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Abstract
This section contains the preface, table of contents, and glossary of symbols and acronyms.

Library of Congress Cataloging-in-Publication Data

O’Sullivan, Créidhe M. M.

Field guide to terahertz sources, detectors, and optics / Créidhe O’Sullivan, J. Anthony Murphy.

p. cm. – (The field guide series ; FG28)

Includes bibliographical references and index.

ISBN 978-0-8194-9167-1

1. Millimeter wave devices–Handbooks, manuals, etc.

2. Terahertz technology–Handbooks, manuals, etc.

3. Infrared equipment–Handbooks, manuals, etc.

4. Submillimeter waves–Handbooks, manuals, etc.

I. Murphy, J. Anthony. II. Title.

TK7876.5.O88 2012

621.381′33--dc23

2012012372

Published by

SPIE

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: +1.360.676.3290

Fax: +1.360.647.1445

Email: books@spie.org

Web: http://spie.org

The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.

First printing

fx0-1.jpg

Introduction to the Series

Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org.

John E. Greivenkamp, Series Editor

College of Optical Sciences

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide Series:

Field Guide to

Adaptive Optics, Robert Tyson & Benjamin Frazier

Atmospheric Optics, Larry Andrews

Binoculars and Scopes, Paul Yoder, Jr. & Daniel Vukobratovich

Diffractive Optics, Yakov Soskind

Geometrical Optics, John Greivenkamp

Illumination, Angelo Arecchi, Tahar Messadi, & John Koshel

Image Processing, Khan M. Iftekharuddin & Abdul Awwal

Infrared Systems, Detectors, and FPAs, Second Edition, Arnold Daniels

Interferometric Optical Testing, Eric Goodwin & Jim Wyant

Laser Pulse Generation, Rüdiger Paschotta

Lasers, Rüdiger Paschotta

Microscopy, Tomasz Tkaczyk

Optical Fabrication, Ray Williamson

Optical Fiber Technology, Rüdiger Paschotta

Optical Lithography, Chris Mack

Optical Thin Films, Ronald Willey

Polarization, Edward Collett

Probability, Random Processes, and Random Data Analysis, Larry C. Andrews & Ronald L. Phillips

Radiometry, Barbara Grant

Special Functions for Engineers, Larry Andrews

Spectroscopy, David Ball

Visual and Ophthalmic Optics, Jim Schwiegerling

Field Guide to THz

The region of the electromagnetic spectrum between microwaves and infrared radiation has come to be known as the “THz gap,” mainly due to the lack of readily available laboratory sources and detectors. For many years technology development was driven by astronomers and planetary scientists, but other potential uses, particularly in medical and security applications, have led to increased activity by the mainstream physics and engineering community in recent times. Because diffraction is important at these frequencies, THz systems cannot be successfully designed using traditional optical techniques alone.

The primary objective of this Field Guide is to provide the reader with a concise description of the quasi-optical techniques used at THz frequencies, as well as the basic principles of operation of the most common THz system components in use today. More detailed accounts of specific devices can be found in the bibliography and references therein.

We would like to thank our families and our colleagues at NUI Maynooth, in particular Neil Trappe, Marcin L. Gradziel, and Ian McAuley of the THz Optics group and also Stafford Withington of the Cavendish Laboratory at Cambridge.

