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MEASUREMENT AND SIMULATION OF PARALLEL PLATE

WAVEGUIDE STRUCTURES IN THE TERAHERTZ REGION

FOR SENSING AND MATERIAL CHARACTERIZATION

APPLICATIONS

Presented by J. Alex Higgins June 14, 2012

Thesis Committee:

Branimir Pejcinovic, Chair

Matrin Siderius, Ph. D.

Lisa Zurk, Ph. D.

NEAR-Lab

OVERVIEW

J. Alex Higgins, [email protected] June 14, 2012 2 / 19

Introduction

Why Terahertz?

Terahertz Sensing and Material Characterization

How Does This Work Contribute?

Background and Theory

Parallel Plate Waveguide

Fourier Transform Mode Matching Technique

FDTD Simulation

TDS and CW-VNA Systems

Results and Discussion

PPW Multimode Radiation Patterns

PPW Resonant Structures (e.g. single notch and notched periodic)

Conclusion

Summary of Results

Summary of Contributions

Future Work

mailto:[email protected]

THE TERAHERTZ GAP


Communicationsand Radar

OpticalCommunications

MedicalImaging

Astro-physics

µ Wave

and RF

mm

Wave Terahertz Infrared Visible Ultraviolet X-ray

Electronics Photonics

1010 1011 1012 1013 1014 1015 1016 1017 1018

Frequency (Hz)

3× 10−2 3× 10−3 3× 10−4 3× 10−5 3× 10−6 3× 10−7 3× 10−8 3× 10−9 3× 10−10

Wavelength (m)

4.135× 10−5

4.135× 10−4

4.135× 10−3

4.135× 10−2

4.135× 10−1

4.135× 100

4.135× 101

4.135× 102

4.135× 103

Energy (eV)

FIGURE 1 – Electromagnetic spectrum indicating the “THz gap”.


TERAHERTZ SENSING AND MATERIAL CHARACTERIZATION


• Biomedicine and security industries

• Biomolecules and explosives have unique spectral signatures in

this region (e.g. DNA, MDMA, RDX, PETN)[1, 2].

• Paper products, plastics, and clothing fibers are virtually

transparent.

• Non-ionizing makes it well suited for health safety scanning of

foods and transportation security.

(A) Detection of illicit substances through paper envelope. (B) Specral fingerprint of explosives(urlhttp://www.pnl.gov).


TERAHERTZ SENSING AND MATERIAL CHARACTERIZATION


• Semiconductor industry

• Characterize current IC device fabrication materials (e.g.

packaging, substrates, isolating dielectric layers).

• Integrate with existing “cheap” CMOS technologies[3].

FIGURE 2 – CMOS mm-wave on-chip antennas and RFICs.[3]


HOW DOES THIS WORK CONTRIBUTE?


PARALLEL PLATE WAVEGUIDE (PPW) TO THE RESCUE!

• Sensing

• False readings are diminished by designing PPW filters that

detect only one material.

• Material Parameter Extraction

• By placing samples laterally inside the PPW the material-EM

field interactions occur over longer distances than in free

space.

y

x

z

PEC

PEC

W

d

l

µ0, ǫ0




• Engineering challenges involved with using PPW

1. Waveguide theory introduces multiple modes of operation

which lead to excess energy loss in dispersion and mode

conversion.

2. Resonance of the PPW structure is dependent on its

geometric parameters; plate separation, notch width, depth,

pitch, and center spacing.




• Engineering challenges involved with using PPW

1. Waveguide theory introduces multiple modes of operation

which lead to excess energy loss in dispersion and mode

conversion.

2. Resonance of the PPW structure is dependent on its

geometric parameters; plate separation, notch width, depth,

pitch, and center spacing.

• The work for this thesis addresses these issues by

characterizing the behavior of PPW operating in a multimode

configuration and investigating the sensitivity of the geometric

parameters of PPW resonant structures.


HATS OFF TO THE MAXWELLIANS


FIGURE 3 – James Clerk Maxwell

MAXWELL’S EQUATIONS

∇× E = −jωµH

∇× H = jωǫE + J

∇ · ǫE = ρ

∇ · µH = 0

(A) George Fran-cis Fitzgerald

(B) Sir OliverJoseph Lodge

(C) Oliver Heavi-side

FIGURE 4 – The Maxwellians[4]


PARALLEL PLATE WAVEGUIDE


y

x

z

PEC

PEC

W

d

l

µ0, ǫ0

FIGURE 5 – Diagram of the geometry for a PPW.

