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FREQUENCY SELECTIVE TERAHERTZ RETROREFLECTORS
BY
RICHARD JAMES WILLIAMS
B.S. (PHYSICS), SOUTHEASTERN LOUISIANA UNIVERSITY, HAMMOND,
LOUISIANA
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF MASTER OF SCIENCE
DEPARTMENT OF PHYSICS AND APPLIED PHYSICS
UNIVERSITY OF MASSACHUSETTS, LOWELL
Signature of Author
Signature of Thesis Supervisor:
Dr. Andrew J. Gatesman
Signatures of Thesis Committee Members:
Dr. Viktor A. Podolskiy
Dr. Anna N. Yaroslavsky
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FREQUENCY SELECTIVE TERAHERTZ RETROREFLECTORS
BY
RICHARD JAMES WILLIAMS
ABSTRACT OF A THESIS SUBMITTED TO THE FACULTY OF THE DEPARTMENT OF PHYSICS AND APPLIED PHYSICS
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE
UNIVERSITY OF MASSACHUSETTS LOWELL 2014
Thesis Supervisor: Andrew J. Gatesman, Ph.D. Adjunct Professor, Department of Physics and Applied Physics
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Abstract
The use of novel optical structures operating at terahertz frequencies in industrial and
military applications continues to grow. Some of these novel structures include gratings,
frequency selective surfaces, metamaterials and metasurfaces, and retroreflectors. A
retroreflector is a device that exhibits enhanced backscatter by concentrating the reflected
wave in the direction of the source. Retroreflectors have applications in a variety of diverse
fields such as aviation, radar systems, antenna technology, communications, navigation,
passive identification, and metrology due to their large acceptance angles and frequency
bandwidth. This thesis describes the design, fabrication, and characterization of a
retroreflector designed for terahertz frequencies and the incorporation of a frequency
selective surface in order to endow the retroreflector with narrow-band frequency
performance. The radar cross section of several spherical lens reflectors operating at
terahertz frequencies was investigated. Spherical lens reflectors with diameters ranging from
2 mm to 8 mm were fabricated from fused silica ball lenses and their radar cross section was
measured at 100 GHz, 160 GHz, and 350 GHz. Crossed-dipole frequency selective surfaces
exhibiting band-pass characteristics at 350 GHz fabricated from 12 um-thick Nickel screens
were applied to the apertures of the spherical lens reflectors. The radar cross section of the
frequency selective retroreflectors was measured at 160 GHz and 350 GHz to demonstrate
proof-of-concept of narrow-band terahertz performance.
! "#!
Acknowledgements
I would like to thank my graduate research advisor Dr. Andrew J. Gatesman for all of his
advice and motivation. I would also like to thank Dr. Thomas M. Goyette for assistance in
data processing and his patience in explaining the inner workings of radar systems. I am
very appreciative to our range technicians Ms. Lucille M. DeRoeck and Mr. Lawrence
Horgan for assisting in the experimental setup and data collection. I would like to thank Dr.
Guy B. DeMartinis for his help with rebuilding the 350 GHz range. I would like to thank my
parents, Joyce and Stephen Williams for all of their love and support. I thank Mr.
Christopher M. Roberts for his insight and willingness to discuss hair-brained ideas. Finally,
I would like to thank Ms. Meghan F. Hennelly for putting up with me through this long,
arduous process, and always believing in me.
We all need to be resources rather than receptacles.
- Dick Lucas
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Dedication
For Lance Corporal Matthew ‘Matty’ Hull.
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Contents
LIST OF TABLES viii
LIST OF FIGURES ix
1. INTRODUCTION 1!1.1 TERAHERTZ RADIATION ...............................................................................................1!1.2 RETROREFLECTORS ......................................................................................................2!
1.2.1 Applications of Retroreflectors .............................................................................4!1.3 FREQUENCY SELECTIVE SURFACES ...............................................................................5!
2. THEORY 6!2.1 RETROREFLECTORS ......................................................................................................6!
2.1.1 Retroreflector Acceptance Angle Comparison.......................................................8!2.2 SPHERICAL LENS REFLECTORS....................................................................................10!2.3 FREQUENCY SELECTIVE SURFACES .............................................................................14!
2.3.1 Passive Frequency Selective Surfaces .................................................................14!2.3.2 Capacitive and Inductive Meshes ........................................................................15!2.3.3 Crossed-Dipole Aperture Band-pass Filter ..........................................................17!
3. METHODOLOGY 19!3.1 DESIGN AND FABRICATION .........................................................................................19!
3.1.1 Spherical Lens Reflector Fabrication ..................................................................19!3.1.2 Frequency Selective SLRs ..................................................................................20!
3.2 BACKSCATTERING PREDICTIONS .................................................................................21!3.3 MEASUREMENT ..........................................................................................................22!
3.3.1 Inverse Synthetic Aperture Radar (ISAR) ...........................................................22!3.3.2 Compact Radar Range Measurements .................................................................23!
4. RESULTS 25!4.1 FREQUENCY SELECTIVE SPHERICAL LENS REFLECTORS...............................................25!
4.1.1 ISAR Imagery.....................................................................................................25!4.1.2 Backscatter Coefficient as a function of Azimuth at 350 GHz .............................29!
4.2 BEHAVIOR OF SLRS WITHOUT FSS .............................................................................31!4.2.1 ISAR Imagery.....................................................................................................31!4.2.2 Backscatter Coefficient as a function of Azimuth................................................38!4.2.3 Elevation Angle Dependence ..............................................................................42!
5. DISCUSSION 45!5.1 FREQUENCY SELECTIVE RETROREFLECTORS ...............................................................45!5.2 SLR AND GROUND PLANE BACKSCATTER COEFFICIENT COMPARISON.........................46!
5.2.1 Backscatter Coefficients at 100 GHz...................................................................46!5.2.2 Backscatter Coefficients at 160 GHz...................................................................46!
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5.2.3 Backscatter Coefficients at 350 GHz...................................................................47!5.3 MEASUREMENT AND PREDICTION MODEL COMPARISON..............................................47!5.4 ALTERNATIVE FABRICATION PROCESSES AND DESIGNS ...............................................48!
5.4.1 Spherical Lens Reflectors for n≠2 .....................................................................48!5.4.2 Frequency Selective Surface Application ............................................................49!5.4.3 Alternative Frequency Selective Retroreflector Designs......................................50!
6. CONCLUSION 51!7. FUTURE WORK 52!8. REFERENCES 53!9. APPENDIX 60!
9.1 ISAR IMAGERY..........................................................................................................60!9.1.1 Frequency Selective Spherical Lens Reflectors ...................................................60!9.1.2 Spherical Lens Reflectors ...................................................................................62!
9.2 AZIMUTH DEPENDENCE ..............................................................................................65!9.2.1 Frequency Selective SLRs ..................................................................................65!9.2.2 SLRs without FSS...............................................................................................67!
9.3 SLR ELEVATION ANGLE DEPENDENCE .......................................................................73!9.3.1 SLRs without FSS at 100 GHz............................................................................73!9.3.2 SLRs without FSS at 160 GHz............................................................................74!9.3.3 SLRS without FSS at 350 GHz ...........................................................................75!
9.4 HFSS SIMULATION DETAILS ......................................................................................75!9.4.1 Monostatic RCS Simulation Setup ......................................................................75!
10. BIOGRAPHICAL SKETCH 77!
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List of Tables
Table 3.1 Predicted backscatter coefficients for six SLRs ranging in size from 8 mm to 2mm in diameter and measured backscatter coefficients of the rough dielectric ground plane and concrete from [47]. ..................................................................................22 Table 3.2 Measurement matrix for each compact radar range showing a comparison of the ground plane elevation angle and the SLR elevation angle. The retroreflectors were oriented such that 25 degrees ground plane elevation corresponded with bore-sight. ...23 Table 4.1 Measured backscatter coefficients of the six retroreflectors and ground plane at 100 GHz, 160 GHz, and 350 GHz. Measurements were listed for HH-polarization at 25 degrees elevation and 0 degrees azimuth...........................................38 Table 9.1 Elevation angle dependence of the measured peak backscatter coefficients of the six SLRs and ground plane at 100 GHz for HH-polarization......................................74 Table 9.2 Elevation angle dependence of the measured peak backscatter coefficients of the six SLRs and ground plane at 160 GHz for HH-polarization......................................74 Table 9.3 Elevation angle dependence of the measured peak backscatter coefficients for the six SLRs and ground plane at 350 GHz for HH-polarization.....................................75
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List of Figures
!Figure 1.1 Electromagnetic spectrum showing the terahertz region between the microwave and infrared. 2!Figure 1.2 Depiction of an electromagnetic wave incident on an object undergoing (a) diffuse scattering, (b) specular reflection, and c) retroreflection. 2!Figure 1.3 A comparison of the reflection characteristics of (a) a planar mirror and (b) a retroreflector for oblique incidence. The planar mirror is subject to the law of reflection and only exhibits retroreflection at zero degrees incidence. 3!Figure 2.1 Common passive retroreflectors illustrating retroreflection and displaying characteristic dimensions including (a) the dihedron reflector, (b) the trihedron reflector, (c) the cat’s eye reflector, and (d) the Luneburg lens reflector. 7!Figure 2.2 350 GHz backscatter coefficients as a function of aspect angle for a square dihedron reflector (w=h=5.01 mm), SLR, and square flat plate (w=h=7.09 mm). The SLR was modeled as a thin circular mirror of diameter 8 mm that retroreflected all energy incident upon it. All three reflectors have the same cross sectional area, and 45 degrees azimuth is bore-sight. 9!Figure 2.3 Coordinate system showing incident radar direction (within x-y plane) for (a) a square dihedron reflector (w=h=5.01 mm), (b) a square flat metal plate (w=h=7.09 mm), and (c) a spherical lens reflector (d=8 mm). 10!Figure 2.4 Thick lens diagram showing cardinal points, lens thickness, radii, and focal lengths. 11!Figure 2.5 Focal length of a ball lens of index of refraction n, radius r, and backside focal length b. 12!Figure 2.6 Focal length of a ball lens (SLR) for (a) n=2, (b) n>2, and (c) n<2. 13!Figure 2.7 Structure of a spherical lens reflector composed of two different sized hemispheres, for the case when the index of refraction is not 2. 13!Figure 2.8 Illustration of (a) a capacitive mesh and (b) an inductive mesh showing periodicity of the unit cell and the gap/width between elements. 15!Figure 2.9 Idealized frequency response of (a) a low-pass filter, (b) a high-pass filter, (c) a band-pass filter, and (d) a band-stop filter. 16!Figure 2.10 (a) Crossed-dipole aperture band-pass FSS made from 12-micron-thick electroplated Nickel. Inset shows the unit cell of the FSS with aperture dimensions. (b) Experimentally measured transmittance spectra of the band-pass filter. Image is taken from [4]. 18!Figure 3.1 Time-domain spectroscopy measurements of fused silica from 0.3 – 2 THz. The solid line is the measured spectra from [44] and the asterisks are the data from [45]. (a) Power absorption coefficient and (b) index of refraction. Plots are taken from [44]. 19!Figure 3.2 Aluminum coating process showing evaporation of aluminum onto fused silica ball lenses sitting in the mask. 20!Figure 3.4 Cross-section representation of a frequency selective spherical lens reflector consisting of a fused silica ball lens with aluminized hemispherical cap and crossed-dipole band-pass filter wrapped around the aperture. 21!Figure 3.4 Orientation of the SLR on the rough dielectric ground plane. 23!
