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Design, development and application of a novel microwave nondestructive evaluation sensor based on metamaterial lens

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Design, Development and Application of a Novel Microwave
Nondestructive Evaluation Sensor Based on Metamaterial Lens
A Dissertation
Presented to
the faculty of the School of Engineering and Applied Science
University of Virginia
In Partial Fulfillment
of the requirements for the Degree
Doctor of Philosophy (Electrical Engineering)
by
Daniel Shreiber
December, 2008
UMI Number: 3348740
Copyright 2009 by
Shreiber, Daniel
All rights reserved.
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APPROVAL SHEET
The dissertation is submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy (Electrical Engineering)
TJ. Shreiber
This dissertation has been read and approved by the examining Committee:
Prof. M. Gupta, dissertatioh advisor
o^u^YH - (^J*u_J-x*-4s
Prof. R. Weikle, committee chair
Prof.f. W.A/Jesser
K •._
/
Dr. R.L. Cravey
Prof. N.S. Barker
Accepted for the School of Engineering and Applied Science:
Dean, School of Engineering and
Applied Science
December, 2008
ABSTRACT
Nondestructive Evaluation (NDE) method is one of the primary tools of inspecting
different materials for structural reliability. Microwave NDE techniques attract more and
more attention from the industry and academia. Microwave NDE techniques have the
potential to penetrate deeper into materials such as composites and other dielectrics as
compared to ultrasonic techniques. Microwave NDE sensors typically operate in two
modes - far field and near field. Although in the far field the standoff distance from the
sample is comfortable to a user, the resolution of such sensor is limited by the diffraction
limit.
This thesis describes design, fabrication and evaluation of a novel microwave NDE
sensor based on a metamaterial lens. It was a purpose of this work to design a novel
Microwave NDE sensor based on a metamaterial lens. The proposed sensor would
combine a comfortable standoff distance from the sample with a subwavelength
resolution. It was shown that in the resonant frequency range of 3 - 4 GHz the designed
lenses can focus below the diffraction limit (0.48 X) and that defects as small as 0.037 X
in diameter in a dielectric sample can be detected. The resolution was further improved
by introducing a metamaterial lens with resonant frequency of 16.75 GHz. Applicability
of the proposed sensor to other samples such as corrosion spot under space shuttle tile
and rippling on the surface of carbon fiber composites was shown. The limitations of the
method were also discussed.
The proposed sensor is a viable alternative to the existing NDE methods and contributes
greatly to advances in the field of non destructive evaluation.
I would like to thank the people of NASA Langley Sensors and Electromagnetics
Branch Dr. Wes Lawrence, Eric Vedeler (branch head), Ken Dudley, Theresa Butler and
many others for shearing their wisdom in the field of electromagnetism and their support
throughout this work.
I want to thank Bob Young of NASA Langley Sensors and Electromagnetics Branch for
providing scientific and technical support to this project all way along. I can not imagine
this project progressing without his help.
I would like to thank the member of my committee Dr. Weikle, Dr. Jesser and Dr. Barker
of ECE UVA, for offering very useful suggestion on how to improve the quality of the
results in the project.
I want to thank my NASA Langley mentor, Dr. Robin Cravey for her support and
advice. Her experience and personality made my stay at NASA Langley a very useful
scientifically and a very pleasant experience. She was always there in the crucial
moments of the project offering a direction to advance.
I want to thank my advisor Dr. Mool Gupta (UVA ECE) for giving me the opportunity to
engage in the exciting field of metamaterials, for his guidance, for showing how the
proper research should be conducted and for his very valuable scientific advices that kept
me on track.
I want to thank my family, my parents Yitzhak and Nina, my wife Marina, my daughters
Mindy and Devora for their support and constant encouragement. I would not be able to
finish this project without their help.
The last but not the least, I would like to thank the Creator of the Universe for making all
this possible.
CONTENTS
List of Figures
i
List of Symbols
vi
1. Introduction
1
2.
Theoretical Background
6
3.
Design and Fabrication of Metamaterial Lens
3.1
3.2
3.3
2-D Lens for Operation at 3.65 GHz
19
3.1.1
Fabrication of the 3.65 GHz 2-D Metamaterial Lens.
19
3.1.2
Modeling of the 3.65 GHz 2-D Metamaterial Lens.
21
Modeling and Fabrication of 3.65 GHz 1-D Lens
23
3.2.1
Fabrication of the 3.65 GHz 1 -D Metamaterial lens.
24
3.2.2
Modeling of the 3.65 GHz 1 -D Metamaterial lens.
24
Modeling and Fabrication of 16.75 GHz 2-D Lens
25
3.3.1
Modeling of the 16.75 GHz 2-D Metamaterial lens.
26
3.3.2
Fabrication of the 16.75 GHz 2-D Metamaterial lens.
27
4. Experimental Setup for the Characterization of Metamaterial Lens
4.1 Determination of the Resonant Frequency.
30
4.2 Determination of the Frequency Dependent Index of Refraction.
33
4.2.1 Lens Operating at 3.65 GHz Resonance Frequency.
33
4.2.2 Lens Operating at 16.75 GHz Resonance Frequency.
34
4.3 Determination of the Focus Spot Size.
36
4.4 Aperture Size Measurement Setup.
38
4.5 NDE Sensor Experimental Setup.
39
4.5.1 Dielectric Sample with Drilled Hole.
41
4.5.2 Corrosion Spot Detection.
43
4.5.3 Surface Rippling of Carbon Fiber Composite Detection.
46
5. Negative Index Material Lens Characterization Results
5.1 Resonant Frequency.
48
5.1.1 3.65 GHz 2-D Lens.
48
5.1.2 3.65 GHz 1-D Lens.
50
5.1.3 16.75 GHz 1-D Lens.
52
5.2 Index of Refraction.
54
5.2.1 3.65 GHz Lens.
54
5.2.2 16.75 GHz Lens.
56
5.3 Focus Spot Size.
59
5.3.1 3.65 GHz 2-D Lens.
59
5.3.2 3.65 GHz 1-D Lens.
62
5.3.3 16.75 GHz Lens.
64
5.4 Aperture Size Dependence of the Focus Spot Size.
67
6. Results and Discussion for Sub wavelength Resolution Measurements
6.1 3.65 GHz 2-D Lens.
70
6.1.1 Dielectric Sample.
70
6.1.2 Corrosion Plate.
74
6.1.3 Carbon Fiber Composite.
75
6.2 3.75 GHz 1-D Lens.
76
6.3 16.75 GHz Lens.
78
6.3.1 Dielectric Sample.
78
6.3.2 Corrosion Spot Detection.
80
7. Limiting Factors for the Lens Performance.
84
8. Summary of Accomplishments
8.1 3.65 GHz 2-D Lens.
90
8.2 NDE Sensor with 3.65 GHz 2-D Lens.
91
8.3 3.65 GHz 1-D Lens.
91
8.4 16.75 GHz Lens.
92
8.5 NDE Detector Based on the 16.75 GHz Lens.
93
8.6 Limitation Factors for the Lens Performance.
94
9. Conclusions and Future Work.
96
Appendix (Journal Publications and Conference Presentations)
A. Journal Publications.
98
B. Conference Presentations.
98
References
99
1
LIST of FIGURES
Fig. 1 Schematic of (a) Laser NDE system, (b) Ultrasonic NDE system.
Fig.2 Comparison of refraction phenomenon in a medium with positive and negative
refractive index.
Fig. 3 Propagation of radiation through a metamaterial lens.
Fig.4 A schematic of a split ring resonator.
Fig. 5 (a) Optical image of a metamaterial lens that was designed and fabricated for this
study, (b) The unit cell.
Fig.6 Dimensions of the 3.65 GHz 2-D metamaterial lens unit cell.
Fig.7 Example of a Corel-Draw file for a section of a metamaterial lens.
Fig. 8 Image of the modeled lens.
Fig.9 Modeling results for transmitted power as a function of incident microwave
frequency (3.65 GHz).
Fig. 10 Assembly process for the 1-D lens.
Fig.l 1 Modeling results for transmitted power as a function of incident microwave
frequency (3.65 GHz 1-D lens).
Fig. 12 Modeling results for transmitted power as a function of incident microwave
frequency (1-D lens).
Fig. 13 (a) Image of a designed metamaterial lens operating at 16-17GHz frequency
range. PCB material- Rogers Duroid 5880 (s = 2.2, tan8 = 0.009) (b) the unit cell.
Fig.14 Dimensions of the 16.75 GHz 2-D metamaterial lens unit cell.
Fig. 15 A schematic of the experimental system for the frequency sweep experiment.
ii
Fig. 16 Photographs of the experimental setup for the 3.65 GHz lens.
Fig. 17 Photographs of the experimental setup for the 16.75 GHz lens.
Fig. 18 Horn antennas used in the experiments (a) for 3.65 GHz 1-D and 2-D lenses and
(b) for 16.75 GHz 2-D lens.
Fig. 19 A schematic of the experimental system for the index of refraction determination
(f= 3.65 GHz).
Fig.20 A schematic of the experimental system for the index of refraction determination
(f= 16.75 GHz lens).
Fig.21 A schematic of the experimental system for the focus spot size determination.
Fig.22 An optical photograph of the experimental setup for the focus spot size
determination (f = 16.75 GHz).
Fig.23 Image of a lens with 1/3 of the aperture area reduced by absorber (f = 16.75 GHz).
Fig.24 A schematic of NDE sensor based on the negative index material lens.
Fig.25 Schematic of the sample (fiberglass, s = 4.8).
Fig,26 Optical image of fiberglass sample.
Fig.27 Optical image of 1 mm hole drilled in the sample.
Fig.28 Optical image of the filler for the 1 mm hole drilled in the test sample.
Fig.29 Aluminum plate with simulated corrosion spots. A square indicates the area
scanned by the sensor based on 3.65 GHz negative index material lens.
Fig.30 Test sample used for the scan with the sensor based on 16.75 GHz negative index
material lens, (a) Corrosion plate and (b) space shuttle tile mounted on the corrosion
plate.
iii
Fig.31 Test system for sensor based on 16.75 GHz negative index material lens. The
sensor was used to scan a space shuttle tile mounted on an aluminum plate with simulated
corrosion spots.
Fig. 32 Image of a carbon fiber composite test sample.
Fig. 33 Magnified image of rippling on the surface of a carbon fiber composite sample
used in our experiments.
Fig.34 Results of the transmission frequency sweep for the 2-D negative index material
lens (experimental setup is shown in Fig. 14).
Fig.35 Non-calibrated results of the transmission frequency sweep for the 1-D negative
index material lens (experimental setup is shown in Fig. 14).
Fig.36 TRL calibrated results of the transmission frequency sweep for the new 2-D
negative index material lens (experimental setup is shown in Fig. 14).
Fig.37 Typical normal incidence and 15 degree scans (experimental setup is shown on
Fig. 18).
Fig. 3 8 A plot showing the frequency dependence of the index of refraction.
Fig.39 S21 phase scan for a 2" sheet of Teflon before the correction.
Fig.40 Index of refraction variation with frequency for a 2" sheet of Teflon after the
correction.
Fig.41 S21 phase scan for the 16.75 GHz negative index material lens before the
correction.
Fig.42 A plot showing the frequency dependence of the index of refraction.
Fig.43 Power scan at 12 mm and 32 mm away from the lens. Dark solid line depicts the 3dB point.
iv
Fig.44 Power scan at 12 mm away from the lens for f = 3.66 GHz and f = 6 GHz. Dark
solid line depicts -3 dB point.
Fig.45 Focused spot size (in X) vs. distance from the lens. The lines represent linear
fitting of the data.
Fig.46 Power scans at focus spot distance for 1-D lens and 2-D for 3.65 GHz lens. Dark
solid line depicts the -3dB point.
Fig.47 Power scan at 14 mm away from the lens. Dark line depicts the -3dB point.
Fig.48 A table of experimentally measured focus spot size dependence on the distance
away from the lens and frequency.
Fig.49 Focused spot size (in cm) vs. distance from the lens.
Fig.50 Focus spot size measurement for the full aperture of the lens.
Fig.51 Focus spot size measurement for 2/3 aperture of the lens.
Fig.52 Relative power scan of the sample as depicted in Fig.8 at f = 3.65 GHz.
Fig.53 Relative power scan of a sample as depicted in Fig.8 f = 6 GHz.
Fig.54 Relative power scan of a sample when two holes were filled alternately (f = 3.65
GHz). The second hole was drilled 3 cm away from the first one.
Fig.55 Relative power scan of a sample when two holes were filled alternately
(f = 6 GHz).
Fig. 56 Relative power scan of a sample when two holes were filled simultaneously
(f= 3.65 GHz).
Fig.57 3-D power scan of the corrosion spot on an aluminum plate as indicated in Fig.28
(a) f = 3.65 GHz and (b) f = 6 GHz.
Fig. 5 8 Relative power scan showing rippling on a carbon fiber composite sample
V
(f= 3.65 GHz).
Fig.59 Comparison of the relative power scans for (a) 1-D 3.65 GHz lens and (b) 2-D
3.65 GHz lens.
Fig.60 Relative power scan of a sample as depicted in Fig.24 (3 mm hole) f = 16.75 GHz.
Fig.61 Relative power scan of a sample as depicted in Fig.25-27 (1 mm hole) f = 16.75
GHz.
Fig.62 Normalized relative power scan of an aluminum plate that contains a corrosion
spot and covered with a space shuttle tile.
Fig.63 Normalized relative power scan superimposed with the scanned area of the
aluminum plate covered with the space shuttle tile.
Fig. 64 Modeling results for transmitted power as a function of incident microwave
frequency for three metals: copper, silver and PEC (3.65 GHz 2-D lens). The PCB
material is FR4.