β =√

k2 − k2c =

√

k2 −(mπ

d

)2

αc,TE =Pl

2P0=

2k2cωµβd

Rs

αc,TM = 2ωǫ

βdRs|Am|2

TRANSVERSE ELECTRIC (TE) MODE

Hz = Bm cos(mπ

dy)

e−jβz

Ex = jωµ

k2cBm sin

(mπ

dy)

e−jβz

Hy = jβ

k2cBm sin

(mπ

dy)

e−jβz

Ey = Hx = 0, m ∈ N

TRANSVERSE MAGNETIC (TM) MODE

Ez = Am sin(mπ

dy)

e−jβz

Ey = −jβ

k2cAm cos

(mπ

dy)

e−jβz

Hx = jωǫ

kcAm cos

(mπ

dy)

e−jβz

Hy = Ex = 0, m ∈ N0


PARALLEL PLATE WAVEGUIDE CONT.


z (mm)

y (m

m)

TE−modeEx−field [Mode = 1]

0 5 10 15 200

0.5

1

1.5

2

−30

−20

−10

0

z (mm)

y (m

m)

TM−modeHx−field [Mode = 1]

0 5 10 15 200

0.5

1

1.5

2

−30

−20

−10

0

z (mm)

y (m

m)

Ex−field [Mode = 2]

0 5 10 15 200

0.5

1

1.5

2

−30

−20

−10

0

z (mm)

y (m

m)

Hx−field [Mode = 2]

0 5 10 15 200

0.5

1

1.5

2

−30

−20

−10

0

z (mm)

y (m

m)

Ex−field [Mode = 3]

0 5 10 15 200

0.5

1

1.5

2

−30

−20

−10

0

z (mm)

y (m

m)

Hx−field [Mode = 3]

0 5 10 15 200

0.5

1

1.5

2

−30

−20

−10

0

FIGURE 6 – Comparison of PPW TE and TM mode field strength distributions.


PARALLEL PLATE WAVEGUIDE CONT.


0 0.2 0.4 0.6 0.8 1 1.2 1.4

0

y (mm)

Ex (

dB)

0 0.5 1 1.50

50

100

φ (°

)

(A) TE1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0

y (mm)

Ex (

dB)

0 0.5 1 1.5−100

−50

0

50

100

φ (°

)

(B) TE2

FIGURE 6 – First two TE field distributions between the plates of the PPW.


FOURIER TRANSFORM MODE MATCHING TECHNIQUE


• The Fourier transform technique is especially well suited for EM

problems since it provides a convenient mathematic

representation of wave scattering, diffraction, and propagation.

• e.g. antenna radiation, diffraction, and interference.

• Fourier transform, mode-matching, and residue calculus offer a

robust set of techniques.

• When applied to solving EM scattering and boundary problems

they obtain simple, analytic, and rapidly converging series

solutions.




• The analysis method for scattering and boundary condition

problems has the following steps[5]:

1. Divide the scattering domain into closed and open regions.

2. Represent the scattered fields in their respective regions in terms of theFourier series and transform.

3. Enforce boundary conditions on the field continuities between regions.

4. Apply the mode-matching technique to obtain the simultaneousequations for the Fourier series modal coefficients.

5. Utilize the residue calculus method to represent the scattered field in afast convergent series.




x

z

r

θs

y

-a a

Eiy

Ery

Ety

Region II

Region I

k

k0

PECPEC

FIGURE 7 – Cross section diagram of a radiationpattern geometry for a flanged PPW.

Ety =

1

2π

∫

∞

−∞

Ety(ζ)e

−j(ζx−κ0z) dζ

Ety(ζ) =

∫

∞

−∞

Ety(x, 0)e

jζx dx

Ety(ζ) =

1

2π

∞∑

m

(cm + δmn) ama2Fm(ζa)

Fm(u) =eju(−1)m − e−ju

u2−

(

mπ2

)2

Hty(ζ) = ζp sin ap(x+ a)

−

∞∑

m

cmζm sin am(x+ a)

1

2π

(

Ipn +∞∑

m

cm

)

= a (ξpδnp − ξncn)




x

z

r

θs

y

-a a

Eiy

Ery

Ety

Region II

Region I

k

k0

PECPEC

FIGURE 7 – Cross section diagram of a radiationpattern geometry for a flanged PPW.

