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Microwave-microwave and infrared-microwave double resonance spectroscopy of ammonia, methanol and trifluoroiodomethane

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O rder N u m b e r 8 8 1 4 8 8 9
Microwave-microwave and infrared-microwave double resonance
spectroscopy of N H , C H O H an d C F I
3
3
3
Peterson, Dean Bailey, Ph.D.
Michigan State University, 1988
UMI
300 N. ZeebRd.
Ann Arbor, MI 48106
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MIC ROW AV E- M IC RO W AV E AND
INFRARED-MICROWAVE DOUBLE RESONANCE
S P EC TR OSC OP Y OF NH g , CHgOH AND CFgl
By
Dean B. Peterson
A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCT OR OF PH ILOSOPHY
Department of Chemistry
1987
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ABSTRACT
MICROWAVE-MICROWAVE AND INFRARED-MICROWAVE DOUBLE RESONANCE
SPECTROSCOPY OF N H g , CHgOH AND CFgl
By
Dean B. Peterson
Double resonance spectroscopy involves the
simultaneous application of two radiations
to a sample at
frequencies that are resonant with transitions in the sample
molecule.
There are many different
resonance methods.
types of double
Two distinct techniques,
level double resonance,
can be discussed.
3-level and 4-
In either case
the higher power radiation is termed the pumping source
(pump)
and the lower power radiation is termed the signal
source
(probe).
The 4-level double resonance technique was used to
study energy transfer by collisions
in rotational energy
levels of NHg with He and Hg as collision partners.
The
rotational transitions were mon it ore d and pumped by
microwave radiation.
The experimental details and results
of the mi cr ow ave -m icr ow ave double resonance study is
presented in the thesis.
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Dean B. Peterson
The 3-level double resonance technique is used for
simplification and assignment of spectra.
An infrared-
microwa ve double resonance experiment was developed using a
Fourier transform infrared spectrometer.
the results
A discussion of
from the double resonance experiment
is given.
An infrared-microwave double resonance spectrometer
has been developed in our laboratory which employs a
powerful mi crowave source,
a cylindrical cavity sample cell,
and a tunable infrared microwave sideband laser.
apparatus,
a ground state microwave transition,
assignment and frequency are normally known,
With this
whose
can be selected
for pumpin g and the infrared spectrometer can then be
scanned to locate vibration-rotation transitions
affected by the pumped micro wa ve transition.
that are
The results of
a study of CHgOH including a lineshape analysis are given
along wi th results from experiments on CF^I.
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To Sue
iv
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ACKNOW LEDGMENTS
I would like to thank Professor Richard H. Schwendeman
for his great help throughout these studies,
advisor,
not only as an
but also as a good friend.
My thanks are also extended to Mr.
Ron Haas for his
work and wit to help me endure the FTIR days.
I wou ld also like to thank the members of the group
throughout the years
for their discussions
A special thanks
and friendship.
is extended to my parents for their
encouragement and be li ef in me.
Finally I woul d like to thank Sue for always bei ng
there.
(IOEO)!
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TABLE
OF
CONTENTS
LIST
OF T A B L E S .............................................. ix
LIST
OF F I G U R E S .............................................. xi
CHAPTER
I.
I n t r o d u c t i o n .................................. I
CHA PTE R II.
Four-Level Mi cr ow av e- Mi cro wa ve Double
Resonance
in NHg-He and NHg-Hg Gas Mixtures.
. . .7
2.1
I n t r o d u c t i o n ...................................... 7
2.2
T h e o r y ............................................. 10
2.3
E x p e r i m e n t a l ...................................... 16
2.4
R e s u l t s ........................................... 21
2.5
R e f e r e n c e s ........... ............................ 25
C HA PT ER III.
a
In fra red-Microwave Double Re sonance Using
Fourier Transform Infrared S p e c t r o m e t e r ..........27
3.1
I n t r o d u c t i o n ..................................... 27
3.2
T h e o r y ............................................ 31
Co herence S p l i t t i n g .......................... 31
Fourier Tr ansform S p e c t r o s c o p y .............. 36
3.3
E x p e r i m e n t ....................................... 44
I n s t r u m e n t a t i o n ......... .. .................. 44
Sample P r o c e s s i n g ............................ 58
3.4
R e s u l t s .......................................... 62
3.5
R e f e r e n c e s ....................................... 67
CHAPTER IV.
Infrared Microwave Sideband Laser
Sp ec troscopy of C H g O H ................................. 68
4.1
I n t r o d u c t i o n ..................................... 68
vi
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4.2
T h e o r y ........................................ 70
General S p e c t r o s c o p y .......................... 70
M e t h a n o l ........................................ 77
4.3
E x p e r i m e n t a l .....................................88
In t r od uc t io n ................................... 88
CO
2
L a s e r ..................................... 88
S i d e b a n d ........................................ 90
4.4
Results and D i s c u s s i o n ..........................99
4.5
R e f e r e n c e s ........................................ 106
CHAPTER V.
Infrared-Microwave Double Resonance with a
Sideband L a s e r ........................................ 108
5.1
I n t r o d u c ti o n ...................................... 108
5.2
T h e o r y ............................................. 112
Methanol
( CH gOH ) ............................... 112
C F g l ............................................. 115
Lineshape Analysis and G e n e r a t i o n .......... 118
Absorption C o e f f i c i e n t ........................ 126
5.3
E x p e r i m e n t a l ...................................... 131
C
( > 2
Sideband L a s e r ............................. 131
Microwave P u m p ................................. 133
Double Resonance S p e c t r o m e t e r ...............134
5.4
Results and D i s c u s s i o n .......................... 138
Infrared-Microwave Double Resonance in
C H g O H ........................................... 138
Infrared-Microwave Double Resonance in
C F g l ............................................. 140
vii
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Lineshapes of Infrared-Microwave Double
Resonance Signals
5.5
CHAPTER VI.
in C H g O H ....................152
R e f e r e n c e s ........................................ 156
Summary and Future W o r k ...................... 158
6.1
Summary
.
...................................... 158
6.2
Future W o r k ...................................... 161
6.3
R e f e r e n c e s ........................................ 166
A P P E N D I X ....................................................... 167
viii
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L IS T
OF
TABLES
Table
2.1
Page
Compa ris on of ca lculated and experimental
values of four-level double resonance
effects in
2.2
NH^-He m i x t u r e s .................... 14
Compar iso n of calculated and experimental
values of four-level double resonance
effects in
2.3
NHg-Hg m i x t u r e s .................... 15
Four-level double resonance effects in
N H g - H e ........................................... 22
2.4
Four-level double resonance effects
in
N H 3-H2 .......................................... 23
3.1
The first ten roots of J (x) = 0 ............54
m
4.1
Selection rules
for asymmetric rotor
rotational t r a n s i t i o n s ....................... 72
4.2
Parameters used to calculate the energy
levels of the ground and Vg = 1 states of
C H g O H .......................................... 83
4.3
Cal cu l at ed energies
the vibrational
4.4
and coefficients for
ground state of CHgOH
Ca lcu la t ed energies and coefficients
. . .86
for
the CO st retching state of C H g O H ........... 87
4.5
Comparison of observed and calculated
frequencies of CHgOH t r a n s i t i o n s ........... 104
5.1
Vibration-r ota ti on parameters for the ground
and v^ = l states of C F g l ..................... 119
xx
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5-2
CHgOH double resonance experimental
r e s u l t s .........................................139
5.3
Pumped ground state rotational
transitions
in C F g l .........................................148
5.4
Parameters for CFgl transitions in the 10 pm
r e g i o n ........................................... 149
x
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L IS T
OF
F IG U R E S
Figure
1.1
Page
Energy level diagram presenting various
3-level and 4-level double resonance
schemes.
The thick and thin arrows
represent pump and signal transitions,
r e s p e c t i v e l y .................................... 3
2.1
An energy level diagram of symmetrically
split levels in ammonia.
increases or decreases
The pump
the absorption
signal intensity depending on whether
k, < k„ or k, > k . Here,
$
X
$
X
the rate constant
2.2
for the p r o c e s s .......... 11
Block diagram of microwave-microwave
four-level double
2.3
k denotes
resonance spectrometer.
.17
Plot of mi crowave detector signal vs.
power/max.
power.
Attenuators before and
after the sample cell were manipulated in
such a way that the microwave power inside
the cell could be changed without changing
the power at the detector.
The results of
this plot show that the pumping transition
could be brought to within 1 - 2 %
saturation at the
of complete
highest p o w e r s ............ 20
Energy level diagram for single and double
r e s o n a n c e ...................................... 33
xi
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3.2
An example of the use of radio frequency
micr owa ve double resonance
simplify spectra.
(RFMDR)
to
The upper trace is a
portion of the normal Stark mo du lat ed
mi crowave spectrum of ethyl formate.
The lower trace is the RFMDR spectrum in
the same region with the radio frequency
pump coincident with a transition.
the three level resonances
Only
in the ground
(v = 0 ) and first excited state
(v = l )
appear strongly in the spectrum.
The
sim plificati on in the RFMDR spectrum is
evident
(from Wodarczyk and Wilson,
(11))
3.3
Diagram of a Michelson
interferometer
3.4
Interferogram taken by a BOMEM DA3.01 FTIR
.37
. . .40
of C H 3 F at 0.02 cm ^ r e s o l u t i o n ............ 42
3.5
Spectrum calculated from interferogram of
CHgF at 0.02 cm ^ resolution.
3.6
. . . . . .
.43
Block diagram of FTIR-microwave double
resonance s p e c t r o m e t e r ........................ 45
3.7
Diagram of optical components
DA3.01
3.8
in BOMEM
FTIR s p e c t r o m e t e r ......................46
Diagram of the Cassegrain mirror arrangement
used to reduce the diameter of the infrared
beam from the BOMEM i n t e r f e r o me te r .......... 49
3.9
Diagram of microwave cavity cell used in
xn
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double resonance e x p e r i m e n t ................. 50
3.10
Diagrams of field lines
modes
for 3 low-order
in circular waveguide.
The solid
lines show electric field directions,
whereas the dashed lines show ma gn eti c
field directions
3.11
(from Moreno
(14))
. . . .52
Plot of reflected power from mi cr ow ave
cavity cell versus mi crowave frequency.
The sharp dips
indicate resonances
in the
c e l l ............................................. 55
3.12
Plot of refl ect ed power versus mi cr owa ve
frequency for one resonance of the TE11
m o d e ............................................. 57
3.13
A comparison of a normal spectrum and a
m od ula ted spectrum of NHg at 0.02 cm
The upper trace is the normal calculated
spectrum of NHg.
The lower trace is the
c alc ula ted spectrum using amplitude
modul ati on and phase sensitive detection
on the interferometer
3.14
s i g n a l ................ 60
A comparison of calculated interferograms
from si mulated spectra.
Trace
(A) was
c a l cu la t ed with a splitting of 5 data
points.
Traces
(B) and
(C) were calculated
with increasing splitting,
respectively
. .64
The variation of energy levels wi t h J and
xiii
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K for a mo le c u le of slight asymmetry.
deviations of the curves
The
from horizontal
lines represent the deviations from the
levels of a symmetric t o p ............... . .73
4.2
Energy levels of a hindered rotor with
three potential minima and various
asymmetries
and barr ie r heights:
symmetric rigid rotor,
(B) symmetric rotor,
(C) asymmetric rotor,
very high barrier,
intermediate barrier,
intermediate
barrier,
(D) asymmetric rotor,
high
barrier,
(E) asymmetric rotor,
very high
barr ie r
4.3
(A)
( 9 ) .................................... 76
A schematic representation of the CHgOH
m o l e c u l e .....................
4.4
78
Vi bra tion-rotation spectra comparing a
symmetric top molecule to an asymmetric
molecul e wi th a torsional barrier.
It
should be noted that the scale of
splitting for the symmetric top is five
times that for the asymmetric top with
internal r o t a t i o n ............................. 84
4.5
A block diagram of an extra-cavity laser
stabilization scheme used on the COg
4.6
A diagram of the sideband modulator.
CdTe crystal
laser.91
The
is inserted between two AlgOg
xiv
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slabs in a brass housing that is matched
to double-ridged
4.7
w a v e g u i d e ...................93
A diagram of the electric fields of the
COg laser and sideband laser as created
by the sideband modulator c r y s t a l ......... 95
4.8
A diagram of the sideband laser
s p e c t r o m e t e r ................................... 96
4.9
FTIR spectrum of the CO stretch band
of
C H g O H .......................................... 100
4.10
A typical scan of the sideband laser
showing four transitions of CH^OH.
COg laser is fixed at the 9P(26)
The
laser
line while the microwaves are swept
4.11
A plot of the ratio of (-/+)
. . . .101
sidebands
versus micr ow av e frequency for two
different
10R(24)
5.1
Three
laser lines
(9P(16)
(o)
and
(x) ) .................................... 103
level energy diagram used for
density matrix c a lc u l a t i o n ................... 121
5.2
Calculated lineshape using a Rabi
frequency of 100 MHz for the pumping
r a d i a t i o n ...................................... 130
5.3
Block
diagram of COg sideband laser
s p e c t r o m e t e r .................................... 132
5.4
Block
diagram of infrared mic ro wa ve double
resonance s pe ct r o m e t e r ........................ 135
xv
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Resonance cavity cell used in infrared
microwave double resonance experiment
to
obtain high mi crowave f i e l d s ...................136
5.6
Absorption spectrum of CHgOH.
laser is on the 9P(24)
laser
The COg
line and the
microwaves are swept from 15.0 to 16.0 G H z . 141
5.7
Double resonance spectrum of CHgOH over
the same region as figure 5.6.
This shows
the se le ctivity of the double resonance
t e c h n i q u e ..................... ................ 142
5.8
Infrared mic ro wav e double resonance
spectrum of CFgl.
9R(16)
The COg laser is on the
laser line.
The pump frequency is
15,287.6 M H z .................................... 144
5.9
Trace A shows the double resonance signal
of CHgO H w it h the pumping frequency on
resonance w it h the pumped transition.
Trace B is 150 MHz off resonance and
Trace C is 300 MHz off resonance.
laser is on the
5.10
The COg
9P(24) laser l i n e ........... 145
Infrared micr ow ave double resonance
spectrum of CFgl.
9R(16)
laser line.
The COg laser is on the
The pumping frequency
is 12,150.0 M H z ............................... 150
5.11
Infrared microwave double resonance
spectrum of CFgl.
The COg laser is on the
xvi
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9R(16)
laser line.
The pump ing frequency
is 9,000.0 M H z .................................. 151
5.12
C alc ul ate d lineshape using different
frequencies.
Rahi
The signal with the largest
amplitude was gen erated using the largest
Rabi f r e q u e n c y ..................................153
5.13
Ex perimental results for the infraredmicr owa ve double resonance on the R(4,1)A
transition of CHgOH,
obtained using
different pump in g powers.
is on the 9P(24)
6.1
The COg laser
laser l i n e .................. 154
Diagram of sideband laser Lamb-dip
s p e c t r o m e t e r ................................... .162
6.2
A plot of a Stark mo dulated Lamb-dip
the 0(5,3)
from
transition of C H g F ................. 165
xvii
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CHAPTER
I
Introduction
High resolution
i.e.,
infrared and mi crowave spectroscopy,
the detection and interpretation
transitions,
has rapidly pr ogressed in
of mol ec ula r
the past
two decades.
There are new developments of higher resolution and faster
acquisition instruments almost daily.
One spectroscopic
tool useful for m an y applications and ext en si ve ly used in
our laboratory is the technique of double resonance.
Double resonance s p ec tr os co py involves the
simultaneous application of two fields
of
sample,
in the sample
bo th resonant w i t h transitions
molecule.
One of the fields,
radiation on the
the pump, must have enough
strength to perturb the system either by changin g the
population distribution of the two levels
involved or by
creating a coherence splitting of the pu mped levels.
two changes will be discussed in more detail
following chapters.
The second field,
These
in the
the probe or signal,
must be weak so not to disturb the related energy levels.
The probe radiation is used only to mon it or the effect of
the pump on the transition
in resonance with the probe.
Double resonance was first used in the micro wav e and
radiofrequency regions
(1-3).
After the advent of the
1
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2
laser,
double resonance was extended to the infrared,
visible,
and ultraviolet regions of the electromagnetic
spectrum.
Since the first
investigation using a laser (4)
man y scientists have used double resonance techniques for a
variety of studies.
There are two types of double resonance systems,
which
can be separated by their mechanisms and the information
obtained from each.
In the first,
the two transitions
in
resonance with the frequencies of the applied fields have a
common level
(the three level s y s t e m ) .
not have a common level;
system.
this
is known as a four level
These two double resonance mechanisms are explained
in Figure 1.1 by energy level diagrams.
system,
The second type does
In the three level
the pumping effect on the energy level in common is
directly m on itored by the changes in the probed transition.
This system is used for investigations to identify
particular transitions.
In the four level system,
the
effects of the pumping radiation on the molecule must be
transmitted to the energy levels of the probe radiation
through intermolecular collisions.
double resonance signals
Observations of these
lead to information about the
collisional process and the collisional
(5).
"selection rules"
The four level double resonance system can also be
used to increase the populations of upper levels associated
with excited vibrational bands.
The four level system is
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n p roh ibited w ith o u t p e r m is s io n .
3
3 Level
3E
TIT
TFT
4 Level
Figure
1.1.
and 4-level
arrows
En e r gy level diagram presenting various
double resonance schemes.
represent pump and signal
3-level
The thick and thin
transitions,
respectively.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
then used to increase the intensity of a hot band or
co mbi nation band transition.
The two different systems
introduced above will be presented in experiments
in this
thesis.
The thesis describes a combination of different
techniques of double resonance used for mole cu lar studies on
NHg,
C H gF, CHgOH,
and CFgl.
The material is p r es en ted in a
chr onological order in the a u t h o r ’s graduate research
program.
Chapter 2 describes a m i c r ow av e-m ic row av e four
level double re sonance experiment pe rformed on NH^-He and
NHg-Hg gas mixtures.
This experiment was used to confirm
results obtaine d earlier by Oka ejt al_.
Chapte r 3 presents
(6-9).
the theoretical foundation of the
i n fr ar ed -m ic ro wa ve double resonance experiments.
The
ba ck gr ou nd theory of Fourier transform infrared spectroscopy
is also given.
Chapter 3 explains the FTIR-microwave double
resonance experiment and gives the results from the study.
Chapte r 4 introduces
the theoretical considerations
used to predict and calculate transitions.
It also
describes the theory of the methanol molecule.
sideband
laser is introduced in Chapter 4,
along with the
use of extra cavity COg laser stabilization.
C Hg OH transitions
The COg
A list of
is given and a comparison of results from
diode laser experiments
(10,11)
is made.
The in fr ared-microwave double resonance experiment
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p roh ibited w ith o u t p e r m is s io n .
5
using the COg sideband laser as the infrared source
pre sen ted in Chapter 5.
Chapter 5 explains
is
the theory of .
CFgl and the lineshape obtained from the double resonance
experiment.
Results form a double resonance study of CHgOH
and CFgl are given.
The final chapter of the thesis is a summary of the
work.
This chapter gives an overall view of the work
accom pli she d and a proposal for future experiments
in the
field of double resonance spectroscopy.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
6
References
1.
T. Yajima,
1668
and K. Shimoda,
K. Shimoda,
3.
A. Battaglia,
J. Phys.
Ronn,
Soc.
A. Gazzini,
Nuovo Cimento,
A. M.
Soc.
Japan.,
15.
(1960).
2.
4.
J. Phys.
14., 1076
Japan.,
14., 954 (1959).
and E. Polacca,
(1959).
and D. R. Lide,
J. Chem.
Phys.
47.,
3669
(1967).
5.
6
. T.
Adv.
Atom.
Mol.
Phys.
9, 127
(1974).
Oka, J.
Chem. Phys. 47, 13 (1967).
T.
Oka, J.
Chem. Phys. 47, 4852
(1967).
. T.
Oka, J.
Chem. Phys. 48, 4919
(1968).
Oka, J.
Chem. Phys.
(1968).
7.
8
T. Oka,
9.
T.
10.
P. W. Daly,
11.
A. R. Fabris,
49, 3135
and T. Oka,
J. Chem.
and T. Oka,
Phys.
J. Chem.
53., 3272 (1970).
Phys.
56., 3168
(1972).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
CHAPTER
II
Four-Level Microwave-M icr ow ave Double Resonance in
NHg-He and NHg-Hg Gas Mixtures.
2.1
Introduction
Four-level mi cr ow av e-microwave double resonance
measurements can be used to determine relative probabilities
of collision induced transitions.
effects,
By observing these
collisional "selection rules"
for different gas
mixtures can be obtained.
In a four-level double resonance process,
equilibrium populations
the
in two molecular levels are
pe rt urb ed b y the absorption of radiation at the resonance
frequency.