Créidhe O’Sullivan

J. Anthony Murphy

Department of Experimental Physics

National University of Ireland,

Maynooth

Table of Contents

Glossary of Symbols and Acronyms xi

Introduction 1

The THz Band 1

The THz Gap 2

THz Absorption in Air 3

Reflection and Transmission 4

THz Sources 5

Natural Sources of THz Radiation 5

THz Generation Techniques 6

Gunn Diodes 8

IMPATT Diodes 9

TUNNETT Diodes 10

Resonant Tunnel Diodes 11

Difference Frequency Generation 12

Electro-optic Crystals (Optical Rectification) 13

Optical Parametric Oscillators 15

Frequency Multipliers 16

Photoconductive Antennas 17

Photomixing 18

Optically Pumped Far-IR Gas Lasers 19

p-Type Germanium Lasers 20

Quantum Cascade Lasers 21

Gyrotrons 22

Synchrotrons 23

Free-Electron Lasers 24

Backward Wave Oscillators 25

Smith–Purcell Emitters 26

THz Detectors 27

THz Detection Techniques 27

Responsivity and Signal-to-Noise Ratio 29

Noise Equivalent Power 30

Shot and Thermal Noise 31

Extrinsic Semiconductor Detectors 32

Photoconductive Detectors 33

Photomixers 34

Schottky Diodes 35

Schottky Diode Mixers 37

SIS Mixers 38

Electro-optic Sampling 39

Semiconductor Bolometers 41

Microbolometer Arrays 43

Transition-Edge Sensors 44

SQUIDs 45

Hot-Electron Bolometers 47

Hot-Electron Bolometer Mixers 48

Pyroelectric Detectors 49

Golay Cells 50

THz Optics 51

Gaussian Beam Propagation 51

Complex Radius of Curvature 52

Gaussian Beam Parameters 53

Beamwidth 55

Edge Taper 56

Truncation and Spillover (Gaussian Beams) 57

Truncation and Spillover (Non-Gaussian Beams) 58

Confocal Distance 59

Far-Field Divergence 60

Ray Matrices and Gaussian Beam Transformation 61

Higher-Order Modes (Cylindrical Coordinates) 64

Higher-Order Modes (Rectangular Coordinates) 65

Mode Coefficients 66

Power Coupling Efficiency 69

Gaussicity 70

Mismatched Beams and Tolerancing 71

Scattering Matrix Formulism 72

Transmission Matrices 73

Linear Scattering Operators 74

Truncation at an Aperture 75

Perfect Lenses and Pure Propagation 76

Reflections at Dielectric Interfaces (Lens Surfaces) 77

Standing Waves in Horn-Fed Systems 78

Cascading Scattering and Transmission Matrices 79

Off-Axis Mirrors (Ellipsoidal) 80

Off-Axis Mirrors (Parabolic) 81

Off-Axis Mirrors (Distortion and Cross-Polarization) 82

Polarizing Grids 83

Roof Mirrors as Polarization Rotators 84

Dual-Beam Interferometers (Tunable Filters) 85

Diffraction Losses in Interferometers 86

Diplexers and Multiplexers 87

Four-Port Dual-Beam Interferometer (Diplexer) 88

Horn Antenna Feeds 89

Corrugated Conical Horns (Scalar Feed) 90

Smooth-Walled Horns (Pyramidal and Diagonal) 91

Conical Smooth-Walled Horns (Single and Dual Mode) 92

Shaped Horns and Multimode Feeds 93

Lens Antennas 94

System Design 95

Modeling Techniques 96

THz Applications 97

THz Imaging 97

THz Spectroscopy 99

THz Time-Domain Spectroscopy 100

Equation Summary 101

Bibliography 114

Index 117

Glossary of Symbols and Acronyms

A

absorbance

A

detector area

A

profiled horn parameter

a

aperture radius

a

horn aperture side length

a

semi-major axis of an ellipse

a

wire radius

An,Anh,Anυ

nth mode coefficient of beam a, nth mode coefficient of orthogonal components

an

mode coefficients for beam n at the input port

ac

alternating current

A12, A21

scattering matrices for an absorbing stop

B

magnetic field

B

magnetic field strength

b

horn aperture side width

b

semi-minor axis of an ellipse

Bn,Bnh,Bnυ

nth mode coefficient of beam b, nth mode coefficient of orthogonal components

bn

mode coefficients for beam n at the output port

BWO

backward wave oscillator

C

capacitance

C

heat capacity

c

speed of light

Ce , Cph

electron heat capacity, phonon heat capacity

c.c.

