STUDY OF THZ SURFACE WAVES (TSW) ON
BARE AND COATED METAL SURFACE
By
GONG, MUFEI
Bachelor of Science in Optoelectronics
Tianjin University
Tianjin, China
1998
Master of Engineering
Nanyang Technological University
Singapore
2001
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
DOCTOR OF PHILOSOPHY
July, 2009
ii
STUDY OF THZ SURFACE WAVES (TSW) ON
BARE AND COATED METAL SURFACE
Dissertation Approved:
Dr. Daniel Grischkowsky
Dissertation Adviser
Dr. R. Alan Cheville
Dr. Weili Zhang
Dr. Albert T. Rosenberger
Dr. A. Gordon Emslie
Dean of the Graduate College
iii
ACKNOWLEDGMENTS
First of all, I want to express my appreciation to Dr. Daniel R. Grischkowsky, my major
advisor, for giving me the chance to do my Ph. D. in one of the best THz group in the
world and always guiding me with his scientific excellence and extremely high standard
throughout my Ph. D. study. I am proud of the quality of the work we did together. It has
been an honor to be a student of his. I am sure the training and scholarship I learned from
Dr.G will keep benefiting me in my career.
I want to give my deep thanks to Dr. Weili Zhang, who is not only my committee
member, but also the advisor of my undergraduate thesis in Tianjin University in China
11 years ago, for his continuous guidance, support and help to me all these years. I am
grateful to all the trust, encouragement and friendship from Dr. Zhang.
I want to send my gratitude to my other current and former graduate committee members,
Dr. Alan Cheville, Dr. Albert T. Rosenberger and Dr. Bret Flanders. All were very
generous, with their time, patience and input. Special thanks to Dr. Cheville, who gave
me a lot of important advices and offered me the facility to learn the new sample
preparation technique.
I also want to thank Dr. Charles Bunting and Dr. James West, who have taught me and
helped me to strengthen the electromagnetic part in my dissertation works.
Dr. Jianming Dai, Yuguang Zhao, Steve Coleman, Jiangquan Zhang, Matthew Reiten and
Abul Azad, thank you for the training, advices and encouragement you gave to me when
I first join the group.
During my hard time, I am so grateful that I have all of you: Adam Bingham, Norman
Laman, Sree Harsha, Jiaguang Han, Xinchao Lu, Ranjan Singh, Suchira Ranmani,
Yongyao Chen, Jianqiang Gu, Zhen Tian and Minh Dinh, all of you have been so
supportive and willing to help. I will remember everyday I had with you and cherish our
friendship.
To my parents, Chun’ai Guan and Chuan Gong, to all my family members and to my
girlfriend, Yongfen Chen, words can never be enough to express my thankfulness to all
the supports to me.
iv
TABLE OF CONTENTS
Chapter Page
1. INTRODUCTION .....................................................................................................1
1.1 Introduction of surface wave study ....................................................................1
1.2 Purpose of this study ..........................................................................................6
1.3 Scope of this report ............................................................................................7
2. EXPERIMENTAL SETUP ......................................................................................10
3. EXPERIMENTAL RESULTS AND DISCUSSIONS ............................................16
3.1 Individual signal...............................................................................................16
3.1-1 Signal on bare metal surface ..............................................................17
3.1-2 Signal on dielectric coated surface ....................................................25
3.2 Signals taken above surface .............................................................................28
4. THEORETICAL TREATMENT .............................................................................39
4.1 The surface wave field on bare metal surface ..................................................39
4.2 The surface wave field on dielectric coated surface ........................................41
4.2-1 The transverse field profile ................................................................41
4.2-2 The dispersion....................................................................................46
4.2-3 The absorption coefficients ...............................................................48
4.2-4 The coupling coefficients ..................................................................53
5. CONCLUSIONS.....................................................................................................62
6. FUTURE WORK .....................................................................................................64
REFERENCES ............................................................................................................65
APPENDICES .............................................................................................................70
Appendix I .............................................................................................................70
Appendix II ............................................................................................................78
v
Appendix III ...........................................................................................................80
vi
LIST OF TABLES
Table Page
1-1 Evanescent Field Extent .......................................................................................4
vii
LIST OF FIGURES
Figure Page
2-1 2D schematic of the system setup .......................................................................11
2-2 3D schematic of surface wave apparatus ............................................................12
2-3 The optical part of the receiver ...........................................................................13
3-1 Reference signal .................................................................................................16
3-2 Surface wave pulse on bare metal surface ..........................................................18
3-3 The diffraction pattern for 0.5 THz, λ = 600 μm ................................................20
3-4 Overlap integral at different distances ................................................................22
3-5 Overlapping of the surface wave field pattern and the diffraction pattern .........23
3-6 THz surface wave pulse on dielectric coated surface with block .......................26
3-7 TSW pulse on coated surface .............................................................................27
3-8 THz surface wave pulses measured at the surface and at 0.6 mm above
surface .........................................................................................................................29
3-9 Comparison of signals measured at the surface and above surface ....................30
3-10 The time domain surface waveforms above dielectric-coated surface with block
.....................................................................................................................................31
3-11 Amplitude fall-off viewed in frequency domain ..............................................32
3-12 Unnormalized frequency dependent field fall-off curves .................................33
3-13 Experimental surface wave fall-off ..................................................................34
3-14 Theoretical fall-off on bare surface ..................................................................36
3-15 Experimental and theoretical surface wave fall-off on coated surface .............37
3-16 Comparison of theoretical and experimental amplitude fall-off at selected
frequencies ...................................................................................................................38
4-1 Theoretical model equivalence of slab waveguide structure ..............................42
4-2 left: Ey field TM0 distribution at 0.5 THz of a plastic slab waveguide; right: field
profile of coated surface (half of the field of the left) ..................................................43
viii
4-3 Theoretical normalized surface wave fall-off curve ...........................................45
4-4 Exponential field fall-off constants calculated with and without perfect conductor
assumption ...................................................................................................................45
4-5 Group velocity and phase velocity ratio to speed of light of the fundamental TM0
mode of dielectric slab waveguide with a thickness of 25μm and an index of refraction of
1.5................................................................................................................................48
4-6 Fraction of power (η) at different frequencies in our surface structure ..............49
4-7 Amplitude absorption due to the dielectric layer................................................50
4-8 Amplitude absorption due to metal αm/2 using analytical method .....................52
4-9 Metal amplitude absorption calculated using approximation method ................53
4-10 Zoomed drawing of the PPWG-Surface wave junction ...................................55
4-11 Electric field functions of the two coupling modes ..........................................55
4-12 The calculated amplitude coupling coefficient of PPWG – SWG junction .....56
4-13 Schematic of the wave propagation at the slit ..................................................57
4-14 Electric field function of the two coupling modes at the slit ............................58
4-15 The calculated amplitude coupling coefficient of the slit .................................59
4-16 The theoretical output spectrum and experimental output spectrum ................60
4-17 The comparison of the time domain curves between experiment and theory ..61
1
Chapter 1 Introduction
1.1 Introduction of surface wave study
Surface waves, which are also called surface plasma polaritons or surface plasmons, are
the propagation modes of an electromagnetic wave which is bounded to the interface
between two mediums. Different terms are used for emphasis on either the quantum or
wave nature. In this study, because in the THz range the wave property is the main aspect
of interest, surface waves will be the most appropriate terminology. The surface wave
propagates along the interface while in the normal direction it has exponential decay on
both sides of the interface (evanescent waves). To satisfy this condition, the dielectric
constant of one of the mediums must be negative. Therefore, the surface wave is mostly
studied on the surface of metal or doped semiconductors. As a solution of Maxwell’s
equations on the medium boundary, the form and the evanescent properties of the surface
wave has a great dependency upon the surface morphology and the ambient dielectric
distribution [2].
The earliest study of surface waves can be traced back to 100 years ago [3]. Since
Sommerfeld and Zenneck [4] did the groundbreaking work on studying surface waves on
a cylindrical surface and flat surface, theoretical models have been successfully built to
2
understand surface waves since the early 20th century. However, because of the limited
availability of experimental techniques in the early days, the experimental study
developed slowly. Especially the fundamental studies which mainly includes source,
coupling configuration, propagation property, de-coupling configuration and detection
are technically difficult in practice.
Technology advances in other fields promoted the research of the surface wave in some
aspects. The surface wave was first studied in radio frequency range [5, 6]. In the 1960s,
after the invention of laser, which provided a new type of light wave source, people
started to study the surface plasmon in the optical range. The development of
semiconductor devices provided sensors for the detection. The coupling, de-coupling and
propagation of the surface wave were the first missions for surface wave researchers. To
couple a freely propagating wave into the surface wave, aperture launching was used first
[6]. In 1968, Otto proposed the prism coupling/decoupling method based on frustrated
total internal reflection [7]. Raether discussed the feasibility of utilizing the surface
roughness for the coupling and decoupling [8]. A lot of progress was made as technology
further advanced. Especially in recent years, thanks to the major development in
microchip fabrication and near-field techniques, researchers are able to study
experimentally and to manipulate the propagation characteristics of surface waves.
People have used bent, thin film coatings, periodic structures and corrugated surfaces to
control the coupling, propagating and decoupling process of surface waves [9-11].
Numerous investigations have been carried out on the development of new optoelectronic
devices, based on the evanescent property of surface waves. The potential applications
3
include bio-material analysis and spectroscopy, near-field microscopy, high density
optical data storage and optical displays.
The propagation of surface waves was also extensively studied in theory; however, the
experiments are difficult to realize because the direct measurement of the bounded
(evanescent) field is difficult in practice. Surface waves have great dependency to the
dielectric constants of the metal and the dielectric on the metal surface. From optical to
the far infrared and THz range, the frequency dependent metal dielectric constant εm =
εm’ + i εm” undergoes drastic change (see appendix II). The difference in metal
conductivity and the consequent metal dielectric constant results in the significant
changes of the surface waves in different frequency ranges.
In optical and near infrared range, according to Drude’s theory, metal conductivity has
small real part and big imaginary part which makes the metal a lossy medium. As a
result, surface waves have small spatial evanescent extension in the air δair and in the
metal δmetal (the distance where the field drops to 1/e of the surface) and short propagation
length Li (the length at which the intensity drops to 1/e), relative to its wavelength as
shown in comparison table below. Therefore, once an optical wave is coupled into the
surface wave, the energy is confined to vicinity of the surface with a relatively short
propagation length. The tightly bound surface wave field in the optical frequency range is
difficult to detect directly. Therefore, the traditional way of studying surface wave in
optical range is first to couple the wave into free space and detect from far field, and then
to use theoretical method to retrieve or reconstruct the field on surface. For the direct
4
measurement of the field, the near-field scanning optical microscope could be a
promising technique for the detection of surface fields [12].
On the other hand, in the microwave and THz range, the real part of metal conductivity is
very high and is equal to its handbook dc value for aluminum, σr = 4 × 107 S/m (the
corresponding conductivity at optical frequencies at λ = 800 nm, σr = 1.2 ×105 S/m). The
real part of metal dielectric constant is a negative constant, while the much larger
imaginary part is proportional to the wavelength.
The spatial extensions δair and δmetal of the evanescent field and the propagation length Li
of the surface wave increase when the conductivity increases. Therefore in THz range,
because metals have high conductivity and behave close to ideal lossless conductor, large
spatial extension and propagation lengths are expected as shown in the table below. The
0.5 THz (λ=600) 1 THz (λ=300 μm) 375 THz (λ=800 nm)
δair δmetal Li δair δmetal Li δair δmetal Li
Al 160 mm 111 nm 137 m 56 mm 78 nm 34 m 1.27 μm
12.6
nm
235 μm
Ag 189 mm 87 nm 210 m 63 mm 59 nm 53 m 0.68 μm
23
nm
267 μm
Au 158 mm 107 nm 141 m 54 mm 74 nm 35 m 0.61 μm
25
nm
117 μm
Table 1-1. Evanescent Field Extent
5
field extends into the air many hundreds of wavelengths. The low loss also enables the
surface wave to propagate for tens of meters.
However, as the conductivity increases, the surface field extends so far into free space
that the surface of the conductor has little confinement to the mode of surface wave. In
fact, as it had been pointed out by many early researchers, in THz and the equivalent far
infrared, the surface wave is difficult to build up on surface because it is so loosely bound
to the surface, that coupling and decoupling occurs simultaneously along the long
propagation length [13]. A solution to this problem is to cover the surface of the
conductor with a thin layer of dielectric or to corrugate the surface such as using gratings.
