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inequality (expr. 5) ensures that there is no 'walkoff between
the copropagating channel 1 and 2 beams due to fibre dispersion, while the right-hand side provides that there will be
many pulses of the modulated light travelling in the fibre.
Thus the copropagating channel 1 wave experiences a modulation in its phase of magnitude A(pl synchronous with the
channel 2 modulation rate, whereas the counterpropagating
channel 1 beam passes many channel 2 pulses and hence has a
constant net phase shift A(j)l/2. Therefore, detection of the
channel 1 interferometer output with a lock-in amplifier synchronous with the channel 2 modulation rate is a measure of
the phase shift A<pl in channel 1 due to crossphase modulation
from channel 2. The square-wave modulation rate of 100 kHz
that was used satisfies expr. 5.
With no light in channel 2 the interferometer output D for
channel 1 is
Ys cos 4>
D = If + lb +
where lf and Ib are the channel 1 intensities in the two directions, •/ is a measure of the coherence of the two beams, <p is
the relative phase between the two arms of the interferometer.
If the interferometer is allowed to drift the detected output will
drift between If + Ib-
+ Ib +
i.e. the peak-to-peak drift is 4 N /(/ / / b )y. This is shown in
Fig. 2a, obtained by square-wave modulation of channel 1
with a light chopper plus synchronous detection. This drift
output serves to calibrate the interferometer phase shift. With
light injected into channel 2 as well, the channel 1 interferometer output is
2 N /(/ / / 6 ) 7 cos
, X(Qt))
AT&T Bell Laboratories
Crawford Hill Laboratory
Holmdel, NJ 07733, USA
where P is the power per channel,
x 1/50
Fig. 2
a Drifting output of interferometer with 1-3 /an beam blocked
b Output signal; output of interferometer with 1-3 nm and 1-5 /an
beams unblocked and phase sensitive detector tuned to modulation frequency of the 1-3 nm laser
c Same as b except 1-3 /im beam is blocked
d Same as b except 1-5 nm beam is blocked
ELECTRONICS LETTERS 22nd November 1984 Vol. 20
22nd October 1984
CHRAPLYVY, A. R., MARCUSE, D., and HENRY, p. s.: 'Carrier-induced
phase noise in angle-modulated optical-fibre systems', J. Lightwave Technol., 1984, LT-2, p. 6110
where Acpl is the added phase change due to crossphase
modulation, Q is the modulation frequency of channel 2, and
X(Qt) is a square wave of frequency Q. For A({)1 <£ n/2 the
output of the lock-in detector tuned to frequency ft will drift
between — 2 N /(/ / / fc )y A(f>1 < D < 2^/(7f Ib)y A</>x as the interferometer phase drifts between <p = — n/2 and (p = + n/2- This
is shown in Fig. 2b. As expected, blocking either the channel 2
laser (Fig. 2c) or the channel 1 laser (Fig. 2d) causes the crossphase modulation signal to vanish. We also verified that we
were not observing stimulated Raman scattering: with either
input to the directional coupler blocked only a very small
amount of noise was measured. Also, the contribution of silica
Raman amplification to the nonlinear phase shift was negligible for the channel 1 and 2 frequency separation used here.1
From eqns. 6 and 7 we see that the ratio of drift amplitude in
Fig. 2b to that in Fig. 2a yields A $ , , the crossphase modulation. For 1 mW of injected channel 2 power this phase shift is
about 0024 rad (1-4°), which agrees well with the predicted
value (eqn. 4) of 0022 rad.
The presence of crossphase modulation places certain
restrictions on various coherent WDM systems. For an Nchannel ASK system,1 and Le = I/a, from eqn. 2 for
a = 0-25 dB/km,
A</> = 0-045P(7V - 1)
To limit the degradation due to phase crosstalk to an
acceptable level (0-5 dB power penalty), A<£< 0-15 rad 3 or
P < 3-3/(N — 1) mW. This restriction on P may render coherent detection of ASK unattractive for WDM systems applications. In frequency-modulated systems the amount of residual
amplitude modulation is restricted by similar arguments. In
phase-modulated systems the only phase noise due to crossphase modulation will arise from residual amplitude noise on
the nominally CW laser output. In most instances this will not
cause noticeable degradation. 1
In conclusion, we have measured the effects of crossphase
modulation in coherent wavelength-division multiplexing
using conventional injection lasers. For two-channel multiplexing, 1 mW of power modulation in one channel produces
a phase shift of 1-4 in the other channel. The measurement
was made using a novel interferometric experimental arrangement that can also be used to measure other weak nonlinear
phase-sensitive effects at low laser power.