Imn =∫

∞

−∞a2κ0Fm(ζa)Fn(−ζa) dζ

Ety =

1

2π

∫

∞

−∞

Ety(ζ)e

−j(ζx−κ0z) dζ

Ety(ζ) =

∫

∞

−∞

Ety(x, 0)e

jζx dx

Ety(ζ) =

1

2π

∞∑

m

(cm + δmn) ama2Fm(ζa)

Fm(u) =eju(−1)m − e−ju

u2−

(

mπ2

)2

Hty(ζ) = ζp sin ap(x+ a)

−

∞∑

m

cmζm sin am(x+ a)

1

2π

(

Ipn +∞∑

m

cmImn

)

= a (ξpδnp − ξncn)




Re(ζ)

Im(ζ

)

R

−am

Γ1

am

Γ6

Γ5

Γ4

BranchCut

Γ2

Γ3

k0

Γ4

Γ7

FIGURE 7 – Contour path in the ζ-plane.

Imn =

∫

∞

−∞

2κ0

[

1− (−1)n ej2ζa

(ζ2 − a2m) (ζ2 − a2n)

]

dζ

∮

f(ζ) dζ =

∮

Γf(ζ) dζ = 0

.

.

.

Imn =2π

a

√

k20 − a2m

amδmn + (I2mn − I1mn)




Re(ζ)

Im(ζ

)

R

−am

Γ1

am

Γ6

Γ5

Γ4

BranchCut

Γ2

Γ3

k0

Γ4

Γ7

FIGURE 7 – Contour path in the ζ-plane.

Imn =

∫

∞

−∞

2κ0

[

1− (−1)n ej2ζa

(ζ2 − a2m) (ζ2 − a2n)

]

dζ

∮

f(ζ) dζ =

∮

Γf(ζ) dζ = 0

.

.

.

Imn =2π

a

√

k20 − a2m

amδmn + (I2mn − I1mn)

cm =

(

δmn −[

(I1mn+I2mn)

2πa(

ξn+√

k2

0−a2

m

)

]T)

−1

(I1pn+I2pn)

2πa(

ξn+√

k2

0−a2

n

)




x

z

r

θs

y

-a a

Eiy

Ery

Ety

Region II

Region I

k

k0

PECPEC

FIGURE 7 – Cross section diagram of a radiation pattern geometry for a flanged PPW.

Ety(r, θ) = ej(kr−

π

4 )√

k2πr cos θ

∑

∞

m (cm + δmn) ama2Fm (−ka sin θ) (9)




0dB

−20

−40

−60

0

30

60

90

270

300

330

TE1

TE3

TE5

(A) First three even symmetric modes

0dB

−20

−40

−60

0

30

60

90

270

300

330

TE2

TE4

TE6

(B) First three odd symmetric modes

FIGURE 7 – Examples of PPW TE radiation patterns using (9) with a = 0.25 mm and ν = 2 THz.


FINITE DIFFERENCE TIME DOMAIN SIMULATION


MIT ELECTROMAGNETIC EQUATIONPROPAGATION (MEEP)

• An open-source implementation of theFDTD method for numerically solvingelectromagnetic problems.

• Available for download at(http://ab-initio.mit.edu/meep).

• A port for the Apple Macintosh was writtenusing the Macports interface(http://www.macports.org).

• Also accessible as a resource tool at theNanoHUB website(http://nanohub.org/resources/Meep).

Some of its key capabilities of are:

• Simulations in 1D, 2D, 3D, and cylindricalcoordinates.

• Distributed memory parallelism on anysystem supporting the MPI standard.

• PML absorbing boundaries.

• Exploitation of simulation symmetries,which reduces computation size.

• Scriptable front-end or callable from a C++library or Python interface.

• Output results in the HDF5 standardscientific data format.

• Arbitrary material and source distributions.

• Field analyses including flux spectra,energy and power integrals.


http://ab-initio.mit.edu/meep

http://www.macports.org

http://nanohub.org/resources/Meep



MIT ELECTROMAGNETIC EQUATIONPROPAGATION (MEEP)

• An open-source implementation of theFDTD method for numerically solvingelectromagnetic problems.

• Available for download at(http://ab-initio.mit.edu/meep).

• A port for the Apple Macintosh was writtenusing the Macports interface(http://www.macports.org).

• Also accessible as a resource tool at theNanoHUB website(http://nanohub.org/resources/Meep).

MEEP!

Some of its key capabilities of are:

• Simulations in 1D, 2D, 3D, and cylindricalcoordinates.

• Distributed memory parallelism on anysystem supporting the MPI standard.