The collisional effect is then monitored in
another two-level system by observing the absorption of a
weak radiation signal at this second resonance frequency.
It is important to understand that these molecular energy
levels are not connected.
Therefore the only possible
effect of one transition on another is through a collision.
A series of four-level double resonance experiments
were done by Oka and co-workers on many different molecules
(1-6).
One particular group of experiments on NHg with
7
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
8
different collisional partners has at tracted a large amount
of attention
( - ).
2
8
The interstellar NHg m o l ec ul es show nonthermal
population distributions
inversion
levels
(9).
among the low lying rotation-
Because NHg mo lecules collide mostly
with H or He atoms or Hg molecules
in interstellar space,
the fundamental data on NHg-Hg and NHg-He collisions are
useful
for the interpret ation of this abnormal stationary
state distribution.
The experimental data have since been compared to
calculated double resona nce effects on the MHg-He system by
Davis and Green
(10) with only partial success and by
Billi ng and Diercksen
(11),
whose results ma tc h the
experimental values.
Billi ng and Diercksen
calculations on the NHg-Hg system,
(12)
also did
but the calculated
results were not in good agreement with the observed values.
The un sa tis fac tor y nature of the comparison between theory
and experiment led Davis
statement
(10)
still suffers
and Green to the following
: "A lthough it is possible that the theory
from some uni den ti fi ed problem,
used have been remarkably successful
experimental results,...
progress
the methods
in predic ti ng detailed
We therefore suggest that further
in understa ndi ng NHg rare gas collisions might
require reexamination of the experimental work".
to test the validity of the experimental data,
In order
we repeated
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e r m is s io n .
9
many of the four-level double resonance me as urements on NHgHe and NHg-Hg mixtures.
Both the NHg-He and NHg-Hg collisional effects were
studied in the mi crowave s p ec tr os co py laboratory at Michigan
State University.
source
(pump)
In this experiment a strong microwave
is tuned to a resonant fr equency of an NHg
inversion transition while a second very weak microwave
source
(signal)
is tuned to a second inversion transition.
The absorption of the signal radiation with the pump turned
off (Io £^)
is compared to the absorption when the pump
source saturates
its transition
(I
on
).
expressed as the ratio AI/I where AI = I
*off
The comparison is
on
-I
„„ and I =
oft
Throug h this observation of AI/I the collisional
"selection rules" can be analyzed.
The next section outlines
the histo ry of the theory
and shows in particular how this applies to the NHg
molecule.
In the following section the experimental
apparatus is described.
Then the final section states the
results of our experiment co mpared to the calculated and
experimental results of previous studies.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
10
2.2
Theory
The energy levels studied in this work are composed of
inversion doublets of ammonia as shown in Figure 2.1.
Many
of the transitions between the inversion doublets fall in
the 20-26 GHz microwave region.
radiation
In Figure 2.1 the pumping
is indicated by the bold arrow
is denoted v g .
There are three possible outcomes which
could result from this experiment.
The first is when the
rate of the parity changing x transition
that of the
and the signal
isgreater than
parity conserving <J>transition.
In this case
the signal absorption should increase when the pump
radiation is turned on.
In the second situation,
of both types of transitions are comparable;
give no change in signal absorption.
the rates
this case would
The final case is when
the $ transition rate is greater than the x transition rate.
This situation would produce an
absorption.
decrease in signal
The observation of this can be shown as AI/I
being either positive or negative.
case were to occur,
Of course,
if the second
the method woul d prove to be useless,
however the probability of these rates being exactly equal
is quite small.
Most of the early theoretical work on the
interpretation of the NH^-He microwave double resonance
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
11
NHq Energy Levels
VP
A
+
B
Figure 2.1.
levels
s
An en e r g y level diagra m of s y m m e t ri ca ll y split
in ammonia.
absorption signal
^
V
The pump
increases
or de creases
the
in tensity de pe nd in g on wh eth er k t < k
or
$
x
® e r e » k denotes
the rate constant
for the process.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
12
experiments was dev eloped by Davis and Green
(10,12,13,14).
Green began the theoretical studies by using the electron
gas model which was created by Gordon and Kim
(15).
In this
study the ammonia mo lec ul e was treated as a rigid top.
Davis and Boggs extended this work by using G r e e n ’s
theory with classical path calculations to obtain degeneracy
averaged cross sections
for the NHg-He collisions as a
function of energy of collision.
Then,
a Boltzmann average
over the collisional energy was pe rf or me d to deter min e rate
constants at room temperature,
determined.
from which the AI/I value was
The calcula ted AI/I values were found to be in
poor agreement with the experimental
results
(4).
Other changes to the theory were made by Davis,
and Mehrot a (10,16,17,18).
These results were still
to give mi xe d agreement wit h the experiments.
Boggs
found
Green then
introduced a Hartree-Fock potential mod if ie d by the addition
of long-range dispersion and induction contributions.
this improvement did not help much,
Davis and Green
When
included
in their calculation the m-d epe nd en ce of the cross sections
for NHg-He collisions
(10),
which also did not change things
very much and wh ich led to the statement quoted above.
this point we began,
at the instigation of T. Oka,
At
a series
of experiments to check the experimental me as ure men ts
performed in O k a ’s laboratory.
G. D. Billing,
L. L. Poulsen and H. F. Diercksen in
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
13
1985 performed an elegant series of calculations on both the
NHg-He and NHg-Hg systems
(11,18).
Both of these
calculations were done by ab initio self-consist ent -fi eld
(SCF) methods.
calculations
potential
The main difference between
these
and those carried out by Davis and Green is the
function used for the collisional
interaction.
The results obtaine d by this me th od are in muc h better
agreement wi th the experimental data reported by Oka,
verified by our work,
and
and with some infrared laser mic rowave
double resonance results reported by Das and Townes
(7).
Table 2.1 presents a comparison of the calculated results of
Davis and Green
(10);
with the experimental
gas mixture.
Billing,
Poulsen and Diercksen
results of Oka
Table 2.2 compares
(1-4),
(18);
for the NHg-He
the calculated and
experimental results for the NHg-Hg system.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
14
Table 2.1. Comparison of calculated and experimental values
of four-level double resonance effects in NH^-He mixtures.
Transit ion
Pump
( , )
1
1
( , )
2
2
( , )
2
1
(3,1)
(3,2)
Calculated AI/I
Signal
Davis
( , )
( , )
(3,1)
(3,2)
( , )
(3,2)
(3,1)
(3,1)
(3,2)
(4,1)
(4,2)
(4,4)
(3,1)
(4,1)
(4,2)
2
1
2
2
2
2 2
-
1
2
3
5
- 1
1
14
3
14
-7
*5
d
Billing et^ a l .
-5.2
-4.5
3.2
0.7
-5.3
1.5
5.6
-5.9
7.9
-5.5
1.3
-2.9
8
0
.
.
Observed AI/I^
Oka®
-3.5
8
6
-2.4
-
1 0 . 0
-
2
.
8
0
.
0
-3.0
-4.2
-0.3
.5
-5.0
4.4
-5.0
-2.5
\
2
0
.
6
0
.
0
0 .
0
a The pump and signal transitions are between the inversion
doublets for the level (J,K).
k AI/I = (Ipumped - Iunpumped )/ Iunpumped where the I ’s
are proportional to the absorption of the radiation.
c Re ference
(10)
^ Refe re nc e
(18)
e References
(4,6)
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
15
Table 2.2. Comparison of calculated and experimental values
of four-level double resonance effects in NHg-Hg mixtures.
Trans xtion
Pump
( , )
2
1
( , )
(3,1)
2
2
(3,2)
(4,1)
(4,2)
(4,4)
3
Calculated AI/I
S ignal
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
Observed AI/IC
Billing and Diercksen^
+
+
+
+
( , )
(3,2)
( , )
( , )
( , )
( , )
( , )
( , )
(3,1)
(3,2)
( , )
( , )
1
b
-
+
+
-
Okae
+5.2
-3.0
+
0
.
6
2
.
6
1 1 . 2
+0.5
+ 2.3
-2.4
+8.3
+4.2
-1.9
1 . 1
The pump and signal tra nsitions are between the inversion
doublets for the level (J,K).
k Sign of Al/I calculated ratio.
£
AI/I = (Ipumped - Iunpumped )/ Iunpumped where the I ’s
are proportional to the absorption of the radiation.
^ Reference
e References
(11)
(5,6)
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
16
2.3
Experimental
The four-level mi cr ow a ve -m ic ro wa ve double resonance
experiment was
introduced by Oka and his co-workers,
and the
meth od and their results are summarized in References
(1-6).
In order to test the va li dit y of the experimental data,
we
repeated m a n y of the four-level double resonance
measurements on these systems.
In our apparatus,
differs somewhat from that used previously,
Hewlett-P ac ka rd
which
a ph as e-locked
(HP) 8690B ba ckward wave oscillator
served as the low-power signal radiation source,
(BWO)
whereas a
phase -l oc ked OKI 24V11 K-band klystron served as the pump
source.
The experimental set-up is shown in Figure 2.2.
The BWO was
frequency locked by using a HP model 8709A
synchronous detector and a HP 8455A reference oscillator.
The klystron was
locked by means of a Mi crowave Systems M0S5
phase lock system.
was always
Radiation from the pump,
whose frequency
lower than that of the signal source,
was
pr e v e n t e d from reaching the detector by means of a slotted
piece of waveguide which could be squeezed until
the longer
dimension was just below the cut-off point for the pump
frequency.
The sample cell was a standa rd X-band wave gu id e Stark
cell and the detector response to the signal radiation was
proc es se d at the Stark mo dul ati on frequency
(33.3 kHz) by
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p roh ibite d w ith o u t p e r m is s io n .
17
FREQ.
STAB.
BVO
V
SYNTH
VACUUM
ATT.
KLY. I
POWER
METER
LINE
STARK
ATT.
FREQ.
STAB.
CELL
FREQ.
METER
=
STARK
MOD
ATT.
LOW
PASS
FILTER!
PHASE
SE N SIT IV E
DETECTOR
PREAMP
DVM
Figure
2.2.
Block
double
resonance
diagram
of
microwave-microwave
four-level
spectrometer.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p roh ibited w ith o u t p e r m is s io n .
18
means of a phase-sensitiv e detector
mo n i t o r e d by a digital voltmeter
(PSD) whose output was
(D VM ).
After determining
that both the pump and signal sources were locked at the
appropriate resonance frequencies,
the low-pass filter was
checked to be sure that no pump signal reached the detector.
The DVM zero was determined by reducing the signal power to
near zero and recording the DVM voltage.
Then,
the signal
was returned to a predet er mi ne d level and the DVM output was
recorded with the pump power at its highest value and at
40db b el ow its highest value.
spurious
The system was tested for
responses by noting no change in the PSD output
when the pump frequency was deliberately tuned off
resonance.
The NHg gas was a specially purified sample obtained
from J. L. Dye of Mi chigan State University.
99.99% pure commercial gas.
The He was a
The sample mixtures were
pr epared by mi xi n g ~5 Torr of NHg and ~500 Torr of He into
one sample bulb and ~5 Torr of NHg and ~5QQ Torr of Hg into
another sample bulb.
Since NHg strongly adsorbs on the
walls of our microwave sample cell,
the actual gas ratios
in
the cell at the time of measurement were probably smaller
than 1/100.
The total p ressure
in the sample cell was
typically 70-80 mTorr for bo t h samples.
All measurements
were carried out at room temperature (~297 K ) .
In order to determine whether the pumping source used
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p roh ibite d w ith o u t p e r m is s io n .
19
(OKI 24V11 klystron)
had sufficient power to saturate a
transition,
the pump was used as a source for a one photon
experiment.
Attenuators bef or e and after the sample cell
were ma ni pu la te d in such a wa y that the microwave power
inside the cell could be changed without changing the power
at the mi crowave detector.
power plot
The resulting absorption vs.
is shown in Figure 2.3.
The results of this plot
show that the pumping transition could be brought to within
1 - 2 %
of complete saturation at the highest powers.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
20
0.80
0.60-
f— 4
<d
a
<30
0.40- *
in
0.20 -
0.00
0.00
0.20
0.40
00
0.80
0.60
P /P m ax
Figure
2.3.
power/max.
cell
were
Plot
power.
the
at
detector.
pumping
complete
microwave
cell
detector
Attenuators
manipulated
inside
the
of
could
The
transition
saturation
in
such
be
changed
results
could
at
before
be
the
a
of
way
signal
and
that
without
this
brought
highest
to
vs.
after
the
the
microwave
changing
plot
show
within
sample
the
that
1- 2%
power
power
the
of
powers.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
21
2.4
Results
The values of AI/I for the NHg-He mixture are compared
to the p re vi ous ly reported values
NHg-Hg m i x tu re in Table 2.4.
in Table 2.3 and for the
Al though there are some minor
differences between the present and previous results,
overall agreement
is very good,
the
especially given the
variation in instrumental arrangement and sample pressure in
the two experiments.
In O k a ’s experiments
two klystrons
we re used to generate the micro wav e frequencies for the pump
and signal
radiations.
The high mi crowave power was passed
through a K- b a n d Stark modulat ion cell in the opposite
direction of the signal micr ow ave radiation,
the low-pass
filter to prevent the pumping radiation from
reaching the detector.
The results show that the AI/I
ratios are small unless the k values
transitions
whereas we used
in the pump and signal
are the same or differ by ±3.
There is no
indication at all of any problem with the previous
e xp er imental work that could explain the differences between
ob served and calculated AI/I values.
experimental
By confirming the
values of AI/I by Oka and co-workers,
the
present data confirm the recent suggestion by Billing et. a l .
that the source of the original discrepancies between theory
and experiment are mainly the result of an inadequate
potential function for collisions of NHg with He or Hg.
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e r m is s io n .
The
22
Table 2.3.
Four-level double resonance effects
Tr an si ti on
Pump
( , )
1
1
( , )
2
1
( , )
2
2
(3,2)
(3,3)
(4,3)
Signal
(5,5)
(7,7)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(9,8)
(5,5)
(7,7)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(9,8)
( , )
( , )
( , )
( , )
(3,3)
(4,4)
(5,5)
( , )
(7,7)
(8,7)
(9,8)
( , )
( , )
( , )
(3,3)
1
1
2
2
1
1
2
2
6
6
1
1
2
1
2
2
6
(5,4)
6
1
1
2
1
2
2
AI/I
3
Oka
-
0
Tr an s i t i o n
*5
Peterson
.
6
0 .
0
0
-3.2
-0.3
0 .
1 . 0
0
-3.5
-3.0
0 .
-5.2
-3.4
0
.
0
0
.
0
0
. 0
-4.2
0
. 0
-2.5
1 . 0
0
.
0
(5,4)
6
0
-2.7
-0.5
0.5
0
-3.9
.
Pump
(6,5)
. 1
-4. 1
-0.4
0.4
-3.2
0.3
-0.3
-1.3
0.5
0 .
1
-2.9
-
-
0 .
0
0 .
0
.
2
0 .
2
0
0
0
.
1 . 1
0
.
0
0
.
0
0.5
-0.5
0
0
0
0
. 0
0.4
-0.9
0 .
(8,7)
0
-2.4
.
8
1.9
-1.3
.
6
0 .
0
0 .
0
0 .
0
(4,4)
(5,5)
(7,7)
(8,7)
( , )
(9,8)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(8,7)
( , )
(9,8)
( , )
( , )
(3,3)
(4,4)
(5,5)
( , )
(7,7)
(9,8)
(10,9)
(3,3)
(4,4)
(5,5)
(7,7)
( , )
(5,5)
(7,7)
( , )
0
0 .
2
-1.3
0 . 0
1
1
0
2
2
.
1.7
0 . 0
1 . 1
1 . 6
0 . 0
0
0 . 0
-
2 .
2
0 . 0
2
2
0 .
8
. 2
-0.4
1
8
0.4
0.5
1.5
0.4
0.3
6
1
8
0 . 0
0.3
0.3
-2.9
0 . 0
8
6
Peterson
0 . 0
0 .
8
8
(9,8)
Oka°
8
6
0
-2.5
0
2 .
.
AI/I^
3
Signal
8
(7,6)
in NHg - He.
0
1 . 1
-
2
.
8
0 . 2
-2.5
0.9
0 . 0
0 .
0 .
0.5
0
1
1 . 0
1 . 2
0
0.4
. 0
0
-1.9
. 6
-1.7
0 . 0
0
0 . 0
0.3
0 . 0
0 . 1
0
1 . 6
.
8
0 .
0
-0.3
0 . 0
-
.
0
0 . 1
0 .
2
1.3
3
The pump and signal transitions are between the inversion
^ doublets for the level (J,K).
AI/I = (Ipumped - Iunpumped )/ Iunpumped where the I ’s
are proportional to the absorption of the radiation.
° References (4,6)
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
23
Transition
Pump
1
1
( , )
2
1
2
(3,2)
.
0
0 .
0
1
1
5.2
2
2
0 .
0
0
.
0
0
.
6
0
.
0
0
.
0
0
.
0
0
. 2
1
1
2
2
1
1
2
2
8.4
-2.3
-0.3
-
0
.
0
0
.
0
.
(6,5)
0
0.4
1 .
-
8
0
.
0
0
.
1
0
.
2
0 .
1
(7,6)
0.3
0.3
-0.7
-
0
. 0
0
. 0
0
. 1
0 .
1
1
0.4
2
2
0
.
0
(8,7)
0
-3.0
0.3
0.7
-0.3
Signal
(3,3)
(4,4)
(5,5)
( , )
(7,7)
(8,7)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(8,7)
(9,8)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(9,8)
(3,3)
(4,4)
(5,5)
(7,7)
(5,5)
(7,7)
6
1 . 0
0
0.5
2.3
o
o
(5,4)
0
Pump
(9,8)
Al/Ib
3
Oka
Q
Peterson
-0.4
-0.3
0.5
6
1
1
2
2
1
1
2
2
0 . 0
0.3
-
1 . 0
0.3
-0.7
0 . 1
0
.
0
0 . 1
0
.
0
0.4
0 . 0
-2.7
-0.9
0
. 2
-
1 . 2
-
0 . 1
O
o
(4,3)
(5,5)
(7,7)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(9,8)
(5,5)
(7,7)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(9,8)
( , )
( , )
(3,3)
(4,4)
(5,5)
(7,7)
(8,7)
(9,8)
( , )
( , )
Oka° Peterson
in NHg-Hg
o
«
o
2
Signal
Transi ti on
Al/Ib
o
o
( , )
Si
o
o
( , )
Four-level double resonance effects
o
o
Table 2.4.
0 . 2
0.3
0.5
0 . 2
0 . 0
-
0 . 1
0 . 0
-
0 . 1
0.3
-
0 . 2
The pump and signal transitions are between the inversion
k doublets for the level (J,K).
AI/I = (Ipumped - Iunpumped )/ Iunpumped where the I ’s are
proportional to the absorption of the radiation.
References (5,6).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
24
theoretical work recently done by Billing et. al.. shows a
much closer correlation to the experimental results than the
previous
theoretical studies.
Another experiment performed
b y Townes and Das also gave similar results.
therefore,
It is,
our conclusion that the reported data in this and
previous work by Oka et. a l . are consistent.
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p roh ibite d w ith o u t p e r m is s io n .
25
2.5
References
1
.
T. Oka,
J. Chem.
Phys.
2
.
T. Oka,
J. Chem.
P h y s . 47,
4852
(1967).
3.
T. Oka,
J. Chem.
P h y s . 48, 4919
(1968).
4.
T. Oka,
J. Chem.
P h y s . 49,
(1968).
5.
P. W. Daly and T.. Oka,
6
.
7.
A. R.
53
3272
(1970).
56,
3168
A. Das and C. H. Townesi, J. Chem.
Phys.
85,
179
(1972).
(1986);
Ph . .D . T h e s i s , University of C al if or ni a at
N. Morita,
1985.
S. Kano and T. Shimizu,
J. Chem.
Phys.
6
8
,
(1978).
A. C. Cheung,
and W.
10.
Phys.
Phys.
3897
9.
3135
J. Chem.
Berkeley,
.
13 (1967).
J. Chem.
Fahris and T. Oka,
A. Das,
8
47,
D. M.
T. Sullivan
Rank,
III,
C. H. Townes,
Astrophys,
S. 1. Davis and S. Green,
J. Chem.
J.
S. H. Knowels,
1 5 7 , L13
Phys.
(1969).
78., 2170
(1983).
11.
G. D. Billing and G. H. F. Diercksen,
145
Chem.
Phys.
105,
(1986).
12.
S. Green,
J. Chem. Phys.
13.
S. L. Davis and J. E.
64, 3463
(1976).
Boggs, J. Chem.
Phys.
69,
2355
(1978).
14.
S. Green,
J. Chem.
15.