Fig.65 Modeling results for transmitted power as a function of incident microwave
frequency for three metals: copper, silver and PEC (3.65 GHz 2-D lens). The PCB
material is Rogers Duroid 5880.
vi
LIST of SYMBOLS
y - damping term
Yj - damping constant with binding frequency COJ
A - a peak to trough distance
A; - spatial period of variation in the source in the i direction
©i - angle of incident radiation
©2 - angle of refracted radiation
X - wavelength
8 -permittivity
eeff - effective permittivity of a composite medium
so - permittivity of free space
e i - permittivity of 1st medium
£2 - permittivity of 2nd medium
[i - magnetic constant, permeability
Ueff- permeability of a composite medium
uo - permeability of free space
H\ -permeability of 1st medium
jj.2 -permeability of 2 medium
co - frequency of radiation
COJ - binding frequency
cop - plasma frequency
coo - frequency of oscillation around equilibrium
vii
G)mp - magnetic plasma frequency
a - lattice parameter
B - magnetic flux density
Bave - magnetic flux density of the metamaterial system
c - speed of light in vacuum
C - capacitance per unit area
D - electric flux density
d' - distance between the concentric rings of SRR
d - gap in SRR ring
dl- distance from point source to the lens
d2 - distance from the lens to the image
e - electron charge
E - electric field
Eti - tangential component of electric field amplitude in 1st medium
Et2 - tangential component of electric field amplitude in 2n medium
Eni - normal component of electric field amplitude in 1st medium
E„2 - normal component of electric field amplitude in 2nd medium
Eos+ - incident S-polarized electric field amplitude
Eos- - reflected S-polarized electric field amplitude
Eis+ - transmitted S-polarized electric field amplitude
fj - electrons per molecule with binding frequency COJ
F - restoring force
h - thickness of the wire
viii
H - magnetic field
Have - effective magnetic field of the metamaterial system
Hti - tangential component of magnetic field amplitude in 1st medium
Ht2 - tangential component of magnetic field amplitude in 2nd medium
Hni - normal component of magnetic field amplitude in 1st medium
Hn2 - normal component of magnetic field amplitude in 2nd medium
k - wave vector
ki - wave vector component in i direction
k'j - wave vector component in i direction inside a metamaterial
1 - thickness of the lens
m - electron mass
meff- effective mass of an electron
n - index of refraction
n - total number of electrons
N - number of molecules
p - dipole moment of one electron
Sn - reflection coefficient
S21 - transmission coefficient
|S n | - absolute value of reflection coefficient
|S21| - absolute value of transmission coefficient
t - time
tl - transmission Fresnel coefficient
t'- transmission Fresnel coefficient inside the metamaterial
ix
t2 - gap between the SRR rings
r2 - radius of a wire
r - radius of an SRR ring
rl - reflection Fresnel coefficient
r' - reflection Fresnel coefficient inside the metamaterial
T - transmission coefficient
Ts - S-polarized transmission coefficient
w - thickness of the SRR ring
x - coordinate
y - coordinate
z - coordinate
Z - impedance of the medium
Zi - number of electrons in molecule
1
CHAPTER I
INTRODUCTION
Non Destructive Evaluation (NDE) methods are essential tools used in inspecting
materials for defects. Defects such as cracks, voids, and debonding can cause system
failures for many industrial applications ranging from aerospace to IC packaging. Critical
systems which operate in extreme environments require frequent inspections to detect
defects before they cause catastrophic results. For example, cracks below a critical size
may be tolerated in aircraft components but require regular inspection. Cracks tend to
grow under the influence of stress, low cycle fatigue and similar effects. When a crack
exceeds the critical size for a particular aircraft component, this component should be
replaced. As another example, IC packages may crack during soldering of surface mounts
[1]. The cracking is initiated by delamination between the chip pad and plastic package.
Once the delamination is initiated during the soldering process, it will grow and
propagate until the bottom pad interface is substantially or fully delaminated. Therefore,
there is a need for a constant NDE monitoring of the IC packages for a possibility of the
delamination formation. So, there is a need for nondestructive methods for variety of
applications. This thesis discusses a new method for defect detections using
metamaterials lens that can provide a subwavelength resolution.
There are a variety of NDE methods currently in use, including ultrasonic, laser,
visual, thermal imaging, and microwave. Each method has its own advantages and
disadvantages. For example, thermal imaging can cause damage to a sample due to high
temperature excursions from flash pulse. Laser methods frequently require a
2
thermal/mechanical load on the sample (Fig. 1(a)). Ultrasonic methods require extensive
data interpretation, and also require a coupling material (Fig. 1(b)). The resolution of
these methods is lower than that of other techniques such as microwave NDE.
(a)
Pulser/receivei^r
•
I
^-Transducer
J
1
I
I
'
-—L--— Crack
(b)
Fig. 1 Schematic of (a) Laser NDE system, (b) Ultrasonic NDE system.
Microwave NDE can provide relatively high spatial resolution compared to many
other NDE techniques and has several other advantages. Microwave NDE techniques
have the potential to penetrate deeper into materials such as composites and other
dielectrics as compared to ultrasonic techniques [2]. Also, microwave NDE is relatively
inexpensive, fast [3] and does not require extensive data analysis.
Microwave NDE sensors typically operate in two modes - far field and near field.
The near field method is generally used at standoff distances below 10 mm, whereas the
far field method is used at higher standoff distances. Although the information obtained
in the far field mode is easier to process but there are some disadvantages of using this
mode. For example, many critical areas that require testing are situated at the edges,
3
corners or joints of a sample and unwanted reflections from these structures can limit the
utility of the method [2]. Also, the resolution of the near field mode is generally better
than that of the far field mode. A major disadvantage of the near field mode is that the
standoff distance has to be maintained relatively close to the sample (which is less
convenient for the user). Although the optimum standoff distance enhances the
measurement sensitivity of the near field mode, small deviations from the optimum
distance can significantly degrade this sensitivity [2]. Far field mode results provide
spatial resolution that is independent of the standoff distance. The spatial resolution in
the near field mode is primarily a function of the probe dimensions and not necessarily of
the wavelength.
The example of utility of microwave and millimeter wave NDE near field
methods was demonstrated when fiber breakage and fiber orientation determination tests
were performed in unidirectional carbon fiber reinforced polymer patches used in the
aerospace industry and civil infrastructure [4]. The strength of such patches is dependent
on the directionality of the carbon fibers and on their orientation in regards with the
position of the patch. Normally carbon fiber composites are impenetrable for microwave
and millimeter wave signals. However, when the orientations of the fiber and the electric
field are orthogonal, the signal easily penetrates the laminate providing the desired
results. The tests were conducted in Ka band (26.5 - 40 GHz) and the standoff distance to
the sample was 1 mm. In general, the near field microwave NDE imaging yielded very
good resolution. A lateral spatial resolution of 0.4 urn was achieved at 1 GHz with a
microstrip line probe [5]. However, the probe was positioned at standoff distances
between 60 (jm and 400 urn, depending on the dielectric constant of the tested material.
4
It is the purpose of this work to develop a new microwave and millimeter wave
NDE sensor which combines the advantages of both the near field and the far field modes
of NDE. This sensor operates at standoff distances typical for the far field mode, the
probe size and resolution are comparable with the near field mode (sub wavelength as
opposed to the far field mode where the resolution is limited by the diffraction limit
which is about the wavelength of the EM wave in use), and the dependence of the
resolution on standoff distance is easily established. Also, the depth of penetration into
the sample under test is inversely proportional to the frequency of the wave [6]. In our
case, the probe size is smaller than the wavelength in use and a sub wavelength resolution
can be achieved. Therefore, longer wavelengths could be used for deeper penetration into
a dielectric without compromising the resolution.
The sensor described above has application to a variety of industries. Most
notably, the aerospace industry can benefit from using this approach. There are modern
aircraft composed largely of composite structures (such as fiberglass) which require NDE
monitoring. Microwave NDE methods have shown great promise in this area [3]. The
sensor under discussion offers a convenient way to implement microwave NDE methods
with relatively high resolution and sensitivity.
The sensor was designed using HFSS Ansoft Software to operate at two
frequencies: 3.65 GHz and 16.75 GHz. The design model was verified experimentally
and several applications for the novel sensor were tested.
A metamaterial lens was designed based on the procedure described by Aydin et
al. [7, 8, 9]. The lens was fabricated and characterized for microwave transmission, index
of refraction and spot size of the focused image from a point source. The computational
5
electromagnetics model for this lens was verified. Non Destructive Evaluation
experiments are conducted with this lens to prove the concept of the novel sensor. Then,
a lens for higher frequencies is designed using the previously verified computational
modeling method, and NDE experiments are conducted with the fabricated lens to show
improvement in imaging resolution of simulated defects. A study of the limitations of the
method is performed.
6
CHAPTER II
THEORETICAL BACKGROUND
The desirable characteristics of the novel sensor under development may be
obtained by the introduction of a negative index of refraction material into the sensing
system. What is a negative index material (NIM)? Peculiar properties such as negative
index of refraction, reversed Doppler effect and other effects were predicted for the
materials with simultaneously negative permittivity (s) and permeability (n) in 1968 [10]
(Fig.2). Such a medium was called "left-handed" because the wave vector k, magnetic
field H and electric field E vectors would form a left handed triplet.
Material with positive refractive
index
Material with negative refractive
index
Fig.2 Comparison of refraction phenomenon in a medium with positive and
negative refractive index.
This fact allows for constructing of a flat lens (see ray diagram Fig.3). It was shown by J
Pendry [11] (and also can be observed from Figure 3) that when we have an "ideal"
negative index material with an index of refraction n = -1 exactly, the sum of the
distances of the object to interface and interface to image equals the thickness of the lens,
dl + d2 = 1
(1)
7
1
Fig. 3 Propagation of radiation through a metamaterial lens
Therefore, manipulating the thickness of the lens and the distance from the source
to the lens, one can adjust the distance d2, which is the standoff distance from the sensor
to the test material. Obviously, in reality it is very hard to obtain exactly n = -1 (due to
the losses in the system which are reflected in the imaginary components of both complex
s and |o, of the material) or we can work at a frequency that renders index of refraction
slightly different from the n = -1 (for our system) but this condition gives a very good
estimate of where to look for the focused spot if the distance from the source to interface
and the thickness of the lens are known. Also, the ideal lens would be called a "perfect
lens" when the diffraction limit for the resolution (about the wavelength in use) will not
apply. However, due to the constraints that were discussed above (inability to obtain
exactly n = -1), the perfect lens is very hard to achieve although some experimental
works show focused spot size of 0.4 A, [7] where X is the wavelength in use. In the optical
spectrum region, it was shown [12] that U6 resolution could be achieved using a silver
thin film of 35 nm as a negative index material lens.
8
It is important to explain how the negative index material lens "defies" the
diffraction limit. If we assume a planar object at z = 0, and the associated electric field to
be E(x,y,0) [13], we can write electromagnetic fields over all space as :
E(x,y,z,t) = ( ^ - ) 2 Jjdk x dk y ^(k x ,k y )exp[i(k x x + ky>; + k z z - ^ ) ]
where © is a frequency of radiation and E(kx,ky)
(2)
is the Fourier transform of spatial
variation of the source. Maxwell's equations impose a condition of:
2
k
o
x
+k
o
y
+k
o
z
\JL/
o
=sju—r- = k0 (dispersionequation). (3)
c
Where k; is a wave vector component, where i can be x, y or z and c is a speed of light.
From the dispersion equation one can see that for large kx and ky, k2 will become
imaginary. The waves with imaginary kz will not propagate in the z direction but along
the surface of the interface (evanescent waves). More precisely, only waves with kx = ky
< ko will propagate. If Ax is a spatial period of variation in the source in the x direction,
then kx = 2it/Ax (similarly for ky). Since kx and ky are inversely proportional to Ax and Ay,
kx and ky are largest when Ax and Ay are small . Therefore, the waves that contain
information about the smallest periods of variation in the source will not propagate and
the resolution is limited by the wavelength in use.
Pendry has shown analytically [11] that for a medium which has n = -1 (or e = -1
and |j, = -1), the diffraction limit does not apply. One of the relevant quantities is the
impedance of the medium Z=
— - where £o and u<> are electrical permittivity and
magnetic permeability in free space. One can see that it retains the positive sign when e =
-1 and n = -1 simultaneously. Therefore, there is a perfect match to free space and no
reflection at both boundaries of the medium. Veselago [10] at the time had derived an
expression for the transmission coefficient of the medium to be
T = tit' = exp(ik'zd) = e x p C - i ^ V 2 -k\ -k2y\) (4)
where this expression for k' z is required by the transport of energy in the z direction (1 is
the thickness of the slab). Pendry demonstrated that in this case evanescent waves will
not decay as is the case with a regular material (evanescent waves do not transmit energy
and, therefore, no energy conservation laws are violated). For an S-polarized wave, the
electric field can be given as:
E os+ = [0,1,0]exp(ikzz + ik x x - icyt) (5)
where k z = iJ(k x + k2 -co2c"2) implies decay when a>2c~2 < k x + k 2 .
At the interface, the reflected and transmitted electric field can be written in the
following form:
E0s- ~ r[0,1,0]exp(-ikzz + ik x x -i<»t) (6)
E 1S+ =t[0,l,0]exp(ik' z z + ikxx-i<»t) (7) index " 1 " denotes electric field inside
the medium.
wherek'z = iJ(k x +k2 -£/uco2c
2
and
E\ICO2C
2
< k x +k2.
tl
and rl
are partial
transmission and reflection Fresnel coefficients and prime denotes parameters inside the
medium. The wave is chosen to be this way due to causality which requires the wave to
decay in the medium away from the interface. By matching the fields at the interface one
can obtain:
t\=
2fjk
*
,
jukz+k\
r\ = ***~k%'
Mkz+k\
(9)
10
V
2Jt'
f=
'—,
k'z+jukz
r'=
-uk
z
^z
k'z+/£z
(10)
The transmission through both surfaces can be calculated by summing up all the
multiple scattering events in the following expression:
l) + tlfr'z exp(3ik\ /) +
T = tlfexp(ik\
z
=
z
tlt'exv(ik\
I)
, K z /
l-r'2exp(2ik'zl)
(11)
Substituting into (11) from (9) and (10) gives:
,. „ ,.
tlfexr>(ik'l)
,.
2uk7
2k\z „.
hmT = km
, yv z ' = h m
<—^
—*
r
«->-i <+} 1 exp(2i*', /) - : / Mz + k'z k\ +ftkz
expO^*z_/)
l-(*''
fjkz
= e x p ( i k y ) = exp(ikzl)
( 12 )
)2 exp(2ik' I)
A similar result can be obtained for the P-polarized field. Therefore we have to
conclude that the negative index medium amplifies evanescent waves. The evanescent
waves contribute to the resolution of the image and, therefore, the diffraction limit for
resolution is not applicable in this case.