• PML absorbing boundaries.

• Exploitation of simulation symmetries,which reduces computation size.

• Scriptable front-end or callable from a C++library or Python interface.

• Output results in the HDF5 standardscientific data format.

• Arbitrary material and source distributions.

• Field analyses including flux spectra,energy and power integrals.


http://ab-initio.mit.edu/meep

http://www.macports.org

http://nanohub.org/resources/Meep



• MEEP has two built-in sourcefunctions, continuous-wave andgaussian-pulse.

• The Gaussian is a useful

representation of optical pulsesbecause of its straightforwardmathematical description andbroadband spectral content.

• The derivative of the Gaussian isused to model the distinct positiveand negative swing (pulse) of theTDS system.

Gaussian Function

f(t) = exp

(

−jωt−[

(t− t0)√2 δt

]2)

Gaussian-pulse Function

∂

∂tf(t) =

j

ωexp

(

−jωt−[

(t− t0)√2 δt

]2)




86 87 88 89 90 91 92 93 94

−1

−0.5

0

0.5

1

Time (ps)

Fie

ld S

tren

gth

(V

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−100

−80

−60

−40

−20

0

Frequency (THz)

Po

wer

Sp

ectr

um

(d

B)

Picometrix

Gaussian Model

FDTD

Gaussian

δ/δt Gaussian

Picometrix

∫ δt Picometrix

FDTD

FIGURE 8 – Gaussian-pulse model compared to TDS system waveform and FDTD source function.


MEASUREMENT SYSTEMS


TIME DOMAIN

SPECTROSCOPY (TDS)

Picometrix T-RayTM 4000

Bandwidth 0.2 - 2 THz

Signal-to-Noise Ratio > 70 dB

Rapid Scan Range 320 ps

Rapid Scan Rate 100 Hz

TABLE 1 – Picometrix T-RayTM 4000 system specifications.

FIGURE 9 – Picture of a TDS input coupling experiment us-

ing quasi-optical Picometrix T-RayTM 4000 system.

CONTINUOUS WAVE VECTOR

NETWORK ANALYZER (CW-VNA)

VDI Extender Modules

Six Bands 75 - 750 GHz

Dynamic Range 80 - 120 dB

Compatible VNAsAglient, Anritsu,

Rhode & Schwartz

Output Power 5 - 7 dBm

TABLE 2 – Virginia Diodes Inc. (VDI) extender module spec-ifications.

FIGURE 10 – Picture of a CW-VNA radiation pattern exper-iment setup using VDI extender modules for the WR1.5 band.


RADIATION PATTERNS


FIGURE 11 – Diagram indicating the PPW ge-ometry and setup for a radiation pattern experi-ment.

m TE (GHz) TM (GHz)

0 - 0

1 107.1 *

2 * 214.1

3 321.2 *

4 * 428.3

5 535.3 *

TABLE 3 – First five PPW cutoff frequencies cal-culated for TE and TM modes at a plate separa-tion of 1.4 mm.

• To maintain TM dominant mode operation d = 75 µm (TM2 = 4 THz)

• Reducing the dimensions of the PPW introduces propagation loss, group

velocity dispersion, and coupling issues[6].


RADIATION PATTERNS


Angle (°)

Fre

quen

cy (

GH

z)

−50 0 50

200

400

600

800

1000

1200

1400

Pow

er S

pect

rum

(dB

)

−60

−50

−40

−30

−20

−10

0

FIGURE 11 – Measured TDS system radiationpattern of a PPW operating in TE mode.

Angle (°)

Fre

quen

cy (

GH

z)

−50 0 50

200

400

600

800

1000

1200

1400

Pow

er S

pect

rum

(dB

)

−60

−50

−40

−30

−20

−10

0

FIGURE 12 – FDTD simulated radiation patternof a PPW operating in TE mode.

• The Fourier transform mode-matching technique was implemented[7].

• A brute-force recursive minimal standard deviation algorithm wasimplemented to match results to their weighted analytic solution.


RADIATION PATTERNS


0dB

−20

−40

−60

0

30

60

90

270

300

330

Analytic 100% TE1

Analytic Multimode

FDTD at 910 GHz

TE1: 51%

TE3: 25%

TE5: 17%

TE7: 7%

FIGURE 11 – PPW TE multimode radiation pat-tern of FDTD simulation compared to weightedanalytic mode contributions.