R. G. Gordon and Y.
Phys.
73., 2740
S. Kim,
(1980).
J. Chem.
Phys.
56., 3122
(1972).
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p rohib ited w ith o u t p e r m is s io n .
26
16.
S.
L. Davis and J. E. Boggs,
J. Chem.
Phys.
75,
3937
(1981).
17.
5.
L. Davis,
Phys.
18.
6
Phys.
L. 1. Poulsen and G. H. F. Diercksen,
98,
397(1985).
D. B. Peterson and R. H.
8
6
. 7241
J. Chem.
1418 (1979).
. D. Billing,
Chem.
19.
71,
J. E. Boggs and S. C. Mehrota,
Schwendeman,
J. Chem.
Phys.
(1987).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
CHAP TE R III
Infrared-Microwave Double Resonance Using a Fourier
Transform Infrared Spectrometer
3.1
Introduction
Infrared-microwave double resonance experiments have
been carried out by a number of different
5).
laboratories
( 1
However all of these experiments have used an infrared
source with a large enough power to saturate,
partially,
a molecular transition.
at least
The effect of the
infrared radiation is to change the populations of pumped
transitions,
w hi ch can be easily observed.
Wi t h this
technique both three-level and four-level double resonance
effects can be seen.
The first reproducible work done by means of the
infrared-microwave double resonance technique was reported
by T. Shimi zu and T. O k a in 1970
laser to pump the
v
g [^Q (8,7)]
( ).
6
They used an NgO
transition of "^NHg and
studied the effect of the pumpi ng on ground state inversion
transitions that were ob served with a K-band microwave
source and standard Stark modulation.
The results showed
that there was a large effect on the populations of the
inversion energy levels directly pumped by the laser
27
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28
radiation and a smaller effect on the populations of other
levels through collisions.
After this work,
many papers
that described applications of the technique of infraredmicrowave double resonance were published.
A different approach was used by H. Jones and F.
Kohler
(2) to pump with infrared radiation and observe
assigned ground state transitions with mic rowave radiation.
They put the mic ro wa ve cell inside the laser cavity and
studied the effects on the laser output of tuning the
microwaves through resonances.
rotational transitions
infrared transition,
By noting the effects of
in the lower and upper levels of the
assignments could be ma de for the
vibration-rotation states pumped by the infrared.
Only
rather weak mic ro wa ve power was needed to obtain strong
effects.
This technique was used to assign some vibration-
rotation transitions in the CF^I molecule.
More will be
said about this in Chapter 5.
The most prolific researcher in the field of infraredmicrowave double resonance has been M. Takami with a number
of collaborators
(5,7-9).
In addition to a variety of
experimental work,
he has published a definitive theory of
double resonance.
His work is the closest to ours in that
the infrared radiation
is weak and the microwave radiation
is stronger.
his experiments still use partial
However,
saturation of the infrared transitions.
Takami also detects
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29
the effect on the mi crowave radiation,
experiments
even though with his
it is not clear which radiation source is the
pump and which is the signal due to their comparable
strengths.
Wit h this brief h is tor y of the technique and its
applications
I
would now like to describe the double
resonance experiments we performed.
experiments,
In the first series of
the radiation source used for the infrared
light was a Fourier transform infrared spectrometer.
this case,
In
the infrared radiation was ob viously very weak
and therefore a very str on g micro wav e source was used.
We
hoped to see an effect on the infrared (vibrational)
absorption that is known as "coherency splitting" or "highfrequency Stark effect";
this splitting will be di scussed in
the next section.
The rationale for the infrared-microwave double
resonance experiments desc ri bed in this thesis has been to
try to exploit the advantages of mi crowave p um pin g wi t h a
tunable infrared source.
The main advantage of this
tec hnique is that rotational
spectra in the ground state
have been assigned and are well understood for many
molecules.
Therefore,
the pumped transitions are well known
and then the vibrational
transitions affected by three-level
double resonance can be easily assigned.
of this technique is that
A second advantage
the spectral co mplexity of the
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30
vibrational band is greatly decreased if only the
vibrational
transitions in coincidence w i t h the ground state
pumped levels are affected.
small number of transitions
This can then
lead to a very
if a modulation scheme is used.
The final advantage me n t io ne d here is the fact that by using
a wid el y tunable mi crowave and infrared source,
there is no
problem with finding a coincidental overlap of a transition
and a laser line.
In the following sections the theory of the double
resonance phenomenon will be discussed along with an
explanation of an experiment employing a Fourier transform
infrared sp ect rometer and an amplified mi crowave source.
Some results will be shown and conclusions about the
experiment will also be given.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
31
3.2
Theory
Coherence Splitting
As stated above,
the effects seen by previous authors
of infrared-microwave double resonance experiments are the
results of changes in population.
The population effect for
an infrared transition is much larger then that for a
mi crowave transition becau se of the difference in energy of
the two levels
distribution,
involved.
According to the Boltzmann
the population ratio of the upper and lower
energy states of a transition
is calculated by the following
equation.
N 2/ N 1 = e x p ( - h v 12/kT)
(3.1)
If the transition is in the infrared region of -1000
cm
the ratio is 0.007,
but for a transition in the
microwave region of -15 GHz,
the ratio is 0.997.
Since the
populations can at most be equalizied by steady-state
radiation,
the population effect on saturation of an
infrared transition can be very large,
whereas
the
population effect for a microwave transition is necessarily
very small.
Since the population change is so small for the
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
32
microwave pump,
another effect must be present to observe an
infrared-microwave double resonance signal.
The phenomenon
observed when using a strong microwave pump is called
coherence splitting.
This splitting effect is created only
with very large radiation powers.
calculated b y Javan
The splitting was first
(10).
For the following explanation let us consider a twolevel system first.
When a two level system is irradiated
with coherent radiation,
the wave functions of the two
separate states are combined linearly in a time coherent
manner
(10).
If the radiation is resonant with the energy
level difference in the two level system as shown in Figure
3.1(A)
the combination takes the form,
$^(t)
where
=
4^(t)
4
*
4
>^(t) and
2
cos (cogt/2) + i^ Ct)S ± d ( Jqt/2)
(3.2)
c o s ( c u g t / 2 ) - i $ (t)sin(uQ t/2)
(3.3)
2
0
1
represent the normalized "stationary
states" but time-dependent wave functions of states
|2> in the absence of radiation.
angular frequency,
element
| > and
1
The factor cog is the
which is related to the transition matrix
between the two states as shown by
Wq /2h = Ip^glE/h = i/q .
(3.4)
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33
2>
A)
1
I
>
3>
A
V = V 23
Ay
B)
2>
1
>
3>
I T
Ay
C)
V
= V2 3 * h v 0 /2
2>
1
Figure
3.1
>
Energy
level
diagram
for
single
and
double
resonance.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
34
This quantity
is co mmonly known as the Habi frequency.
The important outcome of Equations
(3.1)
and
(3.2)
is that
the system nutates betwee n two possible states at a
frequency Vg (the Rabi frequency)
without ever be in g in
either state for any pr olonged amount of time.
Now let us consider how this nutation affects the
double resonance phenomenon.
We will do this in a simple,
quantitative way that can be ve rified by more complex
calculation.
To begin, we
introduce a third level
j3> as
shown in Figure 3.1(B).
If we look at the time-dependent
wavefunctions
|2> and
radiation,
for states
|3> in the absence of
we get the following:
*2(fc) = ^(rJexp^iEgt/h)
(3.5)
$ (t) = ipg(r)exp(-iEgt/h)
(3.6)
and
3
The normal
linear transition betwee n states
|2> and
|3>
involves the time-dependent part of the wave functions and
its frequency l/gg can
shown to obey the Bohr frequency
condition,
h w 23 = E 3
E2 *
(3.7)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
Now,
with the application of the pumping radiation
resonant with the
function for
assume that
the
| > •* | > transition we obtain a wave
1
2
|2> of the form in Equation
transitions between
(3.2).
jl> and |3>
part m a y be ignored so we get an
If we
are forbidden,
equation of the
form,
$ (t) = ** (t )c o s (g>qt/2) .
2
(3.8)
1 2
If this is expanded in exponential form,
* 2 ^
“
exp(- iE t/fi) (exp(io> t/2))/2
2
+
0
(3.9)
exp(- iE t/ft)exp(-i<j t/2) /2,
2
0
Which can be further simplified to
# (t)
= l / 2 ^ (r)exp(-i(E - h v /2)t/fi) +
2
2
2
0
(3.10)
l/2* (r)exp(-i(E + h Vo/2)t/ft)
2
Then,
2
a sp litting occurs when the frequency is calculated
for the
|2> -* |3> transition.
v
(±) = vggt
v
q
/ 2
(3.11)
From this result we can see that the normal one photon
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
transition between states
transitions
|2> and
|3> is split into two
if there is a coincidence between the frequency
of strong pumping radiation and states
Equation
(3.11)
| > and
1
| >.
2
shows that the coherence splitting is equal
to the Rabi frequency
vq
.
The coherence splitting has been used in observations
of mi cr ow av e-microwave and also radiofrequency-microwave
double resonance experiments.
Our interest in this
phenomenon and the development of it for an infraredmicro wa ve experiment came from the work of Wodarczyk and
Wilson
(11).
They described a spectrometer in which a
ra diofrequency pump was used to modulate and thus assign
microwave transitions.
By using the double resonance method
a spectrum could be simplified as shown in Figure 3.2.
then makes the assignment much simpler.
This
We were interested
in using this same idea to simplify infrared spectra.
To do
this a tunable high resolution infrared source was needed,
and a Fourier transform infrared spectrometer was a logical
choice.
Fourier Transform Spectroscopy
The Fourier transform infrared (FTIR)
first developed by A. A. Nichelson
diagram of a Michelson
in 1881
spectrometer was
(12).
The
interferometer is shown in Figure
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37
Figure 3.2
An example of the use of radio fre quency
microwave double
resonance
(RFMDR)
to simplify spectra.
The
upper trace is a portion of the normal Stark m o du la te d
microwave spectrum of ethyl
RFMDR spectrum
formate.
in the ground
is the
is evident
Only the three level
(v= ) and first excited state
0
appear strongly in the spectrum.
RFMDR spectrum
trace
in the same region with the radio frequency
pump coincident with a transition.
resonances
The lower
The simplifica tio n
(v=l)
in the
(from Wo darczyk and W i l s o n s (11)).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 1 I U I L 1 I I I I I
38490
30400
31
-1 U
l l l l l l i m i i i i i n i u n i u
38450
38440
38430
n m i
38420
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39
3.3.
The polychromatic source radiation passes
through an
aperture and is separated into two beams by a beamsplitter.
One beam is directed to a stationary mirror,
beam is sent to a movable mirror.
The two beams are then
reflected back to the beamsplitter,
finally to the detector.
while the other
through the sample,
and
The two reunited beams interfere
constructively or destructively,
depending on the path
difference and the wa ve l e ng th of the light.
The signal at the detector is a function of path
difference
(x) and is known as an interferogram
.
The
interferogram can be des cribed by,
I(x) - I(0)/2 =
Here,
£ B(v>|t)cos(2nvjtx ) .
(3.12)
is the wavenumb er of the kth radiation,
the intensity of the source at
proportional
v
= v^,
and I(x)
is
is
to the intensity of the light leaving the
interferometer for a path difference x.
If we assume a
continuous source of radiation with B(v)dv equal to the
intensity between
v
and
+ dv,
v
I(x) - I(0)/2
then
(3.13)
u
This equation is part of a cosine Fourier transform
pair,
so that
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40
Source
Movable
Mirror
) Dei:,
Fixed Mirror
Figure 3.3
Diagram of a Mi chelson
interferometer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
J
[I(x)
- I( )/ ]cos( nxv)dx
0
2
(3.14)
2
These last two equations define the relationship
between
the interferogram and the normal frequency domain
spectrum.
A typical in terferogram and its normal spectrum
is shown in Figures 3.4 and 3.5 respectively.
The most
important criterion for the success of this experiment is
the resolution available for the infrared source.
The
resolution can be written as a function of path difference,
as follows:
Res (cm
1 )
=
(3.15)
where Ax is the max imu m path difference
example,
in our instrument
(in cm).
For
the maximum possible difference
is 50 cm, wh ic h corresponds to a maxim um resolution of 0.01
cm
Thus,
by using an interferometer arrangement
instead
of a scanning spectrometer we can obtain the spectrum all at
once and at a higher resolution than available with a normal
grating instrument.
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42
0.10E+08 - r -
SIGNAL
0.50E+07 - -
o.no
-0.50E + 07
—0.10E+08
-
100.00
0.00000
100.00
200.00
DATA POINT
Figure 3.4
CHgF at
0
.
300.00
#
Interferogram taken by a BOMEM DA3.01
0
2
400.00
FTIR of
cm ^ resolution.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
Absorbance
2.00 -r-
1.50
- -
1.00
- - -
0.50
0.00
eoo.oo
050.00
-
1000.00
1090.00
1 1 0
(
Wavenumber (c m -1 )
Figure 3.5
at
0
.
0
2
Spectrum calculated from interferogram of CH F
cm ^ resolution.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
^
44
3.3
Experiment
As me nt io ne d above,
our first
infrared microwave
double resonance experiment utilized a strong microwave
source for the pumping radiation and a FTIH spectrometer for
the infrared signal radiation.
The observed do ub le ­
resonance should then be the effect of the mic ro wa ve pump on
the infrared transitions that share a common level with the
micr owa ve transition.
To see this effect
the microwaves
were chopped at 100 kHz and the infrared signal was
pro cessed by a lock-in amplifier at the chopping frequency.
A block diagram of the set-up is displayed in Figure 3.6.
Instrumentation
The FTIR spectrometer used for the double resonance
experiment was a BOMEM model DA3.01.
was a water cooled Globar,
The infrared source
which is a good polychromatic
source in the mi d-i nfr are d region.
The beam of light is
first focused by an off-axis ellipsoid mi rror onto an iris.
The beam then passes
to a flat mirror after which it is
reco llimated by a f/4 paraboloid mirror;
is shown in Figure 3.7.
the optical diagram
The recollimated light is then sent
through the Michelson interferometer,
beamsplitter and two flat mirrors,
which is a KBr
and which has a maximum
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45
M ic ro w a v e
100 KHz
Source
-flL
FTIR
_ D et.
Preanp
MV C e ll
V ecto r
Conp.
A /T l
Proc.
Figure 3.6
FTIR
3.16K H z
Block diagram of FTIR-microwave double resonance
spectrometer.
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46
CCOTCR
U U C
S o v flc t
coHPiin
c o u ra o itjro
B*a +1 snjrrev
ats:/
« * > fA S S A > < /
sotM*c.e
n a r t / i a p o *
/7&SO
o*
r o a c ff'i suitrcu'ttc.
cu*rrcS cc*tf**arn£tjT
Figure 3.7
Diagram of optical
FTIR spectrometer.
components
in BOMEM DA3.01
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47
path difference of 50.0 cm.
Upon recombination,
the beam is
condensed and sent through a sample cell and finally focused
on the detector.
The detector used was a liquid-Ng cooled
mercury cadmium telluride photoconductive detector,
m anu fac tur ed by Infrared Associates.
The signal from the
matched preamplifier was coherently detected at 100 kHz by a
Stanford Research Systems SR510 lock-in amplifier.
The
output of the lock-in amplifier was sent to the analog to
digital converter board on the BOMEM instrument where
it was
sampled at a rate of 3.16 kHz.
The sample used was NHg at a pressure of 300 mtorr.
The path length of the cell was 12 inches.
The NHg sample
was an ultra pure sample obtained from Dr. J. L. Dye.
Ammonia was selected for the sample because it is a
symmetric top with inversion doublets that give strong
mi crowave transitions in the
8
to 26 GHz range.
Ammonia was
also picked because the Vg band is well understood,
so that
predictions of the frequency of the expected double
resonance signals could be made easily.
The diameter of the infrared beam from the
interferometer was reduced by a Gassegrain mirror assembly.
The reason for this was to increase the field strength of
the infrared radiation and still keep the beam collimated.
A more detailed diagram of this apparatus is shown in Figure
3.8.
The shadow of the small mirror had essentially no
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
effect on the infrared beam because a shadow,
diameter,
2
.
cm in
5
in the center of the beamsplitter already exists
from the center quartz beamsplitter piece.
The mount was
designed to be flexible in the Z axis as shown and an
ability to tilt
the mirrors was also available.
With the
Cassegrain mir ror arrangement the beam was condensed and
recollimated from 9 cm to 2.5 cm with very little loss.
As me n t i o ne d earlier,
energy levels
radiation.
the splitting of the pumped
is dependent on the electric field of the
Because of the large Doppler width of the NHg
molecule under study (~35 MHz H W H M ) , the Rabi frequency
needs to be of the order of 35 MHz.
The microwave radiation
was ge nerated by a backward wave oscillator and amplified by
a travelling wave tube amplifier
apparatus,
(TWTA).
With this
the mi crowave power output is ~20 Watts.
To increase the microwave electric field inside the
sample cell a micr ow av e cavity cell was constructed from a
design used by J. Asmussen
(13).
The cell is made of brass
and shown in detail in Figure 3.9.
able to work from 8-18 GHz,
Since the cell had to be
it was designed so that the
length of the cell could be adjusted at one end.
This
arrangement allows the cell to operate as a microwave cavity
over the entire range desired.
Another degree of freedom
was needed for the antenna connection to the cell
in order
to provide the correct coupling between the SMA connector
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49
Cassegrain Mirror S e t u p
FT-IR
B ean
-±L.
Convex
M irro r
■ T r
1 Inch
Figure 3.8
used
Diagram of the Cassegrain mirror arrangement
to reduce the diameter of the infrared beam from the
BOMEM interferometer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
SMA
C onnector
A
I
< ■
>
MV Pin
Screen
Screen
NaCl
Window
Figure 3.9
NaCl
Window
Diagram of microwave cavity cell used in double
resonance experiment.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
and the cell.
For this purpose,
the coupling antenna can be
screwed in or out through a vacuum connection.
the cell consist of NaCl windows
however,
The ends of
for infrared transmittance;
the microwaves are shorted at the windows by gold
plated fine tungsten wire screens each of which transmits
8135 of the infrared radiation.
The microwave cell is also
vacuum tight with a total path length of ~
1 2
inches.
The mode condition inside the cell is also of interest
be ca us e each mode has a different structure.
Diagrams of
the electro-magnetic fields of different modes inside a
cylindrical waveguide are shown in Figure 3.10
diagram shows how drastic the differences are.
(14).
This
A
calculation was done for ten possible modes inside the
cavity.
The equation used to calculate the resonance
wav ele ngt hs was the follpwing:
4
(3.16)
Here,
SL
is an integer that gives the number of half waves
along the axis of the resonator,
the resonator cavity,
p
m ,n
z^ is the half length of
a is the radius of the cavity,
and
is the nth root of an mth order Bessel function which
determ ines the axial field.
is given in Table 3.1
A list of the first ten roots
(14).
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52
Figure 3.10
Diagr ams
of field lines for 3 lo w-order modes
in circul ar waveguide.
directions,
di rec tio ns
whereas
The soli d lines show el e ct ri c field
the dashed lines show m a g n e t i c field
(from Mo reno
(14)).
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53
In order to determine the distribution of the
resonant frequencies for a given length of the resonator
cavity,
the power reflected back from the cell was recorded
as the mi crowave frequency was swept.
A typical plot of the
reflected power versus frequency is shown in Figure 3.11.
The plot also has the as signed modes for each ma jo r
resonance seen on the trace.
The mode with the most
desirable structure is the TE11 mode.
The reason for this
is because it has an electric field maximum in the center of
the cell,
as shown in Figure 3.10.
remember however is that the cell
An important fact to
is designed to be able to
be in resonance at any fr equency between 8-18 GHz;
not all the modes,
however
especially at higher frequencies,
give
good overlap with the in frared radiation.
Another important attribute which was de termined for
the cell was the "Q" value.
The "Q" of the cell
is an
efficiency term and is expressed as,
Q
-
o
energy sto red____
energy lost/cycle
*
' ’
The quantity Q is used as a figure of efficiency for a
resonant circuit.
The Q term comes
into play for the
determination of the electric field inside the cavity as
shown in Equation 3.18,
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'
54
Table 3.1.
The first
No.
ten roots
of J (x) = 0.
ID
Value
Mode
1
1.841
TEU
2
2.405
3
3.054
4
3.832
5
3.832
6
4.201
7
5.136
8
5.318
9
5.332
™
1
«21
™
1
1
"01
T E 31
"21
TS41
"12
5.520
1 0
™
Reference
0
0
2
(14).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
i—
r
1
r
* TE11 mode
□ TM01 mode
0 TE21 mode
<D
£
O
DL
~o
Q )
-4-*
o
Q )
H<D
n
*
8.0
*
8.5
n
9.0
*
i
9.5
*
i
I
i
i
r
10.0 10.5 11.0 11.5 12.0 12.5
Frequency (GHz)
Figure 3.11
Plot of re flected power from m i cr ow ave cavity
cell ver sus m i c r o w a v e frequency.
resonances
The sharp dips
indicate
in the cell.