C. A. Burrus is thanked for fabricating the 1-3 //m injection
laser used in these experiments.
STOLEN, R. H., and BJORKHOLM, j . E.: 'Parametric amplification and
frequency in optical fibers', IEEE J. Quantum Electron., 1982,
QE-18, pp. 1062-1072
3 PRABHU, v. K.: 'PSK performance with imperfect carrier phase
recovery', IEEE Trans., 1976, AES-12, pp. 275-285
SPEED OF 10 m/s
Indexing terms: Optical fibres, Optical transmission
We report the transmission characteristics of high-speedcoated lightguide fibres; the evaluation is based on a total
length of 90 km of single-mode fibre. For this experiment the
line speed was varied from 2 to 10 m/s, and each sample
length obtained from a preform was ~ 10 km. We found that
the average losses of the fibres coated at three different
speeds (2, 5 and 10 m/s) are all ~0-4 dB/km at 1-32 /im.
Introduction: It is known that the preform size depends primarily on its fabrication method (MCVD, LMCVD, VAD and
OVD technique), and the diameter ranges normally between 1
and 2 cm. However, further improvement of the preform processes is likely to result in diameters larger than 2 cm and that
will inevitably require high-speed coating. Fibre coating and
drawing technology has progressed substantially, originally
starting with line speeds of 1 m/s and recently achieving the
coating speed in the excess of 10 m/s. 1 In the past, we first
reported very high strength results of silica fibres in a long
length coated at high speeds, 23 including proof-tested data as
well as the Weibull distributions of the fibre strength. Highspeed coating has a major impact on lightguide fibre cost,
since a significant portion of the cost is attributed to the fibre
manufacturing processes.3 5 It should be pointed out that one
of the noticeable differences in high-speed coating ( > 1 0 m/s)
is the fibre draw tension, which is maintained at a much
higher level than for the low-speed-coating case. The important fact that one has to remember is that the draw tension
increases linearly with draw speed and will thus embed
increased residual stresses in the composite-structured drawn
fibre.6 Therefore, a major concern is the effect of this higher
tension on the fibre loss and other propagation properties.
No. 24
To characterise the transmission performance we examined
a total of ~ 9 0 km length of depressed clad single-mode fibres
that were coated at a rate of 10 m/s. This letter reports the
experimental results for these fibres.
in the case for the fibre drawn at 10 m/s. The cutoff point
varies from sample to sample, ranging from ~ 1-25 to
~ 1-28 nm. It must be noted that this phenomenon was also
observed in the loss curves of the fibres drawn with different
furnace temperatures.
Experiments: The high-speed coating was done on a modified
high draw tower that is capable of applying a uniform thickness layer coating of UV-curable material with good concentricity.7 The draw tower is equipped with a high-frequency
zirconia induction furnace to draw a certain size of an optical
fibre from a silica glass preform. The suscepter surface of the
furnace is constantly monitored at its midpoint by an optical
pyrometer through an open port and maintained at a constant
temperature within a few degrees fluctuation of the set point
using feed-back control. Its temperature was set to 2250°C
and is one of the major parameters for determining the draw
tension that is the critical variable in yielding the desired
results. Our tension measurements showed that with and
without applying coating, both tensions are linearly increased
as the draw speed increases.1 In this case, the tension without
applying coating at the speed of 10 m/s was ~50 g. Using the
fibre draw control system8 we have achieved the standard
deviation for the fibre diameter variation less than 0-5 nm for
125 ^im fibre.