0dB

−15

−30

−45

−600

30

60

90

270

300

330

TDS at 385 GHz

Analytic Multimode

CW−VNA at 385 GHz

FDTD at 385 GHz

TE1: 85%

TE3: 15%

FIGURE 12 – PPW TE multimode radiationpatterns of TDS and CW-VNA system mea-surements, and FDTD simulation compared toweighted analytic mode contributions.


EXCESS LOSS


0.1 0.3 0.5 0.7 0.9 1.1

0

0.1

0.2

0.3

0.4

0.5

Frequency (THz)

α c (dB

/cm

)

TDS TE

1

TE5

TE7

TE3

FIGURE 13 – TDS system measurements compared to theoretic of TE mode conductive attenuation.


EXCESS LOSS


360 365 370 375 380 385 390 395 4000

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (GHz)

Exc

ess

Loss

(dB

/cm

)

FIGURE 13 – Close-up of excess loss beyondthe lowest order TE1 mode.

• Black points indicate radiationpatterns with distinct side lobes.

• Red point indicates a radiation

pattern blurred out by diffraction.

0dB

−20

−40

−60

0

30

60

90

270

300

330

374.3 GHz

377.4 GHz

380.6 GHz

FIGURE 14 – TDS system radiation pattern blur-ring due to excess loss.


RESONANT STRUCTURES


SINGLE NOTCH PARALLEL

PLATE WAVEGUIDE (N-PPW)

d

w

t

z Al

Al

FIGURE 15 – Cross section diagram of the N-PPW resonant structure.

d = 1000 µm (plate separation)w = 412 µm (notch width)t {variable} (notch depth)

NOTCHED PERIODIC PARALLEL

PLATE WAVEGUIDE (NP-PPW)

d

wp

t

g

z Al

Al

FIGURE 16 – Cross section diagram of the NP-PPW resonant structure.

d {variable} (plate separation)w = 112 µm (notch width)t = 93 µm (notch depth)

p = 280 µm (notch pitch)g = 162 µm (center span)


RESONANT STRUCTURES


SINGLE NOTCH PARALLEL PLATE WAVEGUIDE (N-PPW)

250 260 270 280 290 300 310−50

−40

−30

−20

−10

0

10

Frequency (GHz)

Fie

ld S

tren

gth

(dB

)

t/w ≈ 4 t/w ≈ 2 t/w ≈ 1 t/w ≈ 0.5

FIGURE 15 – FDTD simulation results com-parison resonant peak shift for varying N-PPWdepth to width ratios.

t (µm) ν (GHz) t/w ∆ν (%)

206 283 0.5 1.07

412 280 1 0

824 278 2 0.71

2060 277 4 1.07

TABLE 3 – Resonant frequency values of simu-lated FDTD single notch depths.

• The resonant peak increases for smaller depths and decreases for larger.

• The resonant peak shows little dependence on notch depth when thedepth-to-width t/w ratio is greater than 2.


RESONANT STRUCTURES


NOTCHED PERIODIC PARALLEL PLATE WAVEGUIDE (NP-PPW)

470 480 490 500 510 520 530 540 550 560−60

−50

−40

−30

−20

−10

0

10

20

30

Frequency (GHz)

Fie

ld S

tren

gth

(dB

)

FDTD for d = 100 µmFDTD for d = 200 µmTDS for d = 200 µmCW−VNA for d = 200 µm

FIGURE 15 – Comparison of TDS and CW-VNAsystem results and FDTD simulated transmis-sion characteristics of the NP-PPW resonator.

ν (GHz) d (µm)

TDS 498 200

CW-VNA 500 200

FDTD 489 200

FDTD 493 100

TABLE 3 – Resonant peak values for varyingplate separation.

• The resonant peak increases for smaller plate separations.

• Results from the dimensional analysis of the NP-PPW indicate that channel

dimensions deviate from their expected value by σ ≤ 5.


SUMMARY OF RESULTS


• Identifying and characterizing the behavior of PPW multimode

operation

• Multimode operation is identifiable using radiation patterns.

• Energy coupled in to individual modes can be estimated using

radiation patterns.

• Distinct side lobes in the radiation pattern are crucial to correctly

weighting mode estimates.


SUMMARY OF RESULTS


• Investigating the sensitivity of the geometric parameters to PPW

resonant structures

• The N-PPW resonant peak increases for smaller depths and

decreases for larger.

• The N-PPW resonant peak shows little dependence on notch

depth when the depth-to-width t/w ratio is greater than 2.

• The NP-PPW resonant peak increases for smaller plate

separations.