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56
E =
8.151 Q P
Mq E a
(3.18)
tiL
In this equation E is the electric field in the center
of the cavity,
radiation,
P is the power in watts of the microwave
ug is the angular frequency of the radiation,
is the radius and 1 is the length of the cell.
above equation,
a
From the
we can see that the larger the Q value the
larger the effective electric field inside the cavity.
The determination of Q for the cell can be done
experimentally wi th the use of the equation,
Q = fQ/Af
(3.19)
where fg is the resonant frequency and Af is the full width
at half maximum
(FWHM).
These values can be m e a s u r e d by
observing the reflected power from the cell.
A plot of
reflected power versus frequency is shown in Figure 3.12.
From this plot a value for the Q of the cell was determined
to be 2,600.
Now if we use this value of Q and the
dimensions of our cell Equation
(3.18),
we obtain an
electric field E of ~620 V/cm for a mic rowave power of 20 W.
This gives a Rabi frequency of 312 MHz for a transition
dipole moment of 1 Debye.
In our experiment,
it was
necessary to use electric fields smaller than this,
because
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
L_
<D
$
O
CL
TE11 m o d e
"D
CD
ZERO POWER
9.70
9.72
9.74
9.76
9.78
9.80
Frequency (GHz)
Figure 3.12
Plot of reflected power versus microwave
frequency for one resonance of the TE11 mode.
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58
at high electric fields
Typical Rabi
frequencies
the NHg sample would break down.
in our experiments were of the
order of 50 to 150 MHz.
Sample Processing
The mic ro wa ve ra diation applied to the coaxial cell
was chopped by a PIN diode that was controlled by an applied
square wave voltage.
The effect of the m od ul at io n of the
infrared absorption by the pumped microwaves was mon it or ed
wi t h a phase -s en sit iv e detect or at the output of a
preamplifier attached to the infrared detector.
mo dul ati on fr equency was
The
100 kHz and the sampling frequency
for the interferogram was 3.15 KHz,
so that the two
frequencies wer e far enough apart to separate each signal
from the other.
The reason
for modulation of the microwave
pump was to improve the sig nal/noise of the double resonance
signal and to suppress the single resonance spectra.
We
also tried to subtract a spectrum wit h the m i cr ow ave pump on
from one with the mic rowave pump off.
An experiment to check the validity of the mo dulation
scheme was carried out by simp ly modulating the output of
the infrared detector and using the phase sensitive
detection.
The output of the phase sensitive detector was
rec orded in the usual way and sent to the hi g h speed vector
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59
processor for the Fourier transform calculation.
comparison between a normal spectrum at
0
.
0
2
cm
- 1
A
resolution
of NHg and the m o d ul at ed spectrum under the same conditions,
as shown in Figures 3.13(A)
and (B).
The two spectra show
no significant difference.
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60
Figure 3.13
A comparison of a normal spectrum and a
modulated spectrum of NH^ at 0.02 cm” *.
the normal calculated spectrum of NHg.
The upper
trace is
The lower trace is
the calculated spectrum using amplitude modulation and phase
sensitive detection on the interferometer signal.
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61
a.
1000
1200
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62
3.4
Results
The results of our attempts to observe infraredmicrowave double resonance with a high power microwave
source and an FTIR spectrometer were disappointing.
There
was no detectable effect on the infrared transitions known
to be coincident w it h the pumped inversion energy levels in
the ground state of N H g .
Both the modulation experiment and
the simple subtraction experiment showed no double resonance
effects.
Our explanation of this failure and a suggestion
for a future experiment will be described in this section.
First of all
let us go back to the calculation of the
Rabi frequency and the coherence splitting effect.
realize that the entire sp litting effect
If we
is ~300 MHz and the
resolution of our FTIR spectrometer is 600 MHz,
the
observable sp litting will be effectively zero bec au se of the
resolution.
The sp litting signal which should occur has to
be averaged over 600 MHz,
thus no signal at all will be
produced from the coherence splitting unless the Rabi
frequency is further increased or the resolution of the
infrared spectrometer is raised.
The first alternative is
impossible bec aus e at any higher electric field the sample
at 100 mTorr disassociates.
The second solution however is
possible and has been employed in the following chapter by
using the COg sideband system for the infrared source.
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This
63
technique of FTIR as the infrared source could still
pos sibly work on higher resolution instruments made by BOMEM
or a homemade FTIR such as that at Kitt Peak.
Some calculations on the interferogram signal shape
were done using a program written by Peter Wentzell of
Michigan State University.
The results of some simulations
are shown in Figures 3.14 a,b and c.
As can be seen the
larger the splitting the stronger the interferogram becomes.
The sp litting here refers to points of the spectrum and the
calculation is just an inverse Fourier transformation of the
predicted spectrum to obtain the interferogram.
interesting consequence of these simulations
One
is that the
signal at zero path difference is zero in the time domain.
This is no rm al ly the largest signal because under normal
conditions the light at zero path difference does not
de st ru ct iv el y interfere,
but when a mo d u l a t e d signal is
detected at zero path the signal
is zero becau se the average
of all- the light on the sample is zero.
The fact that there
is no zero path burst may cause a strange anomaly to occur
when the phase calculation
Another effect
population effect.
been signal
to noise
is done on the i n t e r f e r o g r a m . .
that has been me ntioned earlier is the
Al though this is very small,
(S/N)
there have
ratios reported at 60000:1
(15).
Our instrument however only has a S/N ratio of 500:1 and
this would not be large enough to see the population change
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64
Figure 3.14
A c omp ar iso n of c al cu la te d in ter fer ogr ams
si m u la te d spectra.
Trace
from
(A) was c a l c u l a t e d w i t h a
sp li tt i n g of 5 data points.
Traces
(B)
ca lcu la te d w i t h in cr e as in g splitting,
and
(C) were
respectively.
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65
’ •° -i
Signal
A
0.0
- 1. 0 -
0.0
Signal
1.0
1
40.0
I
60.0
100.0
80.0
-.
0.0 -
-
1.0
WVWvvvww-
J------ J------ 1------ 1------ 1------ j------ 1------ j------ 1------ 1
0.0
20.0
4041
60.0
80.0
60.0
80.0
100.0
1 .0 —1
Signal
.
J
"
20.0
1
*
1
100.0
Data point n u m b e r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
due to the mi crowave pump.
The main reason for this
di ff er en ce in the signal to nois e ratio is because of the
detector used.
W i t h the FTIR and instrumentation available at
Michigan State University the desired experimental
results
for the infrared-microwave double resonance were impossible
to obtain.
Therefore after m uc h deliberation this project
using the FTIR spectrometer was abandoned until further
funding for a higher resolution
instrument can be found.
should however be pointed out that the experiment may
succeed if the steps outlined above are taken.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
It
67
3.5
References
1. T. Shimizu,
and T. Oka,
Phys.
2.
H. Jones, and F. Kohler,
3.
H. Jones, and J. M. Brown,
4. T. Amano,
5.
J. Mol.
S. Yamamoto,
Matsumara,
. T. Shimizu,
6
7.
8
.
M. Takami,
Takami,
10. A. Javan,
and M.
8
Takami,
and T. Oka,
J. Chem.
Phys.
and H. Kuze,
Phys.
Rev.
F. J. Wodarczyk,
37, 445
J. Mol.
K. Kuchitsa,
H. Jones, and M. Takami,
9. M.
11.
Spec.
Rev.
Spec.
J. Mol.
8
A2,
1177
58,
Spec.
(1970).
125
(1975).
90., 222
(1981).
, 194 (1981).
T. Nakanaga,
J. Chem.
J. Chem.
Phys.
Phys.
74, 4276
H.
Takeo,
83,
53,
C.
1444
2536
(1985).
(1970).
(1981).
J. Chem.
Phys.
78,
1039
J. Chem.
Phys.
78,
2204
(1983).
(1983).
1 0 7 . 1579 (1957).
and E. B. Wilson,
Jr.,
J.
Mol. Spec.
(1971).
12. A. A. Michelson,
13. J. Asmussen,
Amer.
J. Sci.
22., 120
Michigan State University,
(1881).
E.
Lansing,
MI.,
private communication.
14. T. Moreno,
New York,
"Microwave Transmission Design Data",
Dover,
NY.
15. J. W. Brault,
Symposium on Mo lecular Spectroscopy,
State University,
June 1985.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ohio
CHAPTER
IV
Infrared Micr owa ve Sideband Laser Spectroscopy of CH^OH
4.1
Introduction
High resolution infrared spectroscopy gives a wealth
of information about molecular structure.
of the
of
12
l>£
Extensive studies
fundamentals as well as the associated hot bands
c HgF and
13
CH^F have been carried out by means of an
infrared mi crowave sideband laser in the high resolution
infrared sp ectroscopy laboratory at Michigan State
Univer sit y
(1).
This chapter describes a preliminary study
of the CO stretch vibrational band of CHgOH.
had three goals:
This project
the first was to familiarize the author
with the COg laser and sideband system,
the second was to
check the results of a diode laser study done on CH^OH
and,
finally,
(2,3)
the third was to separate the Q branch
transitions whi ch were unresolved in Fourier transform
infrared (4) and diode laser experiments
(2,3).
Methanol has previously been studied by diode laser
spectroscopy
(2,3),
by infrared laser Stark spectroscopy
(5)
and by Fourier transform infrared spectroscopy (4).
However,
because of internal rotation and overlap of other
vi br at ion-rotation bands,
the interpretation of the spectra
6 8
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69
has been very difficult.
For the reasons given above and
for a further und er st and in g of the methanol molecule,
we
decided to obtain spectra of the CO stretch vibrational
band.
In addition to a presentation of data for methanol,
this chapter includes a discussion of the rotation-vibration
theory used for interpretation of the spectra.
discussion emphasizes
The
the asymmetric top case and then
explains the methanol molecule in detail.
The COg sideband
laser is described and the experiment is pre sented with a
discussion of the method of laser stabilization.
Finally,
the data for methanol are compared to the results of
previous studies.
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70
4.2
Theory
General Spect ros co py
Mo lecules
of motion:
in free space undergo m an y different types
translation
in space,
overall rotation,
interatomic vibration.
In addition,
constant
To predict
rapid motion.
molecules,
and
the electrons are in
the energies of
their m o l ec u la r motions must be un derstood and
described.
The Bo rn- O pp en h ei me r approximation allows the
molecular Ham iltonian to be separated into an electronic
part and a nuclear part
( ). It has been shown that to good
6
approximation the Hamiltonian for nuclear motion
HN = HT + HR + H y
is (7)
,
(4.1)
where H^, is the Ha mi ltonian for translational motion,
the rotational Hamiltonian,
HR is
and Hy the vibrational
Ham iltonian for the nuclear motion.
With this convention we
can write the energy of the molecule as the sum of these
contributions;
E = Ee + Ey + ET + ER .
(4.2)
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71
We have,
energy,
in this case taken
vibrational energy,
into account the electronic
translational energy and the
rotational energy.
To calculate the frequencies of vi br ation-rotation
transitions
in one electronic state,
the electronic and
translational energies are not used because they do not
change.
The vibrational energy change is taken into account
by including a difference in the rotationless vibration
energies
in the fitting of the experimental data.
The terra
E v ^j)V is used here to designate the vibrational energy.
For an introduction to the methanol molecule,
the
theory will be explained for the asymmetric rotor case;
i.e.,
I
a
* I,
b
*
X
c
where I , I, , and I are principal
a
b
c
moments of inertia about three orthogonal axes through the
mo lecular center of mass.
A slightly asymmetric top
mol ecule splits the levels labeled by the quantum numbers
±K, which are degenerate in a symmetric top.
A common
parameter used to indicate the degree of asymmetry is R a y ’s
asymmetry parameter
( ),
8
For a prolate symmetric top
(B = C),
k
equals -1, whereas
for an oblate symmetric top (B = A),
k
= +1.
The methanol
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72
molecule is a slightly asymmetric prolate top molecule;
therefore,
it has a k value near -1.
Figure 4.1 shows the
rotational energy of a slightly asymmetric top as a function
of J.
Since K is no longer a good quantum number for an
asymmetric rotor,
the energy levels are labeled by the
quantum numbers K_^ and K + ^, which are the values of
the limiting prolate top and oblate top cases,
|K| for
respectively.
An asymmetric top molecu le can have a dipole moment
component in any or all of the three axis directions;
there exists three types of spectra:
type.
a-type,
thus,
b-type or c-
The intensities of rotational transitions of a given
type are proportional
to the square of the corresponding
dipole moment component.
The selection rules for the three
spectral types can be defined in terms of AK_^ and AK+ ^, as
shown below in Table 4.1
Table 4.1.
(9).
Selection rules for asymmetric rotor rotational
transitions.
Type
A K +l
a
even
odd
b
odd
odd
c
odd
even
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73
CJ)
Q;
c
Id
0
5
10
15
20
J
Figure 4.1.
The variation of energy levels with J and K for
a molecule of slight asymmetry.
curves
from horizontal
lines
The deviations
represent
of the
the deviations
from
the levels of a symmetric top.
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74
The Watson Hamiltonian
for an asymmetric rotor
(10)
is
given as:
Hp = 1/2(B + C ) P 2 + [A - 1/2(B + C)]P
it
a
(4.4)
2
+ 1 / 2 (B - C ) ( P b 2 - P c 2 ) - AjP4
- AJKp2pa2 - ¥ a 4 - 2SJp2(Pb2 " Pc2>
‘ SK [Pa2 (Pb2 - Pc2) + (Pb2 - Pc2)Pa2]
In this equation,
constants,
and Aj,
A, B,
A RJ A J K >
S j
•
and C are the rotational
and
centrifugal distortion constants.
are quartic
The eigenvalues of the
Watson Hamiltonian are the rotational energies for an
asymmetric top molecule.
Methanol
is further complicated by internal rotation
of the OH bond with respect
to the CHg group.
Thus the
hydrogen attached to the oxygen has three possible positions
of equal energy and can tunnel through the potential barrier
between them.
Hence the internal rotation is hindered by
the size of the potential barrier.
It has been shown that
the three-fold potential barrier splits
levels
into a nondege ne ra te
degenerate
(E)
level.
the torsional energy
(A) level and a doubly
The potential barrier height has a
direct effect on the size of the splitting.
Figure 4.2
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
75
shows
the be havior of energy levels with various asymmetries
and barri er heights.
The potential barrier height can be
written as a function of the angle of internal rotation y.
V = ^3. (1 - cos 3 y )
+
I I I
2
Here
(1 “ cos
6
y) + ....
(4.5)
2
Vg + Vg +... . is the maxim um potential of the barrier,
Vg is the am plitude of the dominant term,
m a g ni tu de of
and Vg is the
the six-fold term, which measures
of the hi ndering
potential
the deviation
from asimple sinusoid.
With the
internal rotation energy come two new quantum numbers:
which labels
sublevels
the torsional
for a given n.
levels,
n,
and t, w h i c h labels the
By using the K quantum number the
symmetry species can be relat ed to
t
.
The conven ti on used
is listed below:
A
-*K
+
t
= 3N + 1,
Ex - K
+
t
= 3N,
E
2
- K + t = 3 N + 2
.
Here N is an integer.
To obtain the total rotational Hamiltonian for the
calculation of the rotational part of the total energy in
Equation
(4.2),
it is nece ss ar y to add to the Watson
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
76
S=2
•\
\
20
\>
J=2,K=2/
\\S
5
L -.
J
X
\
2
1
\_
\S=0 .■
S=2
_
1
\
N
10
\
V.
/■
/
J=1,K=1 /
/
1
11
\s=o
A
B
Figure 4.2.
Energy
C
D
levels of a hindered rotor with three
potential minima and various asymmetries
heights:
symmetric
(A)
symmetric rigid rotor,
rotor,
E
and barrier
very high barrier,
intermediate barrier,
(B)
(C) asymmetric rotor,
intermediate barrier,
(D) asymmetric rotor,
(E) asymmetric rotor,
very high barrier
high barrier,
(9).
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
77
Hamiltonian in Equation
Equation
(4.5),
(4.4)
the torsional potential,
and the torsional kinetic energy,
T = F(P - p
) 2
.
(4.6)
In this equation p is the momentum conjugate to the
torsional angle
y
angular momenta.
and P is a function of the rotational
The calculation of the energy levels for
an asymmetric rotor with internal rotation has been reviewed
(9).
However,
as will be discussed in the next section,
special techniques are nece ssa ry for calculation of the
levels for methanol.
Methanol
Methanol is an asymmetric top molecule with an
internal degree of freedom,
hinder ed internal rotation.
in Figure 4.3.
referred to as torsion or
The CHgOH molecule is pictured
The theoretical background work done on
CHgOH and its rotation-internal rotation spectrum has been
elegantly presented in a series of papers by Dennison and
co-workers
(11-16).
The three parameters associated with
the external rotation are the moments of inertia I , I. and
3
D
I
about the three orthogonal axes through the center of
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
78
Q
b
H
H
Figure
4.3.
H
A
schematic
representation
of
the
CH^OH
m o l e c u 1e .
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
79
gravity of the molecule,
as shown in Figure 4.3.
The
internal rotation is hindered by the potential function in
Equation
(4.5).
In methanol,
the ba rr i e r height Vg >> Vg.
is usually chosen to be parallel
CHg group,
The a-axis
to the symmetry axis of the
while the b and c axes are orthogonal to a with b
in the COH-plane.
These axes are also shown in Figure 4.3.
For a proper understanding of the internal
must know how I
a
is shared between I
inertia of the CHg group,
a
rotation we also
0 , the moment of
<2
and Ia ^ = Ia“ Ia » which is
2
essenti al ly the moment of inertia of the OH group.
methanol
1
^
and especia lly Iflj are both small,
complicates the energy calculation.
In
and this
Along with the
parameters already men t i o n ed there is a small product of
inertia,
arising from the asymmetry.
Additional
parameters include centrifugal distortion constants,
parameter Vg,
a set of Kirtman constants
the
that account for
the effect of centrifugal distortion on the internal
rotation,
and of course the center frequency of the
vibrational band.
The most recent calculation of the energy levels for
methanol with the parameters just described has been carried
out by Henningsen
(17).
In his theory,
be described by the quantum numbers
indicates the vibrational
state,
an energy state can
(n,-r,K,J)v , where v
J is the total rotational
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
80
angular mo mentum quantum number,
of the rotational
K represents
the projection
angular momentum on the a-axis,
to label the torsional
level,
and t can be
1
,
2
n is used
or
for the
3
three nearly degenerate torsional states for each level.
Wit h this notati on the energy levels can be written as
E (n*rK, J) V = E yife + B v (nTK ) J ( J + l ) - D v (nTK) J (J+1
2
- HV (nTK ) J (J+l
3
+ (asym.
Equation
(4.7)
) 2
+ W V (htK)
) 3
(17),
(4.7)
split.)
looks similar to a symmetric top energy
level expansion except for the W V (n-rK) and the (asym.
split.)
terms.
The coefficients
in Equation
(4.7)
are as
follows,
Bv (m-K)
= | (B + C) + FV <1 - cos3y> + G y <py2 >
+ L yK<py> - U JkK
2
+ b(
h t
K )
,
D V (n-rK) = D j j - d ( n TK ) ,
(4.8)
(4.9)
W v (n-rK) = | V <l-cos3y> + F<py 2 >
3
+ [A - | (B + C) ] K
2
+ AE(htK).
(4.10)
The term with H(n-rK) is added to get a better representation
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n prohibited w ith o u t p e rm is s io n .
81
of the energies at high J, p is the momentum conjugate to
the angle of internal rotation y shown in Figure 4.3,
and
the bracketed quantities are internal rotation expectation
values.
The constants B, G,
F and A are related to the
moments of inertia of the molecule according to
B =
2
2
V
C =
I
+
a
(4.12)
I a Iv
b - K ab
I
I
4"
4n
c
F =
A =
I
al a
I
2
b
-
I
(4.13)
a
1
2
4i
ab
+ I,
b
2 +
I
V b
(4.11)
*
- W
b
(4.14)
2
j
ab
The terms that are multiplied by Fv> G v and
are
centrifugal interaction terms that affect the internal
rotation.
The constants Dj^ and D j j
centrifugal stretching constants,
are the normal
while b(n-rK) and d(m-K)
represent contributions from the asymmetry.
The first two
terms of W(n-rK) are the expectation values of the potential
energy and kinetic energy of the internal rotation,
while
AE(n-rK) lumps together the rest of the contributions to the
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
82
internal rotation.