With the enhanced confinement introduced by these structures, the surface
electromagnetic wave can be established. In 1950, Goubau [14] and Attwood [15]
predicted the surface wave confinement in dielectric coated cylindrical wire and plane
surface of perfect conductor, respectively. According to Attwood’s analysis of the coated
perfect conductor, the field has a trigonometric form inside the film and an exponential
form outside in the vacuum. In 1953, Barlow and Cullen did an excellent overview of the
surface wave studies in the early half of 20th century [5, 6]. In their works, surface waves
at radio frequencies are discussed in detail.
The effect of coating dielectric films and gratings were further studied. In optical range,
Schlesinger et al experimentally studied the far infrared surface plasmon propagation at
119 μm on germanium coated gold and lead surface [16]. In 1982, Stegeman analyzed
Schlesinger’s experiment in theory by assigning the substrate metal a finite value of
6
dielectric constant [17]. More detailed and generalized theoretical study of absorbing
layers in microwave range have been carried out [18-22]. The grating and corrugation in
microwave and infrared were also studied [23, 24].
THz surface wave (TSW) study was only started in recent years. Researchers applied
techniques in both microwaves and optics to study surface waves. Both the THz
Sommerfeld and Zenneck waves have been studied experimentally [25, 26]. THz surface
propagation using lens coupling has been achieved [27]. Extraordinary THz transmission
through subwavelength hole arrays has been observed and theoretically explained [28,
29]. The coupling and confinement of TSW using gratings and periodic surface structure
have been extensively studied, exciting results were obtained [10, 30-33].
1.2 Purpose of this study
Success on the studies of THz surface wave (TSW) has shown a promising future for
THz plasmonic devices. The observed enhanced transmission and other effects are in fact
due to the interaction between the TSW and the subwavelength metallic structures.
Therefore, it is important to be able to physically picture the actual surface wave field
pattern on the metal surface and how it could be manipulated. However, the experimental
technique to study this fundamental property hasn’t yet been available. The
characteristics such as absorption and dispersion of surface plasmons in the dielectric
coating layer on metal surface have been only studied in theory [34].
7
The THz wavelength has unique advantages in surface wave studies. First, the
conductivities of many metals are large enough in the THz range so that they can be
considered as perfect conductors. Consequently, many simplifying approximations can be
made without losing accuracy. Second, the wavelength in THz range is short enough so
that most quasi-optical devices (such as mirrors, lenses, fibers…) are available with
reasonable dimensions for manipulating and guiding of THz beams. Moreover, despite
the “loosely bound” property of the THz surface wave due to the high metal conductivity,
because of the short wavelength, the spatial extension of THz surface wave is not more
than a few centimeters. Thus, a complete picture of the surface wave field decay is much
easier to measure compared to microwave range. Third, Grischkowsky’s THz antenna
receiver makes it possible to measure the broad band THz surface wave field in a quasi-near
field scale (λ/12).
In this study, the experimental technique has been successfully developed and
demonstrated. The surface wave is experimentally studied on a smooth (but not polished)
metal surface and a dielectric coated metal surface. For both cases, the complete
transverse field profile and the propagation parameters such as absorption and dispersion
are measured. The effect of field confinement induced by the dielectric coating is
demonstrated. The results are favorably compared to the theoretical predictions.
1.3 Scope of this report
In this report, we present our experimental and theoretical studies of the surface waves on
both bare and dielectric coated plane metal surfaces.
8
In Chapter 2, the experimental setup is introduced. The standard THz-TDS system was
modified to directly measure the electrical field distribution near the surface with high
spatial (25 μm/step) and temporal resolution.
In Chapter 3, the measured time domain signals on bare and dielectric coated metal
surface are presented. The results are discussed together with the diffraction effect in the
system. Fourier transforms of the time domain signals are performed to view the surface
wave field in the frequency domain. The quasi-near field measurements are successfully
performed. The observed exponential transverse field decay is in good agreement with
the theoretical predictions.
Chapter 4 is focused on theoretical study. For the bare metal surface, the 1/e surface wave
extension distance, also called skin-depth, is derived. For the coated sample, instead of
using the general electromagnetic wave equation method to analyze the structure [22], we
took advantage of the feature of the high THz metal conductivity, by assuming the metal
to be perfect conductor. The problem is then simplified and easy to solve using a well-established
model, which maintained high precision. The accuracy of the assumption was
verified by comparing our results to the non-simplified solution from literature. The
dispersion and absorption of the film coating structure are also calculated. The overlap
integral method is used for the evaluation of the system coupling. The coupling
coefficients, as well as other system parameters, which are responsible for the reshaping
of the surface wave pulse, are also calculated and estimated.
9
In the second part of chapter 4, the theoretical predictions are verified by the
experimental results. The observed surface wave field shows the exponential fall-off
feature in good agreement with the theory. The input THz reference pulse is used as the
input for the numerical simulation of the surface wave propagation process. The
calculated output surface wave pulse shows excellent agreement with the experimental
measurement.
Chapter 5 and 6 will review the work presented here and draw conclusions about what
has been learned. Future work will also be discussed.
10
Chapter 2 Experimental Setup
The schematic of the experimental setup is shown as the fig. 2-1 below, which shows the
complete lay-out of the modified THz-TDS system. Femtosecond laser pulses generated
by Ti:Sapphire laser are split into two arms: one goes to the transmitter as the pump pulse
Computer
controlled
retroreflector
delay line
Beam splitter
THz receiver
Laser pulse from
Ti: sapphire
M1
Laser beam goes to transmitter
Probing laser beam goes
to receiver
-- Mirrors, Lens
Legends
-- Silicon lens
M2
(2)
y
y/2
Laser Sampling Beam
(LSB)
Al sheet block
PPWG
(1)
Laser excitation Beam
(LEB)
L3
L2
L1
THz transmitter
Figure 2-1. 2D schematic of the system setup
11
and the other goes to the receiver as the probe pulse. At the transmitter side, when the
laser pulses are focused onto the transmitter chip, the THz pulses are generated by the
transmitter with E field vertically polarized. The generated picosecond THz pulses pass
through three silicon lenses L1, L2 and L3 and are focused into the entrance slit of the
parallel plate waveguide (PPWG). The plano-cylindrical lens L3 produces a line focus on
the input air gap between the two Al plates of the PPWG, thereby coupling the THz
pulses into the waveguide. The PPWG is the starting part of the surface wave apparatus,
which is shown in the dashed box 1.
Fig. 2-2 shows the detail of the surface wave apparatus. The THz surface wave (TSW)
propagates on a 24-cm-long by 10-cm-wide by 100-μm-thick sample Al sheet with a bare
or dielectric-coated surface. As shown in the upper right in fig. 2-2. An extension of the
M
y
z
x
23
Al blocking plate
3.5 cm cover Al sheet
Sample Al sheet
Cross-section
Top view
spacer
1.2 mm
Sample Al sheet – Top view
Figure 2-2. 3D schematic of the surface wave apparatus
12
Al sheet is placed into the PPWG on top of the lower plate of the PPWG to couple the
THz wave onto the Al sheet. On top of the sample Al sheet, there is another piece of 3.5
cm long Al sheet with 100 μm separation from the bottom sheet to form the actual
parallel plate structure. The TSW launching part is the aperture outside the left of the
PPWG, the two waveguide sheets make a 1.2 mm slowly opening flare aperture structure
to realize the excitation of the surface wave. This launching configuration is similar to the
earlier Zenneck wave setup [26], however, the newly added 3.5 cm long flexible cover
sheet forms an adiabatic flare opening, which provides better bandwidth coupling
efficiency [35].
It has been theoretically proven that no surface wave launcher can provide a 100%
conversion of the incident power into surface wave power [6]. Therefore, along with the
surface wave, there is always a freely propagating THz wave coming out from the flare.
To eliminate the effect of this part in the received signals, a 3.5 mm-deep adiabatic curve
is intentionally made to the Al sheet in order to create a different propagation path for the
two parts of waves. Then a 10 cm wide Al plate is vertically placed in front of the curve
with 3 mm opening below the edge of the plate at the downstream of the curved surface.
The distance from the blocking plate to the end tip of the Al sheet is 8 cm. However, it is
impossible to completely block the freely propagating wave because diffraction occurs
when the freely propagating wave is passing through the slit. More detailed discussion
will be in Chapter 3.
13
The receiver is located at the end of the sheet to detect the linearly polarized TSW field
that is perpendicular to the sheet surface, as shown in the fig. 2-3. The receiver is
fabricated on a double side polished silicon-on-sapphire (SOS) wafer so that the laser
sampling beam can penetrate the sapphire substrate and irradiate the semiconductor
between the antennas. To enable the direct measurement of the electrical field, the
receiver is modified from the standard THz-TDS system. There is no silicon lens attached
to the receiver chip and no second identical large convex silicon lens in front of the
receiver to focus the incoming THz wave from the L2. Thus the mirror symmetry of the
system, which is a required condition for 100% energy transfer, is compromised. Without
the silicon lens in between, the metal antenna side is closely placed to the edge of the
sheet (distance less than 30 μm) to allow a direct detection of the THz electrical field. As
shown in dashed box 2 in fig. 2-1, a periscope configuration is used to enable the vertical
movement of the receiver. The receiver and two optics (M2 and optical lens) are mounted
on a breadboard so that they can move vertically to measure the TSW field at different
heights relative to the surface. The movement of the breadboard is controlled by a
micrometer knob whose minimum measurable distance is 1/1000 inch (≈ 25.4 μm).
14
Two samples are prepared for the study. They are made of two identically sized (24
cm×10 cm×100 μm) Al sheets. For sample 1 the Al sheet is directly used with its original
bare surface; for sample 2 the Al sheet surface is coated with 12.5 μm polyethylene film.
The refractive index of the film is assumed to be constant n = 1.5 in the frequency range
of interest.
Similar to the standard THz-TDS system, on the receiver side, there is an optical delay
line made up of a computer controlled motorized retroreflector. The movement of the
retroreflector can change the laser path length at the receiver side and consequently
change the timing of the photo-conductive switched receiver. The experiments were
performed in this way: first, the receiver is moved to a pre-selected position. Then, the
system starts to take data by controlling the delay line to scan through a long enough
distance (8 mm ~ 10 mm). Scans are repeated as the receiver is moved to different
positions.
Breadboard
mount
M1
M2
L1
SOS receiver
Si side
Figure 2-3. The optical part of the receiver
15
During the experiment, the receiver changes its position upward or downward as shown
in fig. 2-1. The movement of the receiver mount will change the distance between two
mirrors (M1 and M2) and consequently change the optical path length of the receiver side
as well. For example, if the receiver is moved upward, the distance between M1 and M2
will become smaller. Then the total optical path length on the receiver side will be
smaller. This will make the probe laser pulse arrive the receiver earlier. However, the
arrival time of the THz surface wave pulse remain unchanged. Therefore, the motorized
delay line needs to scan further to compensate the shortened optical path and
consequently the detected signal pulse appears later in time, compared with before
moving the receiver upward. Therefore, when studying the arrival timing of the received
surface wave signal, the path length change induced by the movement of receiver should
to be considered and compensated.
Scanning range and step sizes
The system allows the maximum receiver scanning from 3 mm below the surface to 22
mm above the surface. But the scanning range for most experiments and being compared
as a common range is from 1.65 mm below surface to 1.14 mm above surface, which is
called a complete set of data. Small step sizes (25 μm and 50 μm) were used in the range
of -0.5 mm to +0.5 mm from surface, and bigger step sizes (125 μm and 250 μm) were
used for the other positions.
16
Chapter 3 Experimental Results and Discussions
3.1 Individual Signal
The reference THz pulse in fig. 3-1 is taken with the surface wave apparatus out of the
system. The optical arrangement for the reference pulse is shown in fig. 2-1 and the
schematic diagram in fig. 3-1.
0 5 10 15 20 25 30 35
-30
-20
-10
0
10
20
30
40
50
Average Current (pA)
The focal length of the large convex silicon lens L2 is 15 cm and the receiver is located
about 40 cm left to the L2. The lens L2 collects the collimated THz beam from the
Receiver Si lens L2 Transmitter
Free space (reference)
0 0.5 1 1.5
0
50
100
150
200
250
(THz)
Amplitude (a. u.)
Figure 3-1 Reference signal
17
transmitter located at the right focal plane of L2. L2 focuses the THz beam into a
frequency dependent spot at the left focal plane with beam radius proportional to the
wavelength. For example, the spot size for 0.5 THz is approximately 20 mm diameter and
spot size for 1 THz is around 9 mm. Then, the THz beam continues propagating freely 25
cm illuminating the receiver with a much bigger frequency dependent THz beam spot, for
example, 25 mm for 0.5 THz and 16 mm for 1 THz. As shown in fig. 3-1, both the
bandwidth and amplitude are smaller than those obtained with the standard THz-TDS
systems [36].