Unfortunately, negative index materials do not exist in nature. The electric and
magnetic properties of materials are determined by dielectric permittivity (e) and
magnetic permeability (u). Together these quantities determine the response of a material
to electromagnetic radiation. In order for an electromagnetic wave to propagate in a
regular material both s and u have to be positive at that frequency. Veselago [10] has
shown that a material requires both permittivity and permeability to be negative in order
to exhibit the effects that were discussed earlier. While s is known to be negative for
11
some materials at certain frequencies (for example, s is negative below the plasma
frequency for metals), there are no known natural materials with negative u. Therefore
for many years the idea of a negative index material was considered just a theoretical
construct. More recent developments in this field have changed this assumption.
It was suggested by J. Pendry et al. in 1996 [14] that negative electric permittivity
at microwave frequencies could be achieved by an array of thin metallic wires. The
reaction of a metal to an applied electrical field can be described by a plasma behavior.
Permittivity can be defined from a simple model of harmonically bound charges [15, 16].
Each charge is bound by a restoring force:
F = -ma>20x (13)
where m is a mass of the charge and coo is the frequency of oscillation around
equilibrium. When the electric field is applied, we can write:
-eE(x,t) = m[ x+ y x+ co^x]
(14)
where y is a damping term that represents dissipation of the energy into the system and e
is electrical charge. With the approximation of a small oscillation, the dipole moment of
one electron can be written as (if the field varies as e"ltflt):
,2
p = -ex - —(O)Q -coL -iyco) lE
m
(15)
Assuming N molecules with Z\ electrons in each, fj electrons per molecule with
binding frequency COJ and damping constant yj, the dielectric constant is given by:
S(CO)
.
Ne
v" 1 r /
2
2
•
v-l
/ 1 A
Far above the highest resonant frequency the dielectric constant takes the form:
12
col
p
(17)
a>{a> + iy)
s{co) = \
where cop is a plasma frequency. Equation (17) is approximately independent of the wave
vector k. It is clear that below the plasma frequency, e (oo) will be negative (when y is
insignificant).
In general, the plasma frequency depends only on the total number of electrons n
= NZi. It can be described by the following expression:
(o*2p=-^— ne
£
(18)
m
O eff
where meff is the effective mass of an electron.
For many metals, the plasma frequency is in the ultraviolet part of the spectrum.
Near the plasma frequency (cop), the damping term (y) is very small. However, when we
move to lower frequencies, the dissipation is large (cop ~ y). The dissipation will then
dominate all phenomena and we no longer have the behavior of good plasma [14].
Therefore, if one wants to use microwaves for the sensor it is important to reduce the
value of the plasma frequency to the microwave spectrum in order to obtain plasma
behavior at these frequencies. As it was mentioned before, one way to achieve this is by a
periodic array of thin metallic wires. For this structure, the expression for the plasma
frequency can be rewritten in the following way [14]:
a2p=_ne?_
s0meff
=
- r ^ —
(19)
a ln(a/r2)
where Co is a speed of light, a is a lattice parameter and r2 is a radius of a wire. Equation
(19) shows that the plasma frequency in the case of the thin wires array can be expressed
in the terms of geometrical parameters of the system. The thickness of the wires is very
13
small in comparison with the corresponding wavelength in use. Therefore, when the
incident wave is incident on the composite medium composed of the periodic array of
wires and the air in between, such a medium can be considered homogenous and can be
described by some eeff.
In order to obtain a material with negative permeability, it was suggested in 1999
by J. Pendry et al. [17] that a new resonant structure called split ring resonator (SRR)
exhibits negative magnetic permeability at certain frequencies (Fig.4). The structure,
when SRR was combined with an array of thin metallic wires, paved the way for a design
of an artificial material (metamaterial) that would exhibit the characteristics that are
described above.
0'
Fig.4 A schematic of a split ring resonator
The SRR is built on a scale much smaller than the wavelength in use. The condition for
considering a periodic array of the SSRs to be a homogeneous medium in terms of its
response to an incident wave is:
a « X = 2nc0a>~1 (20)
Otherwise, the internal structure of the medium could diffract. The structures are resonant
due to internal capacitance and inductance which are introduced into the structure. The
gap in each ring prevents current from flowing on any one ring, however, the capacitance
14
between the rings enables current to flow. The effective permeability fieff can be defined
as follows. Bave = jueffju0Have (21) where B is magnetic flux density and subscript "ave"
denotes a parameter of the entire system, so that:
Mo12 ave
A detailed calculation is performed [17] which involves defining a field inside the SRR
cylinder when an external field Ho is applied, calculating the EMF around the
circumference of the cylinder, balancing the EMF and defining B ave and Have through Ho,
induced current per unit length j , metal surface resistance per unit area a and geometrical
parameters of the system. The following expression is obtained for the |xeff:
*«-'-,
2ai "
3
2
1 + a>rju0 K £i0a>2Cr3
(23)
where F is the fractional volume of a cell that is occupied by the interior of the cylinder,
F = ——, r is a radius of the SRR and C is the capacitance per unit area between the two
a
sheets:
£
C = —- =
d'
1
— (24) where d' is a distance between the concentric rings.
d'c0ju0
Hence,
w1
Meff=l
. /
. . . 2 (25)
2oi
3d'c0
1+
2
a>r/J0 ft a>2r3
We can define
15
compis called the "magnetic plasma frequency".
From (25) and (26) it can be seen that the value of ueff is negative between coo and comp the resonance effect. Again, ueff in this case is described mostly in geometrical terms.
A combined periodic structure of SRRs and thin metallic wires paved the way for
the design of a metamaterial which would exhibit the negative index of refraction
characteristics described above. From equations (17) and (25) it is clear that a system
which consists of a periodic array of wires and SRRs can be tuned to have a negative
permittivity and permeability simultaneously at certain frequencies. Equations (19), (24)
and (26) show that the tuning can be performed by adjusting the geometrical parameters
of the metal pattern.
From Maxwell's equations, the index of refraction of a material n can be written:
n = -Jsju (27)
If s and u have the same sign, it is not immediately clear why n must be negative and
why the ray diagram behaves as indicated in Fig.2. In order to answer this question, we
need to recall that boundary conditions require tangential components of E and H and
normal components of D and B to be continuous at the interface:
/I —
tl 5 " ^ f] — "^^ tl
(28) (index t denotes tangential and n denotes normal
£E
\ n\
=£ E
2 n2iM\Hn\
= VlH
n2
component of the field).
Assuming an interface in the x-y plane, it is clear from (28) that the x and y components
of the field will not change when moving into the second medium regardless of the signs
16
of £ and \i, whereas the z component will reverse its direction if the signs of s and \i have
changed [18]. Maxwell relationships give:
kxE = -/uH
°
kxH = -—eE
c
(29)
which combined with (28) leads to the conclusion that when the signs of s and u are
simultaneously negative, the sign of kz is reversed. This corresponds to a mirror reflection
of the k, H and E triplet at the boundary as indicated in Fig.2. This means that the index
of refraction that is determined from the Snell's law will be negative.
In general, the values of s and jx are complex and, therefore, care must be taken in
the application of equation (27). As an example, let's assume that e = u- = -1. Then s and
jo, maybe written as s = u = exp (m). The index of refraction n is thenn = Jeju = exp (in)
exp (irc) = -1. The only condition which applies is that the square roots of s and u must
have positive imaginary parts to maintain a passive material [19].
Experimental verification of a negative refractive index material was first
performed by R.A. Shelby et al. in 2001 [20]. Today metamaterials which exhibit left
handed properties are a hot research topic for many groups around the world.
Metamaterials can be engineered to exhibit a negative refractive index at frequencies that
range from acoustic to visible light. The first lens fabricated for this work, which is
designed to operate at 3 - 4 GHz, has a typical configuration as depicted in Fig. 5.
17
Fig.5 (a) Optical image of a metamaterial lens that was designed and fabricated for this
study, (b) the unit cell.
It is worth pointing out that the term "lens" does not strictly apply to this
metamaterial because it only focuses rays which are originating from a point source as
shown in Fig. 3. This metamaterial will not focus a collimated beam as a lens in
conventional optics would.
In such a material, the index of refraction will be less than 0 for certain
frequencies. This means that phase and group velocity will propagate in the metamaterial
in opposite directions. The energy flow (associated with the group velocity) will still be
directed away from the interface as in the case with a regular material and positive index
of refraction.
The SRR/wire structure is not the only way to produce a metameterial that
exhibits a negative index of refraction or "left-handed" behavior. Other methods include
photonic crystals [21], 2D microstrip transmission lines loaded with series of chip
capacitors and inductors [22], Sievenpiper structures [23] and ferroelastic crystals [24].
18
Although these other structures are implemented into microwave and radiated wave
applications [25], the original SRR/wire metamaterial structure used in this work was
considered useless outside of geometrical optics applications such as in in the microwave
spectrum. This work is the first known application of this structure outside of geometrical
optics.
19
CHAPTER III
DESIGN and FABRICATION of METAMATERIAL LENSES
3.1 2-D Lens for Operation at 3.65 GHz
The first metamaterial lens was designed and fabricated for the purpose of
proving the concept of operation of the novel NDE sensor proposed in this thesis. The
lens was designed to operate at a resonant frequency between 3 and 4 GHz (Fig. 5).
The wavelength of such an EM wave is very long (about 8.2 cm) and the ability of the
NDE sensor to detect real life defects (even with the sub wavelength focusing ability
of the metamaterial lens) is questionable. However, such a lens is relatively cheap and
easy to fabricate since it can be manufactured by means of commercial production of
printed circuit boards (PCB). A model of the lens was created using the
commercially available software package HFSS Ansoft. The model helps to establish
the resonant frequency of the lens and transmission coefficient S21 through the lens.
The results were compared with the experimental results for the lens in order to verify
the validity of the model. Design validation at 3.65 GHz frequency would allow the
use of the model for design of metamaterial lenses for other frequencies.
The design of the lens was based on the design of Aydin et al. [7, 8, 9].
3.1.1
Fabrication of the 3.65 GHz 2-D Metamaterial Lens.
The lens shown in Fig. 5 has the unit cell dimensions as indicated in Fig. 6.
20
Fig.6 Dimensions of the 3.65 GHz 2-D metamaterial lens unit cell.
PCB material - FR4 (s = 4.4, tan8 = 0.02), Metallic structures - copper (30 um
thick), r=1.6mm, d=t=0.2mm w=0.9mm, a=9.3mm, h = 0.9 mm. PCB sheets were 1.8
mm thick.
The overall dimensions of the lens were 40 unit cells in width, 20 unit cells in
height and 10 unit cells in the direction of the wave propagation. In order to assemble
the lens in a 2-D (a "wine-crate") structure, 1.8 mm thick slits were cut halfway
through the height of each PCB sheet in periodic manner between every unit cell (like
in a wine crate) in order to make the assembly possible. The wires were printed on
one side of the PCB and the SRRs on the other. All the technology to fabricate the
lens is commercially available and relatively inexpensive.
The design was implemented in a Corel-Draw structure as in Fig. 7 for 9 long and
40 short perpendicular sheets.
21
Two sides of the PCB sheet
Fig.7 Example of a Corel-Draw file for a section of a metamaterial lens.
The Corel-Draw file was sent to the manufacturer (Agco, Inc in Boulder, CO)
where the files were converted to Autocad and used to etch the required metallized
structures on the PCB boards. The separate sheets were shipped to the lab and the lens
was assembled on site.
3.1.2
Modeling of the 3.65 GHz 2-D Metamaterial lens.
As mentioned before, one of the objectives of this research was to design an NDE
sensor that could be used in industrial applications to detect real defects in real
systems. In order to reach this goal, a suitable metamaterial lens has to be designed.
22
The lens operates at or near specific resonant frequency (which determine the spatial
resolution of the lens). A computational model, once validated, will serve as an
important tool to design such a lens at various frequencies. The NIM lens structure
was modeled using Ansoft's HFSS™ software. The model is presented in Fig. 8:
\
z
X
Fig. 8 Image of the modeled lens.
Three unit cells were used along the direction of the wave propagation which was
found sufficient [26] to describe the behavior of a system. Perfect E boundary
conditions were used for E perpendicular to the z direction and perfect H boundary
conditions perpendicular to y direction. The incident electric field E was directed
parallel to the wires (in the y direction).
Fig. 9 shows the result obtained from the model.
23
Frequency Swmp PR4 (model)
45
5
Frequency (GHz(
Fig. 9 Modeling results for transmitted power as a function of incident microwave
frequency (3.65 GHz).
One can clearly see the resonant peak around the frequency of 2.8 GHz. The
plateau at the frequencies higher than 5.5 GHz indicates positive s and fi at these
frequencies where the lens will behave as an ordinary (positive n) medium which
transmits an EM wave.
3.2
Modeling and Fabrication of 3.65 GHz 1-D Lens.
As will be discussed in the following chapters, NIM lens are very lossy structures.
In an attempt to mitigate the losses, a 1-D lens was fabricated from the original lens
by removing the 9 long PCB sheets which were perpendicular to the propagation
direction of the impinging EM wave. The 40 short sheets were held in place by
grooves made in a dielectric material with s similar to that of the dielectric PCB board
(FR4). Fig. 10 shows the assembly process for the 1-D lens:
24
Fig. 10 Assembly process for the 1-D lens.
3.2.1
Fabrication of the 3.65 GHz 1-D Metamaterial Lens.
The sample holder consisted of two dielectric boards in which 40 grooves of 1.6
mm width were machined. The grooves were located 9.3 mm apart, which coincides
with the unit cell dimension. The PCB boards were situated in a way that the H vector
was perpendicular to the SRRs.
3.2.2
Modeling of the 3.65 GHz 1-D Metamaterial Lens.
Modeling of the 1-D lens was performed in a similar way to that described in
3.1.2. The results of the model are shown in Fig. 11.
The resonant peak appears around 3.4 GHz and the transmission level of the 1-D
lens is about 10 times higher than for the 2-D lens. This result will be further
discussed in the coming chapters.