complex conjugate

CMOS

complementary metal-oxide- semiconductor

CW

continuous wave

D

detectivity

d

diameter

d

distance between the focal point and the apex of a lens antenna

d

propagation distance

D*

specific detectivity

D12, D21

scattering matrices for pure propagation

dc

direct current

DFG

difference frequency generation

E, Ea

electric field

E(t), E(r)

electric field

E, E0

electric field amplitude

E(x, y, z), E(r)

electric field amplitude

e

elementary charge

Ea , Eb

electric field amplitude

Eap

electric field across an aperture

eF

vector field

eG

vector Gaussian field

Eg , EC , EV , EF

energy gap, conduction band energy, valence band energy, Fermi energy

e^h,e^υ

unit orthogonal vectors

Ei, Ej, Ek

electric field amplitude

Einc, Erefl, Etrans

incident, reflected, transmitted electric field

EL, EH

light-, heavy-hole energy

EOP

optical phonon energy

Eout

output electric field

Ep, t, Ep, r, Ep, i

transmitted, reflected, incident electric field amplitude for p-polarization

Es, t, Es, r, Es, i

transmitted, reflected, incident electric field amplitude for s-polarization

ETHz

terahertz electric field amplitude

Ep+,Ep

forward and reverse traveling pth symmetric Laguerre mode

EO

electro-optic

F

Fresnel number

f

focal length

FEL

free-electron laser

FS

free space

FWHM

full width half maximum

G

thermal conductance

g

wire spacing

GBMA

Gaussian beam mode analysis

GBT

Gaussian beam telescope

H, Ha, Hb

magnetic field

h

Planck’s constant

Hm (x)

mth Hermite polynomial

HEB

hot electron bolometer

HIFI

Heterodyne instrument for the far-infrared

HPBW

half-power beamwidth

I

current

I

intensity, transmitted intensity

I

identity matrix

i

1

i

angle of incidence

Ic

critical current

Ix, Iy

x, y component of intensity

I0

incident intensity

IF

intermediate frequency

IMPATT

impact ionization avalanche transit time

IR

infrared

J

free current density

J

rotational state number

J

screening current

K

power coupling coefficient

k

wavenumber (2π/λ)

Kab

power coupling between two beams

kB

Boltzmann constant

KG

power coupling to a pure Gaussian (Gaussicity)

Klost

power lost due to truncation

kP, kS, kI

pump wavevector, signal wavevector, idler wavevector

Kspillover

power lost due to spillover

KXpol

power scattered into the cross-polar direction

L

inductance

L, Lx, Ly

slant length, slant length along x direction, slant length along y direction

l

grating period

Lmn

operator representing a transfer function

Lnn

coupling to reflected modes at port n

Lpm

generalized Laguerre polynomials

lw

walk-off length

lc

coherence length

l1, l2

path length

LO

local oscillator

LT-GaAs

low-temperature-grown gallium arsenide

M

magnification

Mn

nth matrix

me

electron mass

N

multiplication factor of a frequency multiplier

n

number density

n, nsignal, nnoise

number of photons, signal photons, noise photons detected

n, n1, n2

refractive index

n

rms noise level

n

spectral order

noptical, nTHz

optical, terahertz refractive index

NDR

negative differential resistance

NEP

noise equivalent power

NTD

neutron-transmutation doped

OP

optical phonon

OPO

optical parametric oscillator

OPTL

optically pumped THz laser

P, Pi, P0, P

polarization

P(r)

power contained within a radius r

P

vertex-focus distance of a parabola

Pnoise, Psignal

noise power, signal power

P

total power

PCA

photoconductive antenna

p-Ge

p-type germanium laser

q

charge

q(z), q0

complex radius of curvature (also known as complex beam parameter or Gaussian beam parameter)

qin, qout

complex radius of curvature of input, output beam

q1, q2

complex radius of curvature of beam 1, 2

QCL

quantum cascade laser

R(z)