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Figure 3.5 Top down view of the compact radar range system configuration showing quasi-monostatic transceivers, collimating mirror, calibration fixtures, SLR targets on the ground plane, and anechoic chamber walls. Image taken and modified from [49]. 24!Figure 4.1 160 GHz RCS comparison of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization. 26!Figure 4.2 350 GHz RCS comparison of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization. 26!Figure 4.3 Waterfall plot of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS at 160 GHz. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization. 27!Figure 4.4 Waterfall plot of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS at 350 GHz. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization. 28!Figure 4.5 Azimuth behavior of the backscatter coefficient for the six frequency selective SLRs at 350 GHz and 25 degrees elevation for HH-polarization. 31!Figure 4.6 100 GHz HH-polarization ISAR image of (a) the six SLRs (labeled by diameter) on the rough dielectric ground plane, and (b) the ground plane without the SLRs. In both images, the ground plane was oriented at 25 degrees elevation and 0 degrees azimuth (SLR bore-sight). The black box around the 6 mm SLR (4.6a) indicates the approximate area used to determine the backscatter coefficient. 32!Figure 4.7 Waterfall plot of (a) the six SLRs on the ground plane and (b) the ground plane without the SLRs for HH-polarization at 100 GHz. Both images taken at 25 degrees elevation and 0 degrees azimuth. 33!Figure 4.8 160 GHz HH-polarized ISAR image of (a) six SLRs (five visible) mounted on the rough dielectric ground plane and (b) the ground plane without the reflectors. Both images were taken at 25 degrees elevation and 0 degrees azimuth (SLR bore-sight). 34!Figure 4.9 Waterfall plot of (a) the six SLRs (five visible) on the ground plane and (b) the ground plane without the SLRs for HH-polarization at 160 GHz. Both images taken at 25 degrees elevation and 0 degrees azimuth. 35!Figure 4.10 350 GHz HH-polarized ISAR image of (a) the six SLRs on the ground plane and (b) the ground plane without the SLRs. Both images taken at 25 degrees elevation and 0 degrees azimuth. 36!Figure 4.11 Waterfall plot of (a) the six SLRs on the ground plane and (b) the ground plane without the SLRs for HH-polarization at 350 GHz. Both images taken at 25 degrees elevation and 0 degrees azimuth. 37!Figure 4.12 Azimuth backscatter behavior of six SLRs at 100 GHz for HH-polarization and 25 degrees elevation. 39!Figure 4.13 Azimuth backscatter behavior of five SLRs at 160 GHz for HH-polarization and 25 degrees elevation. 40!Figure 4.14 Azimuth backscatter behavior of the six SLRs at 350 GHz and 25 degrees elevation for HH-polarization. 41!Figure 4.15 Comparison of the measured (red) backscatter coefficient of the 8 mm SLR with the model from section 2.1.1 (blue), and the HFSS-IE model (orange). 42!
! $"!
Figure 4.16 Elevation and azimuth angle dependence of the 8 mm SLR’s backscatter coefficient at (a) 350 GHz, (b) 160 GHz, and (c) 100 GHz. 44!Figure 9.1 160 GHz ISAR image of the frequency selective SLRs on the ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarizations. The images were taken at 25 degrees elevation and 0 degrees azimuth and distinguishable reflectors are labeled. 61!Figure 9.2 350 GHz ISAR image of the frequency selective SLRs on the ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarizations. The images were taken at 25 degrees elevation and 0 degrees azimuth and distinguishable reflectors are labeled. 62 Figure 9.3 100 GHz ISAR imagery of six SLRs on the ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarization. ISAR Images taken at 25 degrees elevation and 0 degrees azimuth. 63!Figure 9.4 160 GHz ISAR imagery of six SLRs on a ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarization. ISAR images are taken at 25 degrees elevation and 0 degrees azimuth. 64!Figure 9.5 350 GHz ISAR Imagery of six SLRs for (a) HH, (b) HV, (c) VH, and (d) VV-polarization. Images taken at 25 degrees elevation and 0 degrees azimuth. 64!Figure 9.6 Azimuth dependence of the backscatter coefficient for the frequency selective SLRs at 350 GHz and 25 degrees elevation for HV-polarization. 66!Figure 9.7 Azimuth dependence of the backscatter coefficient of the six frequency selective SLRs at 350 GHz and 25 degrees elevation for HV-polarization. 66 Figure 9.8 Azimuth dependence of the backscatter coefficients of the six frequency selective SLRs at 350 GHz and 25 degrees elevation for VV-polarization. 67!Figure 9.9 Azimuth dependence of six SLRs at 100 GHz and 25 degrees elevation for HV-polarization. 68!Figure 9.10 Azimuth dependence of six SLRs at 100 GHz and 25 degrees elevation for VH-polarization. 68!Figure 9.11 Azimuth dependence of six SLRs at 100 GHz and 25 degrees elevation for VV-polarization. 69!Figure 9.12 Azimuth dependence of five SLRs at 160 GHz and 25 degrees elevation for HV-polarization. 70!Figure 9.13 Azimuth dependence of five SLRs at 160 GHz and 25 degrees elevation for VH-polarization. 70!Figure 9.14 Azimuth dependence of five SLRs at 160 GHz and 25 degrees elevation for VV-polarization. 71!Figure 9.15 Azimuth dependence of six SLRs at 350 GHz and 25 degrees elevation for HV-polarization. 72!Figure 9.16 Azimuth dependence of six SLRs at 350 GHz and 25 degrees elevation for VH-polarization. 72!Figure 9.17 Azimuth dependence of six SLRs at 350 GHz and 25 degrees elevation for VV-polarization. 73!Figure 9.18 Diagram of HFSS monostatic RCS measurement showing a dielectric sphere with incident plane wave and PEC boundary on bottom hemisphere. 76!
!
! %!
1. Introduction
1.1 Terahertz Radiation
Technology in the terahertz range has seen rapid developments in recent years due to
new applications in biomedical imaging [1], remote sensing [2,3], and materials
characterization [4]. The terahertz region of the electromagnetic spectrum, depicted in
Figure 1.1, spans 0.1 to 10 THz, which corresponds to wavelengths between 0.03 and 3 mm.
THz radiation occupies a region of the electromagnetic spectrum between microwave and
infrared radiation, and shares characteristics of each. Like microwave and IR radiation, THz
radiation is non-ionizing and thus has no known detrimental health effects. It is difficult to
scale microwave electronics to the THz region due to excessive output power losses at higher
frequencies; while scaling infrared devices, such as photonic band-gap materials, proves
arduous due to material response at THz frequencies. Due to the difficulty of scaling
microwave and IR mechanisms to the THz, new hybrid techniques and components are
generally required to build THz systems. Conversely, some microwave and optical
techniques are applicable to the THz region and extensive research has been conducted in the
development of new THz devices [5-9]. Such devices include gratings, THz plasmonics,
metamaterials and metasurfaces, and optical components such as retroreflectors.
!
! &!
Figure 1.1 Electromagnetic spectrum showing the terahertz region between the microwave and infrared.
1.2 Retroreflectors
Retroreflectors are structures or surfaces that reflect incident electromagnetic waves
back in the direction of the source regardless of the angle of incidence, with minimum
deviation. An incident electromagnetic wave is reflected along a vector antiparallel to the
incident direction as shown in Figure 1.2c.
Figure 1.2 Depiction of an electromagnetic wave incident on an object undergoing (a) diffuse scattering, (b) specular reflection, and c) retroreflection.
!
! '!
The propagation vectors of the incident and reflected waves are equal in magnitude and
opposite in direction. Two vectors
!
r u and
!
r v are said to be antiparallel if they travel in
opposite directions and their cross-product is zero, i.e.,
!
r u " r v = 0. (1.1)
A planar mirror exhibits specular reflection; an incident electromagnetic wave is reflected at
an angle equal to the angle of incidence as measured from the vector normal to the surface,
and only exhibits retroreflection when the direction of wave propagation is perpendicular to
the planar surface. Figure 1.3 shows a comparison of the reflection properties of a planar
mirror and a retroreflector. An electromagnetic wave is incident upon the reflectors with
angle
!
" i as measured from
!
ˆ n , the vector normal to the reflector surface. The retroreflector
completely backscatters the incident wave regardless of the incident angle.
Figure 1.3 A comparison of the reflection characteristics of (a) a planar mirror and (b) a retroreflector for oblique incidence. The planar mirror is subject to the law of reflection and only exhibits retroreflection at zero degrees incidence.
!
! (!