25
1D frequency sweep model
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
Frequency (GHz)
Fig.l 1 Modeling results for transmitted power as a function of incident
microwave frequency (3.65 GHz 1-D lens).
3.3
Modeling and Fabrication of 16.75 GHz 2-D Lens.
After all necessary experiments were completed with the lenses discussed above
and the principle of operation was proven for the novel NDE sensor based on the
metamaterial lens, a new lens was designed and modeled. The lens had a smaller unit
cell and metallized structures and, therefore, it resonated at a higher frequency. The
idea was to push the conventional PCB production method to its limit and evaluate
the properties of the resulting sensor. Since the transmission loss of the lens is an
issue, the matrix material of the PCB boards was changed from FR4 to the less lossy
Rogers Duroid 5880.
26
3.3.1
Modeling of the 16.75 GHz 2-D Metamaterial Lens.
The lens was modeled in a manner similar to that described in 3.1.2. However, in
this case, the prediction of the operating (resonant) frequency of the lens was made
before the lens was fabricated and tested. As will be shown in the following chapters,
the experimental results of the test to determine the resonant frequency of the lens
(for the 3.65 GHz lens) indicate that a 1-D model predicts the resonant frequency of a
1-D or 2-D lens more accurately than a 2-D model. It is believed that the difference
between 1-D and 2-D modeled results is due to difficulties in setting of an exact unit
cell size for the 2-D lens model. The geometry of the lens prescribes a metallic SRR
structure to extend on one side and to intersect with the edge of the unit cell in the
model. However, such an intersection is prohibited due to the nature of the boundary
condition that is imposed on the edge of the unit cell. Therefore, the size of the unit
cell had to be enlarged in this direction in order to avoid the intersection. The same
results will show that the transmission levels of the 2-D are more accurately predicted
with a 2-D model. The results of the model are shown in Fig. 12.
The model shows a resonance peak at the frequency about 15.9 GHz. This result
will be compared in the further chapters with the experimental results for
characterization of the new lens.
S21 Rogers
_
-5
J
_
10
—
15-
—
...J.
—
-
20-
..
25
.....
—4
30-
35-
40
•
~
^
*
^
45-
50-
10
.... .._
-
\
i
I
i
I
I
12
13
—
• -
—
i
14
15
16
17
19
20
Frequency (Gfe)
Fig. 12 Modeling results for transmitted power as a function of incident microwave
frequency (1 -D lens).
3.3.2
Fabrication of the 16.75 GHz 2-D Metamaterial Lens.
The procedure for fabrication of the new lens was the same as for the previous
lens. The Corel Draw files were created and converted by the manufacturer to
Autocad files that were used to etch the metallized structures on the Rogers. The
separate sheets of the lens were sent to the lab and the lens was assembled on site.
The flexibility of the very thin (1 mm thick) Rogers Duroid 5880 made assembling
the lens in the wine-crate structure somewhat challenging.
It took over 4 full days to finish the assembly. The lens is shown in Fig. 13.
28
380 mm
Fig. 13 (a) Image of a designed metamaterial lens operating at 16-17GHz frequency
range.
PCB material- Rogers Duroid 5880 (e = 2.2, tan5 = 0.009) (b) the unit cell.
The overall dimensions of the lens are: 100 unit cells in width, 60 unit cells in
height and 10 unit cells thick in the direction of the propagation of the impinging EM
wave. The dimensions within the unit cell are shown on Fig. 14.
Fig. 14 Dimensions of the 16.75 GHz 2-D metamaterial lens unit cell.
29
PCB material - Rogers Duroid 5880 (e = 2.2, tanS = 0.009), metallic structure copper (30 um thick), r=0.7 mm, d=t=0.2mm w=0.3mm, a=3.8mm, h = 0.3 mm. PCB
sheets were 1.0 mm thick.
30
CHAPTER IV
EXPERIMENTAL SETUP for the CHARACTERIZATION of METAMATERIAL
LENS
4.1 Determination of the Resonant Frequency.
Before incorporating the lens into the sensor system, the lens was characterized for
several important physical parameters. The resonant frequency of the lens and
transmission level at that frequency, the frequency dependent index of refraction of the
lens (around the resonant frequency), and the minimum focus spot size that the lens can
provide (this determines the resolution of the sensor) were measured.
For all three lenses used in this work (3.65 GHz 2-D, 3.65 GHz 1-D and 16.5 GHz 2-D)
the determination of the resonant frequency was performed in a similar manner.
In order to confirm the resonant frequency of the material a transmission frequency
sweep experiment was performed for a relatively wide range of frequencies ( 3 - 7 GHz
for the 3.65 GHz 2-D and 1-D lenses and 12.4 -18 GHz for the 16.75 GHz 2-D lens).
The equipment used for the frequency sweep experiment consisted of a Hewlett Packard
(HP) 8510 Network Analyzer and two horn antennas. For the first two lenses, two
Atlantic Electronics Limited (AEL) horn antennas, model H-1498 (broad band 2GHz 18 GHz, largest dimension 12.5 cm) were used. For the 16.75 GHz lens, two Waveline,
model 799 horn antennas (broad band 12.4 GHz - 18GHz, largest dimension 5 cm) were
used. The metamaterial lenses were embedded into a fixture that was covered with
absorber in order to maximize the isolation of the two antennas (especially for the 1-D
and 2-D 3.65 GHz lenses). A schematic of the experimental system for the frequency
31
sweep experiment is provided in Fig. 15 and photographs of the 3.65 GHz lens system
are provided in Fig. 16.
Fixture and
absorber
ens
Horn antenna
Trans miter
•n
Network Analyzer
HP8010
Receiver
Fig. 15 A schematic of the experimental system for the frequency sweep experiment.
Fig. 16 Photographs of the experimental setup for the 3.65 GHz lens.
For the 16.75 GHz lens, a full two-port Thru-Reflect-Line (TRL) calibration was
performed before the sweep in order to obtain not only the transmitted power through the
32
lens (S21) but also the reflected power (Sn). Measurement of the both parameters allowed
the absorption in the lens to be calculated. The emitting horn was located 12 cm away
from the lens for both systems.
The photograph of the 16.75 GHz lens system is shown in Fig.17.
Fig. 17 Photographs of the experimental setup for the 16.75 GHz lens.
The horn antennas used for both lens systems are shown in Fig. 18:
(a)
(b)
Fig. 18 Horn antennas used in the experiments (a) for 3.65 GHz lenses and (b) for 16.75
GHz.
As was mentioned in the previous chapter, the results of the experiments under discussion
will be compared to the modeling results for the same lenses and a conclusion will be
derived about applicability of the model in the design of the future systems.
33
4.2 Determination of the Frequency Dependent Index of Refraction.
The index of refraction of the lens is a very important parameter in
characterization of the system that we are proposing. It was mentioned in Chapter II that
the sub-wavelength focusing phenomenon and related mathematical relations were
established for the lens where its index of refraction is exactly -1. Also, we know that in
reality this number is very hard to achieve. Experimental evidence from many works
shows ([9, 12, 13]) that the effect exists even when the diffraction index is close to -1 but
not exactly -1. The maximal transmission will be achieved at a frequency that
corresponds to a value of n that is somewhat different from -1 (the reason for that will be
suggested in upcoming chapters). Therefore, for our purposes, the determination of the
working frequency was a trade off between a reasonable transmission value and a
frequency that corresponded to a value of n that is close to -1.
4.2.1 Lens Operating at 3.65 GHz Resonance Frequency.
The index of refraction for 3.65 GHz lenses was determined from a Snell's law
experiment. The experiment is shown in Fig. 19.
The index of refraction can be determined from Snell's law when the normal distance (12
cm) from the horn antenna edge to outer face of the metamaterial lens and its thickness
(9.3 cm) are known. The transmitted energy was measured by scanning with a monopole
antenna very close to the lens on the other side. Then the horn antenna was tilted 15° to
the right while pointing to the same location on the lens (a laser pointer was used for that
purpose). The transmitted energy was again measured using the scanning monopole
antenna.
metamatenal
horn
monopole
¥
Network Analyzer
Fig. 19 A schematic of the experimental system for the index of refraction determination
(f= 3.65 GHz).
The location of the obtained peak was compared with the scan of the horn antenna
normal to the lens. The shift in the peak position indicated the magnitude of the index of
refraction (from SnelPs law) and its sign. This experiment was repeated for several
frequencies around the resonant peak in order to establish the frequency where the
metamaterial exhibited an index of refraction closest to n = -1.
4.2.2 Lens Operating at 16.75 GHz Resonance Frequency.
For the new lens another (more rigorous) method to measure the frequency dependent
index of refraction was employed. A schematic of the method is shown in Fig. 20.
35
ens
Horn
I.
H
•
Network
Analyzer HP8010
Fig.20 A schematic of the experimental system for the index of refraction determination
(f= 16.75 GHz lens).
The method is based on far-field range measurements of the negative phase change
through the negative index medium. The distance from the emitting horn antenna to the
lens was long enough to accommodate for the far field (D2/ X) requirement (12 cm
distance versus 5 cm largest dimension of the horn antenna). From the phase
measurement the index of refraction can be calculated from the following formula:
A0 = (n-l)koL
(30)
where ko is the free space vector and L is the thickness of the lens and Acp is the
difference in phase between free space transmission and transmission though the lens. In
this case the free space measurement was subtracted during calibration so that Acp could
be measured directly.
The test was first performed with a 2 inch thick sheet of Teflon inserted instead of the
lens in order to verify the validity of the method by comparison with values of the index
of refraction of Teflon at the operating frequencies. The transmission was measured in
36
the frequency range between 16 and 17 GHz. Then the same experiment was performed
with the negative index lens inserted between the horn antennas.
The phase change of transmitted power as measured by the network analyzer is defined
in a way that any 360° or multiple of 360° discontinuity must be corrected before
calculating n. The correction was accomplished by obtaining the phase shift incurred by
one unit cell of the lens from the HFSS model around the frequencies that should render n
= -1. The obtained number was multiplied by 2 (since the wave is traveling from the
medium with n = 1 to the medium with n = -1) and by 10 since our lens has 10 unit cells.
When the correction was performed for Acp, the index of refraction was calculated from
(30).
4.3 Determination of the Focus Spot Size.
We have discussed previously that for a material with n = -1, focusing behavior can be
described by Fig. 3 and Eqn. (1). In real life however, it is very difficult to obtain n = -1
exactly and with no losses incurred. For n negative but not equal to -1, the location of the
focus spot relative to the surface of the lens would vary in comparison with given by Eq.
(1) (especially note the fact that the best transmission occurs at a frequency that renders n
somewhat different than -1). Also the focusing efficiency of the lens in comparison with
the diffraction limit is also unknown. The location of the focus spot and focusing
efficiency of the lens can be determined experimentally. For this purpose the following
test was set up as shown in Fig. 21.
37
metamaterial
I
Transmitting
monopole
e
o
o
<N
Receiving
monopole
Network Analyzer
Fig. 21 A schematic of the experimental system for the focus spot size determination.
In the experiment, the stationary transmitting monopole was positioned arbitrarily at 6
cm away from the lens surface so that it is within the distance specified by Eqn. (1). In
the ideal case, for n = -1, Eqn. (1) gives the distance di for the focused spot as 3.3 cm.
Therefore, the receiving monopole was operated at distances that were closer to the lens
than 3.3 cm. Both the frequency and the scanning distance were varied to find the
optimal focusing. Since the signal which was emitted by the transmitting monopole was
weak (for the 3.65 GHz lens) and the losses in the lens were high, a 20 dB amplifier was
used to enhance the signal before going into the lens. The 16.75 GHz lens was thinner
than the 3.65 GHz lens in the direction of the wave propagation (4 cm vs. 9.3 cm).
Therefore, according to Eqn. (1), the emitting monopole was positioned 1 cm away from
the surface of the lens and the receiving monopole was operated at distances closer than 3
38
cm to another surface of the lens. The receiving monopole was operated at different
distances within the range that was reported above. It was scanned for 20 cm along the
length of the lens.
The monopole's dimensions were comparable with the quarter wave length of the
resonant frequencies of the lenses, which were 8 cm and 1.8 cm respectively. A photo of
the experimental system to detect the focus spot size of the 16.75 GHz negative index
material lens is shown in Fig. 22:
Fig.22 An optical photograph of the experimental setup for the focus spot size
determination (f = 16.75 GHz).
4.4 Aperture Size Measurement Setup.
One of the characterization issues under investigation in this work was a question of
the aperture size (or the area of the lens, in our case) which is required to successfully
implement the suggested method. In other words, how a reduction in the area of the lens
will affect the transmitted signal in terms of the focus spot size. For this purpose, 1/3 of
the aperture area of the 16.75 GHz lens was covered with absorber around the edges of
the lens as shown in Fig. 23.
39
Fig.23 Image of a lens with 1/3 of the aperture area reduced by absorber (f = 16.75 GHz).
The lens with the reduced aperture was inserted back into the system as described in
Fig. 21. The test was performed in the same manner as described in section 4.3 at the
frequency of 16.65 GHz when the receiving monopole was 2 cm away from the surface
of the lens. The results were compared with the scan at the same conditions when the full
aperture area of the same lens was exposed.
4.5 NDE Sensor Experimental Setup.
After all necessary parameters for the lens and the system were established through the
characterization experiments described in sections 4 . 1 - 4.4, the negative index material
lenses were incorporated in the design of a novel NDE sensor. The sensor was designed
as shown in Fig. 24.
40
translation
axis
Hole
(d=3mm)
lens
Transmitting monopole
sample
o
WmMMMk
L^41
Receiving
monopole
amplifier
Network
analyzer
Fig. 24 A schematic of NDE sensor based on the negative index material lens.
As a note, when the 16.75 GHz lens was used in the sensing experiments, the amplifier
depicted in the Fig. 24 was removed since the transmission signal through the lens was
much stronger than the signal through the 3.65 GHz lens, which simplifies the system.
Also, only 2-D 3.65 GHz and 16.75 GHz lenses were used in the sensing experiments for
reasons that will be explained in the following chapters.