wavelength, nm
Fig. 2 Spectral loss curves of a single-mode fibre drawn from a preform
with three different coating speeds
For this particular experiment the furnace temperature was
varied from 2300 to 2150°C in decrements of 50°C to increase
the fibre draw tension at the constant pulling speed. We set
the draw speed to be 5 m/s, and the spectral losses of the
single-mode fibres obtained under this condition are shown in
Fig. 3. It is seen in the Figure that, as the temperature
o o o , fibre drawn at 10 m/s
fibre drawn at 5m/s
2m Is
X X X , fibre drawn at
1-1. .3pQ
1-2 •2250"
1 . 3 _22PO_
, 2150
sample number
Fig. 1 Transmission losses of single-mode fibres at /. = 1-32 pm for
three different coating speeds (2, 5 und 10 m/s)
For these experiments, nine single-mode preforms of
germanium-doped core with fluorine-doped depressed cladding were used. These were fabricated by the MCVD technique, obtaining a A of 0-37% and designed to be a zero
dispersion near 1-31 /mi region. The preform diameter is
~ 1-6 cm and approximately 10 km were drawn from each
preform, producing a combined length of about 90 km of
125 /im-diameter fibre with 8-3 /im core. Fig. 1 shows the
results of fibre transmission loss at the wavelength point of
1 -32 fim in the loss spectrum. As shown in the Figure, the data
points scatter around the value of 0-4 dB/km. Except for an
outlying point, the scattering of measured points is within
measurement uncertainty. Thus it is indicated that there are
practically no differences in the loss for three different coating
speeds—2, 5 and 10 m/s. To eliminate any possible effect of
variations in the properties of the preforms, fibres were drawn
from each preform at the three different speeds. Fig. 2 shows
the loss spectrums of the samples drawn at the different
speeds. In all cases, the thickness of the applied coating is
typically 50 jim. However, one peculiar characteristic we
observed in the curves is that the width of the hump in the
higher-order-mode region (denoted by W in the Figure) where
the wavelength is less than ~ 1-25 ^m is appreciably narrower
speed = 5 m / s
0 4
wavelength, nm
Fig. 3 Spectral loss curves of a single-mode fibre drawn at four different
draw tensions by varying the furnace temperature from 2300 to 2150 C
ELECTRONICS LETTERS 22nd November 1984
Vol. 20
No. 24
decreases, the width of the hump below the cutoff point also
decreases. Thus we believe that this phenomenon is somehow
related to fibre draw tension. More specifically, it seems likely
that it is attributed to mode filtering. According to a periodic
structured-waveguide theory, 9 a guiding condition of modes is
determined by a relation among three parameters—
wavelength, spatial periodicity and diameter fluctuation depth.
For example, if the periodicity is greater than half the wavelength for a given modulation depth, the modes in the waveguide will be scattered out. For increasing tension the fibre
diameter variation tends to be smoother and, therefore, the
higher-order modes in the shorter-wavelength region will be
less filtered out. We believe that this is a plausible explanation
of the reason for the narrower width of the hump in the case
of higher draw tension.
In order to check any discrepancy in performance between
low-speed- and high-speed-coated fibres, we also examined the
other lightguide properties such as cutoff wavelength, zerodispersion wavelength etc. We found that there are no significant differences in the measured results. However, it must be
noted that high-speed coating tends to provide a slightly lower
value of the transmission loss, particularly in the longwavelength region (see Fig. 2).
surements. We also acknowledge W. M. Flegal, AT&T Technologies, Atlanta Works, for providing the preforms.
A T& T Technologies Inc.
Engineering Research Center
PO Box 900
Princeton, XJ 08540, USA
Conclusion: A total of approximately 90 km length of singlemode fibres was produced with coating at 2, 5 and 10 m/s.
The investigation showed that the transmission characteristics
of high-speed-coated fibres remain the same as those obtained
at a low coating speed.
Acknowledgments: The authors wish to express their gratitude
to R. J. Klaiber and L. S. Watkins for their guidance and
encouragement. We also thank T. L. Watros, L. D.