AE(m-K)
= 1/2 V
0
The term AE(n-rK) can be expressed as,
<1 - c o s r> - D KRK
6
+ kjK
4
3
<py >
(4.15)
+ k K <py 2 > + k K < p y 3 > + k <py4 > + k K <l-cos3r>
2
2
3
4
5
2
+ k g K < p y (l - cos3y)> + k ^ < p y2 (l - cos3y)> + d^.
The expectation values are evaluated for the basic
wavefunctions of
0
for the state m-K.
The seven Kirtman
constants are also used to calculate the J-independent
centrifugal effects.
The final
asymmetry of the molecule.
term dp is from the
Table 4.2
lists all of the
parameters used in the energy level calculation by means of
Equation
(4.7).
For the vibrational ground state
(v = 0),
the 20
parameter model described above works well enough to
represent the energy levels of the torsional ground state
= 0) to an accuracy of 0.002 cm * in the range of K <
J < 15.
However,
6
(n
and
for the excited torsional states of the CO
stretch fundamental,
the situation is not as good.
an idea of the complexity of the spectra,
To give
Figure 4.4 is a
line spectrum of a region of the CO stretch in methanol
compared to that of a normal symmetric top molecule.
Henningsen has done a considerable amount of work on
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
83
Table 4.2.
Parameters used to calculate the energy levels
of the ground and Vg =
Parameter
8
1
states of CHg OH.
C H qOH
ground state
*b
I
c
Xal
Xa
kl
35.306262
35.6380
(26)
d
1.2504
1.2523
( )
5.3331
5.3334
( )
373.21
392.35
(30)
8
8
-0.52
d
0.3 8xl 0“4
d
-0.4 8 x l Q ~ 4
d
-1 8. 41x l0-4
d
- 53 .73x lQ
d
2
k3
k4
k5
k
(26)
6
dkk
k
34.2828
2
V3
V
(3)
34.003856
-0.1079
^ ab
CHgOH
ic
v5
1030.084
0
E vib
b
-
4
-8 5. 50 x l0 -4
d
1 37.07xl0-4
d
6 7 . 85xl0~4
d
6
k 7/
V
G
L
d
0
V
V
°JK
- 2 . 38 9x l0~ 3
-6 .5 46x l0-3
- 1 . 168xl0-4
- 1 . 67xl0-4
- 2. 26 xl 0“ 6
d
9.54 xl 0
d
~
6
1.6345xl0-6
DJJ
d
The units for the inertial parameters (I ’s) are
2
47
kgm xlO
. The units for all of the remaining
parameters are cm
b
c
d
Reference
(16).
Reference
(17).
The ground state parameters were assumed for the excited
state.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
84
Asymmetric Molecule
with T orsional B a r r ie r
A<£21
ECH45 E a i>
A(2,1)A(U)
E<£2>
E(2.2i EC24)Eai)
e
t
a
s
A
<2,1)015
E
canoi)
\
\
\ \ i
x
x
\
' ■
\ \
^\
nm \
Top
Molecule
\
\
7
/
L
\ v j A
symmetric
/
'
'
/ / /
- 1
/ z "
A
//
Xa*fa t /u Wto
1033.8 cn
1033.7
Figure 4.4.
“
1 0 3 0 cn
-I
Vibration-rotation spectra comparing a
top molecule to an asymmetric molecule with a
torsional barrier.
It should be noted that the scale of
s plitting for the symmetric top is five
asymmetric top with
internal
times that for the
rotation.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
85
the theory and data analysis of the GHgOH molecule
(4,17,18),
and has come up with J independent constants to
form an equation for the frequencies of the transitions from
v = 0 to the v = 1 vibrational state.
His equation takes
the following form for an R branch transition:
j/(J-J+l) = wv i b (nTK) + SB (J + l ) (J+2) + 2B° (J + l )
- 4D°(J+1
) 3
- SD(J+1) (J+2
2
SH(J+l) ( J+ 2
3
) 2
- 6H°(J+1
) 3
) 3
(4.16)
where
%ib
vv i b (nTK)
+ w l (n T K ^ " W ° ( n TK ) ,
(4.17)
SB (n-rK) = B (n-rK) - B° (n*rK) ,
(4.18)
SD(m-K)
= D (nTK) - D°(m-K),
(4.19)
SH(n t K ) = H (nTK) - H ° ( n TK).
(4.20)
1
1
1
The constants
Henningsen
in Equation
(4.16) were determined by
(17) and are listed in Tables 4.3 and 4.4.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
86
Table 4.3.
vibrational
n T K
0
1
0
O i l
0
0
0
0
0
0
0
0
1
2
13
14
15
16
17
18
19
0
1
1 0
0
2
0
0
2
1
0
2
2
0 2 3
0 2 4
0 2 5
0
2
6
0 2 7
0
2
8
0 2 9
0
2
1 0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
3
0
1
2
3
4
5
6
7
8
9
10
Calcula ted energies and coefficients for the
ground st at e. 3 .
(cm ^ )
127.975
131.851
143.435
162.587
189.072
222.553
262.618
308.841
360.901
418.699
482.396
137.097
142.602
154.183
171.559
194.697
223.820
259.319
301.615
351.077
407.975
472.479
137.097
138.080
145.975
161.136
183.818
214.174
252.264
298.057
351.430
412.166
479.949
-B^(cm ^)
0.806772
0.806768
0.806761
0.806724
0.806684
0.806628
0.806550
0.806443
0.806302
0.806126
0.805920
0.806865
0.806858
0.806861
0.806815
0.806733
0.806622
0.806489
0.806341
0.806183
0.806020
0.805855
0.806865
0.806831
0.806763
0.806696
0.806620
0.806536
0.806443
0.806340
0.806224
0.806094
0.805946
D°(cm
1
xl0 6 )
4.91
6.45
-3.03
1.13
1
.
6
6
1.80
1.81
1.78
1.72
1.67
1.64
1
2
.
8
6
0.69
1.67
1.61
1.51
1.45
1.44
1.47
1.53
1.63
1.75
1
2
.
8
6
3.15
-2.83
-0.15
0.77
1.25
1.54
1.72
1.82
1.87
1
.
8
8
£
Ca lc ul at ed by Henningsen
(16).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Table 4.4.
Calcul ate d energies and coefficients for the
CO stretc hi ng st ate .3 .
n
t
0
1
K
0
O i l
0
0
0
0
0
0
0
0
1
2
13
14
15
16
17
18
19
0
1
1 0
0
2
0
0
2
1
0
2
2
0 2 3
0 2 4
0 2 5
0
2
6
0 2 7
0
2
8
0 2 9
0
2
1 0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
3
0
1
2
3
4
5
6
7
8
9
10
W fcm 1 ')
. . - .
B (cm
)
132.281
136.135
147.651
166.696
193.043
226.375
266.311
312.467
364.559
422.500
486.436
140.719
146.053
157.536
174.922
198.182
227.513
263.264
305.819
355.521
412.625
477.295
140.719
141.906
150.001
165.337
188.156
218.607
256.747
302.544
355.880
416.544
484.237
0.797808
0.797813
0.797827
0.797844
0.797863
0.797873
0.797857
0.797794
0.797666
0.797470
0.797216
0.798126
0.798187
0.798219
0.798177
0.798067
0.797902
0.797703
0.797491
0.797279
0.797078
0.796891
0.798126
0.798029
0.797898
0.797781
0.797671
0.797572
0.797483
0.797403
0.797329
0.797255
0.797172
1
1
1
D 1 (cm
1
xl0
G )
5.22
7.09
-
2
.
8
8
1.07
1.62
1.77
1.79
1.76
1.72
1.67
1.64
12.75
0.14
1.54
1.55
1.48
1.44
1.44
1.47
1.53
1.62
1.74
12.75
3.24
-2.75
0.78
1.25
1.53
1.70
1.80
1.85
1.87
0
.
1
2
£
Calcul ate d by Henningsen
(16).
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
88
4.3
Experimental
Introduction
The generation of microwave sidebands on COg laser
emission was first demonstrated in 1979 by Corcoran et. a l .
(19).
Since then,
there have been m an y improvements on
tunability and power of COg laser microwave sideband systems
(20-23).
The most suitable COg sideband laser for both
linear and non-linear spectroscopy is the one developed by
Magerl et. a l . (24).
The first spectroscopic investigation with infrared
micr owa ve laser sidebands was performed by Magerl e_t a l .
(25) on the SiH^ molecule.
Since this first experiment
several others have been carried out
number of studies
Un ive rsi ty
(26-28)
including a
in our laboratory at Michigan State
(1); both Doppler limited and sub-Doppler
spectroscopy have been performed.
In this chapter an
applicat io n of this technique to the CHgOH molec ul e is
described.
COg Laser
The COg laser used for this experiment includes a 2.0
meter,
semi-sealed plasma discharge tube that contains a
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
89
mixture of COg,
Ng,
and He at a total pressure of -10 Torr.
The plasma is cooled to 5°C by circulating a refrigerated
50-50 mixture of ethylene glycol
in water.
The laser tube
is a 1.7 meter Pyrex glass tube sealed with ZnSe windows at
the Brewster angle.
This arrangement of the windows creates
laser emission that is po larized parallel to the plane of
the optical table.
One end of the cavity is a rotatable
plane grating ruled with 150 lines/mm mo unt ed on a lansing
Research Corp.
rotatable mount.
is a partially transmitting
concave mirror.
translator
The other end of the cavity
(90S reflection)
spherical
The mirror is mounted on a piezoelectric
(PZT) to control the length of the cavity.
The laser radiation
is directed through a cell
containing COg at a pr essure of 10 - 50 mTorr and then
reflected back on itself.
The fluorescence from the COg is
detected at a right angle to the beam by a liquid Ng cooled
InSb photovoltaic detector
(Judson Infrared Inc.
J10D).
By
sinusoidal modulation of the l a s e r ’s end mirror the laser
cavity length is changed and therefore so is the laser
frequency.
The modulation frequency is 250 Hz.
from the fluorescence detector,
The signal
which is the first
derivative of the saturation dip in the fluorescence as a
function of frequency,
sensitive detector
is processed at 250 Hz by a phase
(PSD).
The output from the PSD is fed
back to the operational power supply which controls
the
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
90
piezoelectric translator
back loop.
process
(PZT),
thus co mpleting the feed­
By using this extra - cavity stabilization
the laser frequency is controlled to ± 150 kHz.
Figure 4.5 shows a diagram of the ex tr a-cavity laser
stabilization scheme.
A short experiment was done to obtain the laser
uncertainty.
The experiment consisted of focusing two COg
lasers on a liquid nitrogen cooled Honeywell Radiation
Center Hg-Cd- Te photovoltaic detector.
The output of the
detector was then processed by a spectrum analyzer.
The
stabilization scheme used can control the laser to ± 150
kHz.
The conditions for this experiment wer e that both
lasers were locked by the external fluorescence cell method
described above.
Most of the laser "jitter"
is due to the
dither voltage applied to the PZT to mo dul ate the
fluorescence.
Sideband Generator
The electrooptic crystal used to combine the two
radiations is made of CdTe.
explained in detail
in Dr.
The structure of the crystal
Sang L e e ’s Thesis
(1).
is
The
3
dimensions of our crystals are 3x3x25 mm
.
The sideband
power can be expressed as P , and is related to the incident
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
PSD
AMP
M2
M3
Fluorescence Detector
OPS
Power
Supply
B ■
OSC
Figure 4.5.
CO_ Laser
A block diagram of
P Z T
an e xt ra —cavit y
stabilization scheme used on the CO_
laser
laser.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
laser power by the equation
(29),
Psb = P Lr2/16 •
Here,
<4 -2 1 >
is the incident laser power and T is the single -
pass phase retardation induced by the transverse
ele ct rooptic effect.
This second term is linearly dependent
on the mi c r o w a ve electric field and the length of the
modulator crystal.
proportional
The F term is also inversely
to the wavelength of the COg laser.
The
sidebands that are generated from the crystal are referred
to as plus or minus according to the occurrence of a + or sign in the equation for the frequency of the sideband,
vsb = VC
Here,
Vg^,
, and
0
2
1
vmw •
(4 *22)
are the frequencies of the
2
sideband,
the laser,
and the micro wav e source,
respectively.
A diagram of the mo dulator is shown in Figure 4.6.
The
specifi ca ti on of the crystal size and the design and
adjustment of the housing was done by G. Magerl of the
Technical U n iv er sit y of Vienna.
The radiation from the COg
with its electric field parallel
optical
table.
laser is plane polarized
to the surface of the
The sideband radiation is generated in the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
CdTe
Crystal
Figure 4.6.
crystal
A diagram of the sideband modulator.
The CdTe
is inserted between two AlgOg slabs in a brass
housing that
is matched to double-ridged waveguide.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
crystal and emitted at a polarization that is perpendicular
to the polarization of the incident carrier.
Therefore,
polarizer can be used to partially separate the carrier
laser)
from the two sidebands
(vT ±
L
v
mw
).
a
(COg
A sketch of the
polarizer and radiation is shown in Figure 4.7.
The
separation of the radiation into carrier and sidebands by
means of a polarizer is not perfect
for two reasons.
First,
the carrier power is typically four orders of magnitude
higher than the sideband power,
discrimination that high.
and no polarizer has a
Second,
the carrier radiation
leaving the mod ulator is slightly elliptically polarized,
so
that some carrier ends up having the same polarization as
the sidebands.
Figure 4.8 shows the experimental diagram of a COg
sideband laser spectrometer in the arrangement
absorption spectroscopy.
for
The microwave radiation was
generated by a Varian backward wave oscillator
(BWO)
operating in the 8.0 - 12.4 GHz or the 12.4 - 18.0 GHz
region.
The BWO frequency is controlled by an operational
power supply
(OPS) used to create the helix voltage.
OPS is controlled by the output
from a digital
converter signal from the mi ni computer
The
to analog
(Digital P D P / e ) .
8
The BWO is stabilized by a phase sensitive synchronizer
(Hewlett Packard Model 8709A) which locks the microwave to a
harmonic of a synthesized frequency also controlled by the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
CO
CdTe
Figure 4.7.
Crystal
A diagram of the electric fields of the C 0
laser and sideband
laser as created by the sideband
modulator crystal.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9
96
Power
Supply
Laser
Cavity
PZT
□ et.
Sample Cell
M od.
DET
Polar.
Amp
Pream p
Power
OET
Meter
BWO
PSD 1
PSD 2
TWTA
BWO
Power
Synch.
S tab.
Mod.
MW
Control
A/D 2
Computer
Figure
4.8.
A
diagram
of
the
sideband
TTY
laser
spectrometer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
computer.
The output radiation from the BWO is divided into two
parts by a directional coupler.
One part
is sent to a diode
mi xe r-multiplier for locking to the pr ecisely known
reference frequency.
The other part of the power goes to a
PIN diode where it is switched on and off at 33.3 kHz.
The
switched microwave power is amplified by a traveling wave
tube amplifier
(Varian Model VZM-6991B1 TWTA).
The output
from the TWTA is sent through a coaxial cable to an adapter
to double ridged wa veguide and then to the modulator
crystal.
The microwave radiation leaving the crystal
is
terminated by an absorbing termination for normal operation
or by a tunable short arrangement for operation in the
higher power resonant mode.
The laser radiation is focused by a 10 inch focal
length ZnSe lens in front of the crystal modulator.
the modulator,
After
the radiation is recollimated by another ZnSe
lens with a focal length of 2.5 inches.
This combination of
lenses condenses the beam by a factor of ~ 4 .
The polarizer
used includes six ZnSe windows placed at the Brewster angle
for the sideband radiation,
carrier radiation
which then reflects most of the
(II VI Inc.
polarizer).
A Ge beam splitter divides the sideband radiation into
two parts.
One beam is used as a reference while the other
goes through the sample cell to the sample detector.
The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
reference beam is mon itored by a liquid Ng cooled Infrared
Associates Hg-Cd-Te photoconductive detector.
The output
from a preamplifier is pr ocessed by a phase sensitive lockin amplifier at the reference frequency of 33.3 kHz which is
the PIN diode modulation frequency.
lock-in amplifier
is sent
The signal from the
into a feedback control circuit
designed by Mr. Ma rtin Rabb at Michigan State University.
The microwave power is controlled by this circuit through
partial attenuation during the "on" period of the PIN diode.
The feedback circuit keeps the sideband power at the
reference detector at a constant
level throughout
the
microwave sweep.
The sample pressure used for the linear absorption
experiments was 0.05 - 1.5 Torr.
Most of the experiments
were run at 150 mTorr with a cell that has a 50 cm path
length.
For some of the weaker transitions,
a higher
pressure was used.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
4.4
Results and Discussion
The comple xi ty of the infrared sp ectrum of the
methanol mo lecule
evident
in the CO stretch region
(vg band)
is
in both the FTIR spectra and in absorption signals
from the sideba nd experiment.
of assignment,
transitions
To illustrate the difficulty
a FTIR absorption sp ectrum of the CO stretch
is di splayed in Figure 4.9.
as the center feature
The Q bra nc h shown
is very compact and unresolved.
The
COg sid eba nd laser was also unable to resolve the Q branch;
however,
P and R bra nc h transitions were easily
distinguished.
A total of 26 laser lines were used to search through
and record the vg band of CHgOH.
The num be r of transitions
fit to a Ga ussian lineshape to find the center frequencies
and relative intensities of the absorption signals was 269.
A typical absorption spectrum of methanol taken by the COg
sideband spectrometer
is shown in Figure 4.10.
The sweep
shown here contains both positive and ne gative sideband
absorption signals because we do not employ a monochr oma tor
to separate the two sidebands.
sidebands,
Even without separating the
the spectra can be distinguished by recording
with the laser frequency intentionally displaced from its
center frequency.
In this case the frequencies of
transitions from the positive and negative sidebands will be
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
Methano
0.16
0 .1 4
0.12
A b so r b a n c e
0.10
0.08
0.06
0 .0 4
0.02
0.00
950
970
990
10 1 0
1030
1050
1070
1090
1110
W a v en u m b ers
Figure 4.9.
FTIR spectrum of the CO stretch band of CHgOH.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
cti
a
tafl
•H
CO
15.50 15.70 15.90 16.10
16.30 16.50
Frequency (GHz)
Figure 4.10.
A typical scan of the sideband laser showing
four transitions of CHgOH.
9P(26)
The COg laser is fixed at the
laser line while the microwaves are swept.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
102
shifted in different directions.
An experiment to determine the ratio of (+) sideband
radiation to (-) sideband radiation was carried out.
The
reason for this experiment was to see if both sidebands
existed and to record their relative powers.
The experiment
used a Bausch and Lomb monochro ma tor to separate the two
sidebands.
After leaving the mo nochromator the radiation
was focused onto a liquid Ng cooled Infrared Associates HgCd-Te pho tovoltaic detector.
The detector output was
processed by a phase sensitive lock-in amplifier
R ese arc h System 510)
(33.3 kHZ).
vs.
(Stanford
at the sideband modulation frequency
A plot of the ratios of - to + sideband power
f re quency for two different
Figure 4.11.
laser lines is shown in
The reason for the change with frequency of
the sideband ratio is not understood at this time.
However,
it should be pointed out that both sidebands exist and are
of comparable power.
The measure d frequencies of several transitions are
compared to the results of diode laser measurements by
Sattler et_ al_.
(2,3)
in Table 4.5.
The comparison shows
that the frequencies agree within the experimental error of
the diode laser work,
whic h is an order of magnitude or more
greater than in the present study.
Many of the transitions
seen in the sideband experiment are very weak and do not
appear in the reports of the theoretical calculations
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
103
t
6.00
r
1
-j---- J—
r
5.00
XXX
X
X
^
4.00
\
XX Q
x
I
^
o
3.00
O
X
X
X X
X
o
X
. r— |
•+J
<d
Oh
XX
o
X
* XX
*
X
* X XX
o
o
o°
2.00
o
o
O
o
O
e
o
o
X
XX
1.00
00oo0°o ®°o°
o °
o
O o ooo‘
X
oo
oo
0.00
7.5
8.5
9.5
10.5
11.5
12.5
Frequency (GHz)
Figure 4.11.
microwave
(o) and
A plot of the ratio of
fr equency for two different
10R(24)
(-/+)
sidebands versus
laser lines
(9P(16)
(x)).
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
104
Table 4.5.
Comparison of CHgOH Transitions.
S a tt l e r a
n ,
b
Peterson
R ( 1> 0,0,2)
1036.882
1036.88297
R(5, , , )
1042.749
1042.74944
R ( 5 , 1,0,2)
1042.850
1042.85117
R ( ,0,0,1)
1044.685
1044.68656
R ( 7 ,2,0,3)
1046.377
1046.37772
R ( 7 ,1,0,3)
1046.300
1046.30095
R ( l l , 0,0,1)
1051.832
1051.83457
R ( 1 3 , 1,0,2)
1054.299
1054.29710
Transition
(J j k ,n ,t )
2
0
2
6
81
k
Reference
(2,3),an experimental
accuracy of ±0.004 cm ^
Sideband work done at Michigan State University.