The principle of operation of the sensor is based on the emitted signal from a point
source (a monopole) that is focused by the negative index material lens to a focus spot
that is smaller than the defined by the diffraction limit. The test sample is located a focus
distance away from the surface of the lens. The sample is translated along the translation
axis in the direction perpendicular to the direction of the wave propagation. The sample is
moved in increments of 1 mm and at each stop the reflected signal is registered by the
receiving monopole which is located on the same side of the lens as the test sample about
a wave length aside from the axis of the emitting monopole (as indicated in Fig. 24). The
41
purpose of the experiments was to determine if a reasonably small defect (in comparison
with the wavelength in use) inside the sample can be successfully detected by the sensor.
In other words, the experiment was to determine whether the change in the reflected
signal due to the presence of the defect could be detected.
4.5.1 Dielectric Sample with Drilled Hole.
There were several samples used to test the applicability of the sensor. Since
microwave frequencies were used in the experiments, the most logical test sample would
be a dielectric with a defect inside it. We used a fiberglass bar (e = 4.8) with a hole drilled
through the bar in the direction perpendicular to the direction of the wave propagation. A
schematic of the bar with accurate dimension is shown in Fig. 25.
0.3cm
8cm
Fig.25 Schematic of the sample (fiberglass, s = 4.8).
Note that the hole shown in Fig. 25 is 0.3 cm in diameter and 10 cm in length.
This sample was tested with the sensors based on both 3.65 GHz lens and 16.75 GHz lens
in order to show the improvement of the image quality when a higher operating
42
frequency was used. Also, another sample was made out of the same material to be tested
with the 16.75 GHz lens which had a 1 mm hole (Fig. 26, 27) to demonstrate the
improvement in imaging abilities of the sensor.
u
Fiberglass
sample
Fig.26 Optical image of fiberglass sample.
Fig.27 Optical image of 1 mm hole drilled in the sample.
Holes to
ttach the
sample to
theXYZ
positioner
43
Fillers for the holes were fabricated out of the same material in order to scan the
"flawless" sample as a background. All the results shown for the described samples are a
subtraction of the background scan from the scan with the defect. The filler for the 1 mm
hole with a stem is shown in Fig. 28.
Fig.28 Optical image of the filler for the 1 mm hole drilled in the test sample.
When this sample was tested with the sensor based on the 3.65 GHz frequency, the
operating frequency corresponded to a wavelength of 8.2 cm. Therefore, the introduced
defect constitutes 0.037 h For the sensor based on the 16.75 GHz frequency, the wave
length was 1.8 cm; therefore, the defect constitutes 0.17 A, for the 3 mm hole and 0.056 X
for the 1 mm hole.
4.5.2 Corrosion Spot Detection.
Another important problem that we tried to address using our sensor was detection of
corrosion spots on an aluminum plate. One of the problems that NASA is trying to
address is detection of such corrosion spots on the aluminum skin of the situated under
44
the space shuttle ceramic tiles. For the experiments, an aluminum test plate was
fabricated by Dr. Smith of the NASA Non Destructive Evaluation branch with simulated
corrosion spots. The spots were 5 mm in diameter (average) and 500 urn in depth. The
plate is shown in Fig. 29.
Fig. 29 Aluminum plate with simulated corrosion spots. A square indicates the area
scanned by the sensor based on 3.65 GHz negative index material lens.
Unfortunately, the geometrical parameters of the system for the sensor based on the
3.65 GHz negative index material lens did not allow for the enough space to attach the
space shuttle tile to the Aluminum plate in order to scan them together. Therefore, only
the plate itself was scanned with the proposed sensor in order to demonstrate that the
sensor can detect a corrosion spot 0.5 mm deep. The sensor based on the 16.75 GHz lens
allowed inserting the space shuttle tile into the scan. Therefore, the tests based on this
sensor were performed with the space shuttle tile attached to the aluminum plate. The test
45
sample for the 16.75 GHz lens sensor is shown in Fig. 30 and the test system is shown in
Fig. 31.
(a) Corrosion plate
(b) Shuttle tile mounted on the
corrosion plate
Fig.30 Test sample used for the scan with the sensor based on 16.75 GHz negative index
material lens, (a) Corrosion plate and (b) Space shuttle tile mounted on the corrosion
plate
Network
analyzer
HP 8
Test
sample
Emittini
monopole
XYZ
positioner
Receiving
nopole
Fig.31 Test system for sensor based on 16.75 GHz negative index material lens. The
sensor was used to scan a space shuttle tile mounted on an aluminum plate with simulated
corrosion spots.
46
4.5.3 Surface Rippling of Carbon Fiber Composite Detection.
EM waves in the microwave spectrum generally do not penetrate the carbon fiber
composites since carbon fibers are very conductive (the exception is a composite where
all the fibers are unidirectionally oriented [28]). However, there is a problem that occurs
on the surface of the carbon fiber composite that is of a great importance to the industry.
Due to improper curing procedures, carbon fiber laminates sometimes have ripples on the
surface. The ripple can be very shallow (in fact, before our sample was tested by our
sensor, we didn't notice any ripple at all visually). The problem is that such a ripple
induces disorientation of the carbon fibers or even their breakage causing the laminate to
loose its structural integrity and, in severe cases, can trigger the system failure. We
wanted to demonstrate that our sensor can detect the ripples on the surface. On the carbon
fiber composite a peak to trough height A of 0.2 mm (0.0024 X) was measured.
For this test we used only a sensor based on the 3.65 GHz negative index material lens
since it was sufficient to demonstrate the capabilities of the method, as will be shown in
the further chapters. Our test sample is shown in Fig. 32:
Fig. 32 Image of a carbon fiber composite test sample.
The magnified rippling effect is shown in Fig. 33.
47
A = 0.2mm (0.0024 A)
Fig. 33 Magnified image of rippling on the surface of a carbon fiber composite sample
used in our experiments.
48
CHAPTER V
NEGATIVE INDEX MATERIAL LENS CHARACTERIZATION RESULTS
As discussed in the previous chapter, several important characteristics of the negative
index material lens were evaluated before its incorporation in the proposed NDE sensor.
This chapter presents the results obtained from the characterization experiments in the
sequence of the experiments discussed in chapter IV.
5.1 Resonant Frequency.
5.1.1 3.65 GHz 2-D Lens.
The first lens (shown in Fig. 5) was tested in an experimental setup (Fig. 15) to
determine the resonant frequency and transmission level of the lens by measuring the
transmission coefficient (S21) with the network analyzer. S21 was measured for the span
of frequencies from 3 GHz to 7 GHz in order to determine the resonant response in
transmission through the lens. The result of the experiment is presented in Fig. 34.
From the plot shown in Fig.34 it can be determined that the NIM lens has a resonant peak
at f = 3.625 GHz. The shape of the transmission curve is similar to the one described by
K. Aydin et al [7]. The resonant peak is relatively broad, yielding good transmission in
the range between 3.6 GHz to 3.7 GHz. It was mentioned in the previous chapter that
another characterization experiment was performed to deal with establishing frequency
dependence of the index of refraction of the lens. Once the dependence was established,
we used the frequency that yielded the index of refraction closest to -1 and had a
reasonably good transmission at the same time. The high transmission at frequencies
higher than 5.5 GHz was due to simultaneously positive E and JJ, at these frequencies. At
49
these frequencies our material behaves as a regular medium with an effective positive
index of refraction.
Frequency Sweep
3
3.5
4
4.5
5
5.5
6
6.5
7
Frequency (GHz)
Fig. 3 4 Results of the transmission frequency sweep for the 2-D negative index material
lens (experimental setup is shown in Fig. 15).
It can be observed from Fig. 34 that the transmission at the resonant frequencies is
around -20 dB. Thus, only one percent of the energy is transmitted through the lens.
Clearly, the negative index material is a lossy medium and this is one of the major factors
to be improved in order to utilize the negative index material lens in NDE sensors.
According to Eqn. 1, di is defined as the distance of the point source away from the lens.
d.2 is the standoff distance of the sensor from a sample, and the sum of the two is equal to
the lens thickness 1. Therefore, in order to increase the standoff distance, we want to
50
make the lens as thick as possible. Transmission losses in the negative index material (the
fact that the losses are primarily due to the absorption and not reflection is proven
through the TRL calibration with the second lens) will significantly reduce our ability to
increase the thickness of the lens.
Comparison of the experimental results (Fig. 34) with the modeling of the same lens
(Fig. 8 and Fig. 9) shows strong correlation between the two, both in the location of the
resonant frequency and transmission levels of the lens. Therefore, the proposed model
can be used to design negative index material lenses for different frequencies in the
future.
5.1.2 3.65 GHz 1-D Lens.
As was mentioned in 5.1.1, one of the major issues which must be resolved in order to
utilize the NIM lens in the NDE sensor properly is the high level of transmission loss in
the lens. One of the proposed ways is to reduce the amount of the matrix material and the
metallized structures that interact with the EM wave. This goal can be achieved by
introducing a 1-D lens as shown in Fig. 10 when the plates that are perpendicular to the
direction of the wave propagation are removed from the structure. The same transmission
test as described in 5.1.1 was performed in order to determine the resonant frequency and
transmission level of the 1-D lens. Results were compared with the experimental results
from 5.1.1. The results of the test are shown in Fig. 35.
51
Frequency Sweep
3
3.5
4
4.5
5
5.5
6
6.5
7
Frequency (GHz)
Fig. 3 5 Non-calibrated results of the transmission frequency sweep for the 1-D negative
index material lens (experimental setup is shown in Fig. 15).
The resonant frequency is located at the same value of 3.625 GHz as for the 2-D lens.
The transmission level of the 1-D lens is much higher (-9 dB from the positive index
plateau) than the results shown in Fig. 34 (-20dB) for a 2-D lens. About 10% of the
radiation is transmitted through the 1-D lens. Comparison of the results shown in Fig. 34
and in Fig. 35 yields a conclusion that the use of the 1-D lens is an option that should be
considered when reducing transmission loss through the lens is important.
Comparison of the result in Fig. 35 with the modeling result for the 1-D lens as shown
in Fig. 11 suggests even better correlation between the experimental and modeled value
of the resonant frequency (~ 0.2 GHz difference) and of the transmission levels. It is
believed that the difference between 1-D and 2-D results is due to difficulties in setting of
52
an exact unit cell size for the 2-D lens model. The geometry of the lens prescribes a
metallic SRR structure to extend on one side and to intersect with the edge of the unit cell
in the model. However, such an intersection is prohibited due to the nature of the
boundary condition that is imposed on the edge of the unit cell. Therefore, the size of the
unit cell had to be enlarged in this direction in order to avoid the intersection. As a result,
the periodicity of the unit cell for the 2-D lens was slightly changed as opposed to the 1D lens where such correction was not necessary.
5.1.3 16.75 GHz 1-D Lens.
The resolution and sensitivity of the proposed sensor is highly dependent on the
frequency in use. 2-D and 1-D NIM lenses which are resonant at 3.625 GHz were used to
prove the concept of operation for the proposed sensor. In order to construct a sensor
which could detect smaller defects, or produce higher quality images for the same defect,
a new lens that works as a NIM material at a higher frequency was designed (Fig. 14 and
Fig. 13). The lens was tested in a way similar to discussed in 5.1.1 and5.1.2 (Fig. 15and
Fig. 17). Before the lens was manufactured, it was modeled with the Ansoft HFSS
software package and the resonant frequency was estimated to be 15.9 GHz. Therefore,
the frequency sweep was performed in the range between 11 GHz and 18 GHz. As was
mentioned in chapter IV, the measurement was performed using a TRL calibration in
order to investigate the nature of the losses associated with the lens (whether most of the
energy is absorbed or reflected back). The results of the test are shown in Fig. 36.
53
TRL Calibration of New Lens
Frequency (GHz)
Fig.36 TRL calibrated results of the transmission frequency sweep for the new 2-D
negative index material lens (experimental setup is shown in Fig. 15).
The resonant frequency was determined to be 16.75 GHz. The transmission through the
new lens was much higher than through the 2-D 3.65 GHz lens (-13 dB vs. -20 dB). The
reason is that the matrix material (Printed Circuit Board material) Rogers Duroid 5880 (s
= 2.2, tan8 = 0.009), which was used for the new lens was less lossy than the PCB
material used for the 3.65 GHz lens (FR4 - e = 4.4, tan5 = 0.02). The "plateau" region
where the material exhibits a normal "right-handed" behavior (as in Fig. 34 and 35) was
not reached in this experiment. This region is situated at higher frequencies than 18 GHz
which was the limit for the operation of the horn antennas in use.
The comparison of the experimental result with a 1-D model shows good correlation,
which confirms that the models can be reliably used in the design of the NIM lenses.
54
As was discussed before, the TRL calibration allows us to calculate the percentage of the
emitted energy that is absorbed in the lens versus the amount of the emitted energy that is
reflected back from the lens. The percentage of the emitted energy absorbed by the lens
(S3) can be calculated from the following equation:
K f + \S2i f+1^3 f =1 (31)
The \S\ values are defined as: \s\= 10A([value in dB] /10) (32). Therefore, from Fig. 36
we find that |5 n | 2 = 0.13, and \S2lf= 0.05. According to (31), we derive that |S 3 | 2 = 0.82.
In other words, 82% of the emitted energy is absorbed in the lens. The reasons for these
losses will be discussed in the later chapters.
It is worth noting that the resonant frequency of 16.75 GHz corresponds to a
wavelength of 1.8 cm. This wavelength is about 4 times shorter than the wavelength of
the previous lens and, therefore, has the potential to resolve even smaller defects. This
question will be examined in the next chapter.
5.2 Index of Refraction.
5.2.1 3.65 GHz Lens.
The frequency dependent index of refraction for the 3.65 GHz lens was determined as
described in 4.2.1 (Fig. 19). An example of the result of such a test is shown in Fig. 37
for the frequency of 3.64 GHz.
55
Odeg
3L64GHZO*15I
i
/
09
, '
08
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0.7
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i:
\
y
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f f
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y/
s
15 deg
V
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03
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0.2
\.
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0.1
•
0
0
20
40
BO
i
80
100
170
140
160
position (mm)
Fig.37 Typical normal incidence and 15 degree scans (experimental setup is shown on
Fig. 19).