• Results suggest that the NP-PPW plate separation is less critical a

design parameter for the resonant peak than the geometry and

placement of notches.


SUMMARY OF CONTRIBUTIONS


• Measurements were performed and presented on both

broadband TDS and narrowband CW-VNA systems.

• Custom PPW and fixtures were designed and fabricated for

each experiment.

• A configurable MATLAB package was developed to process

experimental results.

• An analytic solution for the radiation pattern of a flanged

PPW[7, 8] was implemented in MATLAB.




• A brute-force recursive minimal standard deviation algorithm

was implemented in MATLAB to estimate the energy coupled

into each mode.

• FDTD simulations were developed and performed for PPW

radiation patterns and resonant structures.

• Macintosh ports were written for the freely available MEEP

package[9] for Electromagnetic (EM) simulation.




• Contributing published works include:

• 2011 SPIE Defense, Security, and Sensing conference[10]

• 76th ARFTG conference[11]

• 34th MIPRO conference[12]

• 11th IEEE-NANO conference[13]

• 35th IRMMW-THz conference[14]


FUTURE WORK


• PPW Multimode Radiation Patterns

• Refine radiation pattern analytic solution mode weighting algorithm.

• Investigate mechanism behind “blurring” of side lobes in radiant patterns.

• Automate radiation pattern measurements.

• Develop GUI application for radiation pattern matching.

• PPW Resonant Structures

• Investigate mechanism behind N-PPW diminishing returns wrt t/w.

• Run FDTD simulations using NP-PPW dimensional analysis values.

• Investigate effects of modifying NP-PPW center span dimensions.

• Implement NP-PPW analytic solution using Fourier transformmode-matching technique.



QUESTIONS?


REFERENCES


[1] M. Nagel, P. H. Bolivar, and H. Kurz, “Modular parallel-plate thz components for cost-efficient biosensing systems,” SemiconductorScience and Technology, vol. 20, no. 7, p. S281, 2005.

[2] R. Mendis, V. Astley, J. Liu, and D. M. Mittleman, “Terahertz micofluidic sensor based on a parallel-plate waveguide resonantcavity,” Applied Physics Letters, vol. 95, no. 171113, 2009.

[3] F. G. Jr., T. S. Rappaport, and J. Murdock, “Millimeter-wave cmos antennas and rfic parameter extraction for vehicularapplications.” in VTC Fall. IEEE, 2010, pp. 1–6. [Online]. Available:http://dblp.uni-trier.de/db/conf/vtc/vtc2010f.html#GutierrezRM10

[4] B. J. Hunt, The Maxwellians. Cornell University Press, 1991.

[5] H. J. Eom, Electromagnetic Wave Theory for Boundary-Value Problems. Springer, 2004.

[6] R. Mendis, “Thz waveguides: The evolution,” in Infrared Millimeter Waves and 14th International Conference on TeraherzElectronics, 2006. IRMMW-THz 2006. Joint 31st International Conference on, sept. 2006, p. 367.

[7] T. Park and H. Eom, “Analytic solution for TE-mode radiation from a flanged parallel-plate waveguide,” IEE Proceedings-H, vol.140, no. 5, pp. 387–389, Oct 1993.

[8] C. H. Kim, H. J. Eom, and T. J. Park, “A series for tm-mode radiation form a flanged parallel-plate waveguide,” IEEETRANSACTIONS ON ANTENNAS AND PROPAGATION AP, vol. 41, p. 1469, 1993.

[9] A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software packagefor electromagnetic simulations by the FDTD method,” Computer Physics Communications, vol. 181, pp. 687–702, January 2010.

[10] A. Higgins, B. Pejcinovic, C. Cowen, and F. Kernan, “An investigation of parallel plate waveguide terahertz radiation inputcoupling,” SPIE Proceedings, vol. 8023, no. 1, pp. 802 310–802 310–13, 2011.

[11] A. Higgins, F. Kernan, and B. Pejcinovic, “Multimode characterization of parallel plate waveguide,” in Microwave MeasurementSymposium (ARFTG), 2010 76th ARFTG, 30 2010-dec. 3 2010, pp. 1 –5.


http://dblp.uni-trier.de/db/conf/vtc/vtc2010f.html#GutierrezRM10

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GoBack - Portland State Universityweb.cecs.pdx.edu/~higginja/docs/JAHiggins_MS_PDOT.pdf · 2013. 8. 27. · THE TERAHERTZ GAP J. Alex Higgins, [email protected] June 14, 2012 3