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
105
(17,18)
or the data from the diode laser work
(2,3).
These
transitions are most likely higher order torsional states
> 1) or hot band transitions of the CO stretch band.
A full
list of transitions and intensities is presented in the
Appendix.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
(n
106
4.5
References
1.
S. K. Lee,
1986.
2.
J. P. Sattler, T. L. Worchesky,
Infrared Phys. 18., 521 (1978).
and W. A. Riessler,
3.
J. P. Sattler, T. L. Worchesky,
I n f r a r e d .P h y s . JL9., 217 (1979).
and W. A. Riessler,
4.
G. Moruzzi, F. Strumia, C. Bonetti, B. Carli,
F. Mencarglia, M. Carlotti, G. DiLonarado, and
A. Trombetti, J. Mol. Spec. 1 0 5 , 24 (1984).
5.
J. 0. Henningsen,
.
6
7.
8
.
9.
Ph.D.
Thesis,
J. Mol.
Michigan State University,
Spec.
M. Born and J. R. Oppenheimer,
(1937).
83,
70
Ann.
(1980).
Physik,
84, 457
E. B. Wilson, J. C. Decius, and P. C. Cross,
Vibrations", McGraw-Hill, New York, 1955.
B. S. Ray,
Z. Physik,
78,
"Molecular
74 (1932).
C. H. Townes and A. L. Schawlow, "Microwave
Spectroscopy", Dover, New York, 1975.
10. J. K. G. Watson,
J. Chem.
Phys.,
48, 4517
11. J. S. Koehler and D. M. Dennison,
(1940).
12. D. G. Burkha rd and D. M. Dennison,
(1951).
Phys.
(1968).
Rev.,
Phys.
57., 1004
Rev.,
84, 408
13. E. V. Ivash and D. M. Dennison,
(1953).
J. Chem.
Phys.,
21., 1804
14. K. T. Hecht and D. M. Dennison,
(1957).
J. Chem.
Phys.,
26, 48
15. D. G. Burkha rd and D. M. Dennison,
(1959).
16. Y. Y. Kwan and D. M. Dennison,
(1972).
J. Mol.
J. Mol.
Spec.,
Spec.,
3., 299
43., 291
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
107
17.
J. 0.
Henningsen,
J. Mol.
Spec., 85., 282
(1981).
18.
J. 0. Henningsen,
J. Mol.
Spec., 1 0 2 . 399
(1983).
19.
V. L. Corcoran, R. E. Cupp, J. J. Gallagher,
Smith, Appl. Phys. Lett. 16, 316 (1970).
20.
P. K. Cheo and M. G. Gilden,
(1976).
21.
E. Bonek and H.
(1974).
Korechy,
Bonek,
Appl.
Appl.
Phys.
Phys.
22.
G. Magerl and E.
23.
G. Magerl and E.Bonek,
(1979).
24.
G. Magerl, W. Schupita, and E. Bonek,
Electron. Q E - 1 8 . 1214 (1982).
Appl.
25. G. Magerl, E. Bonek, and W.
Lett. 52, 473 (1977).
Phys.
Lett.,
Lett.,
J. Appl. Phys.,
and W.
28,
34, 452
Chem.
Phys.
26.
G. Magerl, W. A. Kreiner, B. Furch, and E. Bonek,
Phys. Austriaca Suppl. 20., 167 (1979).
27.
G. Magerl,
Mol. Spec.
N. McAvoy, J. Osmundson,
U , 473 (1972).
Acta
and W. A. Kreiner,
28. G. Magerl, J. M. Frye, W. A. Kreiner,
Phys. Lett. 42, 656 (1983).
29.
(1976)
IEEE J. Quantum
A. Kreiner,
W. Schupita, E. Bonek,
83, 431 (1980).
626
25., 750
4£, 4901
Lett.,
T.
and T. Oka,
and G. Schiffner,
Appl.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
J.
Appl.
Opt.
CHAPT ER V
Infrare d-M ic row av e Double Re sonance with a Sideband Laser
5.1
Introduction
Infrared-mi cro wav e double resonance has been an
important
investigative tool used for studies of both weak
transitions and very densel y packed vibrational bands.
The
normal scheme of the infrared microwave double resonance
experiment
is to pump a vibration rotation transition with
strong infrared radiation and observe the rotational
transitions
in the excited vibrational state with a weak
microwave source.
However,
this type of experiment
is
limited to vibrational transitions coincident with the
pumping infrared radiation source,
usually a continuous wave
laser w ith wi de ly -sp ace d lasing frequencies.
experiments done in the high resolution
The
infrared
sp ect ros cop y laboratory at Mic hig an State University
utilized a high power microwave source to pump ground state
rotational
transitions and a low power infrared COg sideband
laser to observe vibration rotation transitions.
This
arrangement of co ntinuously-tunable pump and signal sources
enables
the use of the extensive
information available about
ground state rotational transitions,
so that observation of
108
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
109
a double resonance effect usually leads to straightforward
assignment of the excited vibrational band.
is identical
This technique
to the FTIR - microwave double resonance
experiment explained in Chapter 3, except that we now have
replaced the FTIR with a tunable infrared microwave sideband
laser
(IMSL).
Wi th the advent of the sideband laser new experiments
in high resolution laser spectroscopy became possible.
The
use of an electrooptic modulator to generate microwave
sidebands on COg
infrared laser radiation was
first carried
out for spectroscopic investigations by Corcoran et. al.
(1)
and later developed into a practical procedure by Magerl et
a l . (2).
The sideband laser employs a CdTe electrooptic
crystal which mixes microwave and infrared radiation and
generates
frequency tunable coherent
high spectral purity.
infrared sidebands of
The sidebands are the infrared
frequency plus the microwave frequency and the infrared
frequency minus
the microwave frequency.
Thus by changing
the mic ro wav e frequency the frequencies of the sideband
laser can be changed.
The first applications of an IMSL system in the COg
laser region at Michigan State University made use of a
mod ulator designed and adjusted by G. Magerl and were
carried out by S. Lee (3,4).
transitions
In this work a large number of
in the Vg fun damental bands and in the
2
i/g
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
*•
vg
110
bands of
12
parameters
GHgF and
13
were assigned.
including quartic,
sextic,
The molecular
and octic centrifugal
distortion constants were determined.
Lee also used the COg
sideband laser and a wa veguide laser for infrared-infrared
double resonance
(5).
Almost simultaneously,
H.
Sasada used
the IMSL system to measure the frequencies of a number of
transitions
in vibrational hot bands of
In addition to the work at MSU,
IMSL systems
and
6
in the COg
laser region have been used in the laboratories of
and Oka.
( ).
Magerl
Oka and Magerl have also collaborated on many
projects and were the first
to obtain sub-Doppler spectra
(so-called "saturation dips" or "Lamb dips") wi th a
sideband laser system
(7).
The Lamb-dip results demonstrate
that the radiation is sufficiently powerful to saturate
vibration-rotation transitions.
The COg sideband laser has
also been used for ion spectroscopy and infraredrad io fr eq ue ncy double resonance spectroscopy (8,9).
obvious
It is
from this short h istorical overview of the sideband
laser that the IMSL system is an important tool
in the field
of laser spectroscopy.
The topic of infrared-microwave double resonance was
discussed in Chapter 3;
therefore,
only discuss the molecules
the present chapter will
involved in these studies and the
results obtained from the double resonance experiments.
next section will describe the calculations
The
carried out for
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Ill
CHgOH and CFgl.
After that,
the three-level
and the lineshape analysis will be presented.
calculations
Finally,
the
experiments perf or me d on CHgOH and CF^I along with an
explanation of the results from the lineshape calculation
will be covered.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
112
5.2
Theory
Methanol
(CHgOH)
The vibration rotation energies of methanol have been
described in detail
in Chapter 4.
Therefore,
in this
section the theoretical considerations and the parameters
used for calculation of energy levels
in the CO stretching
vibrational state will be di scussed only briefly.
Methanol
is a slightly asymmetric top wi th internal rotation.
The
internal rotation of the OH group can be described by using
two quantum numbers n and
t
.
Henningsen
an equation for the energy levels
parameters
independent of J.
(10) has developed
in methanol which has
The equation is given below.
E ( n , T , K , J ) V = E vibV+ B V (n,T,K)J(J+l)
- D V (n,T,K)J (J+l
2
+ W v (n,T,K)
Here,
3
) 3
splitting)
(1,2,
t
designates the
or 3) for each
K is the projec ti on of the rotational
angular momentum on the a-axis,
state,
- H V (n,T ,K)J (J+ l
level and
three nearly degenerate states
level,
2
+ (asym.
n labels the torsional
torsional
)
(5.1)
v denotes
the vibrational
and J is the angular mo m e n t u m quantum number.
quantity
v
is the center frequency for the v
The
th
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
113
V
V
vibrational b and and B , D , H
listed by Henningsen
(10,11).
V
and W
V
are all constants,
as
The asymmetry is treated as a
perturbation because of its small effect on the energy
levels.
The equation used to calculate the asymmetric
splitting is
asym.
where S
co
splitting =
(K,n)
SC O (K,n)
r
)!
(5.2)
is a rapidly decreasing function of K,
S C O (l,l)
= |(B - C ) CO
S C O (l,l)
= 4 1 . 9 MHz
S°(l,l)
= 4 8 . 6 MHz
S°(2,l)
= 0.0097 MHz
S C °(2,1)
= 0.0065 MHz
Where 1^
(j -
:ls_J
(5.3)
is the overlap integral of the A-state internal
rotation wavefunctions with K = ± 1.
The terms,
Sco and
are splitting constants for the CO stretch and ground
states,
respectively.
By using equation
(5.1)
for the energy levels the
frequencies of the P,Q and R branch transitions can be
calcul at ed by the following three equations,
respectively:
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114
P branch
v(J^J-l)
(5.4)
= i/v i b (nrK) +
SB(m- K) J(J + l ) - 2B C O (nTK)J
- SD(nTK ) J (J+l
2
) 2
+ 4 D COJ
3
- SH(n-rK) J
3
(J + l )
3
+ H C O (nTK ) J ( J 2+ 2)
3
6
Q branch
(5.5)
i/(J*J) = vv i b (nTK) +
SB(nTK)J(J+l)
- SD(m-K)J (J+1
2
) 2
- SH(nTK)J3 (J+l)3 .
R branch
v(J-J+l)
(5.6)
= vv i b (nTK) +
SB(m-K)(J+l)(J+2)
+ 2B (nTK)(J+l)+4D (nTK ) (J + l ) - S D ( n TK ) (J+l ) (J+2
0
0
3
2
) 2
- H 0 ( h t K ) (J+1) ( 6(J+1)2+ 2) - S H( nTK )(J +l) (J+2)3 ,
3
Here,
3
v v i b (nTK) = vvib + W c o (nTK) - W ° ( n TK),
SB(nTK)
= B C O (n-rK) - B°(m-K),
SB (nTK) = D C O (n*rK) - D°(nTK),
S H U t K) = H C O (n-rK) - H ° (n TK) .
Equations
(5.4),
(5.5)
and (5.6) were used by Henningsen to
calculate the frequencies of the rotation-vibration
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
115
transitions of the CO st retching band of CH^OH.
This
calculation was also done in our laboratory and used for
comparison with the experimental results.
CF3I
CFgl is a symmetric top mo lecule with a nuclear
electric qu adrupole moment from the 5/2 spin of the iodine
nucleus.
large
The quadrupole coupling constant
(~2100 MHz).
in CFgl
is very
Use of a rigid rotor approximation for
CFgl with addition of centrifugal distortion effects
associated with the rotation gives
E(J,K)
= B J (J + l ) + (A-B)K
- Dr K
2
- D j J (J+1
2
- Djr J ( J + 1 ) K
4
+ H jjkJ
2
(J+1) K
This equation
2
2
2
(5.7)
) 2
+ HjjJ (J+1
3
+ Hjkk J( J + 1 ) K
is a power series
4
)
3
+ hkkk k
in J(J+1)
6
+ ...
and
K2
.
For
low J and K values the quartic centrifugal distortion terms
are adequate.
and K,
However,
for energy calculations of high J
as with any expansion series,
should be included.
Equation
(5.7)
the higher order terms
does not
include any
effects of the quadrupole splitting caused by the iodine
atom.
R e p r o d u c e d with p e r m i s s io n of t h e c o p y rig h t o w n e r . F u r th e r re p r o d u c tio n p roh ibite d w ith o u t p e r m is s io n .
116
The size of the quadrupole coupling constant makes
pe rt urbation theory inadequate for energy level
calculations.
(12) was used.
Therefore a method developed by Benz et. a l .
By setting up an energy matrix and
di agonalizing it directly,
the energy levels can be
calculated to high accuracy.
The non-zero elements of the
energy matrices used for the calculation are as follows:
<J,K,F|H|J*,K.F> = <J,K,F |H R iJ,K,F>SJ j.
(5.8)
+ < J iK, F |HQ |J ‘,K, F>
<J,K,F|Hr |J,K,F> = B J (J + l ) + (A-B)K
- Djk J ( J + 1 ) K
<J,K,F|HJJ,K,F>
xf
= e. [ 3 K
2
2
- J (J +l) ]x
2
2
- Dr K
2
1
<J,K,F!Hq |J+1,K,F> = - 3 e K [ ( J + l
- Dj J (J+1
) 2
(5.9)
) 2
4
(5.10)
zz
- K ] / X zz
2
1
(5.11)
2
= <J+1,K,F|H q |J,K,F>
(5.12)
<J,K,F|HQ |J+2,K,F>=3e {[(J+l) -K ][(J+2) - K ]} / Xzz
3
2
= <J + 2 ,K,F|H
In these equations,
2
2
2
1
2
|J,K,F>
(5.13)
F is the quantum number for the
square of the total angular momentu m
(vector sum of
rotational and nuclear spin angular momentum ) and x
zz
= eQq
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
117
is the quadrupole coupling constant.
elements of
All other matrix
+ H q are assumed to be zero.
e
- -3_G.(G + l)/4 - 1(1 + 1)J(J H- 1)
el
21(21 - 1)J(J + 1 ) (2J - 1 ) (2J +3)
G
= F (F + l ) - 1(1+1)
Also,
'
- J(J+1),
(5.15)
e 2 = G 1G 2 /[ ! ( 2 1 - 1 ) J + l ) ( J + 2 ) ] ,
(5.16)
G x = F(F+1)
(5.17)
8
G
- 1(1+1)
- J(J+2),
= [(F+ I+ J+ 2) (J + I - F + l ) ( F + J -I +l )( F+ I- J) 1
2
((2J+1) (2J +3
)
]
^
(5.18)
1 / 2
= _______________ G 3 G4____________
G4______________________________
e
, (5.19)
161(21-1)(J + l ) (J+ 2) (2J +3 )[ (2 J+ l) (2 J+ 5) ]1/2
3
G
3
= [(F+I+J+ 2) (F+ I+ J+3 )( I- F+ J+ l) (I -F+ J+ 2
)
G
4
= [(F-I+J+1)(F- I+ J+ 2)( F+ I-J - 1)( F+ I-J
1 /
The possible values of F are J+5/2,
)
]
]
,
1 / 2
2
,
(5.20)
(5.21)
J + 3 / 2 , . . . . |J-5/2|.
A computer program was written to carry out this
calculation for each vibrational state
using the center frequency of the
frequencies were calculated.
(v=0 and v=l).
state,
Then,
the vibrational
The selection rules used for
this calculation are listed below.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
118
AX = 0; AJ = 0, ± 1 ; AF = same as AJ
%
A list of parameters used in the calculation are given
in Table 5.1.
The pa rameters were obtained from an IR-MW
double resonance study by Jones ejt al.. (13,14)
and from a
double resonance experiment done by Fawzy and Schwendeman
(15).
Lineshape Analysis and Generation
To generate the lineshape of the three-level double
resonance signal the density matrix equation of motion must
be used.
This equation can be written as,
p = - | (HP - PH) - k A P .
Here,
p is the partial derivative with respect to time of
the density matrix.
matrix
Each diagonal element of the density
p, when multip li ed by the total number of molecules
in the sample,
state.
(5.22)
Also,
represents a "population"
H is the Hamiltonian of the molecule,
relaxation rate,
energies,
k is the
and kAp is an extra term added to account
for the relaxation.
parts H ^ \
of that particular
For simplicity,
H is divided into two
the contribution from the vibration-rotation
and H ^ \
the contribution from the interaction
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
Table 5.1 Parameters
for CF^I Ground State and
Gr ound State
vib
eQq
B
DJ
°JK
dk
0.0
(cm ^ )
-2140.464 MHz
1517.50
MHz
vj Band
1075.191 cm_1
-2145.214 MHz
1523.26
MHz
0.001 KHz
0.002 KHz
0.006 KHz
0.006 KHz
0.000 KHz
0.000 KHz
References
Band.^
(14,15).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
between the molecules and the two radiant beams,
H = H (0) + H ( 1 ) .
Then,
(5.23)
in a basis that diagonalizes
h
j
S ) =
<5 -2 4 >
and
Hjj^=
Here,
- jj
jCOSM^t
+
(5.25)
Egcosugt).
is the amplitude of the electric field and
the frequency of the m ic ro wav e radiation;
and
is
an<* u 2 are
the corresp ond ing quantities for the infrared radiation.
The indices j and k are confined to a, b,
three levels
involved;
the energy level diagram used for
this calculation is shown in Figure 5.1.
Pbc =
p cjj
and c for the
Only p ^
are non-zero and it is assumed that
= p^ a and
» co^a and
“ 2 " u cb where “ jk = (Ej " Ek ) / h ‘
The matr ix elements for the equation of motion of the
density matrix are as follows:
P
= - i (H^p,
- P . H ^ 15 ) - k
AP
raa
n v ab
ba
ab ba '
aa
aa
(5.26)
v
'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
c>
A
r\j
b>
a>
Figure 5 . 1 .
matrix
Three
level
energy
diagram
used
for
density
calculation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Now we
make
the substitutions,
pba =
dbae
1
’
(5.32)
pcb =
d cbe
2
’
(5.33)
pca =
“ oa6' 1 '” 1 + “ 2 > t '
<5 -3 4 >
and introduce the Rabi frequencies,
= Pab g l
ft
1
and
x
*
= pb c € 2 .
ft
We can then write the following equations
(5.36)
for the
matrix elements by applying the rotating wave approximation:
paa =
L
h
.
<dba - da b ) - k aa4 p aa
(5.37)
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123
*bb =
^cc =
\a
<dab - db a ’
^
+ ^
<dcb ~ db c )- kbbd -bb
(dbo 'dcb> " 1‘« & P «
= i ( “ l - “ba>dba+^
(,W
( 5 ’39)
,bb > + ^
j cb = 1(“ 2 ““ c b )dcb+ L ^ ( P b b -Pc c ) + L ! l
aca = 1(“ 1 + “ 2 - “ ca>d ca+ ^
Now,
<5 ' 3 8 >
if we let d.
.= d*. . +
* J
dba
id*.*, for
1J
1J
dc a - kba dba<5 - 4 0 >
1 ca- k cb dcb < 5 - « >
dcb - k ca<ica
i =a,b,c;
(5.42)
j =a,b,c * i,
where d*. . and d*. *. are both real,
xj
1J
d ba - d ab = 21dbkThen,
if we let
<5 ‘4 3 >
—
and
=
~ “ cb ’
the equations for the diagonal elements are reduced to the
following form:
daa =
- X ldi.k - k a a 4 p aa
<5 -4 4 >
Pbb = + *ldb a “ X 2 dob “ kbb 4pb b
(5.45)
Pec = k 2d cb -k cc4 p cc
‘5 -4 6 >
Since pQa + p ^
A 1 = paa " pb b ’
+ pcc contains no radiation terms,
we let
A 2 = pbb ~ pc c ’
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
and separate each d value
get 8 equations
ij
-
into a real and imaginary part to
for the matrix elements.
+ x 2 d*cb
kll^ 4l
^
*2 3 Xl dba ~ 2 x 2d cb ~ k2 1 C41
3ka = - ^ l di>k ~ ^
abk 3 ^ l ^ a
k 12^42
These are
d2
* ~k 2 2 * i 2 ~ d2 ^ ’
dkk ~ kb adba ■
+
h
a kb 3 - fi“ 2dkk +
+
dkk - k c b dkb ’
dkk
akk 3 <*“ 1 + * “ 2>dka +- ^ - dba
( 5 - 50)
<5 ' 5 1 >
d'ca ' k c b dkk'
Jka 3 - < A“ 1 + 4 “ 2>d'ca +- ^
(5 .48)
<5 ' 4 9 >
- kbadbk •
^kb 3 A“ 2dkb + - £ ■ *2 -
(5*47)
d cb - kc a dka-
d'cb - kc a dk k ‘
<5- 52>
<5' 53)
<5 ’ 5 4 >
i—*
1!