One notices from the plot in Fig.37 that the energy density maximum shifts to the right
when the horn antenna is also shifted to the right, which is indicative of a negative index
of refraction (the monopole is scanned from top to bottom as indicated in Fig. 19 and zero
on the axis is taken to be the first point where the signal is acquired).
The index of refraction can be calculated in the following manner: if h is the position
shift in energy density curve, from the Snell's law: nx sin©! = n2 sin© 2 (32). In our case,
h
sinl5° =« 2 sin ©2 (33) where tan@2 =— (1 is the thickness of the lens). Therefore, the
value of n2 can be obtained from (33).
Fig. 3 8 shows the results of refractive index variation with incident microwave signal
frequency.
Index vs. Frequency
0 ,
--
.
-0.5
-1
-1.5
= .2
„
»
-2.5
-3
-4
*
-I
3.61
1
1
3.6
3.62
'
3.6
•
3.63
'
3.6
!
3.64
1
3.6
1
3.65
1
3.6
i
3.66
Frequency (GHz)
Fig. 3 8 A plot showing the frequency dependence of the index of refraction
From the plot in Fig.38 one can see that the frequency which has the best transmission
of energy through the lens (f = 3.625 GHz) is not the one that gives the index of
refraction closest to n = -1 (f = 3.66 GHz). Therefore, in all subsequent lens
characterization experiments (with this lens), a frequency of 3.65/3.66 GHz was used to
yield an n close to -1.
5.2.2 16.75 GHz Lens.
As was stated in chapter IV, another (more rigorous) method to determine the
frequency dependent index of refraction was used for the 16.75 GHz lens. The method is
described in 4.2.2 and shown in Fig. 20. First the method was tested on a 2" thick sheet of
Teflon. The results are shown in Fig. 39 before the correction (phase) and in Fig. 40 after
the correction (index of refraction obtained from Eqn. 30).
57
Teflon
200
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Fig.39 S21 phase scan for a 2" sheet of Teflon before the correction.
Teflon
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1^
1.41
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17
Frequency (GHz)
Fig.40 Index of refraction variation with frequency for a 2" sheet of Teflon after the
correction.
58
It can be seen that after the correction, the values of n for the Teflon sheet are very close
to the quoted value of n = 1.44 in [27].
When the same experiment was repeated with the negative index lens, the following
results were obtained before the correction (Fig. 41 - phase) and after (Fig. 42 - index of
refraction obtained from Eqn. 30) correction.
Lens
Frequency (GHz)
Fig.41 S21 phase scan for the 16.75 GHz negative index material lens before the
correction.
It can be seen that the data is inconsistent below 16.5 GHz which corresponds to much
lower transmission levels away from the resonance peak as shown in Fig. 36. Therefore,
we will consider the data reliable in the range between 16.5 GHz and 16.8 GHz.
59
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17
Frequency (GHz)
Fig.42 A plot showing the frequency dependence of the index of refraction.
As can be seen, the frequency of 16.75 GHz which has the highest transmission level,
yields an index of refraction that very close to -1; therefore, this was chosen as the
operating frequency in the remainder of the experiments.
5.3 Focus Spot Size.
5.3.1 3.65 GHz 2-D Lens.
The experimental setup to determine the focus spot achievable by the lens is discussed
in 4.3 and shown in Fig. 21. As was discussed in 4.3, the goal of this experiment is to
determine the best focus spot size that can be achieved by the lens and what is the
optimal distance from the lens. This determination will help answer the question whether
the lens can defy the diffraction limit and whether it is applicable in the proposed sensor.
Fig. 43 shows a scan of the normalized power at f = 3.66 GHz at two distances away
from the lens. The focus spot size was determined to be the peak width at half the
maximum power, or the -3 dB point.
60
12 mm away
—
0
50
100
150
- 3 2 mm away
200
position (mm)
Fig.43 Power scan at 12 mm and 32 mm away from the lens. Dark solid line depicts the 3dB point
The best focusing spot size of 0.48 X was achieved for the frequency of 3.66 GHz at a
distance of 12 mm from the lens. A better focusing spot size could possibly be achieved
closer to the lens but this could not be investigated due to mechanical limitations of the
experimental setup.
In order to emphasize the focusing abilities of the lens, scans at two different
frequencies
are compared (Fig.44). At 6 G H z , the metamaterial has positive e and jx and,
therefore the energy transmitted through the material is unfocussed and relatively
unattenuated.
61
0
50
100
150
200
position (mm)
Fig.44 Power scan at 12 mm away from the lens for f = 3.66 GHz and f = 6 GHz. Dark
solid line depicts -3 dB point
From Fig.44 one notices that at the -3 dB point, the spot size for f = 6 GHz is 13.6 cm
(which corresponds to 2.7 X for X = 5 cm) whereas the spot size for f = 3.66 GHz is 3.9
cm (which corresponds to 0.48 X for X = 8.2 cm). Fig. 45 shows the focused spot size
versus distance from the lens for two frequencies (f = 3.64 GHz and f = 3.66 GHz).
The result presented in Fig. 45 is consistent with the result in Fig. 38. Even small
deviations from the value of effective n = -1 are shown to have a serious effect on
focusing abilities of the lens [30]. At 3.66 GHz, the index of refraction was determined to
be n = -1.25. The index of refraction at 3.64 GHz is n = -1.6, which deviates more from
the ideal value of n = -1. Therefore, the focusing abilities of the lens at f = 3.64 GHz
should be less prominent than for f = 3.66 GHz.
focus spot size
OJS i
*
3.66 GHZ
•
3.64 GHZ
—
25
mmswsy fmmMiu
Linear £3.66 GHz)
linear (3.6«GHz)
30
Fig.45 Focused spot size (in X) vs. distance from the lens. The lines represent linear
fitting of the data
Another important conclusion from Fig. 45 is that at f = 3.66 GHz frequency, a
significant change in the distance away from the lens does not bring about a significant
increase in focus spot size of the lens (which is in disagreement with the discussion in
chapter I based on [2]).
5.3.2 3.65 GHz 1-D Lens.
From the comparison of the results presented in Fig. 34 and Fig. 35, one can suggest
that the transmission levels through the 1-D lens operating at 3.65 GHz are about 10
times higher than for the 2-D 3.65 GHz lens. It has previously been discussed that
improving transmission levels through the lens is a crucial factor in making the lens
63
applicable in the proposed NDE sensor. Performing the same procedure as in 5.3.1 on the
1-D lens will help to determine whether the transmission levels were indeed improved.
Figure 46 shows a comparison of the focus spot size obtained for the 1-D and 2-D lens
respectively.
f \
as
Q8
a7
* \
ft
I ae
11
D
*as
i
\
/!
y i
\
\
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2D
\
\
/
0.3
0.2 \
U *•
/
\
\
/
%
0.1
>>,_ 3?^**" *
so
100
ISO
200
Posflion(mn4
Fig.46 Power scans at focus spot distance for 1-D lens and 2-D for 3.65 GHz lens. Dark
solid line depicts the -3dB point
The 1-D lens yielded a focus spot size of 5 cm = 0.7 A, whereas the scan for the 2-D lens
rendered the focus spot size of 4 cm = 0.48 X.
The tests suggest that the transmission through the 1-D lens is indeed could be about
10 times higher than through the 2-D lens (-9 dB versus -20 dB for the 2-D lens based on
non calibrated measurements and modeling results). However, the resolution of the 1-D
lens is lower than the 2-D lens (0.7 A, vs. 0.48 A respectively). The reason for the
64
difference in resolution could possibly be attributed to there being no component of H
perpendicular to the split rings for the 1-D lens at oblique incidence angles. Therefore,
there is no resonant effect in that area of the lens. Some transmission is possible if the
wire mesh in this direction renders a positive e value. 1-D lens aberrations are different
from the 2-D case. Higher power transmission does allow for the construction of a thicker
lens. Greater power transmission through the lens has one important benefit: it allows
better manipulation of standoff distance from the sample which could be important for
industrial applications. Another benefit is that manufacturing a 1-D lens is simpler than
for the 2-D lens. Before construction of the sensor a decision must be made as to which
characteristic is more important for the particular application - a longer standoff distance
from the sample or the resolution of the sensor. Based on this determination a 1-D or a 2D lens could be used.
5.3.3 16.75 GHz Lens.
The same procedure as shown in Fig. 21 was conducted to determine the focus spot
size for the new 16.75 GHz lens. As can be seen from the comparison of Fig. 34 and Fig.
36, the 16.75 GHz lens transmission levels are much higher than that of the 3.65 GHz
lens. This fact was utilized by eliminating the amplifier from the experimental setup
shown in Fig. 21. The results of the scan for the best focusing spot size are shown in Fig.
47.
65
16.6 GHz 1.4 cm away
0
20
40
60
80
100
120
140
Distance (mm)
Fig.47 Power scan atl4 mm away from the lens. Dark line depicts the -3dB point.
As can be seen, the new lens yielded a focus spot size of 0.9 cm or 0.5 X. In terms of
wavelength, this result is similar to the one obtained for the previous lens, but in absolute
values the focus spot is much smaller than before (0.9 cm vs. 4 cm). Therefore, this lens
could be used to detect even smaller defects.
As a note, this lens design pushes the limits of conventional manufacturing of the
printed circuit boards comprising both lenses (the metallized structures on the dielectric
material). This technology is relatively cheap and can be easily used. However, there are
other methods which can be used to manufacture the NIM structures which are more
expensive but allow for a significant reduction in the dimensions of the metallized
structures. Such methods include microlithography [31], nanofabrication [32] and ink jet
lithography [33]. Since the size of the metallized structure is directly linked to the
66
resonant frequency, it is clear that such reduction in size will yield a significant reduction
in focus spot size, which will allow construction of MM lens-based NDE sensors with
even higher resolution and sensitivity.
It can be observed that the best result depicted in Fig. 47 was obtained at the operating
frequency of 16.6 GHz, as opposed to 16.75 GHz where the transmission is the strongest
and the value of n is closer to -1. The reason for this result can be explained with the help
of the table in Fig. 48. The table shows the values of the focus spot sizes as a function of
the distance away from the lens and the frequency (around the resonance).
Frequency
distance (cm)
16.6 GHz 16.65 GHz 16.7 GHz 16.75 GHz 16.8 GHz 16.85 GHz
0.7
1.1
1.1
1.4
1.1
1.3
1.3
1.2
1
1
1.2
1.1
1.1
1.2
1.4
0.9
1.1
1.1
1.2
1.1
1.2
1.7
1.1
1.1
1.1
1.2
1.2
1.4
2
1.2
1.1
1.1
1.1
1.2
1.4
2.2
1.3
1.2
1.2
1.2
1.3
1.4
3
3.1
2.4
1.5
1.4
1.4
1.5
Fig.48 A table of experimentally measured focus spot size dependence on the distance
away from the lens and frequency.
The results can be explained by a combination of two factors. First, the data was not
taken in fine enough spatial increments to determine the best focus spot size for a certain
frequency. Also, the signal being transmitted through the lens, although stronger than for
67
the first lens, was still weak and some interference from the background noise could
potentially distort some results differently at different points away from the lens.
The results for two frequencies are plotted in Fig. 49. One can see that the results are
consistent with the theoretical focus spot size dependence on the distance away from the
lens.
0.5
1
1.5
2
2.5
3
3.5
Distance (cm)
Fig.49 Focused spot size (in cm) vs. distance from the lens.
5.4 Aperture Size Dependence of the Focus Spot Size.
This experiment was described in 4.4. The impact of the aperture (or the lens area) on
the focus spot size was studied with the experimental system shown in Fig. 21. The result
for the full aperture (entire area of the lens) is shown in Fig. 50 and for the 2/3 of the
aperture is shown in Fig. 51.
68
full aperture scanning monopole 2 cm away
0.9-
~ « r •- -ye • •
fcm
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60
20
80
100
120
140
Distance (mm)
Fig.50 Focus spot size measurement for the full aperture of the lens.
0.66 aperture scanning monopole 2 cm away
^
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40
60
80
120
Distance (mm)
Fig.51 Focus spot size measurement for 2/3 aperture of the lens.
140
A slight increase in the focus spot size (0.2 cm or 0.1 A) can be observed due to the
reduction of the aperture size by 1/3. This result is similar to what is expectedfroma
similar system in conventional optics. The absorber that covers 1/3 of the area of the lens
blocks a significant amount of the radiation from propagating through the lens.
70
CHAPTER VI
RESULTS and DISCUSSION for SUBWAVELENGTH RESOLUTION
MEASUREMENTS
6.1 3.75 GHz 2-D Lens.
6.1.1 Dielectric Sample.
The fiberglass sample shown in Fig. 24 was tested in the setup depicted in Fig. 25. The
results of the scan of the sample with a hole normalized to the baseline sample (without a
hole) are shown in Fig. 52.
200 mm scan backrourd subtracted
0.15
-0.15
J
position (mm)
Fig.52 Relative power scan of the sample as depicted in Fig.8 at f = 3.65 GHz.
From Fig. 52 the location of the hole can be determined from the minimum of the plot.
The procedure was repeated at a frequency of 6 GHz, for which the system operates in a
regular far field mode (the distance between the transmitting monopole and the sample
71
was 15.8 cm) to determine the presence of the defect. The result of the scan is shown in
Fig. 53.
200 turn scan backrourid subtracted
0.15
-0.1 S
position (mm)
Fig. 5 3 Relative power scan of a sample as depicted in Fig. 9 f = 6 GHz
It can be seen that it is not possible to determine the location of the hole from the scan
that is presented in Fig.53, which appears to be dominated by edge effects and/or by the
"wine crate" structure of the lens which at this frequency acts like a grating.
In order to investigate the capabilities of this method further, a second hole of the same
diameter was drilled 3 cm away from the first hole. The sample was scanned when both
holes were filled in order to establish the background. Then the sample was scanned with
one hole closed and one hole open and the second time with the other hole open and the
first hole closed. The procedure was repeated when the frequency of operation was
72
changed from f = 3.65 GHz to f = 6 GHz. The results of the experiment are shown in
Fig.54 andFig.55.