3.1-1 Signals on bare metal surface
As introduced in Chapter 2, sample 1 is a 24 cm long, 10 cm wide and 100 μm thick, bare
aluminum sheet; sample 2 is a sheet of the same dimensions, but with a 12.5 μm
polyethylene film coating. The measurements of samples can be carried out by taking
multiple scans with different vertical positions of the receiver from below to above the
surface. Fig. 3-2 (a), (b) and Fig. 3-4 are the THz surface wave signals of sample 1 and 2
taken at the level of surface. The corresponding amplitude spectra are plotted in the inset.
Fig. 3-2 (a) is taken on sample 1, the bare surface without the blocking plate. From the
structure of the coupling mechanism, it is obvious that the received signal is a mixture of
the surface guided wave and the unguided freely propagating wave because the system
structure allows the collinear propagation of both waves. The coupled and uncoupled
THz waves come out together from the flare opening of the PPWG. The surface wave
18
coupling occurs during its entire propagation, and the coupled surface wave propagates
along the adiabatically curved surface. The freely propagating wave comes out from the
1.2 mm flare opening of the PPWG and radiates into free space the surface as a diffracted
wave which keeps spreading as it propagates.
0 5 10 15 20 25 30 35 40
-10
-5
0
5
10
15
20
Average Current (pA)
0 5 10 15 20 25 30 35 40
-6
-4
-2
0
2
4
6
8
10
Average Current (pA)
With the blocking plate with a 3 mm opening perpendicular the surface, as the case of fig.
3-2 (b), the signal amplitude is greatly reduced. This is believed due to blocking the
(b)
(a)
Bare surface with block
Bare surface without block
Transmitter
Receiver
Si lens
Receiver Si lens Transmitter
0 0.5 1 1.5
0
5
10
15
20
25
30
35
(THz)
Amplitude (a. u.)
0 0.5 1 1.5
0
10
20
30
40
50
60
70
80
90
(THz)
Amplitude (a. u.)
Figure 3-2. (a) Surface wave pulse on bare metal surface, no block (b) Surface
wave pulse on bare metal surface with block.
19
majority of the diffracted wave from the flare. However, the reduced signal arrives at the
same time as the unblocked one. This indicates that the received signal still contains
wave that comes along the path of the freely propagating waves. This shows that the
unguided free space waves again “find” their way to overcome the obstacles under the
help of diffraction and propagate to the receiver. The surface wave in the signal, although
is weak, can also be identified and will be shown in the later data processing.
On the bare metal surface, diffraction has a significant contribution to the signal. So it is
necessary to assess diffraction from the waveguide flare and the slit of the blocking plate
in more detail. To simplify the problem, the metal sheet is assumed to be a straight plane
with no curvature. When there is no blocking plate, the only diffraction is from the 1.2
mm wide flare opening of the waveguide, equivalent to single slit diffraction with a
conducting sheet extending in the propagation direction from one edge of the slit. The
diffracted wave from the flare opening propagates 20 cm to the receiver without
disturbance. Because of the Al sheet’s mirror effect, the equivalent diffraction slit width
should be doubled to 2.4 mm, and the Al sheet is the centered symmetric plane. Here, the
Fresnel number F = a2/(Lλ), where a is 1.2 mm, the half width of the slit, L = 200 mm is
the propagation distance and λ is the wavelength. At λ = 600 μm, corresponding to 0.5
THz, F = 0.012 <<1, so it can be considered to be far field diffraction. The far-field half-space
amplitude diffraction pattern of a single slit is described as a (sinθ)/θ function with
the central maxima at the metal surface. Assuming the central peak signal amplitude
taken without blocking plate to be 1, the area defined by the intensity diffraction pattern
stands for the total power from the 1.2 mm slit.
20
0 10 20 30 40 50 60 70 80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
mm
Intensity
(2) no block, at 12 cm
(1) no block, at 20 cm
(3) 8 cm behind the
block (3 mm slit)
3 mm slit
In fig. 3-3, curve 1 shows the power diffraction pattern from the flare opening at the
receiver plane. When the blocking plate is inserted at 8 cm from the receiver,
corresponding to 12 cm from the flare opening, the free space waves diffract 12 cm from
the flare opening and arrive at plane of the 3 mm slit between the plate and metal sheet.
The slit truncates the diffraction pattern to 3 mm; the transmitted wave from the 3 mm
aperture diffracts again as it propagates to the receiver. Curve 2 in fig. 3-3 shows the
diffraction pattern at the blocking plate — it contains the same amount of power as curve
1. Then the transmitted power through the 3 mm slit (the shadowed area) is diffracted to
the receiver 8 cm downstream shown as curve 3, whose area is equal to the shadowed
area. Therefore, according to the calculation conserving the total power, when inserting
Figure 3-3. The intensity diffraction pattern for 0.5 THz, λ = 600 μm: (1). The
1.2 mm flare opening without block, (2) the 1.2 mm flare opening at the
blocking plate, (3) the 3 mm slit of the blocking plate
21
the blocking plate, the peak amplitude at the receiver should change to 1.25 of the
unblocked signal.
In the actual experimental setup, more processes occur besides the diffraction. The
surface wave coupling and decoupling occurs along the entire sample surface. The
adiabatic curve of the sheet interferes with the free space diffraction. The blocking plate
introduces not only the diffraction but also the decoupling of the surface wave. As a
result, the experimental data in fig. 3-2 clearly show that the received signal has much
more reduction when the blocking plate is inserted in the system, than predicted in the
simple calculation above.
The surface wave launching/coupling efficiency is determined by the overlap integral of
the excitation field (the diffracted wave field) and the surface wave field [6]. A well-known
fact is that THz surface wave (TSW) is weakly coupled to the bare metal surface
due to the high metal conductivity, resulting in the TSW exponential fall-off field
extending transversely from a few tens to hundreds of millimeters above the metal
surface, as shown in Table 1-1. Therefore at the 1.2 mm flare opening of the PPWG, the
coupling to surface wave is very low because of the small overlap integral of the two
field patterns. As the propagation distance increases, the diffracted (sinθ)/θ pattern
expands whereas the exponential surface wave field pattern remains the same, because it
is the single mode solution determined by the constant metal conductivity. The coupling
of the two fields increases at first as the diffracted wave field is expanding closer to the
extent of the TSW field giving a larger overlap integral. The diffraction field pattern
22
keeps expanding and becomes much larger than the TSW field pattern, then the coupling
decreases as the two fields are becoming less overlapping. Fig. 3-4 below shows the
overlap integral at different distances for 0.5 THz. From the figure, 175 cm gives the
optimal coupling.
0 5 10 15 20 25 30 35 40 45 50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Diffraction distance (m)
Overlap integral
1.75 m
Fig. 3-5 below shows the transverse intensity and field profile at a few selected distances.
For λ = 600 μm on an aluminum surface, the TSW field pattern is constant and is shown
as the dotted line, with 1/e amplitude value of 160 mm. The diffraction patterns at 80 cm,
175 cm and 500 cm and 5000 cm from the flare opening are plotted as solid lines. At 80
cm, the two fields are normalized for comparison. At 175 cm, the overlap integral
between the free space diffraction and the surface wave has the maximum value of 0.825,
as the two patterns have their most overlapping shapes. Furthermore, for a propagation
distance of 500 cm and finally at 50 m, the spatial extension of the two waves have
Figure 3-4. Overlap integral of the surface wave field pattern and the diffraction
pattern at different distances
23
become so different that they are considered to be well separated and no longer coupled.
Therefore, in the measurement on sample 1 with only 20 cm propagation distance, the
signal actually contains only a small portion of surface wave while the majority remains
0 100 200 300 400 500 600
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
Intensity
Diffraction 80 cm
TSW profile
Diffraction 175 cm
Diffraction 500 cm
Diffraction 50 m
0 100 200 300 400 500 600
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
mm
Normalized field
TSW profile
Diffraction 175 cm
Diffraction 500 cm
Diffraction 80 cm
Diffraction 50 m
Figure 3-5. Overlapping of the surface wave field pattern (dashed line) and
the diffraction pattern (solid line). (a) Intensity. (b) Amplitude.
(a)
(b)
24
as the uncoupled freely propagating wave. The TSW is predicted to propagate 137 m
before the intensity drops by 1/e. For this distance the 1/e extent of the diffracted wave
amplitude is 2800 cm, compared to the unchanging extent of the TSW with a 1/e
amplitude extent of 16 cm. In summary, an optimum long (>1000λ) distance is a desired
condition for the best coupling of surface waves, however it is impossible to obtain a pure
surface wave signal since there is no 100% overlap integral throughout the entire surface.
An important point is that the two waves propagate with the same phase velocity to 1 part
in 108. Consequently, for λ = 600 μm, the coherence length for energy exchange between
the two waves is the stunning value of 108λ = 60 km, which raises the question as to
whether or not these waves can ever be completely decoupled.
More loss is introduced with the blocking plate in the system. The large spatial extension
of the THz surface wave results in a large portion of the wave energy getting truncated by
the blocking plate. Moreover, the 3 mm slit opening of below the blocking plate is
simultaneously an aperture decoupler which couples the surface wave back into the free
space.
Although there is predicted radiation loss of the surface wave at the surface bending [11],
it believed to be an insignificant loss factor in this experiment because not much energy
is actually coupled into the surface wave. However, the surface bending is responsible for
the signal reduction because it creates an indirect path for the diffracted wave from the
PPWG flare opening so that even less energy finally gets its way through the slit.
Therefore, the measured surface wave after the blocking plate is lower in amplitude.
25
3.1-2 Signals on dielectric coated surface
In the measurement of sample 2, as shown below in fig. 3-6, the presence of the dielectric
coating greatly compresses the spatial extension of surface wave and consequently
greatly improves the surface wave coupling. Therefore, the signal is much stronger. The
dielectric coating confines the surface wave field to within only a few wavelengths from
the surface so that the wave can pass through the slit and arrive at the receiver. The signal
of sample 2 also shows that the pulse has been stretched to 25 ps long with a positive
chirping feature, where high frequencies arrive latter in time. This is also evidence that
the dielectric film is guiding the wave with dispersion. The relative smooth spectrum of
the signal shows no sharp low-frequency cut-off or any unusual oscillations, indicating
single TM0 mode propagation in the dielectric with zero cutoff frequency.
Compared with the reference spectrum, the amplitude spectrum of frequency from 0.5 ~
0.7 THz of film-coated surface wave is higher than the reference. The first reason is that
the free space signal has low transfer efficiency as mentioned at the beginning of this
chapter. However, the surface wave apparatus has a confocal Si lenses arrangement
which provides better coupling from the free space into the waveguide system. The
second reason is the surface waves on the dielectric coated surface propagate in more
tightly guided mode so that more energy is preserved during the propagation.
26
0 5 10 15 20 25 30 35 40
-20
-10
0
10
20
30
40
50
Delay (ps)
Average Current (pA)
On the coated surface, diffraction is no longer the dominant effect in the received signals
compared to the case of bare metal surface. The comparison is made in the fig. 3-7, the
top curve (a) is the signal taken without block, and the middle curve (b) is taken with the
blocking plate. It shows when the blocking plate is inserted, no major change happens to
the signal as it does on the bare metal surface. This indicates that with the improved
coupling due to the dielectric film, more energy is being carried by the surface wave
mode and propagates closely along the surface, whereby the blocking plate can have very
limited influence. The unguided freely propagating part of the wave that can be blocked
or diffracted can be obtained by subtraction of the curve in (b) from the curve in (a). As
shown in (c), the freely propagating wave is the small leading part of the signal which
propagated along the shorter straight line path.
Figure 3-6 THz surface wave pulse on dielectric coated surface with block
Dielectric coated surface
with block
Receiver
Si lens Transmitter
0 0.5 1 1.5
0
50
100
150
200
250
300
THz
Amplitude (a. u.)
surface wave
reference
27
0 5 10 15 20 25 30 35 40
-20
-10
0
10
20
30
40
Average Current (pA)
0 5 10 15 20 25 30 35 40
-20
-10
0
10
20
30
40
Average Current (pA)
0 5 10 15 20 25 30 35 40
-10
0
10
Delay (ps)
Average Current (pA)
Receiver
Si lens Transmitter
Receiver
Si lens Transmitter
Dielectric coated surface
without block
Dielectric coated surface
with block
(a)
(b)
(c)
0 0.5 1 1.5
0
50
100
150
200
250
300
350
400
THz
Amplitude (a. u.)