In these equations,
(2k
aa
+
kb b )/3
<k bb + 2 k c c )/3
k 22
k 21 = <k cc - kb b )/3
ii
CM
H
Now,
<k aa ‘ kb b )/3
we set all of the time derivatives to 0 (i.e.,
assume a steady state).
Then,
we can write the equation
matrix form,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in
125
AL = C.
(5.55)
the matrices A,
0
k ab
j/2
0
k12
0
"X2
~ Au^
0
- V 2
0
0
0
- x 2 /2
0
0
0
0
AtOg
0
0
-xx/2
k
0
-A*!
0
0
0
(5.56)
0
k ab
x 2/2
k ca
- V 2
0
k21
0
"X1
0
0
k22
0
0
0
0
-Xj/2
0
0
0
0
0
-x2/2
~ a“ 3
*x/2
d* ,d‘ ‘
* ba’ ba’ ca’ ca’
(-k
11A1 -k12
ca
Xj/2
*
0
0
2*2
k cb
A o>2
-Ao 2
k cb
2 ,d c b ’d 'cb >
©
o
o
o
©
(Ai
to>
A=
and C are
2xx
0
11
L,
-k21il “k22A2 ,0,0)
(5.57)
(5.58)
With this system the matrix elements of L can be
calculated.
By using the correct density matrix elements
the absorption coefficients can be found.
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126
Absorption Coefficient
The absorption coefficient
(y) is related to the in­
quadrature component of the polarization with frequency
(P_
s
(2 )
')
by the following equation:
y - -( 4-nta
)(
p (2)
s ) .
(5.59)
€0
To calculate y from the density matrix p, we use
P = N tr( P jj ) .
(5.60)
For the three level system described above we get
P = N[ Pb a (Pba + Pa b ) + ^ c b ^ c b
+ Pb c5 ] *
(5.61)
Since,
pba= <dba + i d bk
pab= <dba - i d ba >e + 1 “ l t
“ d
-
pba+ pab= d;)a<s‘ i“ l t+ e i“ lt >
(5 ’ 62>
<5 ' 6 3 >
+
(5.64)
= 2d! cosu.t + 2d !‘ sina>.t .
ba
1
ba
i
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127
Also,
'clT
(dcb + id-cb )e' 4“ 2 t '
{ 5 . 6 5 )
pbc= <d cb + idci,)ei” 2 t '
<5 ‘6 6 >
pcb + pb c = 2d*cbC O S u2 t + 2d cbsintl,2t
’
(5.67)
so
P - 2N ( Pk^Cdj^cosojjt + d^sinoijt)
+
" c b ^ ' c b 0 0 3 ^
+
dcbs i n w 2t)3
(5.68)
*
Here P equals the induced polarization of the sample.
oscillation of the polarization leads to emission,
This
which has
the form
E g = 2N "“ l* [ pb a (dj)asinto1t - db a c os u1t)
c
* 2N
(5.69)
u o b (<*c bs i n u 2t - d ^ c o s u 2 t)]
c
At the infrared detector this emission beats with the
infrared radiation of frequency ug*
The output of the
detector is proportional to the component of the product of
Eg and E ^
that has zero frequency.
proportional
to P cjjdcb * ‘ .
Therefore,
This component
is
with this information
the absorption coefficient can be calculated.
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128
(5 .7 0 )
Equation
(5.70)
calculates
the absorption at the infrared
detector.
In the infrared region the Doppler effect
important,
is very
and therefore Doppler averaging must be done for
a proper lineshape.
This
is carried out by convoluting a
Gaussian function with the data obtained in the absorption
coefficient calculation.
The Doppler averaging equation can
be written as
00
(5.71)
Here
(5.72)
with
Here,
p
2
2k fiT/M
.
(5.73)
v is the component of the velocity of the mol ecule in
the direction of the radiation,
coefficient calculated for
Yj is the absorption
B o l t z m a n n ’s
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129
constant,
T is the absolute temperature,
m ol ec ul ar mass.
and M is the
Since the lineshape of interest is in the
frequency domain,
the Doppler averaging was carried out
the frequency domain.
The result
in
is
00
(5.74)
where f(v)
(5.75)
with
(5.76)
Here Avp is the Doppler half-w id th at half-height.
The
integration was done nu me ric all y and carried out to three
Doppler widths from the center frequency.
This calculation
was done for many different Rabi frequencies and pressures
by the computer program,
VAX computer.
DBRSIR,
written
in FORTRAN for the
The lineshape shown in Figure 5.2 was
calculated with the follo wing parameters:
Infrare d Rabi frequency = 0.001 MHz
Mi crowave Rabi frequency = 100.0 MHz
Po pulation difference for IR transition = 0.99
Population difference for MW transition = 0.004
Dopp le r half width at h al f max.
= 34.5 MHz
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130
I
-2 5 0
'
I
-1 5 0
1
I
1
-5 0
I
50
*
I
150
8
"
250
Frequency (GHz)
Figure 5.2.
100 MHz
Calculated lineshape using a Rabi
frequency of
for the pumping radiation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
131
Relaxation rates for all transitions = 3 MHz.
The results of additional calculations with this
program will be described below.
5.3 Experimental
COg Sideband Laser
The infrared-microwave double resonance experiment
described below was ac comp lished by using a COg sideband
laser system for the infrared source.
laser was described in Chapter 4.
The COg sideband
A diagram of the
spectrometer used is shown in Figure 5.3.
The COg sideband
laser was used in the tunable traveling wave mode;
therefore,
the infrared power was very low.
The microwave radiation used for sideband generation
was phase locked by a Hewlett Packard model 8709A
synchronous detector to a harmonic of the output from a PTS
model 500-M7010 ra dio frequency synthesizer.
locking was explained in Chapter 4.
that
This scheme of
The only difference is
in this case the mic ro wav e frequencies are referenced
to the PTS synthesizer instead of to the Hewlett Packard
synthesizer.
The frequency of the COg laser is locked to
the Lamb dip in the fluorescence from an extracavity cell
that contains COg.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
PIT
Laser
Cavi ty
Stab.
Sample Ce
Mod.
DET
Polar.
Amp
Preamp
Power
DET
Meter
Iso.
PSD
Att.
BWO
TWTA
PSD 2
BWO
Power
-
Synch.
Stab.
UW
Uod.
Control
A/D
2
Computer
Figure
5.3.
Block
diagram
of
sideband
TTY
laser
s p e c t roine ter.
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133
For the double resonance experiment,
the sideband
laser beam is not mo du lat ed and the radiation
is not divided
into reference and signal beams.
The power of the sideband
radiation is still kept constant,
however,
by controlling
the microwave power applied to the electrooptic modulator.
The detector used as the reference is a microwave
power meter thermistor head connected to a microwave power
meter.
The thermistor samples the mi crowave power by means
of a directional
amplifier
is sent
coupler after the traveling wave tube
(TWTA).
The voltage output from the power meter
to the PIN diode control circuit which adjusts the
mi cr owa ve power by con trolling the attenuation by the PIN
diode.
This experimental setup controls the sideband power
only by controlling the mi cr owa ve fluctuations;
COg
therefore
laser fluctuations have no effect on the reference loop
and are not taken into account.
The reason for the changes
in control are to allow modula tio n by chopping the microwave
pumping radiation.
Mic rowave Pump
The mic rowave
(pump)
backward wave oscillator
radiation source was a Varian
(BWO).
The BWO was phase locked by
a Hewlett Packard synchronous detector to a harmonic from a
HP 8455A reference oscillator,
as described in Chapter 4.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
134
The microwaves were then amplified by a Varian traveling
wave tube amplifier
(TWTA).
The microwave radiation was
100SJ amplitude mo dulated at 33.3 kHz by a PIN diode,
as
exp lained in Chapter 4, but the microwave frequency was not
swept.
To reduce fluctuations,
the microwave radiation was
mo ni to re d at the output of the TWTA by a thermistor through
a directional coupler
(40 db total attenuation).
of the power meter was sent
The output
to a PIN diode control circuit
similar to that described above.
This kept
the microwave
power constant and reduced the noise at the IH detector.
Double Resonance Spectrometer
The double resonance specrometer is shown in Figure
5.4.
The pumping microwaves were modulated and the infrared
signal was processed at the modulation frequency by a lockin amplifier.
The signal at the output of the lock-in
amplifier was the difference between the infrared signals
with the microwave pump on and off.
The signal was sent to
an analog to digital converter and stored in a PDP-8
computer.
The spectrometer was computer controlled as
disscussed in Chapter 4.
The microwave cell used for the
double resonance experiment
is the cavity cell explained in
Chapter 3 and is shown again in Figure 5.5.
cavity cell which increases
This cell
is a
the electric field inside if
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
135
Po w e r
Supply
PZT
Power
Meter
3W 0
G e t.
Mod.
so.
Mod.
BWO
TWJA
Polar.
Stab.
P o w er
Get.
MW
Cell
M eter
Amp
BWO
PSD
TWTA
BWO
Pow er
Stab.
Synch.
MW
C o n tro l
C o m p u te r
Figure 5.4.
TTY
Block diagram of infrared mi cr ow av e double
resonance spectrometer.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
136
SMA
C onnector
A
>
I
f l
MW Pin
Screen
Screen
NaCl
Window
NaCl
Window
Figure 5.5.
Resonance cavity cell used in infrared
microwave double resonance experiment
mi crowave
to obtain high
fields.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
137
adusted to the proper dimensions.
The adjustment
is made by
mini mi z i ng the refl ect ed power back from the cell as
explained in Chapter 3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
138
5.4
Results and Discussion
Infrared-Microwave Double Resonance in CHgOH
The essential results of the CHgOH infrared microwave
double resonance study are shown in Table 5.2.
Here the
experimental results are compared to values calculated by
using Henningsen's parameters
listed,
(10,11).
Of the 8 transitions
four are Q branch transitions that had not been
experimentally determined before.
The number of transitions
constraints listed below:
is somewhat
limited by the
The infrared source used is
limited to a spectral coverage of ±(8 - 18 GHz)
COg laser line.
from each
The microwave pumping source used had to be
in the other microwave b a n d from that of the sideband
microwave generator;
i.e.,
if the X-band (8.0 - 12.4 GHz)
mic rowave generator was used for sidebands,
(12.4 - 18.0 GHz)
then the P-band
generator was used for the pumping
mic rowave and vice versa.
This was because our laboratory
has only one BWO in each region.
Another reason for the
limited number of double resonance signals is the rather
large
(~0.8 cm *) CHgOH rotational constant
(B).
This
allows only a small number of ground state rotational
transitions to be pumped with an 8-18 GHz microwave source.
Figure 5.6 shows a one photon trace over a 1 GHz scan.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
Table 5.2
CH^OH Double Resonance Experiment Results.
Pump
lower-upper
Probe
IR trans
Experiment
(cm 1 )
Theory'*'
(cm
)
(J,k)-(J,k)sym
(J , k ) t ,n ,sym
(2,0)-(3,l),E
R( 2,0)2, 1, E
1038.8316
1038.831
(4,1) — (4,1) ,A
R( 4, 1~)3,0,A
1041.7829
1041.789
(4,3)-(5,2) ,A+
R(5 ,2~)2,0,A
1042.7351
1042.747
(4,3)-(5,2),A+
R ( 5 ,2 + )2,0,A
1042.7393
1042.739
(4,3)-(5,2),A+
Q (5,2 ~ ) 2,0,A
1033.1712
1033.175
(4,3)-(5,2),A~
Q(5,2*) 2, 0, A
1033.1763
1033.175
(4,3)-(5,2),A+
Q (4,3)1,0,A
1034.0357
1034.035
(2,0)— (3 , 1 ) ,E
Q ( 3 , 1)1,0,E
1034.2645
1034.264
Theoretical predictions by J. 0. Henningsen
(io,n).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
There are two absorption signals shown here.
the double resonance signal
has its lower energy level
is given.
In Figure 5.7
The transition which
in common with one of the pumped
ground state levels is present in the double resonance
signal.
The comparison betwe en the two figures
illustrates
the se le ct iv it y of the double resonance experiment.
double resonance signal
The
is co ns iderably smaller than the one
photon ab sorption signal;
however,
the signal to noise
ratios for the two signals appear to be about the same.
The
reason for the de creased noise in the double resonance
experiment
is because we mo dulate the mo lecules
experiment rather than mo du la te the source.
in this
Therefore the
source noise contribution to the total noise of the signal
is greatl y reduced.
Inf rared-Microwave Double Resonance
in CF^I
There have been many attempts to u n der st and and assign
the 10 pm region of the CF^I molecule;
however,
attempts have met with limited success
(12-17).
all of these
The
greatest progress was made by Jones e_t al_. , who used a
double resonance technique to gain an und er st an di ng of the
mi d- in f r a re d bands of CF^I
(13,14).
What we had hoped to be
able to do was to pump sel ec tiv el y the ground state
rotational transitions and probe the
band transitions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
141
m
15.00
15.25
15.50
15.75
16.00
Frequency (GHz)
Figure 5.6.
on the 9 P ( 24)
A b s or p t i o n sp e c t r um of CHgOH.
laser line and the mic ro wa ve s
The COg
laser is
are swept
from
15.0 to 16.0 GHz.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
CO
15.00
15.25
15.50
15.75
16.00
Frequency (GHz)
Figure 5.7.
Double resonance specrtrum of CH^OH over the
same region as Figure 6.
double resonance
This shows
the selectivity of the
technique.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
143
The information about the ground state rotational
transitions is already known,
in an assignment of the
typical
and could in principle assist
band transitions.
A plot of a
infrared mic row ave double resonance spectrum
obtained by our technique is shown in Figure 5.8.
the CHgOH study,
signals.
Unlike
Figure 5.8 shows many double resonance
Possible reasons for these groups of double
resonance signals are discussed below.
To u nd er st and the signal seen we must first review the
vibration rotation theory as applied to CF^I.
The hyperfine
splitting associated with the quadrupole moment of the
iodine nucleus greatly increases the complexity and number
of the rotational
transitions
in the ground and
v ib ra ti on al ly excited states of CF^I.
These transitions are
closely spaced and because of the large Rabi frequency of
the pumpin g radiation,
more than one transition can be
pumped at the same time.
An experiment was done on a methanol transition to
determine the relationship between the mi crowave pumping
radiation frequency and the ground state rotational
transitions pumped.
A plot was created of the lineshapes
recorded at different mi crowave pumping frequencies.
is displayed in Figure 5.9.
This
The results of the experiment
show that a small signal still exists even wit h pumping ~30G
MHz off resonance.
The lineshape here also shows the off
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
144
r—H
<d
d
m
•p H
CO
8.20 8.40 8.60 8.80 9.00 9.20 9.40
Frequency (GHz)
Figure 5.8.
CFgl.
In fr a re d m i c r o w a v e doubl e
The C 0 2 laser is on the 9R(16)
re so na nc e s pe ct ru m of
laser line.
The pump
fre qu en cy is 15 ,28 7. 6 MHz.
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
145
Figure 5.9.
Trace A shows
the double resonance signal of
CHgOH with the pumping frequency on resonance with the
pumped transition.
Trace B is 150 MHz off resonance and
Trace C is 300 MHz off resonance.
9P(24)
The COg
laser is on the
laser line.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Signal
146
T
T
T
Signal
Signal
T
15.00
15.20
15.30
5.40
Frequency (GHz)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
147
resonance pumping effect.
It should be noted here that
the
size of the Rabi frequency of the pumping radiation depends
on both the electric field and the dipole transition moment
for the pumped transition.
By using the m e thod of energy calculations discussed
in the theoretical section of this chapter,
the energy levels for CF^I.
we can calculate
A list of frequencies of the
p ossible pumped transitions is shown in Table 5.3.
The
table illustrates the possiblity of multiple level pumping.
This could contribute to the large number of double
resonance signals seen.
The final reason for the complexity of the double
resonance signal oberved is the large number of vibrational
bands whi c h overlap in the 10 pm region.
fundamental,
combination,
center frequencies,
(18),
These bands are
and hot bands and their estimated
as determined by previous experiments
are given in Table 5.4.
It is apparent that the double resonance signals and
center frequencies cannot be easily determined under the
conditions
of plots
of the CF^I case.
For future reference,
a series
is given for the CFgl infrared m i c rowave double
resonance experiment.
These are shown in Figures 5.8,
5.10,
and 5.11.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
148
Table 5.3 P umped Ground State Rotational
T ransitions
in
CF 1 .
3
Lower-■Upper
Frequency*"
(J.k.F)
- (J,k,F)
3,3,4.5
4,3,5.5
11990.763
-309.237
3, 3, 3. 5
4,3,4.5
12000.323
-299.677
3,2,3.5
4,2,4.5
12097.288
-202.712
3,0,1.5
4,0,2.5
12104.064
-195.936
3,2,4.5
4,2,5.5
12106.689
-193.311
3,0,2.5
4,0,3.5
12118.500
-181.500
3,1,2.5
4,1,3.5
12126.159
-173.841
3,1,1.5
4,1,2.5
12137.483
- 162.517
3,0,0.5
4,0,1.5
12140.427
-159.573
3,1,3.5
4,1,4.5
12149.526
-150.474
3,2,2.5
4,2,3.5
12151.686
-148.314
3,0,3.5
4,0,4.5
12165.904
- 1 3 4.096
3,1,4.5
4,1,5.5
12186.965
-113.035
3,1,0.5
4,1,1.5
12189.439
-110.561
3,0,5.5
4,0,6.5
12202.991
-97.009
3,3,2.5
4,3,3.5
12204.011
-95.989
3,0,4.5
4,0,5.5
12215.800
-84.200
3,1,5.5
4,1,6.5
12219.283
-80.717
3,2, 1.5
4,2,2.5
12243.071
-56.929
3,2,5.5
4 , 2 , .5
12266.886
-33.114
3,2,0.5
4,2,1.5
12339.021
+39.021
3, 3, 5. 5
4 , 3 , .5
12342.283
+42.283
3,3, 1.5
4,3,2.5
12438.590
+138.590
3,3,0.5
4,3,1.5
12595.461
+295.461
6
6
(MHz)
Offset**
(MHz)
C a l c u l a t e d by the program described in the text;
the
parameters are those in the first entry in Table 5.4.
A s s u m i n g pumping frequency of 12300.0 MHz.
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149
Table 5.4 Parameters
, -1
u/cn
Band
G. S
.
Dj(MHz)
0 .0
1523.29
0 .0 0 2
0.006
-2145.214
1075.191
1517.50
0 .0 0 1
0.006
-2140.464
1145.212
1520.69
0.005
0.015
-2147.65
1079.66
1516.67
0 . 0 0 0
0.008
-2145.214
1046.0
1521.13
0.0015
0.006
-2142.91
1075.269
1516.53
0.013
0.006
-2145.214
1074.78
1520.78
0.013
0.006
-2145.214
1075.256
1514.90
0 .0 0 2
0.006
-2145.214
3 1075.42
1516.95
0 .0 0 1
0.006
-2145.214
3 1075.168
1512.43
0 .0 0 0
0.006
-2145.214
1
2
O '/
2 v g 3
*
6
3
3
y
3
.
v3
1
.
v
6
(MH z )
eQq
1
.
v5
r
3
v x
V
Dj
in 10pm Region.
B(MHz)
V1
4
for CF^I Transitions
1
Reference
(19).
Reference
(15).
Reference
(14).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Signal
150
14.00
14.50
15.00
15.50
16.00
Frequency (GHz)
Figure 5.10.
of CFgl.
Infrared microwave double resonance spectrum
The CC
> 2
p umping frequency
laser
is on the 9R(16)
laser
line.
The
is 12,150.0 MHz.
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151
14.00
14.50
15.00
15.50
16.00
Frequency (GHz)
Figure 5.11.
of CFgl.
Infrared microwave double resonance spectrum
The C O
2
pumping frequency
laser
is on the 9R(16)
laser
line.
The
is 9,000.0 MHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
152
Lineshapes of Infrared Microwave Double Resonance Signals
in
CHgOH
The theory for lineshape calculation of the double
resonance signal was explained in the theoretical section
above.
By u sing the DBRSIR program w i t h experimental data,
we can approximate the Rabi
pump.
frequencies
involved in the
Figure 5.12 shows t h e o r e t i c a l l y - c a l c u l a t e d plots of
double resonance effects vs.
frequencies
f r equency for the Rabi
of the microwave radiation.
shown here is at highest Rabi frequency;
lowest Rabi frequency.
lineshapes
the smallest
is at
One of the two trends in the
is an increase in signal amplitude with an
increase in Rabi frequency.
obvious,
The largest signal
The second trend,
which is less
is variation of the s p l itting in the seven cases.
