Numerical analysis and designs of terahertz photomixer and photoconductive antennas

ANTENNA ON A HYBRID GaAs MEMBRANE AND SI LENS SUBSTRATE FOR A TERAHERTZ PHOTOMIXER 67 5.1 Introduction ..... 2.4 Radiation patterns of the antennas on a semi-infinite Si substrate: a s

Ph.D Dissertation

Numerical Analysis and Designs of Terahertz Photomixer and Photoconductive Antennas

by Truong Khang NGUYEN

Ajou University Department of Electrical and Computer Engineering

February 2013

Numerical Analysis and Designs of Terahertz Photomixer and Photoconductive Antennas

by Truong Khang NGUYEN

Ajou University Department of Electrical and Computer Engineering

February 2013

Numerical Analysis and Designs of Terahertz Photomixer and

Photoconductive Antennas

by Truong Khang NGUYEN

A Dissertation Submitted to the Department of Electrical and Computer Engineering in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy in Electrical Engineering

Ajou University February 2013 Approved by:

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to my advisor Professor Ikmo Park, who gave me a passion for Antenna field that is really an important thing at the start of my graduate study His serious and dedicated personality in work has made me a high admiration I can not repay for his kindness and every effort to guide, support and encourage me during the course of this study

I am also thankful to the members of the dissertation defense committee, Professor Sangin Kim, Professor Sang Min Lee (F Rotermund), Professor Youngbae Park, and Professor Haewook Han for their comments and suggestions, which are very crucial for the successful completion of this dissertation

I am indebted to Professor Hanjo Lim, who gave me the valuable opportunity to study and research in Ajou University

Special thanks are extended to all of my colleagues whose enlightening discussions and interest made this work invaluable Thanks are also given to my Vietnamese student friends who have shared my difficulties in far-from-home life

Finally, I would like to give my respect and thanks to my family, most of all, my parent and my wife, Thi Duyen Pham, for their encouragement and endless love Their love, understanding and prayer have made this work possible

Jesus always hears our prayers.

ABSTRACT

Terahertz (THz) science and technology have made significant progress in the past decades However, the use of THz waves was not fully realized due to the absence of practically suitable and efficient signal sources The THz radiation can be generated by using short laser pulses or using an optical beat for the pump of the photoconductive antenna The physical mechanism of the former technique can be divided into two groups, ultrafast surge effects and nonlinear optical effects The latter technique was preferred to as photomixing or optical heterodyne A common method to detect THz radiation is through Electro-Optic Sampling (EOS) measurement to determine the THz electric field In both THz pulsed and CW photomixing systems the antenna is one of the most important elements to couple radiation into or collect radiation from free space However, an efficient antenna design for THz applications has been a difficult subject of huge interest The effort

on new kinds of integrated antennas with new devices in order to increase the power and the efficiency of the radiated structured is the main goals of our work

In this work, we numerically studied and investigated the characteristics of several antenna types for both THz pulsed and CW photomixing systems We proposed some antenna design which obtaining high total efficiencies to partly solve the low output problem Besides, the issue of improved antenna directivity was also particular considered

in this work This work was completed with a special topics of photoconductive antenna used in a THz pulsed system The results that we obtained contribute in providing a more throughout understanding about the important role of antenna in the radiation of the THz