0 0.5 1 1.5
0
50
100
150
200
250
300
350
400
THz
Amplitude (a. u.)
Figure 3-7. TSW pulse on coated surface without block. (b) TSW pulse on coated
surface with block (c) The freely propagating wave given by subtraction of TSW
pulse (b) from TSW pulse (a). Inserts show corresponding spectra
The freely propagating wave
28
3.2 Signals taken above surface
Signals at different heights above the surface are measured by moving the receiver. As
introduced in the fig. 2-1, the time delay effect of the movement of the receiver has to be
compensated to indicate the actual arrival time of each signal before presenting the THz
signals in time domain. For example, in the fig. 3-8 (a), the lower curve was taken at the
surface and the upper curve was taken 0.60 mm above the surface. From the figure it can
be seen that there is an apparent time delay between the two signals. As shown in fig. 2-1,
when the receiver is moved upward by 0.60 mm, then the distance between M1 and M2
becomes shorter by 0.60 mm, and therefore the optical sampling pulse will arrive the
receiver 0.60 mm/c = 2.00 ps earlier. However, the arrival timing of the THz pulse signal
remains the same. Therefore in order to measure the signal, the sampling pulse will need
to “wait” 2.00 ps longer to be synchronized with the surface measurement and so the time
delay is created. Therefore, in order to compensate for this time delay, the signal above
the surface needs to be moved to 2.00 ps earlier in time (to the left) relative to the signal
on the surface, as shown in fig. 3-8 (b).
The fig. 3-8 (b) shows that after removing the effect of position change of the receiver,
the peaks in the surface wave pulse at 0.6 mm above the surface are aligned precisely
with the corresponding ones in the pulse on the surface except for their smaller
amplitudes. This indicates that the signal above the surface actually arrives at the same
time as the one on the surface which is expected according to the plane wave mode
profile, because the entire wavefront propagates with the same velocity.
29
0 5 10 15 20 25 30 35 40
-20
-10
0
10
20
30
40
Delay (ps)
Average Current (pA)
600 micron above surface
at surface
0 5 10 15 20 25 30 35 40
-20
-10
0
10
20
30
40
Delay (ps)
Average Current (pA)
at surface
600 micron above surface
As the receiver moves above the surface, the signal amplitudes of both sample 1 and
sample 2 decrease. The dielectric film covered sample 2 exhibits stronger confinement of
Figure 3-8. THz surface wave pulses measured at the surface and at 0.6 mm
above surface (a) before compensating the time delay caused by receiver
movement. (b) after compensation
(a)
(b)
30
the surface wave than the bare surface and hence results in a faster fall-off of the surface
wave field. Fig. 3-9 shows the comparison of signals measured at the surface and above
0 5 10 15 20 25 30 35 40
-4
-2
0
2
4
6
8
10
12
Delay (ps)
Average Current (pA)
3.4 mm above surface
at surface
0 5 10 15 20 25 30 35 40
-20
-15
-10
-5
0
5
10
15
20
25
30
35
Delay (ps)
Average Current (pS)
3 mm above surface
at surface
Figure 3-9. Comparison of signals measured at the surface and above surface (a)
bare surface – sample 1 with block. (b) dielectric coated surface – sample 2 with
block
(a)
(b)
31
the surface. In fig. 3-9 (a), for the bare surface - sample 1, the upper curve is measured at
3.4 mm above the surface, the amplitude drops 50% of the lower curve at the surface,.
For sample 2, shown in fig. 3-9 (b), when the Al surface is coated with a 12.5 μm
dielectric (n = 1.5), the field extension of the surface wave is greatly compressed. At 3
mm above the dielectric-coated surface, the amplitude drops to 20% of the surface signal.
As the receiver keeps moving, more signals are taken, a clear trend of TSW field fall-off
is observed. In below fig. 3-10, the time domain signals are plotted according to their
corresponding receiver positions. It clearly shows a snapshot of the entire surface wave,
and gives the field fall-off profile above the surface. Because all the time shifts have been
compensated, in fig. 3-10, the displayed relative positions of the waveforms in time
0
1
2
3 10 20 30 40 50 60
-15
-10
-5
0
5
10
15
ps
mm
Figure 3-10. The time domain surface waveforms above dielectric-coated
surface with block.
32
reflect their actual arrival timing. This again shows that the THz surface waves at
different height above the surface hit the receiver at the same time. It is also worth
noticing that in the fig. 3-10, the long ringing tail of high frequency components fade
away, as the wave extends higher into the space. The frequency dependency of the
fringing field fall-off is again a nature of the guided surface wave, which is better
presented in frequency domain.
Fourier Transforms are performed on all the above time domain signals so that the
amplitude spectra of the signals taken at different receiver positions are obtained. By
putting the spectra together in the order of their corresponding receiver positions, the
amplitude fall off of the surface wave can be compared in frequency domain. Fig. 3-11
shows the spectra from surface to 6 mm above the bare metal surface without blocking
plate.
-2
0
2
4
6
0.2
0.4
0.6
0.8
1
1.2
0
10
20
30
40
50
60
70
80
90
mm
THz
Figure 3-11. Amplitude fall-off viewed in frequency domain
mm
THz
33
Therefore, for each individual frequency, by picking out the amplitude points at all
positions from the spectra in fig. 3-11, a spatial amplitude fall-off distribution can be
obtained, as shown in fig. 3-12
0
1
2
3
4
5
0.4
0.6
0.8
1
1.2
0
10
20
30
40
50
60
70
80
90
mm
0
1
2
3
4
5
0.4
0.6
0.8
1
1.2
0
5
10
15
20
25
30
35
40
mm
THz
Because the amplitude has its maximum value at the surface, all the amplitudes are
usually normalized to the amplitude at the surface to show a clearer comparison. The
normalized amplitude fall-off curves for each individual frequency from 0.2 to 1.2 THz
are plotted fig. 3-13 (a) for bare metal without block, (b) for bare metal with block. Fig.
3-13 (a) and (b) show the experimental results of the frequency dependent field
distribution on the bare metal surface without and with blocking plate, respectively. Both
of the two situations show that the detected surface wave field has maximum strength at
the surface, and then the field decreases with the increase of the distance from the
surface. The field strength increases when the distance is greater than certain value,
Figure 3-12. unnormallized frequency dependent field fall off curves: a- bare
metal surface without block, b- bare metal surface with block
a b
THz mm THz mm
34
0
1
2
3
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
0
1
2
3
4
5
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
however for some lower frequencies the increase happens outside of the margin of the
figure for it takes longer distance. Both the decrease and increase are frequency
dependent. The field distribution with the blocking plate has poor signal to noise ratio
which causes the trend less obvious.
As discussed earlier, both surface wave coupling and free space diffraction occur to the
bare metal surface case. Therefore, the theoretical field distributions of these two effects
are worked out and plotted. Fig. 3-14 (a) is the surface wave field fall-off on aluminum
surface. High metal conductivity in THz results in loosely bound surface wave field,
therefore the fields are hanging far away above the surface and show a slow fall-off
curve. Fig. 3-14 (c) is the far field diffraction pattern of the waveguide flare opening
which corresponds to the unblocked case. After diffracting 20 cm away from the flare
opening, the diffraction pattern is widely spread across the vertical plane and also results
Figure 3-13. Experimental surface wave fall-off (a) bare surface without
block. (b) bare surface with block
THz mm THz mm
(a) (b)
35
in almost flat field distribution within 4 mm from the surface. Fig. 3-14 (d) is the
diffraction pattern of the 3 mm slit of the blocking plate which corresponds to the case
with block, short distance and wider slit width results in narrower first order diffraction
peaks, especially at frequency higher than 1 THz, the second order diffraction peaks even
show up.
The bare metal surface case is a combination of weakly bound surface wave and strong
free space diffraction, therefore both features of surface wave and diffraction can be
found in the experimental field patterns. In the case of bare surface without blocking
plate as shown in fig. 3-13 (a), the field decrease from the surface maximum shows that
there is coupled surface wave existing in the signal. The field increase at some distance
from surface is believed to be due to the diffraction. Also, because the wave has long
propagation length on the surface, the diffracted wave expands closer to the surface wave
pattern, which is, the surface wave field pattern fig 3-14 (a) has similar distribution as the
far field diffraction of the flare opening fig. 3-14 (c). Therefore, the condition does allow
a better surface wave launching which is confirmed in the fig. 3-13 (a). Due to the same
reason, when blocking plate is inserted, the launching condition is worsen and results in
lower signal amplitude. The field pattern before normalization below clearly shows the
change.
Comparing with the theoretical fall-off curve of bare Al surface of fig.3-14 (a), the actual
field falls much faster than the theoretical prediction. This discrepancy is not surprising
because it has been observed and reported by many earlier researchers [13, 22, 23, 27,
36
37-40]. T. Jeon of our group had the similar observation [26]. According to the theory,
surface waves are modeled on ideal flat metal surface. So in experiment, extremely
optically smooth and flat surface is needed to satisfy the theoretical prediction of large
spatial field extension. Surface roughness of the sample Al sheet also increases the
0
0.5
1
1.5
2
2.5
3
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
0
0.5
1
1.5
2
2.5
3
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
0
1
2
3
4
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
0
1
2
3
4
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
(a) (b)
(c) (d)
THz
mm
THz
THz THz
mm
mm mm
Figure 3-14. (a) Theoretical fall off on bare surface. (b)Theoretical fall off
reduced with a factor of 28. (c) Diffraction pattern from the flare. (d) The
diffraction of 3 mm slit.
37
confinement to surface plasmon and results in smaller spatial extension and propagation
length. In the study conducted in ref. 25, the observed field fall-off is 28 times faster than
the theoretical prediction. Because we are using the same type of Al sheet in this study, in
fig. 3-14 (b), 28 is used as an empirical factor to re-plot the theoretical fall-off curve. It
clearly shows a better agreement with the experiment. However, whether the factor is a
frequency dependent number still remains for further investigation. When the blocking
plate is in the system, the secondary diffraction in fig 3-14 (d) shows a much under-sized
field pattern compared to that required by surface wave. Therefore, the coupling doesn’t
really happen efficiently which results in rather noisy field pattern.
In fig. 3-15 (a), the “loosely bound” field on bare metal surface has become to “tightly
bound” field due to the thin layer of dielectric film. As discussed in the introduction, the
thin film provides strong confinement to the surface wave energy and therefore, its spatial
extension above the surface is largely reduced in all frequencies.
0
0.5
1
1.5
2
2.5
3
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
0
0.5
1
1.5
2
2.5
3
0.4
0.6
0.8
1
1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mm
Figure 3-15. (a) Experimental surface wave fall-off on coated surface.
(b) Theoretical fall off on coated surface
(a) (b)
mm mm
THz
THz
38
Excellent agreement between experiment and exponential field fall-off of dielectric-coated
surface can also be observed in fig. 3-15 (a) and (b). As shown in fig. 3-16, the
theoretical exponential field fall-off e−αy and experiment field fall-off curves at a few
selected frequencies are re-plotted. Again, the frequency dependent field fall-off agrees
reasonably well with the corresponding theoretical fall-off.
0 0.5 1 1.5 2 2.5 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
vertical direction (y axis): mm
Normalized field amplitude
0.3 THz
0.4 THz
0.5 THz
0.6 THz
0.8 THz
1.1 THz
In summary, with the dielectric film, surface plasmons exhibit a much better guided
characteristic and more robust to the perturbation such as bending of the surface. The thin
dielectric coating is proved to be an excellent solution to the enhancement of THz surface
plasmons which is very important to the further applications of surface plasmons.
Figure 3-16. Comparison of theoretical and experimental amplitude fall-off at
selected frequencies
α = 0.27 mm-1
α = 0.49 mm-1
α = 0.76 mm-1
α = 1.10 mm-1
α = 1.96 mm-1
α = 3.74 mm-1
39
Chapter 4 Theoretical Treatment
The objective of the theoretical work is to understand the propagation process of the THz
pulse on both bare metal surface and dielectric coated surface. For the bare metal surface,
since the diffraction effect has been discussed in chapter 3, only the calculation of the
transverse profile of the surface wave field is introduced here. For the dielectric coated
surface, it includes four parts: 1. The transverse field profile of the propagating mode.
With the comparison with the experimental results, this process justifies the correctness
of the simplified theoretical model. 2. The dispersion relation, which accounts for the
frequency dependent phase delay. This process introduces chirping into the input pulse
and explains the long lasting ringing feature in the output signal. 3. The absorption. This
process introduces amplitude attenuation to the input signal. 4. The coupling between
different elements of the system. The last 3 processes are responsible for the reshaping of
the output signal.