1.2.1 Applications of Retroreflectors
Retroreflectors predominantly find use in the visible spectrum as nighttime/low-
visibility environment markers such as road signs, road markers, and clothing. For this
application the retroreflector is highly visible above background objects such as roads,
buildings, and vegetation, allowing a road sign or pedestrian to be visible to a driver in poor
visible conditions [10-12]. Nighttime running apparel and Fireman’s jackets are lined with
retroreflective patches that increase the “observability” of the runner or fireperson as a direct
result of the retroreflective patches redirecting the incident light back towards the observer.
The study by Luoma et al determined that a nighttime motorist was able to identify an
approaching pedestrian wearing retroreflectors on their wrists and ankles, and on major joints
at distances of 156 m and 169 m, respectively. Approaching pedestrians with torso-mounted
retroreflectors were identifiable at 96 m and pedestrians without retroreflectors were only
identifiable at 40 m.
Retroreflection is a key phenomenon in the field of metrology as it can be used to
ascertain relatively accurate x-y-z coordinates of objects [13,14]. NASA’s Apollo 11, 14,
and 15 missions placed several retroreflector arrays on the Moon to measure the Earth-Moon
separation as well as variations in the Moon’s rotation as part of the Lunar Laser Ranging
Experiment [15]. The retroreflector arrays were installed by the Apollo astronauts at
multiple locations on the lunar surface, and by using pulsed lasers, the Earth-Moon
separation distance can be determined. Rotational anomalies can be observed by tracking the
motion of the aforementioned reflector arrays.
!
! )!
Optical retroreflectors also have applications in passive identification comparable to
radio frequency identification (RFID) tagging [16]. Research into tunable retroreflector
arrays as optical identification tags has increased in recent times [17,18]. Mechanically
controlled dielectric spacer layers within the retroreflector array [18] and smart polymers
[16,17] have been used to turn on/off a retroreflecting element in the array. The ability to
turn a retroreflector on or off through modulation gives rise to arrays of retroreflectors that
can spell out words or display patterns at the users behest. Aside from identification and
tracking, retroreflectors have found use in the detection of atmospheric pollutants [19] (e.g.
NO2 and CO) via the absorption method [20].
1.3 Frequency Selective Surfaces
A frequency selective surface (FSS) was used in this work to impart frequency
selective properties to the terahertz retroreflectors. A passive FSS exhibiting band-pass
behavior at 349 GHz was applied to the retroreflectors. With improved application
techniques, more complicated FSS designs with multiple tailored resonances could be used to
encode a barcode-like frequency signature into the retroreflector [21]. An FSS can be
excited in one of two ways; via the interaction of an incident electromagnetic wave with the
periodic elements (passive array), or driven excitation of the elements by individual voltage
generators (active arrays) [22]. FSS also have uses in creating ultra-thin, wide-band
electromagnetic absorbers [23,24,25], multiband absorbers [21,26,27], and in shaping the
radiation pattern of antennas [28,29].
!
! *!
2. Theory
2.1 Retroreflectors
Similar to frequency selective surfaces, retroreflectors can be developed as either
passive or active devices. An active retroreflector takes the form of electrically loaded
circuits such as van Atta reflectarrays [30,31] and electrically modulated trihedron arrays
[32], both of which require external power sources. Passive retroreflectors use geometry to
retroreflect incident waves and are generally subdivided into corner reflectors and spherical
lens reflectors (SLRs). Corner reflectors, such as dihedron and trihedron reflectors, redirect
an incident electromagnetic wave back towards the source via multiple reflections based
reflector geometry [33]. SLRs, including the cat’s eye and Luneburg lens reflector (graded
index SLR), use refraction via a spherical lens to focus the incident electromagnetic wave
onto a reflective cap. The wave is reflected by the cap and is then refracted back into the
direction of the source with minimal deviation [34]. The passive retroreflectors described
above are presented in Figure 2.1.
!
! +!
Figure 2.1 Common passive retroreflectors illustrating retroreflection and displaying characteristic dimensions including (a) the dihedron reflector, (b) the trihedron reflector, (c) the cat’s eye reflector, and (d) the Luneburg lens reflector.
Corner reflectors are perhaps the most well-known and readily available
retroreflectors due to their simplistic design and ease of manufacturing, however the SLR has
been shown to have a much wider acceptance angle [30]. The acceptance angle is defined as
the angular extent over which the retroreflector backscatters towards the source. For a
dihedron reflector, retroreflection is confined to the plane perpendicular to the corner crease.
A trihedron reflector behaves similarly with the benefit that retroreflection is no longer
confined to the perpendicular plane.
!
! ,!
2.1.1 Retroreflector Acceptance Angle Comparison
The performance of a retroreflector is characterized by how much incident
electromagnetic energy it returns to the source relative to its surroundings. One way to
compare a retroreflector’s performance to other objects such as a dihedron, is to compare
their radar cross section (RCS). The RCS of a scatterer is defined as
!
" = limr#$ 4%r2 Es
2
E02 , (2.1)
where E0 and Es are the incident and scattered field intensities, respectively. The backscatter
coefficient
!
"0 is determined by normalizing the RCS to the illuminated area of the scattering
body. The peak RCS for a rectangular dihedron of height h and width w, is given in Eq. 2.2,
while the angular dependence of a square dihedron (h=w) was previously developed [35].
!
"dihedron =8#h2w2
$2 (2.2)
It has been suggested [36,37] that the peak RCS for an SLR on bore-sight can be modeled as
a perfect circular mirror of diameter d.
!
"SLR #$ 3d4
4%2 (2.3)
The azimuth dependence of the SLR, assumed here to only depend on its capture area, is
shown in Figure 2.2 in comparison with a similar sized (same cross sectional area) square
dihedron as described in [35]. Also shown in Figure 2.2 is the RCS of a similar sized flat
metal plate. Figure 2.3 illustrates the orientation of the reflectors in the coordinate system
used in Figure 2.2.
!
! -!
Figure 2.2 350 GHz backscatter coefficients as a function of aspect angle for a square dihedron reflector (w=h=5.01 mm), SLR, and square flat plate (w=h=7.09 mm). The SLR was modeled as a thin circular mirror of diameter 8 mm that retroreflected all energy incident upon it. All three reflectors have the same cross sectional area, and 45 degrees azimuth is bore-sight. !!
!
! %.!
!!
Figure 2.3 Coordinate system showing incident radar direction (within x-y plane) for (a) a square dihedron reflector (w=h=5.01 mm), (b) a square flat metal plate (w=h=7.09 mm), and (c) a spherical lens reflector (d=8 mm). !2.2 Spherical Lens Reflectors
A SLR consists of a low-loss dielectric ball lens and a highly reflective cap placed at
the focal length of the lens. The focal length of the ball lens can be derived from the thick
lens formula [38],
!
f0 = " f =nr1r2
(n "1)[n(r2 " r1) " (n "1)d], (2.4)
!
! %%!
where n is the index of refraction of the lens, f0 is the front side focal length, f is the backside
focal length, d is the thickness of the lens, r1 is the radius of the front surface, and r2 is the
radius of the back surface.
Figure 2.4 Thick lens diagram showing cardinal points, lens thickness, radii, and focal lengths.
For a ball lens, the lens parameters are:
!
r1 = r for the convex surface (front),
!
r2 = "r for the
concave surface (back),
!
d = 2r is the thickness of the lens, and f is the focal length of the
lens. Substitution of the lens parameters into Eq. 2.4 yields
!
f =nr
2(n "1). (2.5)
!
! %&!
Figure 2.5 Focal length of a ball lens of index of refraction n, radius r, and backside focal length b.
The focal length is determined to be the radius of the ball lens upon substitution of
!
n = 2 into
Eq. 2.5. Another way of expressing Eq. 2.4 is in terms of the backside focal length, the
distance between the backside of the ball lens and the focal length.
!
b = f " r =(2 " n)r2(n "1)
(2.6)
For the case of
!
n = 2, the backside focal length is zero, indicating that the distance from the
backside of the ball lens to the focal length is zero. When designing a SLR, the reflecting
surface is placed at the focal length of the ball lens, and when
!
n = 2 this coincides with the
backside of the hemisphere. For
!
n < 2, Eq. 2.6 yields a positive backside focal length (
!
b > 0)
and so the reflecting surface must be positioned further away from the backside of the ball
lens. When
!
n > 2, Eq. 2.6 gives a negative backside focal length, this indicates that the focus
is inside the lens.
!
! %'!
Figure 2.6 Focal length of a ball lens (SLR) for (a) n=2, (b) n>2, and (c) n<2.
For a dielectric sphere of index of refraction
!
n " 2 an SLR may still be fabricated in a
number of ways. If a dielectric sphere with
!
n < 2 is available, the ball lens has a focal length
!
f > r and should be suspended above the reflective cap such that the reflective cap coincides
with the backside focal length. In general, an SLR with
!
n " 2 can be manufactured by using
two different sized hemispheres of the same material as given by
!
r1 = (n "1)r2 , (2.7)
where
!
r1 and
!
r2 are the radii of the front and back hemispheres, respectively [14].
Figure 2.7 Structure of a spherical lens reflector composed of two different sized hemispheres, for the case when the index of refraction is not 2.
!
! %(!
Luneburg lens reflectors are another type of SLR that use a dielectric ball lens with a
radially dependent index of refraction (Figure 2.1d) [39]. The graded index lens improves
the RCS of the SLR by increasing the acceptance angle. In practice the manufacture of a
Luneburg lens is restricted to composite, stepped-index ball lenses [36,39].
2.3 Frequency Selective Surfaces
2.3.1 Passive Frequency Selective Surfaces
For passive arrays there are two processes that induce frequency selectivity. One
method involves the interference of electromagnetic waves within a multilayer dielectric
structure where the transmission response is controlled by the permittivity, thickness,
spacing, and number of layers [40]. The other technique incorporates resonant interaction
between an incident electromagnetic wave and a two-dimensional array of periodic
conducting elements or apertures in a conducting screen.
In this work, the FSS of choice was the capacitive/inductive resonant grid. As stated
earlier, this type of FSS is fabricated from either a periodic array of conducting segments on
a substrate (capacitive resonant mesh/grid) or as a periodic array of apertures in a conducting
screen (inductive resonant mesh/grid). In this instance the frequency response is determined
by the geometry of the segments/apertures.