By u s i n g this second feature the Rabi frequency for the
pumped transition can be estimated.
An experiment was carried out on the R(4,1)A
transition
in CHgOH to determine the effect
fr e quency on the lineshape.
of this experiment.
of Rabi
Figure 5.13 shows the results
As the plot shows,
there is a
n o ticeable change in the signal as pre d i c t e d by the double
resonance calculation done earlier.
Wit h this reassurance
that the theoretical prediction is e x p erimentally
observable,
an experiment
to obtain the electric field
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■
-2 5 0
]
-1 5 0
r
r
-5 0
.
1
.
50
(
150
1
1
250
M H z Offset
Fi g u r e 5.12.
C a l c u l a t e d l i n e s h a p e u s i n g d i f f e r e n t Rabi
frequencies.
The signal w i t h the largest a m p l i t u d e was
g e n e r a t e d u s i n g the largest Rabi frequency.
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154
i
14.90
15.00
1---------- 1----------r
15.10
15.20
15.30
15.40
Frequency (GHz)
F i gure 5.13.
Experimental
results for the infrared-
m i c r o w a v e double r e s o n a n c e on the R ( 4 , 1 ) A tran s i t i o n of
CHgOH,
o b t a i n e d u s i n g d i f ferent pum p i n g powers.
The C0„
M
laser is on the 9P(24)
laser
line.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
155
strength inside the cell can be done.
This experiment was
accomplished by comparing the observed lineshape to that of
a calculated signal.
the cell,
For this particular frequency and Q of
the electric field was ~350 V/cm.
The lineshape experiment and calculation were
performed to characterize further the application of
infrared microwave double resonance with a high power
mi c r o w a v e source and a low power infrared source.
be evident by now that
the results obtained w i t h this method
for the CHgOH molecule were not useful,
themselves,
It should
for the CF^I case.
at least by
We conclude,
therefore,
the technique of infrared microwave double resonance is
e xperimentally difficult and has some fundamental
shortcomings,
but it can give information that is
u nobtainable in any other way.
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that
156
5.5
1.
2.
References
V. J. Corcoran,
R. E. Cupp,
J. J. Gallagher,
T. Smith,
Phys.
16., 316
G. Magerl,
Lett.,
3.
S. K.
Lee,
S. K.
E. Bonek,
52, 473
Spec.,
4.
Appl.
Skatrud,
(1970).
and W. A. Kreiner,
Chem.
Phys.
(1977).
R. H. Schwendeman,
1 1 7 . 416
Lee,
Lett.
and W.
and G. Magerl,
J. Mol.
(1986).
R. H. Schwendeman,
and F. C. DeLucia,
R.
L. Crownover,
J. Mol.
Spec.
D. D.
1 2 3 , 145
(1987).
5.
S. K.
Lee,
Ph.D.
Thesis,
Michigan State University,
1986.
.
6
H. Sasada and R. H.
331
7.
.
G. Magerl,
J. M. Frye,
Lett.,
Y. T. Chen,
42,
F. Scappini,
Mol.
Spec.
117.
Spec.,
W. A. Kreiner,
A. Kreiner,
J. M.
June 1987.
Frye,
and T. Oka,
106, 436(1984).
10.
J. 0. Henningsen,
J. Mol.
Spec.,
85., 282(1981).
11.
J. 0. Henningsen,
J. Mol.
Spec.,
1 0 2 . 399
12.
H. P. Benz,
Spec.,
21,
Appl.
Symposium on M o l ecular
Ohio State University,
W.
and T. Oka,
656(1983).
and T. Oka,
Spectroscopy,
9.
J. Mol.
(1986).
Phys.
8
Schwendeman,
A. Bauder,
and Hs.
(1983).
H. Gunthard,
J. Mol.
156(1966).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J.
157
13.
H. Jones and F. Kohler,
14.
F. Kohler,
80.. 56
15. W.
16.
Spec.,
and H. D. Rudolph,
58.,125
J.
(1975).
Mol.
Spec.,
(1980).
Fawzy,
317
H. Jones,
J. Mol.
and R. H. Schwendeman,
J. Mol.
Spec.,
120,
(1986).
H. H. Ritze and V. Stert,
J. Mol.
Spec.,
94,
215
(1982).
17. P. K. Wahi,
1 1 4 . 305
18.
H.
19.
and V. B. Kartha,
K. Burczyk,
Phys.,
55,
255
H. Hollenstein,
2,
Spec.,
79, 941
and M. Quack,
(1985).
S. W. Walters and D. H. Whiffen,
Trans.
J. Mol.
(1985).
Burger,
Mol.
V. A. Job,
J. Chem.
Soc.,
Faraday
(1983).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER
VI
S ummary and Future Work
6.1 Summary
This chapter presents an overview of the results
obtained by the different experiments p e r formed for this
thesis
in the high resolution
infrared and microwave
s pec t r o s c o p y laboratory at Michigan State University.
The
experiments p r e sented in the previous chapters are diverse
in nature,
but had a common goal,
which was to develop and
apply double resonance techniques to m o l ecular systems for a
better u n d erstanding of these systems.
This goal was
reached for the microwave- m i c r o w a v e double resonance study,
but only partially achieved in the infrared-microwave double
resonance experiments.
The micro w a v e - m i c r o w a v e double resonance studies on
NHg-He and NHg-Hg were four level double resonance
experiments.
The information gained concerned the molecular
collisional processes of NHg with He and NHg with Hg.
The
results of the m i c r o wave-microwave double resonance
experiment
( ) were complementary to earlier experimental
1
work done by Oka e_t a_l. (2-6) .
The more recent
theoretical
calculations show that O k a ’s and our experiments were
158
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159
carried out correctly.
and Townes
(7),
selection rules"
A further experiment,
done by Das
gives similar results on the "collisional
developed by Oka.
It is our conclusion
that this work on NH^-He and NHg-Hg collisions
can only be
further understood by additional theoretical calculations.
The FTIR-microwave double resonance experiment
described in Chapter 3 was not so successful,
very interesting possibilities.
realized,
but has some
If the experiment could be
the data from such a double resonance study would
be very important for complex molecules.
Therefore,
I
b elieve that this experiment should be tried again after
steps are taken to increase the signal to noise ratio of the
FTIR spectrometer.
The uses of the COg sideband spectrometer in Chapters
4 and 5 show its importance in the field of high resolution
infrared spectroscopy.
The CH^OH one photon study of the CO
stretching fundamental b a n d agrees in essence w i t h the
experimental work p r evio usly completed by Sattler et_ a l .
(8,9),
but has more accurate frequencies
for the transitions
and also m a n y additional transitions not reported earlier.
A list of the infrared transitions measured and their
relative intensities is given in the Appendix.
The infrared-microwave double resonance experiment
w ith a high power m i c rowave source and w i t h the COg sideband
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160
laser as an infrared source worked very well.
The results
obtained by this m e thod provided some p r e v i o u s l y
unidentified Q-branch transitions
CHgOH.
in the CO s tretch band of
The selectivity of the m e t h o d was not as high as
needed to unravel the complex spectrum of CF^I.
The problem
associated with the s t r o n g m i c rowave pumping radiation
the br o a d range of the pump.
is
The multi-level p umping
problem exists because of the large Rabi frequency needed to
overcome the Doppler w i d t h of the infrared transition.
One
possible way to p roceed is to employ sub-Doppler
spectroscopic conditions in the infrared region.
This can
be achieved by Lamb-dip experiments similar to those
described in the next section.
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161
6.2 Future Work
In this section we propose an extension to the
infrared-microwave double resonance studies described above.
The extension involves use of partial saturation of Lamb-dip
conditions
for the infrared absorption.
To understand the
L amb-d ip experiment we must first describe the process of
D oppler averaging associated with infrared transitions.
Since the half - w i d t h at half-height of a line is given by
A v d = 2j~ G)°j
p_kT_ln2
]
1 /
2
,
(6.1)
as the f r e quency is increased so is the Doppler width.
In
the m i d - i n f r a r e d region the Doppler width is much larger
than the pressure b r o a d e n i n g for low pressure gases whereas
in the centimeter m i c rowave region
ex t r e m e l y low pressures.
it is smaller except
The Doppler b r o a d e n i n g is due to
the different velocities of the molecules
of the incident radiation.
distribution,
for
in the direction
If we can eliminate the velocity
we can eliminate the Doppler b r oadening of the
line.
One w ay to reduce the effect of the velocity
distribution
cell
twice,
is to pass the radiation through the sample
as shown in Figure 6.1.
feature in Figure 6.1,
apart
The only additional
from the reflection of the beam
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162
Power
Supply
Loser
Co vi t y
PZT
Stab.
Amp
Polar.
Power
Meter
BWO
PSD
BWO
Power
TWTA
Stab.
UW
Control
A/ D
Figure
Computer
1
6
. .
1
Diagram of sideband
TTY
laser Lamb-dip
spectrometer.
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163
back through the cell,
is the use of the Fresnel Rhomb to
a llow the two beams to be coincident.
The rhomb converts
the plane polarized incoming beam to circularly polarized
radiation.
After passing through the cell and reflection,
the second passage through the rhomb converts the circularly
pol a r i z e d radiation to plane polarization again,
the polarization plane 90° to the original.
but with
Therefore,
a
polarizer can separate the incoming and outgoing beams.
If for this experiment we call the direction of the
radiation beam the z axis,
then the molecules with the
ve l o c i t y component v along the z axis experience two Doppler
shifted electric fields,
E(v)
= E +cos(1+v/c)wt + E_cos(l-v/c)ut,
(6.2)
where u is the laboratory frequency of the laser and E + and
E_ are the electric fields of incoming and reflected laser
radiation,
respectively.
While molecules wit h v * o are
resonant w ith only one of the two laser fields,
molecules
wit h v = 0 are resonant for both fields and experience twice
the saturation.
dips.
This
These Lamb-dips
leads
(10),
to the generation of saturation
as they are called,
are Doppler
free and therefore have muc h smaller line widths.
By using the Lamb-dip technique muc h smaller microwave
fields would be required to see the double resonance e f f e c t ’
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
164
of the infrared transitions.
Smaller m i c rowave fields would
pump only one specific transition instead of p umping many
off-resonance transitions at once.
The infrared mic r o w a v e sideband laser has been shown
by Magerl e_fc al.
saturation dips.
(11)
to have sufficent power to produce
We have also been able to see such dips by
using a Stark m odulation scheme.
in the Q(5,3)
Figure 6.2.
A plot of saturation dips
transition in the Vg band of CHgF is shown in
This spectrum was recorded b y employing square-
wave modulation of an electric field between 0 and 20
volts/cm.
The Stark field splits the m o l e c u l a r transitions
into their m components,
thereby causing an amplitude
m o dulation of the absorption.
this study is shown
The experimental setup for
in Figure 6.1.
The sideb a n d radiation
was not amplitude mo d u l a t e d for this experiment,
change is from the Stark effect.
so the only
The square wave Stark
m o dulation could be replaced with square wave amplitude
modulation of a microwave pump.
This procedure would
modul a t e only those transitions which h a d an energy level in
common with one of the pumped levels.
dips are less than 1 MHz wide,
Since the saturation
microwave Rabi frequencies of
this magnitude should be sufficient.
The infrared-microwave
experiment using the Lamb-dip technique might be a useful
technique to try with the CFgl molecule.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
165
11.270
11.275
11.280
Frequency (GHz)
F i gure 6.2.
Q(5,3)
A plot
of a Stark m o d u l a t e d L a m b - d i p from the
t r a n s i t i o n of CHgF.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
168
6.3 References
1.
D. B. Peterson,
8 6 . 7241
and R. H. Schwendeman,
J. Chem.
(1987).
2.
T. Oka,
J. Chem. Phys.
47, 4852
(1967).
3.
T. Oka,
J. Chem. Phys.
48., 4919
(1968).
4.
T. Oka,
J. Chem. Phys.
49, 3135
(1968).
5.
P. W. Daly,
6.
A. R.
Phys.
and T. Oka,
J.
Fabris and T. Oka,
Chem. Phys.
J. Chem.
53., 3272
Phys.
(1970).
56., 3168
(1972).
7.
A. Das,
8.
J. P. Sattler,
T.
Infrared Phys.
18, 521
J. P. Sattler,
T.
Infrared Phys.
19,
9.
E.
and C. H.
10.
W.
11.
G. Magerl,
Appl.
Lamb,
Phys.
Townes,
J. Chem.
L. Worchesky,
179 (1986).
and W. A. Riesler,
and W. A. Riesler,
(1979).
Jr.,
Phys.
Rev.
J. M.
Frye,
W. A. Kreiner,
Lett.,
85,
(1978).
L. Worchesky,
217
Phys.
47., 656
1 3 4 A . 1429 (1964).
and T. Oka,
(1983).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix
This Appendix lists the transition frequencies that
were measured for the CO stretch band of the CHgOH molecule
Because the two sidebands were not separated,
absolute m i c rowave frequency
transitions.
only an
(GHz) can be given for the
The list is displayed by laser line and
microwave frequency.
The intensities of all of the
transitions are estimated as weak
(S) or very strong
10R(6)
(W), m e dium
(M),
strong
(VS).
laser line at 966.250360 cm
11305.853
10R(8)
(W)
11708.119
(W)
laser line at 967.707233 cm ^ .
10165.744
(W)
11479.206
(W)
10866.616
(W)
11800.336
(W)
11310.655
(W)
12047.633
(W)
10R(10)
12C 160 2 laser line at 969.139547 cm
10477.897
10R(14)
(W)
11712.375
(M)
12C 160 2 laser line at 971.930258 cm
10066.798
(W)
10755.910
(W)
10925.326
(W)
167
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
168
1ORC16)
1 0 R ( 18)
12C 160 2 laser line at 973.288516 cm"1 .
9435.340
(W)
9936.347
(M)
9645.237
(W)
10728.197
(M)
12C 160 2 laser line at 974.621939 cm"
10423.763
10R(20)
1
(W)
12C 160 2 laser line at 975.930493 cm"
1
•
9372.400
(W)
11002.632
(W)
9650.966
(W)
11727.015
(W)
9915.174
(W)
11920.473
(W)
10668.733
(W)
10R(22)
■1
12C 160 2 laser line at 977.213922 era" •
9820.005
(W)
11744.501
(W)
10690.437
(W)
11762.194
(W)
10R(24)
12C 160 2 laser line at 978.472285 cm'
■1
10983.395
(W)
11146.605
(W)
11055.214
(W)
11635.553
(W)
10R(26)
-1
12C 160 2 laser line at 979.705420 cm'
9588.984
(W)
11086.345
(M)
9682.722
(W)
11436.595
(W)
9892.476
(W)
11512.685
(M)
10976.495
(W)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
169
10R(28)
12C 160 2 laser line at 980.913210 cm
1.
9822.575
(W)
11213.743
(M)
10291.176
(W)
12038.836
(W)
10R(30)
12C 160 2 laser line at 982 .095530 cm ^ .
9416.936
(M)
10685.815
(M)
9765.589
(W)
11236.097
(M)
9913.104
(W)
11758.493
(W)
10234.634
(M)
12045.813
(W)
10458.351
(M)
10R(32)
12C 160 2 laser line at 983 .252249 cm ^ .
9414.117
(W)
10684.151
(M)
9770.055
(W)
11234.037
(M)
9918.509
(W)
11754.391
(W)
10276.537
(M)
12029.626
(W)
10461.579
(M)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
170
9P(36)
12C 160 2 laser line at 1031.477430 cm *.
12381.834
(S)
15701.569
(S)
12634.805
(S)
15781.546
(M)
12749.212
(M)
15925.403
(S)
12752.750
(S)
16166.109
(S)
13124.729
(M)
16331.344
(VS)
13270.547
(W)
16589.616
(VS)
14488.296
(W)
16701.968
(VS)
14835.297
(M)
16870.761
(VS)
14978.103
(M)
16969.188
(VS)
15505.948
(S)
17121.908
(VS)
i
laser line at 1033.487999 cm- 1 .
12540.211
(VS)
16203.403
(VS)
12680.676
(S)
16413.347
(VS)
12798.580
(M)
16694.627
(VS)
12938.955
(S)
16923.222
(S)
13159.644
(S)
17155.847
(M)
13320.842
(S)
17236.524
(VS)
13549.288
(S)
17338.715
(M)
13726.006
(S)
17650.241
(VS)
13817.301
(M)
17857.348
(S)
13931.411
(S)
17984.468
(S)
16082.096
(VS)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
171
9P(32)
12C 160 2 laser line at 1035. 473616 cm 1 .
12410.960
(W)
15221.521
(W)
12640.439
(W)
15334.099
(W)
13001.789
(W)
15453.679
(W)
13062.504
(M)
15670.059
(M)
13191.916
(M)
15780.409
(W)
13296.670
(W)
16107.860
(W)
13535.398
(M)
16264.618
(W)
13676.345
(W)
16608.048
(M)
14089.519
(W)
16713.887
(W)
14349.908
(M)
16962.424
(W)
14532.375
(S)
17430.548
(M)
15131.742
(M)
17775.637
(W)
9P(30)
laser
line at 1037 .434110 cm- 1 .
12668.429
(W)
15832.121
(W)
12930.127
(W)
16067.268
(W)
13264.369
(W)
16168.172
(W)
13533.622
(W)
16522.189
(VS
14203.592
(W)
16765.686
(W)
15432.282
(M)
16869.674
(W)
15585.126
(W)
17294.410
(S)
15701.754
(S)
17843.447
(W)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
172
9P(28)
laser line at 1039. 369314 cm
12485.147
(W)
15876.409
(VS)
12747.843
(M)
16094.408
(S)
12997.548
(M)
16407.361
(M)
13414.586
(VS)
16858.452
(M)
13683.217
(W)
17110.369
(W)
13952.292
(M)
17606.367
(S)
15101.267
(M)
17805.142
(W)
laser line at 1041..279074 cm
9P(26)
9P(24)
1
•1
9611.117
(W)
15721.398
(VS)
10138.663
(W)
16072.848
(W)
10541.298
(M)
16345.408
(M)
14650.566
(M)
16976.601
(W)
15199.525
(S)
-1
12C 160g laser line at 1043 .163239 cm*
9355.457
(VS)
13484.538
(S)
9529.798
(S)
13600.605
(M)
10076.012
(W)
14216.101
(M)
10453.621
(S)
14439.049
(M)
10628.454
(S)
15104.427
(M)
10754.866
(M)
15292.709
(W)
11115.109
(W)
15939.769
(W)
11583.446
(W)
16592.505
(M)
11942.081
(W)
16926.228
(W)
12412.931
(VS)
17267.867
(M)
12518.536
(VS)
17761.467
(M)
12657.404
(S)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
173
9P(22)
9P(2Q)
laser line at 1045. 021669 c m - 1 .
10045.980
(VS)
14716.785
(W)
10176.217
(M)
15618.843
(VS)
12937.511
(VS)
16870.117
(M)
13066.316
(W)
12C 160 2 laser line at 1046. 854234 cm- 1 .
9395.477
(VS)
14279.281
(S)
9665.978
(S)
14797.637
(M)
9964.665
(W)
14976.298
(S)
11382.806
(VS)
15111.939
(W)
11523.258
(M)
15342.307
(W)
11800.129
(M)
16159.497
(W)
12582.089
(S)
16332.686
(W)
12841.071
(M)
16428.638
(W)
13139.600
(W)
16586.694
(S)
13963.856
(W)
16755.001
(S)
laser line at 1048,.660809 cm
9P(18)
9493.822
(W)
11931.094
(W)
9902.895
(W)
12627.631
(M)
9988.791
<W)
12872.796
(W)
10389.278
(W)
14300.555
(M)
10935.575
(W)
14522.827
(M)
11156.419
(M)
14907.046
(W)
11269.952
(W)
15212.984
(W)
11407.281
(W)
15623.208
(M)
11570.069
(W)
15725.552
(S)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
174
9P(16)
laser line at 1050. 441282 cm"
9530.259
(S)
10678.409
(M)
9701.715
(S)
10961.088
(M)
9928.068
(S)
11878.128
(S)
10084.209
(S)
11965.029
(M)
laser line at 1052. 195545 cm
9P(14)
9 P ( 12)
1
■1
•
9417.868
(S)
11122.938
(W)
9695.514
(W)
11267.514
(M)
9873.130
(S)
11365.653
(M)
10239.099
(M)
11744.097
(M)
10577.813
(W)
12072.052
(M)
10821.332
(S)
12C 160 2 laser line at 1053..923503 cm
-1
«
9492.153
(W)
10212.493
(M)
9589.169
(W)
11783.491
(W)
9765.349
(M)
10538.906
(W)
10001.415
(W)
11196.796
(VS
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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