L'Esperance and E. A. Sigety (BL-MH) for their help in mea-
24th October 1984
PAEK, LT. c , and SCHROEDER, c. M.: 'Optical fibres coated with a
UV-curable material at a speed of 12 m s\ Electron. Lett., 1984,
20, pp. 304-305
PAEK, L\ c , and SCHROEDER, C. M.: 'High speed coating of optical
fibers with UV curable materials at a rate of greater than 5 m sec',
Appl. Opt., 1981, 20, pp. 4028-4034
PAEK, u. c , and SCHROEDER, C. M.: 'High strength in a long length
for fiber coated at a speed of 5 m,'s\ J. Lightwave Techno!., 1984,
LT-2, pp. 354-357
speed coating of optical fibres with thermally curable silica resin
using a pressurised die', Electron. Lett., 1982, 18, pp. 713-715
INAGAKI, N., and CHIDA, N.: 'High speed fiber drawing'. Technical
Digest of IOOC83, Japan 1983, paper 27A4-1
PAEK, u. c , and KURKJIAN, C. R.: 'Calculation of cooling rate and
induced stresses in drawing of optical fibers', J. Am. Ceram. Soc,
1975, 58, pp. 330-335
SMITHGALL, D. H., and FRAZEE, R. E. : 'High speed measurement and
control of fibre-coating concentricity', Bell Syst. Tech. J., 1981, 60,
pp. 2065-2080
SMITHGALL, D. H.: 'Application of optimization theory to the
control of the fiber drawing process', ibid., 1979, 58, pp. 1425-1436
DABBY, F. w., KESTENBAUM, A., and PAEK, u. c : 'Periodic dielectric
waveguides', Opt. Commun., 1972, 6, pp. 125-130
Piezoresistance: For a gauge made in isotropic material the
gauge factor (fractional change in resistance AR/R per unit
strain e) is given by
Indexing term: Piezoelectric devices and materials
A theoretical model for piezoresistance in polysilicon is
described. Grain size, orientation and doping dependence
effects are included. Predictions of gauge factor using the
model give reasonable agreement with experimental results
and enable optimum processing parameters to be chosen for
a given grain size.
Introduction and theoretical model: Recent studies in
piezoresistance of polysilicon1'2 have shown that it has the
advantage of high gauge factor and ease of deposition on
insulator coated substrates. However, the dependence of gauge
factor on structure is not well understood.
In this letter a theoretical estimate of gauge factor is made,
taking into account grain size, texture and doping level, which
is in reasonable agreement with experimental results. The
model used allows the optimum doping level to be predicted
for a given grain size. The p-type polysilicon material is
assumed to have grains of length L, separated by thin grain
boundaries with associated depletion regions. These barriers
are assumed to be trapping centres and insensitive to strain. 3
G = 1 + 2v + —
where v is Poisson's ratio. Eqn. 2 can be expressed in terms of
compliance coefficients S^5 and piezoresistance coefficients nd
(where nd incorporates high doping effects6).
In the case of an anisotropic homogeneous material eqn. 2
where i = 1 and d = / for longitudinal strain, and i = 2 and
d = t for transverse strain.
The values of nd and So- can be calculated for an arbitrary
direction using the following equations: 5
S,j = Si2 + ( S t l - Sl2 - |S 44 K/, 2 / 2 + mfm] + nf n])
Su = S , , + (S 44 + 2Sl2 - 2Sl iX/f mf + If "if + mf nf)
n, = nli
Resistivity calculations: Doping segregation was assumed not
to be present and thus the depletion widths w are given by
QJ2N (for LN > Qt), where N is the average doping concentration (centimetre" 3 ) and Qt is the density of trapping states
(centimetre" 2 ). Using the assumptions of this model the following equation for resistivity of the films can be found:
Pg +
ELECTRONICS LETTERS 22nd November 1984
+ l\ n\ + m\n\)
m\ m\
The current is assumed to be in the x' direction in the transformed co-ordinate system, defined by 6, <j>, if/ as shown in
Fig. 1. The direction cosines /,-, mh nt of the transformation are
defined by
where p, pg and pb are the resistivities of the film, grain and
barrier, respectively, and S is the grain boundary thickness.
Numerical values used in eqn. 1 were taken from Mandurah's
experimental work.4
+ 2(TT44 + nl2 ~ niXil\m\
n, = nl2 + ( 7 i n - 7r12 - TI
(2w + d)
[L P=
= l2 m2
./ 3
Piezoresistance in polysilicon: Using the assumptions of this
model in conjunction with eqn. 1, the fractional change in
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