!
! %)!
Figure 2.8 Illustration of (a) a capacitive mesh and (b) an inductive mesh showing periodicity of the unit cell and the gap/width between elements.
2.3.2 Capacitive and Inductive Meshes
The capacitive and inductive mesh FSS are complimentary geometric structures with
inverse frequency response [41]. An electromagnetic wave incident on a capacitive mesh
FSS at sufficiently high frequencies will be reflected; while at sufficiently low frequencies
the wave will be transmitted. A high frequency wave with wavelength !<<p-g, where p is
the periodicity of the unit cell and g is the gap between elements, sets up an almost uniform
oscillating current in each conducting element and as such the current distribution over most
of the conducting element is the same as if the wave were incident upon a continuous
conducting sheet. This uniform current flow in the conducting segments produces a reflected
wave like a mirror. At low frequencies governed by !>>p-g, the incident wave is unable to
set up current in the conducting segments and the incident wave does not interact with the
mesh, leading to high transmission. The impedance of the capacitive mesh is given by
!
ZC =1j"C
, (2.8)
!
! %*!
where
!
" is the angular frequency of the incident electromagnetic wave, and C is the
effective capacitance of the mesh. From Eq. 2.8 it is evident that for high frequencies the
mesh is a low impedance surface and behaves like a short circuit, reflecting the incident
wave. For low frequencies the capacitive mesh is a high impedance surface and has little to
no effect on the incident wave [42]. Based on this description, the capacitive mesh FSS
functions as a low-pass filter (Figure 2.9a).
Figure 2.9 Idealized frequency response of (a) a low-pass filter, (b) a high-pass filter, (c) a band-pass filter, and (d) a band-stop filter.
The inductive mesh FSS is the complimentary structure to the capacitive mesh FSS
and exhibits inverse behavior. A high frequency incident wave with !<<p-w, where p is the
periodicity of the unit cell and w the width of the conducting gap between apertures, is
unable to set up currents in the conducting screen and the wave is transmitted. At low
frequencies with !>>p-w, the incident wave sets up near uniform oscillatory currents in the
conducting screen and is largely reflected. The impedance of the inductive mesh is given by
!
! %+!
!
ZL = j"L , (2.9)
where
!
" is the angular frequency of the incident wave, and L is the effective inductance of
the mesh. From Eq. 2.9 it is evident that the mesh behaves as a high impedance surface for
high frequency incident waves and as a low impedance surface for low frequency waves. At
low frequencies the inductive mesh acts like a short circuit and reflects the incident wave
while at high frequencies the wave is transmitted. Based on this description, the inductive
mesh FSS functions as a high-pass filter (Figure 2.9b).
2.3.3 Crossed-Dipole Aperture Band-pass Filter
The FSS employed in this work was a band-pass filter with a center frequency of
349 GHz, consisting of periodic crossed-dipole shaped apertures in a 12-micron-thick Nickel
screen. The crossed-dipole aperture dimensions are shown in Figure 2.10a where the length
of the dipole is 400 microns, the width of the dipole is 68 microns, the periodicity of the unit
cell is 700 microns, and the screen thickness is 12 microns.
!
! %,!
Figure 2.10 (a) Crossed-dipole aperture band-pass FSS made from 12-micron-thick electroplated Nickel. Inset shows the unit cell of the FSS with aperture dimensions. (b) Experimentally measured transmittance spectra of the band-pass filter. Image is taken from [4].
As shown in Figure 2.10b, the FSS has a maximum transmittance of nearly 100% at 349 GHz
and has a full width at half maximum of 50 GHz between 325 GHz and 375 GHz. The FSS
in Figure 2.10a is a resonant inductive mesh filter. The dimensions of the crossed-dipole
apertures are tailored such that the filter is transparent at the resonant frequency of the filter
and otherwise opaque [43].
!
! %-!
3. Methodology
This section describes the methods used to design, fabricate, and characterize the
terahertz SLR and the frequency selective SLR. Material selection and fabrication techniques
for the SLRs are discussed. SLRs based on fused silica ball lenses were fabricated and their
radar cross-section measured at terahertz frequencies.
3.1 Design and Fabrication
3.1.1 Spherical Lens Reflector Fabrication
Six SLRs with diameters ranging from 2 mm to 8 mm were fabricated from
commercially available fused silica ball lenses. Fused silica was used as it is a low-loss
material and has an index of refraction of approximately n=1.951 from 0.3 – 2 THz [44].
Figure 3.1 Time-domain spectroscopy measurements of fused silica from 0.3 – 2 THz. The solid line is the measured spectra from [44] and the asterisks are the data from [45]. (a) Power absorption coefficient and (b) index of refraction. Plots are taken from [44]. An aluminum fixture was machined to mask one hemisphere of the ball lenses and the
unmasked hemisphere was coated with approximately 2500 angstroms of evaporated
!
! &.!
aluminum as measured by an Alpha-Step IQ Surface Profiler. Aluminum was chosen for the
reflective coating as it has a reflectivity of "99% from 0.1 – 45 THz [46].
Figure 3.2 Aluminum coating process showing evaporation of aluminum onto fused silica ball lenses sitting in the mask.
3.1.2 Frequency Selective SLRs
The method for attaining frequency selective retroreflective behavior was the
application of a planar 349 GHz band-pass filter FSS to the aperture of the SLRs. The band-
pass filter (Figure 2.10a) was cut into small segments and fastened to the aperture of the
SLRs. As the band-pass filter was applied to the aperture of the reflectors, only frequencies
within the pass-band transmitted into the reflector while frequencies in the stop-bands
scattered from the filter. Due to the difficulty of application, the filter did not perfectly
conform to the ball lens’ spherical surface. No special folding techniques were used to
reduce sharp edges in the wrapped filter.
!
! &%!
Figure 3.4 Cross-section representation of a frequency selective spherical lens reflector consisting of a fused silica ball lens with aluminized hemispherical cap and crossed-dipole band-pass filter wrapped around the aperture.
3.2 Backscattering Predictions
For an SLR to be observable in a real-world environment, its backscatter coefficient
should show significant contrast with its surroundings. To this end, the SLRs in this study
were measured on a rough dielectric ground plane with a backscatter coefficient similar to
that of rough concrete at 100 GHz [47] which was assumed to exhibit a similar
backscattering coefficient as rough concrete at 160 GHz and 350 GHz as well.
The predicted backscatter coefficients (log scale) for the six SLRs, as determined by
normalizing Eq. 2.3 to the area of the scattering body, are presented in Table 3.1 for 100
GHz, 160 GHz, and 350 GHz. The backscatter coefficient for the rough dielectric ground
plane at 100 GHz, 160 GHz, and 350 GHz in addition to the #0 of rough concrete at 100 GHz
from [47] is also shown. At 100 GHz, the predicted #0 of the SLRs is 32 dB – 45 dB greater
than the ground plane’s #0, while at 160 GHz and 350 GHz, the SLRs are predicted to
backscatter 28 dB – 41 dB and 34 dB – 47 dB more than the ground plane, respectively.
!
! &&!
Table 3.1 Predicted backscatter coefficients for six SLRs ranging in size from 8 mm to 2mm in diameter and measured backscatter coefficients of the rough dielectric ground plane and concrete from [47].
Freq/Diam 8 mm 6 mm 5 mm 4 mm 3 mm 2 mm Ground Plane
Concrete
100 GHz 18.5 dB 16 dB 14.4 dB 12.4 dB 9.9 dB 6.4 dB -26 dB -26.7 dB 160 GHz 22.6 dB 20.1 dB 18.5 dB 16.5 dB 14 dB 10.5 dB -18 dB N/A 350 GHz 29.3 dB 26.9 dB 25.3 dB 23.3 dB 20.8 dB 17.3 dB -17.5 dB N/A
3.3 Measurement
3.3.1 Inverse Synthetic Aperture Radar (ISAR)
The RCS of the SLRs was determined by analyzing their inverse synthetic aperture
radar (ISAR) imagery. ISAR is a radar measurement technique that generates an image of a
target object by Fourier processing its coherent backscattering properties. A target is placed
on a rotational stage and a fixed transceiver, located some distance from the stage, measures
the object’s backscattered amplitude and phase as a function of target rotation and frequency.
A two-dimensional Fourier transform of the collected data produces a two-dimensional
image of the object. The cross range resolution of the resulting images is:
!
"Rc =#2"$
, (3.1)
where
!
" is the wavelength and
!
"# is the angular extent over which the image was
processed. The image’s range resolution is:
!
"Rr =c2#
, (3.2)
where c is the speed of light and
!
" is the bandwidth [48].
!
! &'!
3.3.2 Compact Radar Range Measurements
The six SLRs were mounted on a 4 ft. diameter rough dielectric ground plane and
measured in three compact radar range systems operating at center frequencies of 100 GHz,
160 GHz, and 350 GHz. Each measurement composed of a -60 to +60 degree azimuth sweep
at a fixed ground plane elevation angle. The RCS measurements were taken at 5, 15, 25, 35,
and 45 degrees elevation and the reflectors were oriented such that a ground plane elevation
of 25 degrees and 0 degrees azimuth coincided with SLR bore-sight (Figure 3.4).
Table 3.2 Measurement matrix for each compact radar range showing a comparison of the ground plane elevation angle and the SLR elevation angle. The retroreflectors were oriented such that 25 degrees ground plane elevation corresponded with bore-sight.
Ground Plane Elevation Angle (
!
"el ) Retroreflector Elevation Angle (
!
"el ) 5 degrees -20 degrees 15 degrees -10 degrees 25 degrees 0 degrees (bore-sight) 35 degrees +10 degrees 45 degrees +20 degrees
Figure 3.4 Orientation of the SLR on the rough dielectric ground plane.
!
! &(!
A schematic of the compact radar range system is presented in Figure 3.5 that depicts
the quasi-monostatic (0.3 degree bistatic angle) measurement system with calibration pylons,
collimating mirror, target under investigation, and anechoic chamber walls. Each of the three
ranges used were fully polarimetric.