Gaussian beam phase radius of curvature

R

radius

R

reflectivity

R

resistance

R

surface radius of curvature

r

complex reflection amplitude coefficient

Rin, Rout

phase radius of curvature

rin, rout

ray displacement

Rsurf

surface radius of curvature

rT

truncation radius

RV

responsivity

R1, R2

surface radius of curvature

R1, R2

distances to foci of an ellipse

RF

radio frequency

rms

root-mean-square

RTD

resonant tunnel diode

S,Sa, Sb, Sc

full scattering matrix

s

phase error

S11, S12,

scattering matrices

S21, S22

SIS

superconductor–insulator–superconductor

SNR

signal-to-noise ratio

SNRdB

signal-to-noise ratio in dBs

S/N

signal-to-noise ratio

SPR

Smith–Purcell radiation

SQUID

superconducting quantum interference device

T

temperature

T

transmittance

T

fractional power transmission

t

complex transmission amplitude coefficient

T, Ta, Tb, Tc

full transmission matrix

Tb, Ts

bath, heat sink temperature

Tc

critical temperature

Te

edge taper

Te (dB)

edge taper expressed in dB

Te, Tph

electron temperature, phonon temperature

T11, T12,

transmission matrices

T21, T22

TCR

thermal coefficient of resistance

TE, TM

transverse electric, magnetic

TES

transition edge sensor

THz-TDS

terahertz time-domain spectroscopy

TUNNETT

tunnel injection transit time

u(x, y, z), u0

non-plane-wave part of the electric field, constant

V, Vrms

voltage, root-mean-square voltage

υ

vibrational state number

Vbi

built-in potential

Vgap

gap voltage

w, w(z)

Gaussian beam radius

wm

beam radius at a mirror

w0, w0,a, w0, b

Gaussian beam waist radius

w0,in, w0,out

Gaussian beam waist radius

WG

waveguide

x

path length

xc

point of intersection, x coordinate

yc

point of intersection, y coordinate

zc

confocal distance, Rayleigh range

α

absorption coefficient

α

diffraction parameter

α

incident beam polarization angle

α, α(T)

thermal coefficient of resistance

α

tilt of grid wires

β

mode balance constant

βtrans, βrefl

transmitted, reflected beam polarization direction

χ

electron affinity (volts)

χ(2),χijk(2)

second-order susceptibility

Δ

path length difference

ΔIF

IF bandwidth

Δmax

path length difference for maximum transmission

Δmin

path length difference for minimum transmission

ΔSSB

single-sideband path length difference

Δ1, Δ2

energy gap of a semiconductor

ΔE

energy gap

Δx

lateral shift

Δz

relative displacement

Δz

position of beam waist behind aperture

Δθ

cone angle

Δν

bandwidth

δν

frequency of successive transmission bands

ε0

permittivity of free space

Φ0

flux quantum

ϕ

grid inclination angle

ϕc

critical emission angle

ϕm, ϕsc, ϕB

metal, semiconductor, barrier work function

ϕ0(z), ϕin, ϕout

Gaussian beam phase slippage

γ

Lorentz factor (1/(1β2),β=υ/c), υ is velocity

γ

reflection coefficient at an interface

ηspillover

Gaussian beam spillover efficiency

λ

wavelength

λFEL

wavelength of radiation from an FEL

λIF, λLO, λs

IF, LO, signal wavelength

λw

wiggler magnet spacing wavelength

ν

frequency

νIF, νLO, νs

IF, LO, signal frequency

νTHz, νpump

terahertz, pump frequency

θ

angle from normal

θ

angle with respect to propagation axis

θ

incident field polarization angle

θ

grid tilt angle

θ′

projected grid tilt angle

θc

critical angle

θin, θout

ray angle with respect to normal

θ0

asymptotic beam growth angle

θ1, θ2

angle of incidence, reflection

σ

absorption cross-section

τ

transmission

τdiff

diffusion time

τep, τpe, τes

electron-phonon, phonon-electron, electron-substrate energy transfer time

τp

pulse length

ω, ω1, ω2, ω3

angular frequency

Ψn

nth Gaussian beam mode

Ψmn (x, y, z)

Gaussian–Hermite beam mode amplitude (rectangular coordinates)

Ψpm (r, ϕ, z)

Gaussian–Laguerre beam mode amplitude (cylindrical coordinates)

ΨnSC

nth scattered Gaussian beam mode

ψa, ψb, ψF

scalar field

ψG

scalar Gaussian field

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