4.1 The surface wave field on bare metal surface
The surface wave function on metal surface contains a propagation term in the direction z
along the surface and an exponential decay term in the direction of the surface normal y.
Therefore, it is described as:
40
E E e ikz ze kym y = − − 0 m = 1, 2
Where z axis is the propagation direction along the surface, y axis is the direction of
surface normal. kz is the wavevector in z direction, which is also known as propagation
constant, kym is the coefficient of the exponential field fall-off in the medium on either
side of the surface, here m = 1 stands for the metal and m = 2 stands for the dielectric or
air. kz and ky can be determined using the metal-dielectric boundary conditions[41]
From the ref 41, given the complex dielectric constants on both side of the interface, the
wave vectors of the surface wave have the relationships below:
2 2 ( )2 1, 2 .
1 2
1 2
+ = =
+
=
m
c
k k
c
k
z ym n
z
ω
ε
ε ε
ω ε ε
Where ε1 = ε1’ + i ε1” is the complex dielectric constant of the metal, and ε2 is the
dielectric constant of the dielectric outside the metal surface, which is air in this case. ω
is the angular frequency and c is the speed of light. From (4 -2) it can be seen that both kz
and kym are frequency dependent. Once kym is calculated, the theoretical field fall-off
curve as fig. 3-13 (a) can be plotted.
Furthermore, the 1/e field fall-off distances (skin depth) on both sides of the interface are:
(4 - 2)
(4 - 1)
41
2
1
1 2
2
2
1 2
so,
m 1, 2
1
ε
ε ε
ω
δ
ε
ε ε
ω
δ
δ
+
=
+
=
= =
c
c
k
metal
air
zm
In microwave and THz range, |ε1”| >> | ε1’| >> ε2, furthermore, the Drude complex
dielectric constant of metal can be expressed to an excellent approximation as
ε ω
σ
ε
σ
ε ε ε
0 0
1 1 1' i " dc + i dc
Γ
= + ≈ −
Where σdc is the dc conductivity of the metal, ε0 is the vacuum permittivity and Γ is the
damping rate. By using all the above approximations, a much simplified expression for
the above skin depths can be obtained as:
dc
metal
dc
air
c
c
ω ε ωμ σ
δ
ω ε μ
σ
ε
ε
ω
δ
1 0
0
2
0
3
2
1
2
"
2
2 " 2
≈ =
≈ =
4.2 The surface wave field on dielectric coated surface
4.2-1 The transverse field profile
The dielectric coated metal surface structure is shown in the fig. 4-1 (a). General modal
analysis to this 3-layer structure is often complicated in theory because of the complex
(4 - 3)
(4 - 4)
(4 - 5)
42
metal conductivity [15, 17, 22]. However, in THz range the problem can be viewed in a
much simpler way.
In THz range, the real part of the metal conductivity is high and can be considered to be
frequency independent constant and to be equal to the handbook dc value (for aluminum,
σr = 4 × 107 S/m), in contrast to metallic conductivity at optical frequencies, at λ = 800
nm, σr = 1.2 ×105 S/m [42]. Therefore, as shown in the fig. 4-1 (a), the dielectric coated
metal surface can be viewed as a classic waveguide structure --- dielectric slab
waveguide on perfect conductor, also called grounded dielectric film waveguide. To
solve the wave field in this type of waveguide, the perfect conductor plane can be treated
as a symmetric plane. Then the problem is equivalent to solving a waveguide that is
combined by the film and its mirror image, which is actually a free-standing dielectric
slab waveguide with twice thickness as shown in fig. 4-1 (b). Therefore, the problem
(a)
Metal, σ
h βz Dielectric film ε
z
y βz
2h
Dielectric film, ε
(b)
βz
z
y
βz
Figure 4-1. Theoretical model equivalence of slab waveguide structure, if the
conductivity in (a) is infinite, then its field distribution is equivalent to the
upper half of (b)
43
of the surface wave is simplified to the model analysis of a dielectric slab waveguide. The
detailed solution of modes and wave vectors is standard and can be found in appendix I.
Both theoretical [2] and experimental work [43] has shown that in our very thin (~λ/20)
dielectric slab waveguide setup, only the dominant TM0 mode is coupled into the
waveguide and therefore our surface waveguide structure is working in single mode
propagation. According to the field solution in Appendix I, the transverse electrical field
inside the slab has cosine form while the field outside the slab decays exponentially
(evanescent wave). Therefore, once the transverse field fall-off constant and the wave
vector are calculated, the problem is then solved.
The left chart in fig. 4-2 shows a typical TM0 mode Ey field solution of a 25 μm dielectric
slab (n = 1.5) waveguide at 0.5 THz. Inside the film, the Ey field is a small portion of a
cosine curve which falls off from its apex. At the dielectric-air boundary, the
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
1
1.2
mm
Ey field
Ey field distribution at 0.5Thz, of 25um thick, n=1.5 slab waveguide
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
1
Ey field distribution at 0.5THz, of 12.5um thick, n=1.5 surface waveguide
mm
perfect metal
ground plane
Figure 4-2. left: Ey field TM0 distribution at 0.5 THz of a plastic slab
waveguide; right: field profile of coated surface. (n =1.5)
Field inside the
dielectric slab of
twice thickness
Perfect metal
ground plane
Field inside the
dielectric film
Field in
free space
Field in
free space
44
Ey field has a jump because of the discontinuity of the dielectric constant. Outside the
film, the Ey field fall-off is the function e yo y −α where the fall-off constant αyo= 7.64 cm-1.
As for our case, which is a metal surface overcoated structure with 12.5 μm dielectric
film, the field profile on the right is half of that of dielectric slab waveguide on the left.
In the dielectric slab structure, electromagnetic fields propagate in the TM0 mode both
inside and outside the slab with the same wave vector. Therefore, although a perfect
conductor does not support the surface wave, when it is covered with a thin dielectric
film, a guided surface wave can be established. Thus, the wave that is propagating on the
dielectric coated metal surface is in fact the same as the guided mode of the
corresponding dielectric waveguide. The surface wave here is the same as the evanescent
field of the guided mode outside the dielectric layer.
As shown in fig. 4-3, the exponential fall-off outside the film is plotted against frequency
to compare with the experimental measurement shown in fig. 3-15 (b). Because our
sample film is only 12.5 μm thick, the cosine function inside the film is not detectable.
Our approach of treating metal as a perfect conductor at THz frequencies has greatly
simplified the problem. Earlier researchers solved the general wave equation of the
45
0
0.2
0.4
0.6
0.8
1
1.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
mm
0 0.5 1 1.5 2 2.5 3
0
50
100
150
200
250
300
THz
1/cm
Comparison of alfa calculated using our method and ref 21
perfect conductor model
Ref 21method
Figure 4-3. Theoretical normalized surface wave fall-off curve
Figure 4-4. Exponential field fall-off constants calculated with and without
perfect conductor assumption
THz mm
Ref. 21 method
46
surface wave on coated metal using the actual frequency dependent metal dielectric
constant, which must be used for the optical range[22]. The general solutions of
exponential fall-off decay constants on coated metal are compared to our simplified
solutions in fig. 4-4. Not surprisingly the two curves almost overlap which proves that the
perfect-conductor treatment is an accurate assumption in THz, similar to the usual
approach in microwave theory to derive the modes of metal waveguides.
4.2-2 The dispersion
Using the method described in Appendix I, the frequency dependent wave vector βz(ω) of
the guided mode can be calculated. Therefore, given the propagation length, the
frequency dependent phase delay can be calculated.
If the signal at the input end of the film waveguide is described using its electrical field:
Eref(ω) , then at the output end, the electrical field Eout(ω, z) can be written as [43]:
i z z
out ref E (ω, z) = E (ω)TC e− β z e−α
Where ω is the angular frequency, βz is the wave vector of the surface wave mode at ω.
Both the wave inside the film and outside the film propagates with the same wave vector.
α is the amplitude attenuation of the waveguide at ω. T is the transmission coefficient, C
is the coupling coefficient.
(4 - 6)
47
As discussed previously, the dispersion in signal pulse can be understood in the
dispersion of the dielectric slab waveguide whose field distribution is frequency
dependent. Therefore, the fraction of power that propagates inside and outside the
dielectric slab is also a function of frequency. The fraction of power can be calculated
using the mode parameter method in Appendix 1. The higher the frequency, the bigger
fraction of power is held inside the slab. Furthermore, bigger portion of energy inside the
slab, the closer the propagation speed to the speed of light of bulk dielectric; the less
portion of energy inside the slab, the closer the propagation speed to the speed of light in
free space. This explains why in the surface wave signal on dielectric coated surface, the
lower frequency components travel faster than the higher frequency ones.
Once βz(ω) is obtained, the phase velocity
z
p β
v =ω , and the group velocity
z
g d
d
β
v = ω [2]. Fig. 4-5 shows the calculated group velocity and phase velocity as
functions of frequency. Both group velocity and phase velocity decrease as frequency
increases, which is in agreement with the experimental results.
With respect to the energy exchange between the TSW and the freely propagating
diffracted wave traveling at c, the coherence length Lc at 0.5 THz from fig. 4-5 is λ/2 =
0.0025 Lc, Lc = 200λ, Lc = 120 mm or 12 cm which is ½ our guided wave path,
consequently the waves can decouple. At 1 THz the coherence length shortens
considerably to λ/2 = 0.01 Lc, Lc = 50λ = 50 × 0.3 = 15 mm = 1.5 cm.
48
0 0.5 1 1.5
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
THz
ratio to c
phase velocity and group velocity for over coated surface waves
phase velocity
group velocity
Therefore, when the βz(ω) is obtained, the phase change due to the propagation can be
calculated as βzL where L is the length of the thin film waveguide which is 20 cm in our
case. The phase delay as a function of frequency will be applied to the phase term of the
corresponding frequency of the input signal spectrum. The amplitude term will be
discussed in the next two sections.
4.2-3 The absorption coefficients
The absorption α of the thin film over-coating contains two parts: the absorption of the
dielectric film αg,L and the absorption of the metal due to its finite conductivity αm.
g L m α =α +α ,
Figure 4-5. Group velocity and phase velocity ratio to speed of light of the
fundamental TM0 mode of dielectric slab waveguide with a thickness of 25
μm and an index of refraction of 1.5
(4 - 7)
49
1) The dielectric absorption αg,L
Based on the definitions of model parameters in equation (5) to (8) in appendix I, we
have V, U, W and as model parameters. Then using these parameters, in ref [1], the
fraction of power in the core can be calculated:
2 2 2 4 3 4 2
2 2 2
1
n n V n W n WU
n n U
co cl co cl
co cl
+ +
η = −
Fig. 4-6 shows the fraction of power as a function of frequency for our 12.5μm surface
waveguide structure.
0 0.5 1 1.5
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
frequency THz
Fraction of Power
Fraction of Power for 12.5 um, n=1.5 film on perfect conductor
The power absorption coefficient due to the dielectric layer is [44]:
Figure 4-6. Fraction of power (η) at different frequencies in our surface
structure
(4 - 8)
50
g
l
g l l v
v
α =ηα ,
Where αl is the absorption of the bulk dielectric, in our experiment, the dielectric is
polyethylene, whose absorption is lower than 1 cm-1 [45]. In this calculation we use
frequency independent value 1 cm-1 as the value of αl. vl is the group velocity of bulk
material and vg is the mode group velocity within the waveguide layer. We have [1]:
1 2 (1 )
1
/
2 η
β
− −
=
=
n k
c
v
v c n
co
g
l co
0 0.5 1 1.5
0
0.005
0.01
0.015
0.02
0.025
0.03
Frequency: THz 1/cm
Amplitude absorption due to the dielectric 12.5um, n=1.5 coated surface
(4 - 9)
(pg 243, table 12-2[1])
Figure 4-7. Amplitude absorption due to the dielectric layer
(4 - 10)
51
Given fraction of power (η) and group velocities, using equation 5, the amplitude
absorption αg,l/2 due to the dielectric layer can be calculated as a function of frequency,
as shown in fig. 4-7.
2) The metal absorption αm
i) Analytical method
The Joule heat is generated by the surface current induced by the surface wave mode
field near the metal. This can be treated using a simple approximation method. The detail
analytic calculation is described in the Appendix III. The analytic result for the metal
absorption can be written as:
In below figure, the amplitude absorption due to the metal is plotted.