Figure 3.5 Top down view of the compact radar range system configuration showing quasi-monostatic transceivers, collimating mirror, calibration fixtures, SLR targets on the ground plane, and anechoic chamber walls. Image taken and modified from [49].
!
! &)!
4. Results
This section presents the THz backscatter results for the SLRs with and without the
349 GHz band-pass filter. Imagery developed from ISAR measurements and plots of the
azimuth dependence of the six retroreflectors at 100 GHz, 160 GHz, and 350 GHz are shown.
The measured azimuth dependence of the reflectors is compared to the model outlined in
section 2.1 and a simulation performed in the HFSS suite [50]. Also, the peak backscatter
coefficients as a function of elevation angle are presented. This section clearly indicates that
a frequency selective retroreflector operating at THz frequencies was realized.
4.1 Frequency Selective Spherical Lens Reflectors
4.1.1 ISAR Imagery
The RCS measurements at 160 GHz and 350 GHz of the SLRs were collected with
and without the 349 GHz band-pass filter attached to their aperture. ISAR images of the
frequency selective retroreflectors versus the non-frequency selective retroreflectors are
shown for 25 degrees elevation and 0 degrees azimuth in Figures 4.1 and 4.2, for 160 GHz
and 350 GHz respectively. The 160 GHz measurement falls outside of the pass-band of the
FSS and it is expected that the backscatter coefficients will be much smaller than the 350
GHz measurements. Since the 350 GHz measurements falls almost in the center of the pass
band with nearly 100% transmittance, it is expected that the SLRs will still be clearly visible
above the ground plane’s return. Three-dimensional representations of the ISAR images in
Figures 4.1 and 4.2 are given in Figures 4.3 and 4.4 for 160 GHz and 350 GHz, respectively.
!
! &*!
Figure 4.1 160 GHz RCS comparison of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization.
Figure 4.2 350 GHz RCS comparison of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization.
!
! &+!
Figure 4.3 Waterfall plot of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS at 160 GHz. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization.
!
! &,!
Figure 4.4 Waterfall plot of the six SLRs (a) without the 349 GHz band-pass FSS and (b) with the 349 GHz band-pass FSS at 350 GHz. Both images are taken at 25 degrees elevation and 0 degrees azimuth for HH-polarization.
!
! &-!
From Figures 4.1b and 4.3b it is evident that the inclusion of the FSS successfully
masked the SLRs with diameters below 8 mm, however there appears to be some small
return from the 8 mm diameter reflector relative to the ground plane. At 350 GHz, the
frequency selective FSS are still visible above the ground plane, yet their return is diminished
somewhat by the addition of the band-pass filter (see Figures 4.2b and 4.4b). Figures 4.3 and
4.4 show the effect of the band-pass filter on the RCS of the SLRs. In Figure 4.3 (160 GHz)
the filter reduces the RCS such that the SLRs are indistinguishable from the ground plane,
whereas Figure 4.4 (350 GHz) shows that even though the filter reduced the RCS of the
SLRs, they backscatter much higher than the ground plane. Comparison of Figures 4.1b and
4.2b (4.3b and 4.4b) clearly shows that a frequency selective retroreflector was realized at
terahertz frequencies.
4.1.2 Backscatter Coefficient as a function of Azimuth at 350 GHz
The backscatter coefficients for the six frequency selective SLRs as a function of
azimuth angle are presented in Figure 4.5 at 350 GHz. The backscatter coefficients were
determined by selecting an area of the image corresponding to each SLR (see lower left
scatterer in Figure 4.6a) from the HH-polarized ISAR image, summing the RCS of each pixel
in the selected area, and then dividing by the total area selected.
!
"0 =
RCSii=1
#
$
AREAii=1
#
$ (4.1)
In Eq. 4.1,
!
" is the total number of pixels that collectively represent one scatterer. Due to
the size of the reflectors and the resolution of each system, the area approximating the SLRs
!
! '.!
in the ISAR imagery was slightly larger than the actual area of the reflectors and as such the
backscatter coefficient is underestimated by approximately 1 dB – 2 dB.
The backscatter coefficients are plotted for HH-polarization at 25 degrees elevation
and are compared to the azimuth backscatter behavior of the supporting ground plane. The
inclusion of the FSS diminished the backscatter coefficient of the retroreflectors to between
3 dB and 24 dB above the ground plane. Without the FSS applied, the SLRs were 14 dB –
36 dB above the ground plane. Application of the FSS also introduced erratic azimuth
behavior. The azimuth behavior of the frequency selective SLRs for HV, VH, and VV-
polarizations (see Figures 9.6-9.8 in Appendix) show that for some azimuth angles the SLRs
are indistinguishable from the ground plane, and for others the SLRs backscatter up to 16 dB
higher than the ground plane. It is believed that the erratic variations in #0 for the HV, VH,
and VV-polarizations is due to the folds and sharp edges in the applied FSS filter, as well as
the distortion of the crossed-dipole apertures on the spherical surface.
!
! '%!
Figure 4.5 Azimuth behavior of the backscatter coefficient for the six frequency selective SLRs at 350 GHz and 25 degrees elevation for HH-polarization.
4.2 Behavior of SLRs without FSS
4.2.1 ISAR Imagery
Figures 4.6, 4.8, and 4.10 show ISAR images of the backscattering behavior of the six
SLRs mounted on the rough dielectric ground plane at 25 degrees elevation and 0 degrees
azimuth (retroreflector bore-sight) for center frequencies of 100 GHz, 160 GHz, and 350
GHz. Three-dimensional representations of the ISAR images are shown in Figures 4.7, 4.9,
and 4.11 to further illustrate the contrast between the retroreflectors and the ground plane.
ISAR images of HV, VH, and VV-polarization are shown in Figures 9.3-9.5 of the
Appendix. The ISAR images clearly show the large contrast between the RCS of the
retroreflectors and the ground plane.
!
! '&!
Figure 4.6 100 GHz HH-polarization ISAR image of (a) the six SLRs (labeled by diameter) on the rough dielectric ground plane, and (b) the ground plane without the SLRs. In both images, the ground plane was oriented at 25 degrees elevation and 0 degrees azimuth (SLR bore-sight). The black box around the 6 mm SLR (4.6a) indicates the approximate area used to determine the backscatter coefficient.
!
! ''!
Figure 4.7 Waterfall plot of (a) the six SLRs on the ground plane and (b) the ground plane without the SLRs for HH-polarization at 100 GHz. Both images taken at 25 degrees elevation and 0 degrees azimuth.
!
! '(!
The retroreflectors in Figure 4.6a have been labeled by diameter and the black box
around the 6 mm SLR illustrates the effective area used to the determine the backscatter
coefficient. The RCS of the ground plane without the reflectors is shown in Figure 4.6b. In
comparison with Figure 4.6a, the SLRs backscatter significantly more than the ground plane
at 100 GHz, indicating that all reflectors would be highly visible to a THz radar system in
comparison to background clutter comparable to concrete. Figure 4.7 is a three-dimensional
depiction of the ISAR image in Figure 4.6 that reaffirms the high contrast between the
retroreflectors and the ground plane. The measurements were repeated at 160 GHz where all
reflectors except the 2 mm diameter SLR backscattered higher than the ground plane (Figure
4.8 and Figure 4.9).
Figure 4.8 160 GHz HH-polarized ISAR image of (a) six SLRs (five visible) mounted on the rough dielectric ground plane and (b) the ground plane without the reflectors. Both images were taken at 25 degrees elevation and 0 degrees azimuth (SLR bore-sight). !
!
! ')!
Figure 4.9 Waterfall plot of (a) the six SLRs (five visible) on the ground plane and (b) the ground plane without the SLRs for HH-polarization at 160 GHz. Both images taken at 25 degrees elevation and 0 degrees azimuth.
!
! '*!
The measured RCS of the SLRs at 350 GHz is shown in Figure 4.10 and Figure 4.11
with all reflectors backscattering substantially higher than the ground plane. The 100 GHz,
160 GHz, and 350 GHz backscatter coefficients for the six SLRs are presented in Table 4.1
and are compared to the return from the ground plane. All retroreflectors backscattered
approximately one order of magnitude higher than the ground plane and in some cases up to
4 orders of magnitude higher.
Figure 4.10 350 GHz HH-polarized ISAR image of (a) the six SLRs on the ground plane and (b) the ground plane without the SLRs. Both images taken at 25 degrees elevation and 0 degrees azimuth. !!
!
! '+!
!!!
! !Figure 4.11 Waterfall plot of (a) the six SLRs on the ground plane and (b) the ground plane without the SLRs for HH-polarization at 350 GHz. Both images taken at 25 degrees elevation and 0 degrees azimuth.
!
! ',!
Table 4.1 Measured backscatter coefficients of the six retroreflectors and ground plane at 100 GHz, 160 GHz, and 350 GHz. Measurements were listed for HH-polarization at 25 degrees elevation and 0 degrees azimuth.
Freq/Diam 8 mm 6 mm 5 mm 4 mm 3 mm 2 mm Ground Plane 100 GHz 7.9 dB -1.8 dB -7.1 dB -4.6 dB -3.9 dB -13.6 dB -26 dB 160 GHz 11.1 dB -1.7 dB -9.6 dB 12.3 dB -9.2 dB N/A -18 dB 350 GHz 19.4 dB 11.5 dB 8.1 dB 8.8 dB 9 dB 3.3 dB -17.5 dB
A comparison of the measured backscatter coefficients from Table 4.1 and the
predicted backscatter coefficients from Table 3.1 shows that the SLRs backscatter somewhat
less than the predicted values. This discrepancy may arise due to the simplicity of the model,
as it does not account for material losses or any effect due to spherical aberration. ISAR
images for VV-polarization show similar results while the cross-polarization measurements
(HV, VH) show very little backscatter (see Appendix section 9.2.2). It was expected that the
cross-polarization measurements showed very little backscatter as the incident wave
undergoes a single bounce when retroreflected by an SLR.