200 mm scan backround subtracted
0.15
"tote 8cm
~hote5cm
•0.16
\
\
position (mm)
location of holes
Fig.54 Relative power scan of a sample when two holes were filled alternately (f = 3.65
GHz). The second hole was drilled 3 cm away from the first one.
Fig. 55 shows that although a change in the hole's location causes some significant
changes in the energy density, it is still very hard to verify the existence of the hole in the
sample at 6 GHz. Part of this difficulty comes from the edge effects that remain even
after the background is subtracted. At the same time one can identify the location of the
hole when the sample is tested at f = 3.65 GHz, a resonant frequency for this material.
From the analysis of the results presented in 6.1.1, it can be concluded that the concept of
operation of the novel NDE sensor was proven.
73
200 m m scan backround subtracted
0.15
hole 8cm
hole 5cm
-0.15
position (mm)
Fig.55 Relative power scan of a sample when two holes were filled alternately
(f=6GHz)
A defect only 0.037 X in size was detected which shows very high sensitivity of the
sensor. In comparison, when the same defect is observed with a non resonant wavelength
(where the NIM lens behaves as a positive diffraction index medium) the same defect
could not be resolved.
These experiments help determine the sensitivity of the sensor. Based on the
characterization experiments described above, the focus spot size of the sensor was
determined to be 4 cm in diameter. To test the resolution of the sensor, two 3 mm holes
were drilled in the sample at a distance of 4 cm apart. They were plugged (for the
background scan) and then both unplugged. The result of the scan is shown in Fig. 56.
74
position (mm)
Fig. 56 Relative power scan of a sample when two holes were filled simultaneously
(f = 3.65 GHz).
It can be seen that the two holes can be clearly resolved by the NDE sensor under
discussion. Therefore, the resolution of the sensor is of the size of the focus spot.
6.1.2 Corrosion Plate.
One of the ways to apply the NDE sensor is as described in 4.5.2. In order to confirm
that the obtained results are indeed the detected spot, the experiment was repeated at the
frequency of 6 GHz. The results of the test are shown in Fig. 57. One can clearly see the
corrosion spot on the image obtained at the frequency of 3.65 GHz whereas at the
frequency of 6 GHz the corrosion spot can not be detected.
75
Corrosion
spot
(a)f = 3.65
(b)f = 6GHz
Fig.57 3-D power scan of the corrosion spot on an aluminum plate as indicated in Fig.29
(a) f = 3.65 GHz and (b) f = 6 GHz.
The elongation of the corrosion spot in Y direction can be attributed to the physical
dimensions of the receiving monopole in use, since the monopole detects some signal
from the corrosion spot even when the spot is moved out of the center of the radiation.
This problem can be corrected for the corrosion spot size under investigation by using a
sensor with shorter wavelength which will render smaller physical dimensions of the
monopole.
6.1.3 Carbon Fiber Composite.
The sample and the problem under consideration were described in 4.5.3. The results
of the test are shown in Fig. 58.
76
position (mm)
Fig.58 Relative power scan showing rippling on a carbon fiber composite sample
(f= 3.65 GHz).
On the carbon fiber composite a peak to trough height A of 0.2 mm (0.0024 X) was
measured. It is worth noting that this rippling was not noticeable visually when one
looked at the sample but it was detected first by our sensor.
6.2 3.75 GHz 1-D Lens.
We have mentioned before that the reason to investigate the 1-D NIM lens was that it
possibly provides a better signal transmission than the 2-D NIM lens constructed from
the same material. In 5.3.2 it was shown (Fig. 46) that the focus spot size of the 1-D lens
is larger than of the 2-D lens. The purpose of the following experiment is to determine
how this difference in the spot size translates into a difference in the image quality. For
77
that purpose the 3.65 GHz NIM lens was used in the experimental setup depicted in Fig.
24 with the same fiberglass dielectric sample as shown in Fig. 25. The comparison of the
scans for 1-D and 2-D lenses is shown in Fig. 59:
200 m m s c a n n o r m a l i z e d
0.2
I
0.15
(a)
1-D
^jv^y^n
0.05
-0.15
-0.2
position (mm)
200 m m s c a n n o r m a l i z e d
0.2
0.15
0.1
(b)
T^N -D
0.05
A^VW
:>
22
A
2\r*~&
7T
82
1 )2
i: »2
1
V2.
1i 52
V S2
-0.05
-0.1
-0.15
-0.2
position (mm)
Fig.59 Comparison of the relative power scans for (a) 1-D 3.65 GHz lens and (b) 2-D
3.65 GHz lens.
78
It can be seen that the image in Fig. 59 (b) (2-D NIM lens) is sharper than in Fig. 59 (a)
(1-D NIM lens). This is an expected result that confirms our prediction when the focus
spot sizes of both lenses were measured.
Again, it is worth mentioning that both lenses could be used in the system depending on
the requirements of a particular system. For example, if a greater standoff distance from a
sample is needed (which could be achieved by manipulating the thickness of the lens),
the 1-D NIM lens could be used if a reduction in image quality can be tolerated.
6.3 16.75 GHz Lens.
6.3.1 Dielectric Sample.
The absolute value of the focus spot size is much smaller for the 16.75 GHz lens than
for the 3.65 GHz lens due to the reason explained in 5.3.3.
It was mentioned in 4.5.1 that the same dielectric sample was used in the setup for both
the 3.65 GHz and 16.75 GHz NIM lens in order to demonstrate the improvement in the
image quality. The result of the scan for the 16.75 GHz is shown in Fig. 60.
Comparison of Fig. 60 and Fig. 52 shows significant improvement in the image of the
hole obtained with the 16.75 GHz lens. The peak width at half the maximum power of the
hole image is 10 mm for the 16.75 GHz lens versus 40 mm for the 3.65 GHz lens. This is
consistent with the focus spot size of each lens respectively.
Another sample similar to the previous one but with a hole diameter of 1 mm (Fig. 2628) was constructed to demonstrate the improvement in the sensitivity of the sensor when
the new 16.75 GHz lens was used. The results of the experiment are shown in Fig. 61.
79
3 m m hole scan
2.5
• ' , V ; '
""...'.-
•":'-•.:••
•••:
•-".•••"•••
*:••-*••
80
••'••&KJiA*'V'
100
Position (mm)
Fig.60 Relative power scan of a sample as depicted in Fig.25 (3 mm hole) f = 16.75 GHz.
One MM f l a w
2
1
Displacement Along Sample in mm
Fig.61 Relative power scan of a sample as depicted in Fig.26-28 (1 mm hole) f = 16.75
GHz.
80
One can easily identify the hole location at 40 mm away from the start of the scan. The
change in the relative power signal at the hole is 0.18 dB. It is anticipated that a smaller
diameter hole (sub-millimeter) can be detected; however, manufacturing a proper size
filler for the hole to scan the background proved to be impractical with the tools
available. An alternate solution, if the sample is big enough and the distance between the
sample and the lens is maintained precisely the same during the test, is to use another part
of the sample (without the hole) as a background. It is advised for future work to use a
laser-based device which will help to automatically maintain a constant distance between
the sample and the lens. Then, the "flawless" part of the sample can be used as the
background.
6.3.2 Corrosion Spot Detection.
In section 4.5.2 we addressed the issue of investigation of a corrosion spot on an
aluminum plate. The geometrical dimensions of the system and characteristics of the 3.65
GHz lens did not allow the shuttle tile to be inserted between the lens and the plate.
Fortunately, the new (16.75 GHz) system allows for such insertion as shown in Fig. 30
and Fig. 31. The normalized relative power scan is shown in Fig. 62.
corrosion spot normalized
81
Distance (mm)
Fig.62 Normalized relative power scan of an aluminum plate that contains a corrosion
spot and covered with a space shuttle tile.
The background was subtracted from the scan along the corrosion spot. A scan along a
line that is above the corrosion spot (where the entire focus spot does not "touch" the
corrosion spot) was used as a background. For the purpose of illustration, the plot is
superimposed with the picture of the plate to show the relative size of the corrosion spot
versus its indication on the plot. The superimposed picture is shown in Fig. 63.
Fig. 63 shows that the peak width at half the maximum power of the scan is 8 mm, versus
5 mm diameter of the actual corrosion spot, which is a fairly good approximation.
82
corrosion spot normalized
0
10
20
30
40
50
60
70
Distance (mm)
Fig.63 Normalized relative powci si;an superimposed with the scanned area of the
aluminum plate covered with the space shuttle tile.
It has been mentioned before that the problem of corrosion detection on the shuttle skin
under a shuttle tile is an actual problem under investigation by NASA. Current research
effort is concentrated on using NDE sensors based on radiation in the terahertz region.
There are certain problems associated with this method that can be addressed with the
help of the NIM lens. First, it is harder to penetrate a material with terahertz radiation
(especially if the environment is humid) [34]. Second, even with the wavelengths
associated with the terahertz radiation, the edge effects from the ridges of the aluminum
skin significantly affect the results [35]. Introducing the NIM lens into the system would
allow usage of a longer wavelength which can penetrate further into the material under
test without compromising the sensitivity of the sensor. Also, since the focus spot size of
83
this sensor will be smaller than the wavelength in use, such an approach could minimize
the interference due to edge effects with the image from the sample.
Clearly, in order to achieve the stated goals, the losses in the lens must be minimized
(as previously discussed). The next chapter discusses the nature of the losses and what
are the limitations of the system associated with the losses.
84
CHAPTER VII
LIMITING FACTORS for the LENS PERFORMANCE
In general, losses are correctly identified as the major limiting factor for the
performance of the NIM lens and the NDE sensor system which is based on it. It was
shown in section 5.1.3 that 82% of the emitted energy is absorbed in the lens. The
importance of minimizing the losses is twofold. First, the more energy which can
propagate through the lens, the more flexibility there is with the thickness of the lens that
can be used. As shown in Eqn. 1, a thicker lens allows the NDE sensor to be maintained
at a larger standoff distance away from the sample since the sum of the distance from the
point source to the lens and from the lens to the image (the focus spot) is equal to the
thickness of the lens (for the ideal lens). The distance from the lens to the focus spot is
the standoff distance to the sample since we want the smallest possible area of the sample
to be irradiated during the test (similar to near field imaging). The smallest area is defined
by the focus spot formed by the NIM lens.
The second important characteristic of the lens affected by the losses is the ability of
the lens to focus. We have discussed the ability of the NIM lens to defy the diffraction
limit. This ability was attributed to the fact that the NIM lens enhances evanescent waves
[11]. The proof was analytically shown for the ideal lens (with no losses). It was shown
[36] that if we introduce a very small loss to the NIM material's effective e and \i it will
affect the ability of the NIM lens to focus below the diffraction limit. The imaginary parts
of the permittivity and permeability were assumed to be a = 10"5. Therefore, for the NIM
material: e = u- = -l+cri = -l + 10"5i. The same analysis as J. Pendry did for the ideal lens
[11] (Eqn-s (3) - (12)) was carried through with the values of e and u corrected for the
85
losses. Assuming ky = 0, the suppression of the lens's ability to restore the evanescent
waves was analyzed. For this purpose, the deviation of the transmission coefficient tl (kx)
with and without the losses was studied. The evaluation can be performed with the help
tl(k x ,g-)-tl(k x ,0)
tl(k x ,0)
where tl (kx,o) is the transmission of an individual component with the wave number kx
of a criterion function C (kx,o) where C(k x , <r) =
(we are discussing only evanescent wave vectors here) when s" = u" = c. If C (k x ,o")«l,
then the components with the wave vector kx have been effectively restored and
contributed to the resolution of the lossy slab. ForCT= 10"5 and the thickness of the
material 1 = X, one can show that the condition of C (k x ,a)«l is fulfilled only for
\kx\ < kxmax = 2k0. Namely, the evanescent waves with wave vectors higher than kxmax
will not be restored which, in turn, will diminish the resolution of the image. Therefore,
we can conclude that the losses in the lens will affect its focusing abilities. It is worth
noting that the derivation above does not prohibit the lens from focusing better than the
diffraction limit (clearly, the experiments presented in the previous chapters and many
other works demonstrate the sub-wavelength focusing [7], [37]). Rather, it states that the
resolution of the image is limited by the losses and can only approach the ideal lens
condition.
There are two major factors that are believed to be responsible for the losses in the
NIM medium: the absorption in the dielectric PCB matrix of the lens, and ohmic losses
in the metallized surfaces of the lens. In the literature, opinions differ as to the relative
importance of each of these loss factors. Some [16] note that when they stack 40 plates of
FR4 (9.3 cm long and 1.8 mm thick each) together without any metal on the surface, the
created block of dielectric would absorb 40% of the radiation. Some [39] provide
86
simulations that show that there are almost no losses associated with the metallic parts
but an imaginary part of the 8 of the PCB is responsible for the losses. Others [40] present
the simulations of a 3 unit cell (in the direction of the wave propagation) NIM medium
made of the Rogers 5880 Duroid that show exactly the opposite result. The validity of the
Ansoft HFSS model was proven with some experiments. The authors [40] have compared
3 simulations where the varying parameters were the loss tangent of the Rogers PCB and
conductivity of the copper in the metallic parts of the structure. In the first one, they
realistically modelled the material with the known finite conductivity of copper and the
loss tangent of the Rogers material. The result for the loss (S21 parameter) was -1.3
dB/cm. In the second model, the loss tangent of the Rogers was reduced to 0 and the
result was S21 = -1.2 dB/cm. In the third model, the conductivity of the metal was kept
infinite while the loss tangent of the Rogers was returned to its original value. In this case
the result was that S21 = -0.1 dB/cm. These results lead to a conclusion that the finite
conductivity of the copper is the main factor causing losses in the NIM medium. The
authors in [40] are cautious to restrict this result to their specific sample.
This result could also explain the peculiar fact that the best transmission through the
lens was not at the frequency that was supposed to render the index of refraction closest
to -1. In fact, at this frequency, the strongest resonance would yield the strongest currents
at the SRR and, if the major losses are due to the finite conductivity of the metal, the
losses at this frequency will be greater than those somewhat away from -1.