η
ε
λσ
π
η
ω μ ε
ω ε
σ
α ωμ
h
c n
h
n m
2 2 4 4
0
2
0 0
0
2
= 0 = (4 - 11)
52
0 0.5 1 1.5
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Frequency: THz
1/cm
metal absorption, analytical method
original
simplified
ii) Approximation method:
To simplify the calculation, the metal absorption can also be approximated using the
metal absorption of dielectric filled parallel plate waveguide (PPWG). Consider the
dielectric coated surface wave guide system as a PPWG with top plate removed. Details
are introduced in appendix III. The obtained approximation is:
v n
v PPWG
m
g
PPWG l
m
SW
m
α = 0.5ηα ≈ 0.5ηα
This result gives the amplitude attenuation constant (due to the metal) of the surface wave
as fig. 4-9 shows the curve of SW
m α versus frequency which agrees well with the result of
the analytical method in fig. 4-8:
Figure 4-8. Amplitude absorption due to metal αm/2 using analytical method
(4 - 12)
53
0 0.5 1 1.5
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
metal absorption using approximation method
Frequency: THz
1/cm
approximation method
analytical method
4.2-4 The coupling coefficient
When THz pulse propagates in the surface wave apparatus, it will go through a number of
junctions of different waveguide elements, such as cylindrical lens coupling to parallel
plate waveguide (PPWG) and PPWG to thin film coated surface waveguide. At each
junction, THz energy is transferred from one element to the other. Since the energy is
carried by guided modes of the corresponding elements, the coupling at the junctions is
eventually the coupling of modes between different waveguide elements.
Figure 4-9. Metal amplitude absorption calculated using approximation
method
54
Two coupling processes are considered here: 1. The coupling between the PPWG and the
thin film surface waveguide. 2. The coupling at the aluminum sheet block.
The well-known overlap integral is used to calculate the power coupling coefficient
between two waveguide elements [46].
∫ ∫
∫
→ →∗
⋅
=
E ds E ds
E E ds
A 2
2
2
1
2
[ 1 2 ]
Where E1 and E2 are the mode fields of the two waveguides, s denotes the integration
over the waveguide cross section. Here A is the normalized power coupling coefficient;
the amplitude coupling coefficient is the square root of A.
1). The coupling between the PPWG and the thin film surface waveguide.
As fig. 4-10 shows, this process contains two steps: (1) Quasi-TEM mode in the PPWG
couples into the quasi-TEM mode in the flare, which can be considered as an adiabatic
structure PPWG. (2) the quasi-TEM mode in the flare couples into the surface TM0 mode
of the surface waveguide. For region (1), according to the work of J. Zhang and
Grischkowsky, the coupling can be considered to be unity for adiabatic compression
shape waveguide [35]. So its coupling coefficient is not calculated. For region (2), the Ey
field of the quasi-TEM in the flare and the TM0 mode in the thin film surface waveguide
are shown in (4 - 14) and fig. 4-11:
(4 - 13)
55
The detailed definitions of the parameters are listed in the appendix.
(2) (1)
12.5μm film
1.2mm
y
z
100μm
y
Quasi-TEM
Ey
12.5 μm
film space
1
2.25
y
Same as fig. 4-2 (right)
PPWG
TM0
Ey
12.5 μm
film space
2.25
1
Surface wave
Figure 4-11. Electric field functions of the two coupling modes
0< y< 12.5 μm
12.5 μm < y < 1.2 mm
y > 1.2 mm
=
0
2.25
1
y1 E
= − y
yd
y
e y
y
E
0
cos( )
2 α
β 0 < y < 12.5 μm
12.5 μm < y < ∞
(4 - 14)
Figure 4-10. Zoomed drawing of the PPWG-Surface wave junction
56
In PPWG, the E field is perpendicular to the waveguide plates and has the same value
over the entire cross section. When the bottom plate is covered by a thin film, the E field
in the space can still be considered to be the same as the film can be treated as
perturbation. However, the field in the film needs to satisfy the boundary condition,
namely, the ratio of the E field inside and outside the film should equal to the inverse
ratio of the dielectric constants. In our case the ratio is 2.25. The calculated normalized
amplitude coupling coefficient is shown in fig. 4-12.
0 0.5 1 1.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
coupling of PPWG to SWG
2). The coupling at the aluminum sheet block
Figure 4-12. The calculated amplitude coupling coefficient of PPWG – SWG
junction
57
When the surface wave is propagating along the dielectric coated surface, as discussed
previously, its field extension into the free space above the surface is frequency
dependant. Lower frequency component has longer extension. When the wave runs into
the aluminum sheet block as shown in fig. 2-2 and fig. 4-13, the wave front will be
truncated by the block. Only the part of the wave that is below the slit height (3 mm in
our experiment) can pass through and re-establish the surface wave. In other words, the
Al shim stock sheet
12.5 μm thin film
Al sheet block
Wave front
3 mm
Figure 4-13. Schematic of the wave propagation at the slit
=
− y
yd
y
e y
y
E
0
cos( )
1
α
β 0 < y < 12.5 μm
12.5 μm < y < ∞
= −
0
cos( )
0
2
y
yd
y
e y
y
E α
β 0 < y < 12.5 μm
12.5 μm < y < 3mm
y > 3 mm
(4 - 15)
58
aluminum block acts as a spatial window filter which can be described using a binary
function and applied to the overlap integral to calculate the coupling coefficient. The two
E fields for overlap integral are shown mathematically in (4-15) and graphically below:
The calculated amplitude coupling coefficient of the slit is shown in the fig. 4-15.
Because the thickness of the slit is negligible, it works as a perfect block which maintains
the part of the wave front that falls onto the slit and completely blocks the rest part that
falls onto the metal sheet. Therefore, the function for the slit is the same as the input
wave front in the slit opening area and is zero at rest part. As shown in the right fig. 4-15.
The product of the above two coupling coefficients gives the parameter C in the equation
(4 - 6).
y
Same as fig. 4-2
Ey
2.25
Mode field of the slit
Figure 4-14. Electric field functions of the two coupling modes at the slit
12.5 μm TM0
film space
1
Surface wave Slit
3 mm
1
59
0 0.5 1 1.5
0
0.2
0.4
0.6
0.8
1
Frequency: THz
Coupling coefficient of 3 mm slit
So far the main mechanisms that are responsible for the signal reshaping have been
calculated. It includes the absorption of the dielectric material and metal, the dispersion
in the film and the coupling coefficient at the main junctions. The Fresnel’s transmission
coefficient of the silicon cylindrical lens is also estimated to be 70%. Other uncalculated
coefficients are believed to be frequency independent factors and will only have slight
effect on the pulse magnitude. Therefore, given a free space reference signal, the output
signal can be theoretically worked out. In fig. 4-16, it shows comparison of theoretical
output surface wave spectrum and the actual experimental surface wave spectrum. The
two spectra are normalized to match their peaks for comparison.
Figure 4-15. The calculated amplitude coupling coefficient of the slit
60
0 0.5 1 1.5
0
10
20
30
40
50
60
70
80
90
100
Frequency (THz)
Normalized Amplitude
The calculated spectrum shows good agreement with the experimental spectrum. From
the figure, compare with the experimental spectrum (dotted curve), the theoretical one
(solid curve) has more low frequency component remaining than the experimental one.
We believe this is because that waveguiding system always works as a high-pass filter, in
which lower frequency is much easier to get disturbed since it has more energy
propagates as the fringing field and there are still a few loss factors not yet considered
due to the system complexity.
Finally, inverse Fourier transform is performed to the calculated spectrum so that the
theoretical time domain signal can be obtained. In the above figure, the solid theoretical
time domain curve is compared to the red dotted time domain experimental signal.
Figure 4-16. The theoretical output spectrum (solid line) and experimental
output spectrum (dot) on dielectric coated surface
61
Excellent agreement is obtained which shows that the surface wave on dielectric coated
surface is well understood.
0 5 10 15 20 25 30 35
-15
-10
-5
0
5
10
15
Delay (ps)
Average Current (pA)
Figure 4-17. The comparison of time domain curves between experimental (dot)
and theoretical (solid line)
62
Chapter 5 Conclusions
The objective of this project is to study the propagation of THz surface waves and the
field confinement effect of the dielectric coating. During the past one and half years,
standard THz-TDS system was modified to be capable of measuring the transverse
electrical field in subwavelength resolution. A good quality thin film coated aluminum
sample was made and THz surface wave field profile was measured for the first time. The
experimental results are analyzed in both time domain and frequency domain. Theoretical
models were built and have excellent agreement with the experimental results. Compared
with general surface wave model, our approach provides a much simpler way of
calculation with better physical insight and no loss of accuracy.
In the experimental part, the uniqueness of the THz wave granted the success of this
study. In microwave and lower radio frequency range, the long wavelength and high
metal conductivity make it more difficult to bind the surface wave. In the optical range,
on the other hand, the short wavelength and low metal conductivity make the surface
wave field difficult to observe. The THz wavelength enables reasonable dimensions of
sample size and measurement range. Metal still has high conductivity in THz frequency
so that significant changes in surface wave confinement can be observed.
63
In our study, the THz surface system is modified to make the receiver movable so that the
surface wave field distribution can successfully measured in subwavelength scale. The
sample of metal sheet with a tightly attached subwavelength dielectric layer was
successfully made. Comparing with the bare metal surface measurement, the surface
wave on the dielectric coated surface is significantly compressed to a few wavelength
ranges. The THz surface wave field pattern was directly measured for the first time.
In the theoretical part, we developed an improved simple approach for THz surface
waves on both bare metal surface and dielectric coated surface. In the past, the wave
equations of surface wave on dielectric coated metal surface have complicated forms
because the complex metal dielectric constant introduces more complicated boundary
conditions. With the perfect conductor assumption in THz range, the metal boundary can
be conceptually removed and the film coating on metal surface becomes equivalent to
dielectric slab waveguide with twice thickness. The solutions to the latter have relatively
simple forms which maintain the high accuracy. The theoretical model based on the
perfect conductor assumption is proved to be correct and much simpler than the general
equation solving method. Therefore in THz, the complicated dielectric coated metal
surface can be studied using the classical mode analysis for dielectric slab waveguide.
64
Chapter 6 Future Work
The study has demonstrated the effect of a thin dielectric layer on the THz surface wave.
The success of this study has opened THz surface wave research in two ways:
First, dielectric coating has shown extraordinary effectiveness in enhancing the surface
wave attachment to the metal surface. Precise characterization of the film coating has
provided the possibility of a new technique in high sensitivity THz surface wave
spectroscopy.
Second, recent surface wave or surface plasmon studies mostly focus on the transmission
or reflection property in the surface normal direction in the far field. The experimental
study presented here demonstrates a new approach of high precision near field study in
the direction along the surfaces which could offer more fundamental understanding and
physical insight to the surface wave phenomena. For example, the intensively studied
transmission enhancing hole arrays can be studied in this system to measure the surface
wave propagation between the hole arrays. Together with the theory of overlap integral of
surface waves [29], it can explain the mechanism of the enhanced transmission.
65
Reference
1. Snyder, A.W. and J.D. Love, Optical Waveguide Theory. 2000: Kluwer Academic
Publishers.
2. Balanis, C.A., Advanced Engineering Electromagnetics. 1989: Wiley.
3. Sommerfeld, A., Über die Fortpflanzung ebener electrodynamischer Wellen längs
eines Drahtes. Annalen der Physik und Chemie, 1899(67): p. 233.
4. Zenneck, J., Über die Fortpflanzung ebener elektromagnetischer Wellen längs
einer ebener Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie.
Annalen der Physik 1907(23): p. 846.
5. Barlow, H.M. and A.L. Cullen, Surface Waves. The Proceedings of the Institute
of Electrical Engineers, 1953. 100: p. 329.
6. Barlow, H.M. and J. Brown, Radio surface waves. International monographs on
radio. 1962, Oxford: Clarendon Press.
7. Otto, A., Excitation of nonradiative surface plasma waves in silver by the method
of frustrated total reflection. Zeitschrift für Physik A Hadrons and Nuclei, 1968.
216(4): p. 398-410.
8. Raether, H., Surface Plasmons and Roughness, in Surface Polaritons, V.M.
Agranovich and D.L. Mills, Editors. 1982, NORTH-HOLLAND PUBLISHING
COMPANY: AMSTERDAM - NEW YORK - OXFORD. p. 331.
9. Ebbesen, T.W., et al., Extraordinary optical transmission through sub-wavelength
hole arrays. Nature, 1998. 391(6668): p. 667-669.
10. Huang, C.-P. and Y.-Y. Zhu, Plasmonics: Manipulating Light at the
Subwavelength Scale. Active and Passive Electronic Components, 2007. 2007: p.