4.2.2 Backscatter Coefficient as a function of Azimuth
The monostatic backscatter coefficients for the six SLRs as a function of azimuth
angle are shown for 100 GHz, 160 GHz, and 350 GHz in Figures 4.7-4.9. The backscatter
coefficients are plotted for HH-polarization at 25 degrees elevation and are compared to the
azimuth backscatter behavior of the supporting ground plane. The backscatter coefficient of
the SLRs at 100 GHz (Figure 4.12) is 8 dB - 34 dB above the ground plane. The peak
backscatter coefficients of the 5 mm, 4 mm, and 2 mm SLRs are shifted from 0 degrees
azimuth towards +40 degrees azimuth, which may indicate that those reflectors were slightly
misaligned on the ground plane.
!
! '-!
Figure 4.12 Azimuth backscatter behavior of six SLRs at 100 GHz for HH-polarization and 25 degrees elevation.
The backscatter behavior of the retroreflectors as a function of azimuth angle at 160
GHz is shown in Figure 4.13. Finding the 2 mm diameter SLR from the ISAR image proved
too difficult and so the backscatter coefficient is not reported. It is shown in Figure 4.13 that
the 6 mm and 3 mm reflectors have a peak backscatter coefficient aligned towards +40
degrees azimuth, yet the SLRs backscatter 5 dB - 30 dB above the ground plane.
!
! (.!
Figure 4.13 Azimuth backscatter behavior of five SLRs at 160 GHz for HH-polarization and 25 degrees elevation. At 350 GHz the backscatter coefficients of the six SLRs (Figure 4.14) were 14 dB -
36 dB above the ground plane, further illustrating the high contrast seen in the ISAR
imagery. An inspection of Figure 4.14 shows that the 8 mm, 3 mm, and 2 mm diameter
SLRs have a peak backscatter coefficient aligned with 0 degrees azimuth, however the peak
backscatter coefficient of the 6 mm and 4 mm SLR were closer to -60 and +40 degrees
azimuth, respectively. The azimuth behavior of the backscatter coefficients for VV-
polarization was similar to the HH-polarization measurements while the cross-polarization
measurements showed little backscatter (see Figures 9.15-9.17). While the 25-degree
elevation measurements are shown, the backscatter coefficients at the other elevation angles
showed similar results.
!
! (%!
Figure 4.14 Azimuth backscatter behavior of the six SLRs at 350 GHz and 25 degrees elevation for HH-polarization. In Figure 4.15, the azimuth dependence of the backscatter coefficient for the 8 mm
diameter SLR at 350 GHz is compared to the model outlined in section 2.1.1 and a
simulation using the HFSS integral equation solver (HFSS-IE). The HFSS simulation is
described in Appendix 9.4. From Figure 4.15 it is shown that the suggested model outlined
in section 2.1.1 overestimates the backscatter coefficient of an 8 mm fused silica SLR at 350
GHz. The model from section 2.1.1 is approximately 10 dB greater than the measured data
on bore-sight and shows a sharper azimuth drop-off. This discrepancy is due to the
simplicity of the model, which is discussed in section 5.3. The HFSS-IE simulation shows
better agreement than the circular mirror model, however the backscatter coefficient is
overestimated by approximately 6 dB.
!
! (&!
Figure 4.15 Comparison of the measured (red) backscatter coefficient of the 8 mm SLR with the model from section 2.1.1 (blue), and the HFSS-IE model (orange).
4.2.3 Elevation Angle Dependence
The elevation angle dependence of the backscatter coefficient for the 8 mm SLR was
analyzed at 100 GHz, 160 GHz, and 350 GHz. Figure 4.16 shows the elevation and azimuth
angle dependence of the 8 mm SLR’s backscatter coefficient at 350 GHz, 160 GHz, and 100
GHz. Figure 4.16 suggests that the peak backscatter coefficient for the 8 mm SLR was
oriented near: 15 degrees elevation and -15 degrees azimuth at 350 GHz (Figure 4.16a), 5
degrees elevation and 0 degrees azimuth at 160 GHz (Figure 4.16b), and between 15 and 25
degrees elevation and 20 degrees azimuth at 100 GHz (Figure 4.16c). This evidence suggests
alignment errors when mounting the SLRs on the ground plane. A summary of the elevation
angle dependence of all six is given in Appendix 9.3.
!
! ('!
!
! ((!
Figure 4.16 Elevation and azimuth angle dependence of the 8 mm SLR’s backscatter coefficient at (a) 350 GHz, (b) 160 GHz, and (c) 100 GHz.
!!!!!!!!!!!!!!!
!
! ()!
5. Discussion
The results of the retroreflector measurements starting with the performance of the
frequency selective SLRs at 160 GHz and 350 GHz are discussed. A comparison of the SLR
backscatter coefficients with the rough dielectric ground plane at 100 GHz, 160 GHz, and
350 GHz is then presented. The prediction model is compared to the measured data, then
alternative designs and fabrication processes are considered.
5.1 Frequency Selective Retroreflectors
The application of the band-pass filter to the aperture of the SLRs successfully
masked the reflectors at 160 GHz. This was the desired result as the measurement at 160
GHz was outside of the pass-band of the filter. At 350 GHz, approximately the center of the
pass-band, the retroreflectors were still visible above the ground plane; this is an effect of the
band-pass filter allowing radiation to pass into and out of the SLR. It is noted that the
application of the filter diminished the backscatter coefficient of the SLRs by 12 dB – 23 dB,
however they still returned 3 dB – 24 dB more than the ground plane. As evidenced in
Figure 4.5, the inclusion of the filter also had a detrimental effect to the azimuth performance
of the reflectors. As the FSS was wrapped around small spheres, it proved difficult to reduce
sharp edges and retain the integrity of the crossed-dipole pattern. As the geometry of an FSS
is important to the function of the filter, the introduction of sharp edges and loss of pattern
integrity were expected to influence the backscatter coefficient.
!
! (*!
5.2 SLR and Ground Plane Backscatter Coefficient Comparison
5.2.1 Backscatter Coefficients at 100 GHz
The ISAR images in Figure 4.6 show considerable contrast between the
retroreflectors and the rough dielectric ground plane at 100 GHz. The peak backscatter
coefficients for the SLRs ranged from 12 dB to 34 dB more than the ground plane for the 2
mm and 8 mm reflectors, respectively. This indicates that even a 2mm THz retroreflector
could be visible in a real-world environment. The azimuth dependence of the SLRs, shown
in Figure 4.12, implies that not all retroreflectors were aligned with 0 degrees azimuth, as
intended. The 8 mm and 6 mm diameter SLRs appear to have been properly aligned,
however the 5 mm, 4 mm, and 2 mm diameter SLRs appear to be aligned towards +40
degrees azimuth.
5.2.2 Backscatter Coefficients at 160 GHz
The 160 GHz measurements of the SLRs also show substantial contrast with the
ground plane, indicating that the retroreflectors backscattered much more than a rough
concrete surface at 160 GHz. It is noted that the backscatter coefficient for the 2 mm
diameter SLR was not reported due to the difficulty in determining its position on the ground
plane from the ISAR imagery (Figures 4.8a and 4.9a). It is suspected that this reflector was
poorly aligned during the measurement process. The peak backscatter coefficients for the
SLRs were measured to be between approximately 8 dB and 30 dB higher than the ground
plane. It is worth noting that the peak backscatter coefficients for the 6 mm, 5 mm, and 3
mm SLRs were unexpectedly lower at 160 GHz with the 5 mm and 3 mm SLRs
backscattering less at 160 GHz than at 100 GHz. The azimuth dependence of the SLRs at
!
! (+!
160 GHz indicates that only the 8 mm SLR was properly aligned with 0 degrees azimuth
(Figure 4.13).
5.2.3 Backscatter Coefficients at 350 GHz
The peak backscatter coefficients of the SLRs at 350 GHz range between 21 dB (2
mm SLR) and 38 dB (8 mm SLR) above the ground plane (Figures 4.10 and 4.11). At 350
GHz, all retroreflectors were highly visible compared to the ground plane. This indicates that
an SLR as small as 2 mm in diameter could potentially represent a significant THz scatterer
in a real-world environment. As with the 100 GHz and 160 GHz measurements, some of the
retroreflectors were not aligned as intended. Figure 4.14 shows that while the 8 mm, 3 mm,
and 2 mm SLRs appear to be well aligned with 0 degrees azimuth, the 6 mm and 5 mm SLRs
appear to be aligned towards –60 degrees azimuth, and the 4 mm SLR towards +35 degrees.
5.3 Measurement and Prediction Model Comparison
The prediction model presented in section 2.1.1 models an SLR on bore-sight as a
circular mirror. The reasoning for modeling an SLR on bore-sight as a circular mirror is that
the illuminated reflecting surface has a circular cross-section. The azimuth dependence of
this model, shown in Figures 2.2 (green line) and 4.15 (blue line) is modeled by scaling the
area of the circular mirror at oblique angles. If the illuminated area on bore-sight is a circle,
then at oblique angles it is elliptical. What is shown is that the circular mirror model
overestimates the peak backscatter coefficient (on bore-sight) by approximately 10 dB when
!
! (,!
compared with the measured data. It is also shown that scaling the circular area with azimuth
leads to a faster reduction in the backscatter coefficient than the measurement.
These discrepancies show that the model is not accurate and is oversimplified. The
circular mirror analogy does not take into account the ball lens material, and therefore does
not account for material losses. The index of refraction of the ball lens does not factor into
the prediction model, and as discussed in section 2.2, the index of refraction plays an
important role in the focal length of the sphere. In the ideal case of an SLR with index of
refraction
!
n = 2, the focal length of the lens is the back hemisphere of the lens. As a low-
loss material with
!
n = 2 was not available, it should be expected that the backscatter
coefficient of the measured SLRs would be somewhat lower than the prediction model with
the SLRs suffering from spherical aberrations. At oblique angles the reflective cap becomes
more visible to the incident wave and therefore contributes to the backscatter coefficient of
the SLR. The circular mirror model does not account for the emergence of the reflective cap
and will overestimate the decrease in the backscatter coefficient at oblique angles.