Clearly, the issue of the source of the losses in the medium is not resolved and it was
decided to investigate this issue using the Ansoft HFSS model which was verified
experimentally with the 3.65 GHz NIM lens as was shown in the previous chapters. We
87
decided to take a more comprehensive approach, noting experimentally that mere change
of the PCB material from the FR4 to Rogers 5880 Duroid yielded a significant drop in the
losses (-20 dB vs. -13 dB respectively). This occurred even though in terms of the
wavelength, the lens made of Rogers was thicker in the direction of the wave propagation
than the FR4 lens (2.1 X vs. 1.15 X).
The plot in Fig. 64 shows a comparison of results for three different metals used in the
models. The varying parameter in the system is the conductivity of the metal. Whereas
the PCB material in all three cases is FR4 with the s = 4.4 and the loss tangent tan 8 =
0.02, the conductivity of the metal in the NIM material was changed from copper to
silver to perfect electrical conductor (PEC). The following results for the S2i parameter
were obtained.
„,. „„m„a,.ic„n PR/1 matriv
S21 comparison FR4 matrix
M
IMJ*?
,-*i
*3
V^-^f^i
-20
sfe;
^
-30
O
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; -V^-W*.-:*
&
-Cu
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-40
121^-
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._.:.: ^.;]-«^ V^-— £KT*^- v « -
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3
3.5
4
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y-~- • .V»- • •• -*•• P . * J ^ V : ^ ? » '
4.5
5
5.5
6
6.5
7
Frequency (GHz)
Fig.64 Modeling results for transmitted power as a function of incident microwave
frequency for three metals: copper, silver and PEC (3.65 GHz 2-D lens). The PCB
material is FR4.
88
A clear conclusion from Fig. 64 is that the transmission levels in the three models are
the same regardless of a metal that is used in the NIM material fabrication. However,
when the PCB material is changed from FR4 to Rogers Duroid 5880 (s = 2.2 and the loss
tangent tan 8 = 0.009) and the same three cases are calculated for the same metals, the
result looks very different as shown in Fig. 65:
Comparison Rogers S21
Fig.65 Modeling results for transmitted power as a function of incident microwave
frequency for three metals: copper, silver and PEC (3.65 GHz 2-D lens). The PCB
material is Rogers Duroid 5880.
From Fig. 65 one can clearly see that when Rogers Duroid 5880 is chosen to be the
material for the PCB matrix, a change in the metal would lead to a significant change in
the transmission levels of the NIM material.
A comparison of Fig. 64 with Fig. 65 leads to the following conclusion: the reasons for
the losses in the lens are complex. They are really a combination of factors, with the two
89
prime ones being losses in the dielectric and losses due to the finite conductivity of the
metal parts. When the PCB material is very lossy (such as the FR4), the choice of a metal
with a better conductivity will not make much of a difference since a lot of energy will be
already absorbed by the dielectric. On the other hand, when the PCB material is not that
lossy (such as Rogers Duroid 5880), the choice of a metal with a higher conductivity will
help to reduce the losses in the NIM material.
90
CHAPTER VIII
SUMMARY of ACCOMPLISHMENTS
The goal of this work was to design and prove the concept of operation of a novel Non
Destructive Evaluation sensor that operates in the microwave and millimeter wave
spectrum to provide subwavelength resolution. The sensor is based on a Negative Index
Material lens and it has the following advantages: the sensor operates at standoff
distances typical for the far field mode, the probe size and resolution are subwavelength
in size, comparable with the near field mode (as opposed to the far field mode where the
resolution is limited by the diffraction limit which is about the wavelength of the EM
wave in use), and the dependence of the resolution on standoff distance is easily
established. Also, the depth of penetration into the sample under test is inversely
proportional to the frequency of the wave [6].
In order to achieve this ultimate goal, the concept itself should be tested first and the
issues that might stand in the way of the implementation of the idea should be studied.
Therefore, the progress of this work can be summarized by the following milestones
(presented in chronological order):
8.1 3.65 GHz 2-D Lens.
A negative index material lens with the resonant frequency of 3.625 GHz was
designed, fabricated and characterized for its resonant frequency, index of refraction and
focus spot size.
The characterization of the lens confirmed the resonant effect at 3.625 GHz when S21 =
-20 dB which indicates that the lens is a very lossy structure. The frequency dependent
negative index of refraction was demonstrated around the resonant frequency and a focus
91
spot size of 0.48 X (below the diffraction limit) was obtained. The obtained results
showed that a NIM lens was fabricated and it had all the necessary qualities to be tested
in an experimental setup for the novel NDE sensor.
Also, a numerical model to determine the resonant frequency and transmission level of
the lens was developed and confirmed experimentally with the fabricated NIM lens. This
model allowed for the design of a new NIM lens for a higher resonant frequency and,
therefore, for a higher resolution.
8.2 NDE Sensor with 3.65 GHz 2-D Lens.
A novel NDE sensor was designed based on the NIM lens. The concept of operation of
this novel sensor was proved by applying the sensor to a dielectric test sample containing
a simulated defect.
The defect (a through hole with diameter of 3 mm) was detected which renders the
sensitivity of the method to be 0.037 X. Two holes 4 cm apart were detected which
renders the resolution of the sensor to be 0.48 X (consistent with the focus spot size of the
NIM lens).
The applicability of the sensor was tested with two conducting materials (Al plate and
carbon fiber composite) when a corrosion spot with a diameter of 5 mm (0.06 X) on an Al
plate and surface rippling on carbon fiber composite with a peak to trough height A of 0.2
mm (0.0024 X) were detected.
8.3 3.65 GHz 1-D Lens.
As has been discussed before, the fabricated 2-D lens is a very lossy structure. A
technique proposed to reduce losses was substitution of the 2-D lens with a 1-D lens. A
1-D lens based on the same structure as before was characterized and tested in the NDE
sensor setup. The results suggested that although transmission levels for the 1-D lens are
much higher than for the 2-D lens (~ -9 dB vs. ~ -20 dB), the focus spot size of the 1-D
lens was bigger than of the 2-D lens (0.7 X vs. 0.48 X). The difference was attributed to
having no component of H perpendicular to the split rings for the 1-D lens at oblique
incidence angles. Therefore, there is no resonant effect in that area of the lens. Also,
some transmission is possible if the wire mesh in this direction renders a positive e value.
The NDE sensor based on a 1-D lens was tested on the same dielectric sample as before
and the result demonstrated inferior resolution to the 2-D lens, as was expected. The
conclusion from this experiment is that although a resolution of the image obtained with
an NDE sensor based on the 1-D lens is inferior to the image obtained with the 2-D lens,
the benefits of the 1-D lens (such as a possible significantly higher power transmission)
are important when a thicker lens is required. This would occur when a longer standoff
distance from the sample is more important than a better resolved image.
8.4 16.75 GHz Lens.
The resolution and sensitivity of the proposed sensor is highly dependent on the
frequency in use. Since the obtained focus spot size is typically a fraction of the
wavelength, a higher frequency will render a smaller spot size. 2-D and 1-D NIM lenses
having resonance at 3.625 GHz were used to prove the concept of operation for the
proposed sensor. In order to detect smaller defects or obtain higher quality images, a new
lens that works as a NIM material at a higher frequency was designed.
The numerical HFSS Ansoft model (confirmed experimentally before) was used to
design a new lens with resonant frequency at 16.65 GHz. This frequency was chosen
93
because the dimensions of the metallic parts of the lens at this frequency are close to the
manufacturing limits of traditional methods employed to make PCBs.
A new lens was designed and fabricated based on Rogers Duroid 5880 matrix material.
The operating frequency of the lens was 16.75 GHz. Transmission through the new lens
was significantly improved as compared to the first one (-13 dB vs. -20 dB) and no
amplifier was required to perform corresponding part of the tests. The improvement is
attributed to the fact that the new matrix PCB material is less lossy than the previously
used FR4.
The losses in the lens were evaluated when the levels of transmission and reflection
were determined using the TRL calibration (Sn and Sn). It was shown that the lens
absorbs 82% of the incident radiation.
A more rigorous method to measure a frequency dependent index of refraction of the
lens was used for this lens than for the previous one. Variation of index of refraction on
operation frequency dependence was established using phase measurements. Index of
refraction was shown to be negative in the range of 16.4 -17 GHz.
The focus spot size of the new lens was determined to be 0.9 cm (0.5 X). In the
absolute value, this result is more than four times smaller than the focus spot size
obtained from the 2-D lens working at 3.65 GHz. Therefore, smaller sized defects can be
detected with the NDE sensor based on the new lens.
8.5 NDE Sensor Based on the 16.75 GHz Lens.
The resolution of the defect detected with the new lens was improved by about 3 times
as compared to the first sensor (with the same defect). Also, a smaller defect (1 mm in
diameter through hole) was detected. It is very possible that an even smaller defect could
94
be detected by the new sensor but due to limitations in fabrication of a filler (to allow for
a background scan), 1 mm was the smallest flaw tested. This problem can be resolved in
the future if the NDE sensor is enhanced with a laser device that helps to maintain a
constant distance between the sample and the sensor. In that case the background
information can be taken from a scan of a part of the sample that is known to have no
defects.
A corrosion spot with a diameter of 5 mm (0.28 X) under a space shuttle tile on an Al
plate was detected. This problem is of special interest to NASA. Currently, NASA
Langley research is concentrated on the detection of the corrosion spots under space
shuttle tiles using Terahertz radiation. From personal communication with Dr. Eric
Madaras of the Non Destructive Evaluation Branch of NASA Langley who leads this
project it was obvious that some problems with this method still exist. For example, it
was mentioned that the edge effects from the rims of the aluminum skin possess a
challenge to successful resolution of the images. Also, humidity could present a problem
in this frequency range of radiation. It is clear that incorporation of a NIM lens could
potentially alleviate these problems since such a lens would reduce the radiation focused
spot size and reduce the edge effects significantly (as was shown at the frequencies used
for the experiments in this work). Alternatively, a lower frequency could be used, which
would improve the penetration of the radiation into the sample since the lens will reduce
the focus spot to a sub wavelength size.
8.6 Limitation Factors for the Lens Performance.
A comprehensive study of the limitation factors for the lens performance was
undertaken based on an Ansoft HFSS numerical model that was experimentally
95
confirmed in this work. It is known that losses in the lens are the major limitation on the
performance of the lens. The reasons for the losses are a subject for an intensive scientific
discussion between research groups. Losses have been attributed to both the PCB matrix
material and the metallic parts of the system. Our comprehensive study showed that both
factors are responsible for the losses. Namely, the improvement of the conductivity of the
metallic parts would help to reduce the losses only if the matrix material is not very lossy
itself. As an example, the conductivity improvement will work with Rogers Duroid 5880
PCB material but will not work with FR4. Some of the results were confirmed
experimentally when two lenses that were used in this work (manufactured from two
different PCB materials) were compared for the transmission losses.
96
CHAPTER IX
CONCLUSIONS and FUTURE WORK
The purpose of this work was to design a novel NDE sensor that has certain advantages
over existing sensors. This was accomplished by incorporating a NIM lens that, based on
theory, should provide all necessary characteristics to achieve the stated goal. Indeed, it
was shown that in the frequency range of 3 - 4 GHz the designed lenses can focus below
the diffraction limit and that defects as small as 0.037 A, in diameter can be detected.
Although the principle of operation of the novel NDE sensor was successfully proven,
some issues pertaining to the performance of the NIM lens need further study in order to
improve its performance as part of a NDE sensor. The major obstacle in the way of
improvement of the proposed method is the substantial transmission loss in the lens. The
problem is twofold: these losses affect the focusing qualities of the lens and reduce the
allowed thickness of the lens (which, in turn, places limits on the standoff distance from
the sample, as was explained before). Therefore, the future work on this project should be
concentrated on reducing the losses. The present research has demonstrated that there are
two major factors that contribute to the losses in the system: the PCB matrix material
losses and the finite conductivity of the metallic parts of the system. These factors
prescribe the two directions of future research. The first is investigation of alternative,
less lossy substrate materials. The second is researching methods of increasing the
conductivity of the metallic parts of the NIM lens, by using higher conductivity metals
such as silver, or by using alternative methods of metallization of the SRRs and the wires
on this material. A separate topic for the research could be exploring the ways to
miniaturize the SRR and wire features even further (through alternative methods of
97
metallization) in order to reduce the resonant wavelength even further. In this way,
smaller defects can be resolved by the proposed NDE sensor. Also, use of a laser device
that would maintain a constant distance between the sample and the sensor is
recommended. This would allow the background scan to be performed on a different part
of the same sample, and thus eliminate the necessity of fabricating a filler for the
background scan.
The proposed sensor is a viable alternative to the existent NDE methods and
contributes greatly to advances in the field of non destructive evaluation. Based on the
results obtained in this work, the proposed sensor can be used in the following
applications: inspection of integrity of buildings and bridges, detection of defects in wood
that is used in furniture manufacturing, detection of corrosion on the metal - dielectric
interface, IC packaging, rippling on carbon fiber composites, inspection of integrity of
the armor made of ceramics, defects in the aircraft wiring and many others.
98
APPENDIX (JOURNAL PUBLICATIONS and CONFERENCE PRESENTATIONS)
A. Journal Publications.
D. Shreiber, M. Gupta and R. Cravey, "Microwave Nondestructive Evaluation of
Dielectric Materials with a Metamaterial Lens", Sensors and Actuators A: Physical,
vol.144 no. 1 (2008)48.
D. Shreiber, M. Gupta and R. Cravey, "Comparative Study of 1-D and 2-D Metamaterial
Lens for Microwave Nondestructive Evaluation of Dielectric Materials", passed internal
NASA review.
D. Shreiber, M. Gupta and R. Cravey, "Improved Imaging with a Non Destructive
Evaluation Sensor Based on a Metamaterial lens", to be submitted.
B. Conference Presentations.
D. Shreiber, M. Gupta and R. Cravey, "Microwave Sensor for Dielectric Materials with a
Metamaterial Lens", ICONIC 2007 (International Conference on Electromagnetic NearField Characterization and Imaging, St. Louis, MO 2007).
D. Shreiber, M. Gupta and R. Cravey, "Metamaterials for Defect Sensing", NASA
Aviation Safety Technical Conference, St. Louis, MO 2007.
Naval Research Lab, Invited Seminar, Washington, DC 2008.
99
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