13.
66
11. Hasegawa, K., J.U. Nockel, and M. Deutsch, Curvature-induced radiation of
surface plasmon polaritons propagating around bends. Physical Review A
(Atomic, Molecular, and Optical Physics), 2007. 75(6): p. 063816-9.
12. Yin, L., et al., Surface plasmons at single nanoholes in Au films. Applied Physics
Letters, 2004. 85(3): p. 467-469.
13. Klopfleisch, M. and U. Schellenberger, Experimental determination of the
attenuation coefficient of surface electromagnetic waves. Journal of Applied
Physics, 1991. 70(2): p. 930-934.
14. Goubau, G., Surface Waves and Their Application to Transmission Lines. Journal
of Applied Physics, 1950. 21(11): p. 1119-1128.
15. Attwood, S.S., Surface-Wave Propagation Over a Coated Plane Conductor.
Journal of Applied Physics, 1951. 22(4): p. 504-509.
16. Schlesinger, Z., B.C. Webb, and A.J. Sievers, Attenuation and coupling of far
infrared surface plasmons. Solid State Communications, 1981. 39: p. 1035.
17. Stegeman, G.I. and R.J. Seymour, Surface plasmon attenuation by thin film
overlayers in the far infrared. Solid State Communications, 1982. 44(9): p. 1357-
1358.
18. Ufimtsev, P.Y., R.T. Ling, and J.D. Scholler, Transformation of surface waves in
homogeneous absorbing layers. Antennas and Propagation, IEEE Transactions
on, 2000. 48(2): p. 214-222.
19. Ling, R.T., J.D. Scholler, and P.Y. Ufimtsev, The Propagation and Excitation of
Surface Waves in an Absorbing Layer. Journal of Electromagnetic Waves and
Applications, 1998. 12(7).
20. Ling, R.T., J.D. Scholler, and P.Y. Ufimtsev, Errata On: the Propagation and
Excitation of Surface Waves in an Absorbing Layer. Journal of Electromagnetic
Waves and Applications, 2000. 14(10).
67
21. Ufimtsev, P.Y. and R.T. Ling, New results for the properties of TE surface waves
in absorbing layers. Antennas and Propagation, IEEE Transactions on, 2001.
49(10): p. 1445-1452.
22. Schlesinger, Z. and A.J. Sievers, IR surface-plasmon attenuation coefficients for
Ge-coated Ag and Au metals. Physical Review B (Condensed Matter), 1982.
26(12): p. 6444-6454.
23. Mills, D.L. and A.A. Maradudin, Surface corrugation and surface-polariton
binding in the infrared frequency range. Physical Review B, 1989. 39(3): p. 1569.
24. Hibbins, A.P., J.R. Sambles, and C.R. Lawrence, Grating-coupled surface
plasmons at microwave frequencies. Journal of Applied Physics, 1999. 86(4): p.
1791-1795.
25. Jeon, T.-I., J. Zhang, and D. Grischkowsky, THz Sommerfeld wave propagation
on a single metal wire. Applied Physics Letters, 2005. 86(16): p. 161904-3.
26. Jeon, T.-I. and D. Grischkowsky, THz Zenneck surface wave (THz surface
plasmon) propagation on a metal sheet. Applied Physics Letters, 2006. 88(6): p.
061113-3.
27. O'Hara, J., R. Averitt, and A. Taylor, Prism coupling to terahertz surface plasmon
polaritons. Opt. Express, 2005. 13(16): p. 6117-6126.
28. Qu, D., D. Grischkowsky, and W. Zhang, Terahertz transmission properties of
thin, subwavelength metallic holearrays. Opt. Lett., 2004. 29(8): p. 896-898.
29. Qu, D. and D. Grischkowsky, Observation of a New Type of THz Resonance of
Surface Plasmons Propagating on Metal-Film Hole Arrays. Physical Review
Letters, 2004. 93(19): p. 196804-4.
68
30. Nazarov, M., et al., Surface plasmon THz waves on gratings. Comptes Rendus
Physique, 2008. 9(2): p. 232-247.
31. Williams, C.R., et al., Highly confined guiding of terahertz surface plasmon
polaritons on structured metal surfaces. Nature Photonics, 2008. 2(3): p. 175-179.
32. Nazarov, M., et al., THz surface plasmon jump between two metal edges. Optics
Communications, 2007. 277(1): p. 33-39.
33. Mukina, L.S., M.M. Nazarov, and A.P. Shkurinov, Propagation of THz plasmon
pulse on corrugated and flat metal surface. Surface Science, 2006. 600(20): p.
4771-4776.
34. Zhizhin, G.N., et al., Absorption of surface plasmons in "metal-cladding layer-air"
structure at terahertz frequencies. Infrared Physics & Technology, 2006.
49(1-2): p. 108-112.
35. Zhang, J. and D. Grischkowsky, Adiabatic compression of parallel-plate metal
waveguides for sensitivity enhancement of waveguide THz time-domain
spectroscopy. Applied Physics Letters, 2005. 86(6): p. 061109-3.
36. Reiten, M.T., Spatially Resolved THz Propagation, in Electrical Engineering.
2006, Oklahoma State University: Stillwater. p. 227.
37. Begley, D.L., et al., Propagation distances of surface electromagnetic waves in
the far infrared. Surface Science, 1979. 81(1): p. 245-251.
38. Koteles, E.S. and W.H. McNeill, Far infrared surface plasmon propagation.
International Journal of Infrared and Millimeter Waves, 1981. 2(2): p. 361-371.
69
39. Steijn, K.W., R.J. Seymour, and G.I. Stegeman, Attenuation of far-infrared
surface plasmons on overcoated metal. Applied Physics Letters, 1986. 49(18): p.
1151-1153.
40. Saxler, J., et al., Time-domain measurements of surface plasmon polaritons in the
terahertz frequency range. Physical Review B, 2004. 69(15): p. 155427.
41. Raether, H., Surface Plasmons on Smooth and Rough Surfaces and on Gratings
1988, Berlin Heidelberg New York London Paris Tokyo: Springer-Verlag. 136.
42. Zhao, Y. and D. Grischkowsky, Terahertz demonstrations of effectively two-dimensional
photonic bandgap structures. Opt. Lett., 2006. 31(10): p. 1534-1536.
43. Mendis, R., First Broadband Experimental study of planar Terahertz Waveguides
in Electrical Engineering. 2001, Oklahoma State University: Stillwater.
44. Gallot, G., et al., Terahertz waveguides. J. Opt. Soc. Am. B, 2000. 17(5): p. 851-
863.
45. Mendis, R. and D. Grischkowsky, Plastic ribbon THz waveguides. Journal of
Applied Physics, 2000. 88(7): p. 4449-4451.
46. Lesurf, J.C.G., Millimetre-wave Optics, Devices and Systems. 1990: Adam Hilger,
Bristol and New York. 251.
47. Zhao, Y. and D.R. Grischkowsky, 2-D Terahertz Metallic Photonic Crystals in
Parallel-Plate Waveguides. Microwave Theory and Techniques, IEEE
Transactions on, 2007. 55(4): p. 656-663.
48. Mendis, R. and D. Grischkowsky, THz interconnect with low-loss and low-group
velocity dispersion. Microwave and Wireless Components Letters, IEEE, 2001.
11(11): p. 444-446.
70
Appendixes
Appendix I Model analysis of dielectric coated surface
In our study, the surface waveguide structure is shown in below fig. A-1(a). h = 12.5 μm,
εd = 2.25, and the metal underneath is assumed aluminum.
Method 1 and 2 assume in THz, aluminum is perfect electrical conductor (PEC), σ
=∞.
y
z
(a)
Metal, σ,
εm
h Dielectric film εd
x
Air, ε0
2h
Dielectric film, εd
(b)
y
z
x
Figure A-1. Equivalent wave guiding structures
71
To solve the wave equations in this structure (a), we refer to the solution in ref.[2], it is
possible to first solve the wave equations in a free-standing dielectric slab waveguide of
twice thickness of the same material, as shown in fig. A-1 (b), then apply the boundary
condition (perfect conductor boundary at the plane of symmetry) to eliminate unsuitable
modes and select the correct modes for (a)
Two methods of solving the dielectric slab waveguide are introduced here.
1. Direct wave equation method. [2]
The Helmholtz wave equation is used in the dielectric slab waveguide structure. The
formats of the solution to the Helmholtz equation in slab structure include: TE and TM
Ey field Ez field
cos(βydy) sin(βydy)
exp(-αy0y)
+h
-h
y
z
exp(αy0y)
Figure A-2. Perpendicular (Ey) and tangential field (Ez) of TM0 mode of
dielectric slab waveguide[2], it should be noted that the TM0-Ez field is
much smaller ~ 0.05 than the TM0-Ey field
72
modes. In our scope of studying, to couple free space wave into surface, it requires that
the electric field vector lie within the incidence plane, therefore, only TM field need to be
considered. Furthermore, because of the symmetry of the structure, the solutions have
two types of symmetric modes: even and odd. As shown in fig A-2. However, with the
existence of PEC plane in the center, the only allowed modes are TM even mode which
satisfies the boundary condition as tangential electrical field to be zero on the PEC plane.
Below figure shows the E field profile of the fundamental even mode, where the
tangential field Ez is zero at the plane of symmetry. It will be discussed later that the
waveguide is running under single mode (TM0) propagation.
The field solution of TM even mode is listed below:
73
0
0
( )
1
0
0
0
cos( )
sin( )
cos( )
0
0
0
0
0
0
2 2 0
0
0 0
0
0
0 0
0
0
2 2
=
=
= −
= − −
=
=
=
=
=
−
= −
= −
=
+
+
+ + − −
+ + − −
+ + − −
+
−
−
−
z
y
y j z
m
yo
x
y j z
z z m
y j z
m
yo z
y
x
d
z
d
y
j z
yd
d
m
d
d yd
x
j z
yd
d
m
d d
d d z
z
j z
yd
d
m
d d
d yd z
y
d
x
H
H
H B e e
E j B e e
E B e e
E
H
H
H A y e
E j A y e
E A y e
E
yo z
yo z
yo z
z
z
z
α β
α β
α β
β
β
β
μ
α
β β
ωμ ε
ωμ ε
α β
β
μ
β
β
ωμ ε
β β
β
ωμ ε
β β
Where the superscript d in all field variables refer to fields inside the dielectric and 0+ is
for fields in vacuum above the dielectric. Am
d and Bm
0+ is field amplitudes which will be
evaluated at the boundary. βz is the wave vector in propagation direction z. βyd and αyo
are y components of wave vector inside the film and in the air, respectively. These three
0 < y <h
In the film
y >h
In the air
74
parameters are unknown and have to be determined in order to have the complete wave
field expression. From the above fields inside and outside the film, it can be seen that in
this structure, only Ey, Ez and Hx field are not zero. In addition, inside the film the fields
are trigonometric functions and outside the film they are exponential functions. By
enforcing boundary conditions, the βz, βyd and αyo can be determined by numerically
solving the simultaneous equations below (Eq. (8-160), (8-167) and (8-168) in ref.[2]):
2 2 2
0 ( h) ( h) a y yd α + β =
h h h yd yd yo
d
β β α
ε
ε
0 ( ) tan( ) =
( ) 0 0
2 2
0
2 2 2
0 α + β = β − β =ω μ ε − μ ε y yd d d d
Where 1 0 0 = − r r a ωh μ ε μ ε
For TM even mode, the cutoff frequency is
( )
0 0 4 μ ε −μ ε
=
d d
c m h
m
f where m = 0, 2, 4, ….
Substitute h = 25 μm, εd = εrε0 = 2.25 × 8.854 ×10-12 F/m, μd = μ0 = 4π×10-7 H/m, we
have
fc = m × 2.68 THz
(A-1)
(A-2)
(A-3)
(A-4)
75
Therefore, for the dominant mode TMz
0 (m=0), fc = 0, which means all frequency can
have unattenuated propagation in this mode. For the second lowest mode (m = 2) is fc =
5.36 THz, which is higher than the highest frequency of our system. Thus TM0 is the only
mode that is allowed in our surface waveguide system.
2. Mode parameter method [1]
Another method published in Snyder and Love’s book is a more general method for
dielectric waveguide with symmetric structures. First it defines some dimensionless
parameters base on the waveguide refractive index profile and cross-sectional geometry.
Then, the quantities of interest (such as wave vectors, attenuation constants, group
velocities, fraction of power in the dielectric and etc.) are worked out as expressions in
Snyder and Love’s notation.