5.4 Alternative Fabrication Processes and Designs
5.4.1 Spherical Lens Reflectors for n!2
One potential source of error for the SLR design is the choice and availability of
material. Fused silica was used for the SLRs due to its low-loss and index of refraction being
close to
!
n = 2. As fused silica has an index of refraction
!
n =1.951, the design of the
retroreflector must be changed in order to optimize the backscatter coefficient.
As outlined in section 2.2, Eq. 2.5 governs the focal length of a ball lens. In the case
of fused silica, the focal length of the ball lens is approximately 1.026r. For the 8 mm fused
!
! (-!
silica SLR, the focal length is approximately 104 microns behind the back surface of the lens.
In order to create an optimized SLR from a fused silica ball lens, the lens would have to be
suspended 104 microns from the reflecting cap.
As suspending the ball lens above the reflecting cap is difficult to manufacture, the
alternate choice is to use a solid lens of different sized hemispheres (see Figure 2.7). From
Eq. 2.7 it is determined that the front hemisphere should have a radius 95.1% of that of the
hemisphere with the reflective cap. If the coated hemisphere has a 4 mm radius, then the
front or aperture hemisphere should have a radius of 3.804 mm. By reducing the aperture
hemisphere to accommodate the use of fused silica via this method, the effective aperture of
the retroreflector is decreased, thus reducing the backscatter coefficient.
5.4.2 Frequency Selective Surface Application
The frequency selective retroreflector design consisted of a fused silica ball lens with
a band-pass FSS wrapped around the aperture of the reflector. Due to the size of the SLRs it
proved difficult to conform the filter to the sphere’s surface. As such, folds and sharp edges
were present in the filter, which lead to the diminished backscatter performance.
A modification to the fabrication method to remove the unwanted reflections due to
edges and folds in the filter is to etch the filter directly onto the sphere. It has been shown
that sub-micron sized features can be patterned onto a spherical surface using topographically
directed photolithography (TOP) and near-field contact-mode lithography and an
elastometric membrane mask [51]. Near-field contact mode lithography is capable of
patterning features on a spherical surface up to a 65-degree arc while TOP has been used to
pattern features in an 85-degree arc. For arcs greater than these, the features begin to lose
!
! ).!
integrity and deform. Other methods include step and flash imprint lithography (SFIL) and
ion beam proximity printing (IBP), which are capable of patterning high fidelity 0.5 micron
sized features on curved surfaces [52].
5.4.3 Alternative Frequency Selective Retroreflector Designs
With the ability to pattern the FSS onto the sphere directly, coating the entire sphere
in aluminum and then etching the band-pass filter into one hemisphere can achieve the same
design presented here. An alternative design for achieving frequency selective retroreflection
is the application of a band-stop filter (Figure 2.9d) as the reflecting surface. In this example,
only frequencies within the stop-band will be retroreflected whereas frequencies outside of
the stop-band will be transmitted and the reflector will scatter like a homogeneous dielectric
sphere. With improvements in etching techniques, more complicated filter designs with
multiple resonances may be applied to effectively encode a barcode signature into the
retroreflector [21,26,27]. A retroreflector with multiple tailored resonances could yield a
retroreflector with a specific frequency signature that can be used as a method of passive
identification similar to RFID [53].
!
! )%!
6. Conclusion
SLRs exhibiting frequency selective retroreflection at terahertz frequencies have been
manufactured and characterized. The frequency selective nature was imparted by the
addition of a FSS band-pass filter with a center frequency of 349 GHz. The addition of the
band-pass filter reduced the backscatter coefficients of the retroreflectors, however not so
much as to make them indistinguishable with the ground plane. Alternative designs for
achieving and improving the performance of frequency selective retroreflectors have been
discussed.
The backscatter coefficients of six fused silica SLRs have been reported for 100 GHz,
160 GHz, and 350 GHz. All retroreflectors backscattered approximately one order of
magnitude higher than the ground plane and in some cases up to 4 orders of magnitude
higher. The measured backscatter coefficients are within 10 dB - 20 dB of the predicted
values with possible sources of deviation including material properties and prediction model
simplicity. It is evident that a better analytical model is needed to describe the retroreflection
phenomenon for SLRs to account for the refractive index of the lens and material losses. The
measured backscatter coefficients were 5 dB - 34 dB higher than a rough dielectric ground
plane modeling concrete. This indicates that such retroreflectors have the potential to be
visible to a THz radar system deployed in a real-world environment.
!
! )&!
7. Future Work
Now that a proof-of-concept frequency selective retroreflector has been presented, the
next step is to optimize the backscatter response. The main detriment to the backscatter
coefficient is due to the application of the planar band-pass FSS to the aperture of the
reflectors. Optimization of the frequency selective SLRs may be achieved by etching the
FSS directly onto the sphere via the lithography techniques mentioned in section 5. Beyond
this, retroreflectors with multiple tailored resonances would be developed as a method of
passive identification of objects using a remote THz sensing system.
!
! )'!
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!
! *.!
9. Appendix
9.1 ISAR Imagery
This section presents ISAR imagery for the frequency selective SLRs at 160 GHz and
350 GHz, as well as the SLRs without the band-pass filter at 100 GHz, 160 GHz, and 350
GHz. The ISAR imagery is shown for HH, HV, VH, and VV-polarizations at 25 degrees
elevation and 0 degrees azimuth, and all distinguishable reflectors are labeled.
9.1.1 Frequency Selective Spherical Lens Reflectors
ISAR images of the frequency selective SLRs are shown in Figures 9.1 and 9.2 for
160 GHz and 350 GHz. The 160 GHz HH-polarized measurement shows that the 8 mm, 3
mm, and 2 mm SLRs are somewhat visible above the ground plane, whereas the 6 mm, 5
mm, and 4 mm SLRs are completely masked by the ground plane. The cross-polarized (HV
and VH) images indicate that the 8 mm, 4 mm, 3 mm, and 2 mm SLRs show small contrast
with the ground plane, whereas the SLRs are completely masked by the ground plane in the
VV-polarization measurement. The emergence of some SLRs in the cross-polarized
measurements is likely due to sharp folds in the applied filter.
The 350 GHz ISAR imagery in Figure 9.2 shows that all six SLRs backscatter higher
than the ground plane for HH-polarization, however only the 8 mm, 6 mm, and 3 mm SLRs
backscatter higher than the ground plane for VV-polarization. Again, due to the folds in the
applied filter, several (8 mm, 6 mm, and 5 mm) SLRs are slightly visible in the cross-
polarization measurements. While only the 8 mm, 6 mm, and 3 mm SLRs backscatter higher
!
! *%!
than the ground plane for the VV-polarization measurement at 0 degrees azimuth, the other
SLRs begin to show higher contrast with the ground plane at oblique azimuth angles.
Figure 9.1 160 GHz ISAR image of the frequency selective SLRs on the ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarizations. The images were taken at 25 degrees elevation and 0 degrees azimuth and distinguishable reflectors are labeled.
!
! *&!
Figure 9.2 350 GHz ISAR image of the frequency selective SLRs on the ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarizations. The images were taken at 25 degrees elevation and 0 degrees azimuth and distinguishable reflectors are labeled.
9.1.2 Spherical Lens Reflectors
ISAR images of the SLRs at 100 GHz for 25 degrees elevation and 0 degrees azimuth
are shown in Figure 9.3. The HH and VV-polarization measurements (Figure 9.3a,d) show
six SLRs without the band-pass filter mounted on the rough dielectric ground plane. The
SLRs in both the HH and VV-polarization images show similar RCS, however the ground
plane scatters slightly higher for VV-polarization. It is evident from the cross-polarization
images (Figure 9.3b,c) that the SLRs are not visible above the ground plane. This indicates
that the incident wave does not undergo polarization rotations during retroreflection from a
SLR.
!
! *'!
The 160 GHz and 350 GHz ISAR images are presented in Figures 9.4 and 9.5. In
Figures 9.4a,d the 2 mm SLR is not visible above the ground plane. The cross-polarization
images for both the 160 GHz (Figure 9.4b,c) and the 350 GHz (Figure 9.5b,c) measurements
show that the SLRs are not visible above the ground plane. As with the 100 GHz cross-
polarization measurements, the 160 GHz and 350 GHz cross-polarization measurements
indicate that the incident wave does not undergo polarization rotations.
Figure 9.3 100 GHz ISAR imagery of six SLRs on the ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarization. ISAR Images taken at 25 degrees elevation and 0 degrees azimuth.
!
! *(!
Figure 9.4 160 GHz ISAR imagery of six SLRs on a ground plane for (a) HH, (b) HV, (c) VH, and (d) VV-polarization. ISAR images are taken at 25 degrees elevation and 0 degrees azimuth.
Figure 9.5 350 GHz ISAR Imagery of six SLRs for (a) HH, (b) HV, (c) VH, and (d) VV-polarization. Images taken at 25 degrees elevation and 0 degrees azimuth.
!
! *)!
9.2 Azimuth Dependence
In this section the azimuth dependence of the frequency selective SLRs is presented
for 350 GHz, and for the SLRs without the band-pass filter at 100 GHz, 160 GHz, and 350
GHz. Backscatter coefficient measurements below the ground plane are determined by
locating the SLR on the HH-polarization ISAR images.
9.2.1 Frequency Selective SLRs
The azimuth dependence of the backscatter coefficients of the six frequency selective
SLRs on the dielectric ground plane are shown in Figures 9.6-9.8 for HV, VH, and VV-
polarizations. The cross-polarization measurements show that the SLRs backscatter up to 20
dB above the ground plane, while the VV-polarization measurement shows backscatter
coefficients up to 21 dB higher than the ground plane. For some azimuth angles, the
backscatter coefficients drop below the ground plane.
!
! **!
Figure 9.6 Azimuth dependence of the backscatter coefficient for the frequency selective SLRs at 350 GHz and 25 degrees elevation for HV-polarization.
Figure 9.7 Azimuth dependence of the backscatter coefficient of the six frequency selective SLRs at 350 GHz and 25 degrees elevation for HV-polarization.
!
! *+!
Figure 9.8 Azimuth dependence of the backscatter coefficients of the six frequency selective SLRs at 350 GHz and 25 degrees elevation for VV-polarization.
9.2.2 SLRs without FSS
The azimuth dependence of the six retroreflectors at 100 GHz and 25 degrees
elevation are shown in Figures 9.9-9.11 for HV, VH, and VV-polarization. The cross-
polarization measurements show that the SLRs backscatter up to 13 dB above the ground
plane, however in comparison to the co-polarization measurements (HH and VV), the cross-
polarization measurements show the SLRs backscattering 10 dB - 28 dB below the co-
polarization measurements.
!
! *,!
Figure 9.9 Azimuth dependence of six SLRs at 100 GHz and 25 degrees elevation for HV-polarization.
Figure 9.10 Azimuth dependence of six SLRs at 100 GHz and 25 degrees elevation for VH-polarization.
!
! *-!
Figure 9.11 Azimuth dependence of six SLRs at 100 GHz and 25 degrees elevation for VV-polarization.
The azimuth dependence of five SLRs at 160 GHz is shown in Figures 9.12-9.14 for
HV, VH and VV-polarizations. The VV-polarization measurement (Figure 9.14) shows
similar azimuth dependence to the HH-polarization measurements in Figure 4.13. The cross-
polarization measurements show that the SLRs backscatter up to 10 dB above the ground
plane for a select few azimuth angles, but in general are indistinguishable from the ground
plane. The backscatter coefficient of the 2 mm SLR is not reported as it proved difficult to
locate on the ISAR imagery.
!
! +.!
Figure 9.12 Azimuth dependence of five SLRs at 160 GHz and 25 degrees elevation for HV-polarization.
Figure 9.13 Azimuth dependence of five SLRs at 160 GHz and 25 degrees elevation for VH-polarization.
!
! +%!
Figure 9.14 Azimuth dependence of five SLRs at 160 GHz and 25 degrees elevation for VV-polarization.
The backscatter coefficients of the six SLRs as a function of azimuth angle are shown
in Figures 9.15-9.17 for HV, VH, and VV-polarization at 350 GHz and 25 degrees elevation.
The VV-polarization measurement shows similar characteristics as the HH-polarization
measurement in Figure 4.14. The cross-polarization measurements (Figures 9.15 and 9.16)
show that the SLRs are masked by the ground plane for a majority of azimuth angles. For
some azimuth angles, the cross-polarization measurements show backscatter coefficients up
to 10 dB above the ground plane.
!
! +&!
Figure 9.15 Azimuth dependence of six SLRs at 350 GHz and 25 degrees elevation for HV-polarization.
Figure 9.16 Azimuth dependence of six SLRs at 350 GHz and 25 degrees elevation for VH-polarization.
!
! +'!
Figure 9.17 Azimuth dependence of six SLRs at 350 GHz and 25 degrees elevation for VV-polarization.
9.3 SLR Elevation Angle Dependence
9.3.1 SLRs without FSS at 100 GHz
The elevation angle dependence of the peak backscatter coefficients for the six SLRs
without the FSS are shown in Table 9.1 for HH-polarization at 100 GHz. The maximum
peak backscatter coefficient occurs as the elevation angle approaches bore-sight for all SLRs
except for the 6 mm and 4 mm reflectors. The peak backscatter coefficient for the 4 mm
SLR occurs at 35 degrees ground plane elevation (+10 degrees SLR elevation), while the 6
mm SLR’s peak backscatter coefficient was measured at 15 degrees and 35 degrees ground
plane elevation (-/+ 10 degrees SLR elevation). This information indicates that the 4 mm
SLR was misaligned in elevation, however the 6 mm SLR measurement may indicate a
transgression in extracting the backscatter coefficient from the measured RCS. At 45 degrees
!
! +(!
ground plane elevation the backscatter coefficient of the 2 mm SLR was not reported as it
was completely masked by the ground plane.
Table 9.1 Elevation angle dependence of the measured peak backscatter coefficients of the six SLRs and ground plane at 100 GHz for HH-polarization.
GP Elevation!
SLR Elevation!
8mm! 6mm! 5mm! 4mm! 3mm! 2mm! Ground Plane!
5 deg! -20 deg! 4.1dB! -6.7dB! -13.3dB! -13.6dB! -17.8dB! -26.6dB! -41.8dB!15 deg! -10 deg! 3.5dB! 1.8dB! -4dB! -3.8dB! -8.7dB! -16.2dB! -29.9dB!25 deg! 0 deg! 7.9dB! -1.2dB! -3dB! -4.1dB! -3.5dB! -8.5dB! -25.3dB!35 deg! +10 deg! 6.3dB! 1.8dB! -6.1dB! -3dB! -6.9dB! -9.6dB! -23.4dB!45 deg! +20 deg! 4.5dB! -0.4dB! -5.9dB! -9.4dB! -7.9dB! N/A! -21.3dB!
9.3.2 SLRs without FSS at 160 GHz
! The peak backscatter coefficients of the six SLRs at 160 GHz presented in Table 9.2
show that none of the six SLRs were aligned with 25 degrees elevation. The 8 mm, 6 mm,
and 2 mm SLRs exhibit peak backscatter at 5 degrees ground plane elevation, while the 5
mm, 4 mm, and 3 mm SLRs show peak backscatter coefficients at 15 degrees ground plane
elevation. The 2 mm SLR was only distinguishable from the ground plane at 5 degrees
ground plane elevation, and the 3 mm SLR was not distinguishable from the ground plane at
45 degrees ground plane elevation.
Table 9.2 Elevation angle dependence of the measured peak backscatter coefficients of the six SLRs and ground plane at 160 GHz for HH-polarization.
GP Elevation!
SLR Elevation!
8mm! 6mm! 5mm! 4mm! 3mm! 2mm! Ground Plane!
5 deg! -20 deg! 18.5dB! 10.6dB! 4.3dB! -2.6dB! -8dB! -10.4dB! -46.3dB!15 deg! -10 deg! 10.9dB! 7.2dB! 4.3dB! 4.7dB! 0.4dB! N/A! -23.4dB!25 deg! 0 deg! 11.2dB! 5.4dB! -0.4dB! 2.9dB! -2.6dB! N/A! -17.8dB!35 deg! +10 deg! 8.8dB! 3.7dB! 2.3dB! 1.1dB! -3.7dB! N/A! -17.8dB!45 deg! +20 deg! 6dB! 2.2dB! 1.4dB! -0.7dB! N/A! N/A! -13.9dB!
!
! +)!
9.3.3 SLRS without FSS at 350 GHz
The peak backscatter coefficients for the six SLRs at 350 GHz are presented in table
9.3 for HH-polarization. The 5 mm, 4 mm, 3 mm, and 2 mm SLRs exhibit peak backscatter
coefficients at 5 degrees ground plane elevation, which indicates that they were misaligned
by at least 20 degrees. The 3 mm SLR shows a higher backscatter coefficient than the 4 mm
SLR at 5 degrees ground plane elevation. It is inferred that bore-sight of the 4 mm SLR is
between 0 and 5 degrees ground plane elevation. Bore-sight for the 8 mm SLR appears to be
directed towards 15 degrees elevation, while the 6 mm SLR is between 25 and 35 degrees.
Table 9.3 Elevation angle dependence of the measured peak backscatter coefficients for the six SLRs and ground plane at 350 GHz for HH-polarization.
GP Elevation!
SLR Elevation!
8mm! 6mm! 5mm! 4mm! 3mm! 2mm! Ground Plane!
5 deg! -20 deg! 20.2dB! 14.4dB! 16.9dB! 16.6dB! 16.9dB! 10.8dB! -25.8dB!15 deg! -10 deg! 21.7dB! 14.3dB! 11.1dB! 8.7dB! 6.7dB! 1.8dB! -18.8dB!25 deg! 0 deg! 19.4dB! 15.1dB! 11.4dB! 11dB! 9dB! 3.7dB! -15.6dB!35 deg! +10 deg! 19.8dB! 15.1dB! 11.5dB! 9.9dB! 7.3dB! 2.5dB! -14.2dB!45 deg! +20 deg! 18.3dB! 13.6dB! 10.1dB! 8.5dB! 7.3dB! 1.5dB! -12.5dB!
9.4 HFSS Simulation Details
This section details the electromagnetic simulation of an 8 mm diameter SLR with the
HFSS integral equation solver. The development of the SLR model and the numerical RCS
calculation are presented.
9.4.1 Monostatic RCS Simulation Setup
The monostatic RCS simulation setup consisted of an 8 mm diameter SLR and an
incident plane wave of frequency 350 GHz. The SLR was composed of two silicon dioxide
hemispheres with relative permittivity
!
"r = 4 and slightly different diameters joined together.
The bottom hemisphere had a diameter of 8 mm and a perfect electrical conductor boundary
!
! +*!
(PEC) assigned to the outer surface. The top hemisphere had a diameter of 8 mm minus 4
angstroms to avoid assignment of the outer surface as a PEC boundary when united with the
bottom hemisphere. Figure 9.18 shows the SLR model with an incident plane wave and PEC
boundary assignment on the bottom hemisphere. An incident plane wave is incident upon
the SLR from the top with zero-phase position coinciding with the outer surface of the top
hemisphere. The plane wave is incident from the z-axis and the incident angle is varied from
0 to 90 degrees with a step size of 3 degrees. The monostatic RCS is then calculated by
inserting a far-field infinite sphere radiation surface.
Figure 9.18 Diagram of HFSS monostatic RCS measurement showing a dielectric sphere with incident plane wave and PEC boundary on bottom hemisphere.
!
! ++!
10. Biographical Sketch
Richard Williams was born in Sunderland, Tyne and Wear, United Kingdom. He
immigrated to New Orleans, Louisiana in 1997, and went on to obtain his B.S. in Physics
from Southeastern Louisiana University in 2009. While at Southeastern he worked on
gravitational wave physics for the LIGO project and had a summer placement at the Institute
for Gravitational Research (IGR) at the University of Glasgow, Scotland in 2008. After
graduation, Richard began studies at the University of Massachusetts Lowell and has been
working at the Submillimeter-Wave Technology Laboratory for the past four years.