Given the frequency of electromagnetic wave f, the half thickness of the dielectric
waveguide ρ (which equals to h in method 1), the refractive index of the dielectric
(core) nco and the refractive index of surrounding medium (cladding) ncl, we define:
1. Waveguide and fiber parameter V (Eq. 11-47, pg.227 ref.[1])
( ) ( )
2 2 2 1/ 2 2 2 2 2
co cl co cl V = n − n = ρ k n − n
λ
πρ
Where
c
f
k
π
λ
2π 2
= =
2. Profile height parameter
(Eq. 11-48, pg.227 ref. [1])
(A-5)
76
{1 }
2
1
2
2
co
cl
n
n
= −
3. Modal parameters Uj and Wj (Eq. 11-49, pg.227 ref. [1])
2 2 2 1/ 2
2 2 2 1/ 2
( )
( )
j j cl
j co j
W k n
U k n
= −
= −
ρ β
ρ β
Where βj is the wave vector both inside and outside of the dielectric, which is the βz in
method 1, clearly we have (Eq. 11-50, pg.228 ref. [1])
U 2 W 2 2k 2 (n2 n2 ) V 2 j j co cl + = ρ − =
For TM modes, it has (Table 12-2, pg.243 ref. [1])
j j
co
cl
j U U
n
n
W tan 2
2
=
Equation (8) and (9) form up simultaneous equations and can be solved numerically.
Once Uj and Wj are solved, according to the tables on page 242 and 243 in ref. [1], the
field distribution and other quantities can be calculated accordingly.
Example
Fig. A-3 is the identical result of applying the above two methods on a silicon slab
waveguide. In this example, half thickness of the slab (h or ρ) is 65μm, refractive index is
3.42.
(A-6)
(A-7)
(A-8)
(A-9)
77
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
0
2
4
6
8
10
12
Normal E field at 0.3THz for n=3.42, 130um thick dielectric slab
cm
E field a.u.
From the figure, it shows the fundamental TM0
z mode. Inside the slab waveguide, E field
is a cosine function, while in the air, the field is an exponential function. Then for a 65μm
silicon waveguide on PEC plane, the field distribution is just simply cut the below figure
into half through the center (0 cm vertical line).
Method 3 treats aluminum as normal metal with complex dielectric constant m εˆ
This method was worked out by Schlesinger and Sievers [22]. In their paper, they tried to
directly solve the wave equations in the surface waveguide (fig. A-1(a)) with complex
Figure A-3. Ey field distribution of TM0
z mode in a silicon slab waveguide
Dielectric slab
of twice
thickness
78
metal dielectric constant. The complex wavevector βz is solved numerically, as given in
below equation 9. Then the exponential decay constant in the perpendicular direction can
also be calculated using the same relation in equation (3) in method 1.
−
−
+
−
−
+
−
−
+
−
−
+ +
−
+
−
+
−
−
+
≈ − −
4
2
3
1/ 2 3 / 2
2
2
2
2
2
1/ 2 3 / 2
2( ˆ )
( 1)
( ˆ)
( 1)
( ˆ )
( 1)
( ˆ )
2( 1)
2 ˆ
)
1
(
2
1
( ˆ ) ( ˆ )
( 1)
2 ˆ
1
ˆ 1
x x
x x
c
m
d d d
d m
d
m
d
m
d
d
d
m
d
d m
d
m
z
ε
ε
ε
ε ε
ε ε
ε
ε
ε
ε
ε
ε
ε
ε
ε
ε ε
ε
ε
ω
β
Where z βˆ
is the complex wave vector of surface wave, εd is the dielectric constant of
overlayer, m εˆ is the complex dielectric constant of substrate metal. At 1THz, for
aluminum we have ˆ = −3.3×104 + i6.4×105 m ε . x in the equation is 2πh/λ. Where λ is the
wavelength of surface wave, h is the thickness of overlayer and c is the speed of light.
From this equation, the real part of z βˆ
corresponds to the βz calculated in method 1 and 2.
Appendix II Metal conductivity
According to simple Drude model, the frequency-dependent complex dielectric constant
is given in SI units as[47].
/ ( )
/( )
' "
2
0
= − + Γ
= +
= +
∞
∞
i
i
i
p
m
m m m
ε ω ω ω
ε σ ε ω
ε ε ε
Where the corresponding Drude complex metal conductivity is given by
(A-10)
(A-11)
79
/( ) 2 /( )
0 = iΓ + iΓ = i + iΓ m dc p σ σ ω ε ω ω
In above equations, 0 ε is the vacuum permittivity, ∞ ε is the contribution of the bound
electrons, ωp is the plasma angular frequency and Γ is the damping rate, which is defined
as Γ = 1/τ where τ is the average collision time.
In the optical and near infrared range, metal conductivity has small real part and big
imaginary part which makes the metal lossy medium.
On the other hand, in the microwave and THz range, ω/Γ<<1, as a result, the Drude
complex conductivity and dielectric constant of metal can be expressed to an excellent
approximation as
ε ω
σ
ε
σ
ε ε ε
σ σ
0 0
' " dc dc
m m m
m dc
i + i
Γ
= + ≈ −
≈
Within this accurate approximation, in the THz range, the metal conductivity is equal to
its handbook dc value which is very high and can be considered as ideal conductor. The
real part of metal dielectric constant is a negative constant, while the much larger
imaginary part is proportional to the wavelength. Therefore in the THz range, metals
have high conductivity and behave like ideal lossless conductor.
(A-12)
(A-13)
80
Appendix III Metal absorption
1) Analytical method
Due to the uniformity along the x axis as shown in the above structure in fig. A-4, there
are only 3 field components need to be solved in the Maxwell’s equations: Ey, Hx and Ez.
According to the (8-62) on ref [2], page 377, the power absorbed and dissipated as heat
by the metal surface, denoted as Pc is
0
1 2
2
1
= = = c x y H
dz
dP
P
σδ
x
y
z
h
βz
σ
Figure A-4 Surface waveguide structures
(A-14)
81
Where σ is the conductivity of the metal and
ωμσ
δ
2
≈ is the skin depth of good
conductor.
The power flow inside the dielectric layer Pz1 is
= ∫ ×
∧ h
z z y x P a E H dy
1 0 Re[ ]
2
1
Similarly, the power flow outside the dielectric layer (in the air) Pz2 is
P a E H dy h y x
z z Re[ ]
2
1
2 = ∫ × ∧ ∞
Therefore we have the total power flow P:
z1 z 2 P = P + P
The metal power absorption αm is defined similar to equation 4- 9,
( )
( ) 0
P z
dz
dP
P z P e
m
mz
=
= −
α
α
(A-15)
(A-16)
(A-17)
(A-18)
82
Where vl is the group velocity of bulk material and vg is the mode group velocity within
the waveguide layer. As the expression of Hx and Ey, are all known, after substituting into
the above equations,
η
β
β
β
ωε
σ
ωμ
α ⋅
+
=
h
h
yd
yd
z
d d
m
2
sin 2
2
Where η is the fraction of power within the dielectric layer, μd = μrμ0 = 4π×10-7 H/m (μr =
1 for non-ferrites), εd = n2ε0 =1.52 ×8.854 ×10-12 F/m, for aluminum σ = 4×107 S/m βyd is
the wave vector in the y direction inside the film and it has:
z yd d d β 2 + β 2 =ω 2μ ε
Equation A-19 can be simplified by making some approximations. For h in μm, we have:
sin 2βydh ≈ 2βydh
βz ≈ β0 = 0 0 ω μ ε
Substitute the above into 20, the simplified expression of amplitude absorption αm/2 is:
2) Approximation method
In a dielectric filled parallel plate waveguide (PPWG), as shown in below fig. A-5(a),
when studying the metal loss due to the finite conductivity, our surface wave case can be
2 2 4 4 4
0
2
0 0
0
2
0
PPWG
m m n
h
c n
h
n ηα η
ε
λσ
π
η
ω μ ε
ω ε
σ
α ωμ = = ≈
(A-19)
(A-20)
(A-21)
(A-22)
83
approximated that one of the metal plates has been removed (fig. A-5(b)). Under this
approximation, the loss due to the finite metal conductivity can be acquired in 3 steps:
First the loss is reduced to half of the loss of PPWG because there is only one metal plate.
Second it needs to be multiplied by the fraction of total power within the film because the
power is flowing both inside and outside the film. Third, the power is no longer
propagating with the bulk dielectric group velocity (c/n) but approximately with c
because the majority energy is hanging outside the film. Therefore, the velocity ratio is
also needed as a correction factor [44]. From fig. 4-2 it shows that although the E field
inside the film is a cosine function, for such a small thickness h compared to the
wavelength, the field variation is almost flat. This can be approximated to be uniform,
which is just the same as the TEM mode in PPWG.
For fig. A-5(a), the metal plate amplitude loss αm for TEM mode propagation can be
written as [48], attenuation coefficient:
h
PPWG nR
m
0 α = η
h
(b)
h
σ n σ σ ε
(a)
(amplitude loss)
Figure A-5. Using parallel plate waveguide to approximate surface waveguide
(A-23)
84
And the corresponding power attenuation coefficient is twice PPWG
m α . Where n = 1.5 is the
index of refraction of the dielectric, R = 10.88 ×10-3[107/(σλ0)]1/2 for TEM mode. h =
12.5 μm is the thickness of the dielectric, σ = 4×107 S/m for aluminum and
= ≈ 377(
0
0
0 ε
η μ is the impedance of free space.
For the surface waveguide, the amplitude loss is ½ that of the PPWG multiplied by the
fraction of power η (equation (4 - 8)) within the dielectric layer of thickness h and the
velocity ratio. The approximated metal amplitude attenuation coefficient in surface
waveguide is:
v n
v PPWG
m
g
PPWG l
m
SW
m
α = 0.5ηα ≈ 0.5ηα
This result gives the amplitude attenuation constant (due to the metal) of the surface wave
as fig. 4-8 shows the curve of SW
m α versus frequency which agrees well with the result of
the original analytical method:
0.9( / 2)
10
0.5 1.44 10 7
5
m
PPWG
SW m
m n h α
η
σλ
α = ηα = × − × × ≈
(A-24)
(A-25)
VITA
Gong, Mufei
Candidate for the Degree of
Doctor of Philosophy
Dissertation: STUDY OF THZ SURFACE WAVES (TSW) ON BARE AND COATED
METAL SURFACE
Major Field: Electrical Engineering
Biographical:
Born in Mudanjiang, P. R. China, son of Gong, Chuan and Guan, Chun’ai.
Education:
B.S. Optoelectronics, 1998, Tianjin University, China.
M. Eng., 2001, Nanyang Technological University, Singapore.
Completed the requirements for the Doctor of Philosophy in Electrical
Engineering at Oklahoma State University, Stillwater, Oklahoma in July, 2009.
Experience:
Worked as electronic designer in 3rd Research Institute of China Aerospace Science &
Industry Corp. (CASIC), Tianjin, China – Aug 1998 to May 1999
Professional Memberships:
Student Member of Optical Society of America (OSA)
ADVISER’S APPROVAL: Dr. Daniel Grischkowsky
Name: Gong, Mufei Date of Degree: July, 2009
Institution: Oklahoma State University Location: Stillwater, Oklahoma
Title of Study: STUDY OF THZ SURFACE WAVES (TSW) ON BARE AND
COATED METAL SURFACE
Pages in Study: 84 Candidate for the Degree of Doctor of Philosophy
Major Field: Electrical Engineering
Scope and Method of Study: The focus of the research was to investigate the propagation
characteristics (such as field distribution, attenuation and group velocity) of terahertz
surface waves on bare and dielectric coated metal surface. The experiment was carried
out on a modified standard terahertz time-domain spectroscopy system. Surface waves
were coupled into the metal surface using the parallel plate waveguide coupling
mechanism. The picosecond terahertz pulses were generated and detected using the
Grischkowsky photo-conductive transmitter and antenna driven by a femtosecond laser.
Findings and Conclusions: Surface waves at microwave and terahertz frequencies are
weakly guided on bare metal surface due to the high metal conductivity. Detailed
wave coupling analysis and experiment has shown that on a bare metal surface,
the majority of energy remains to be uncoupled freely propagating waves. The
spatial extent of the terahertz surface wave collapses two orders of magnitude
upon the addition of the sub-wavelength dielectric layer on the metal surface.
Simple theory in terahertz range gives an accurate explanation to this effect.
Direct experimental measurements of the terahertz surface wave on an aluminum
surface covered with a 12.5 μm thick dielectric layer have completely
characterized the wave. The measurements of the frequency-dependent
exponential fall-off of the evanescent wave from the surface agree well with
theory.