TABLE OF CONTENTS

Page

ABSTRACT i

TABLE OF CONTENTS ii

LIST OF FIGURES iii

LIST OF TABLES iv

I INTRODUCTION 1 1.1 Terahertz radiation and sources 1

1.2 Terahertz photoconductive antenna 2

1.3 Terahertz photomixer antenna 4

1.4 Substrate for terahertz antenna design 8

1.5 Thesis organization 9

1.6 References 10

II TERAHERTZ RESONANT ANTENNAS ON SEMI-INFINITE AND LENS SUBSTRATE 13 2.1 Introduction 13

2.2 Antennas and substrate geometries 16

2.3 Antenna characteristics 18

2.3.1 On semi-infinite substrate 18

2.3.2 On extended hemispherical Si lens substrate 21

2.4 Summary 27

2.5 References 30

III TERAHERTZ SELF-COMPLEMENTARY ANTENNAS ON LENS

3.1 Introduction 33

3.2 Antenna geometries for comparison 36

3.3 Antenna characteristics in a broadband THz frequency 38

3.4 Summary 46

3.5 References 47

IV ANTENNA ON A GaAs MEMBRANE STRUCTURE FOR HIGH TOTAL EFFICIENCY 49 4.1 Introduction 49

4.2 Antennas and membrane configurations 51

4.3 Antenna characteristics 53

4.3.1 Geometry effects of the GaAs membrane substrate on the antenna performance 53

4.3.2 Effects of the bias line structure on the antenna performance 60 4.4 Summary 64

4.5 References 65

V ANTENNA ON A HYBRID GaAs MEMBRANE AND SI LENS SUBSTRATE FOR A TERAHERTZ PHOTOMIXER 67 5.1 Introduction 67

5.2 Antennas configurations 70

5.3 Antenna characteristics with a modified PBG bias line 73

5.4 Photomixer antenna characteristics with a non-contact lens substrate 78 5.5 Summary 85

5.6 References 86

VI ANTENNA ON A GaAs MEMBRANE COVERED BY A FREQUENCY-SELECTIVE SURFACE FOR A TERAHERTZ PHOTOMIXER 88 6.1 Introduction 88

6.2 Description and modeling of the structure 91

6.3 THz photomixer and antenna characteristics 93

6.3.1 Effect of the size of cavity in a GaAs substrate 94

6.3.2 Effect of the number of holes in a array 97

6.3.3 Effect of the quartz substrate supporting the hole array 99

6.4 Final design and simulated results 102

6.5 Summary 102

6.6 References 103

VII INVESTIGATION OF ANTENNA DESIGN PARAMETER EFFECTS ON A TERAHERTZ PHOTOCONDUCTIVE DIPOLE ANTENNA 106 7.1 Introduction 106

7.2 Antenna design 108

7.3 Antenna characteristics 109

7.3.1 Bias line length effect 109

7.3.2 Center dipole length effect 117

7.4 Summary 119 7.5 References 120

8.1 Summary and key distributions 123 8.2 Future works 125

LIST OF FIGURES

Page

Fig 1.1 Electromagnetic spectrum 3

Fig 1.2 (a) Photoconductive switch for broadband THz systems and (b)

photomixer for narrow band THz systems 4

Fig 1.3 Equivalent circuit of the photomixer integrated with a THz antenna 6

Fig 1.4 Antenna on (a) a substrate lens and on (b) a thin membrane 8

Fig 2.1  Geometries of the four resonant antennas: (a) full-wavelength

dipole, (b) full-wavelength dual-dipole, (c) half-wavelength

single-slot, and (d) full-wavelength four-leaf-clover-shaped antennas 17

Fig 2.2 (a) Antenna on a semi-infinite substrate; (b) antenna on an extended

hemispherical lens substrate structure 17

Fig 2.3 Input impedance of the (a) dipole, (b) dual-dipole, (c)

single-slot, and (d) four-leaf-clover-shaped antennas on a semi-infinite Si

substrate 19

Fig 2.4 Radiation patterns of the antennas on a semi-infinite Si substrate: (a)

single-dipole, (b) dual-dipole, (c) single-slot, and (d)

four-leaf-clover-shaped antennas at the resonant frequency of around 1.0 THz 22

Fig 2.5 Directivities of the (a) single-dipole, (b) dual-dipole, (c) single-slot,

and (d) four-leaf-clover-shaped antennas on a lens at the resonant

frequency of around 1.0 THz, for varying values of the ratio of the

extension layer thickness to the radius of the hemisphere (T/R) 24

Fig 2.6 Radiation efficiencies of the antennas on a lens as functions of the

ratio of the extension layer thickness to the radius of the hemisphere

(T/R): (a) single-dipole, (d) dual-dipole, (c) single-slot, and (d)

four-leaf-clover-shaped antennas at the resonant frequency of around

1.0 THz 26

Fig 2.7 Radiation patterns of the four antennas on the extended

hemispherical lens with radius of R = 4.5 λ (λ = 300 μm) at the

resonant frequency of around 1.0 THz, plotted at the optimum T/R;

(a) single-dipole, (b) dual-dipole, (c) single-slot, and (d)

four-leaf-clover-shaped antennas 28

Fig 3.1 Geometries of the self-complementary antennas: (a) bowtie, (b)

log-periodic, (c) log-spiral, and (d) a hemispherical lens substrate

structure 35

Fig 3.2 Input impedance of the antenna on a lens with R = 5.0 λo and T/R =

0.3: (a) bowtie, (b) log-periodic, and (c) log-spiral 37

Fig 3.3 Directivity of the antenna for various T/R with fixed R = 5.0 λo: (a)

bowtie, (b) log-periodic, and (c) log-spiral 39

Fig 3.4 Radiation efficiency of the antenna for various T/R with fixed R =

5.0 λo: (a) bowtie, (b) log-periodic, and (c) log-spiral 40

Fig 3.5 Directivity of the antenna for various R with fixed T/R = 0.3: (a)

bowtie, (b) log-periodic, and (c) log-spiral 42

0.3: (a) bowtie, (b) log-periodic, and (c) log-spiral 45

Fig 3.7 Radiation pattern of the antenna at fmax with fixed R = 7.0 λo and T/R

= 0.3: (a) bowtie (2.18 THz), (b) log-periodic (2.28 THz), and (c)

log-spiral (2.18 THz) 46

Fig 4.1 Antenna geometry: (a) top and (b) side view 52

Fig 4.2 The relationship of antenna characteristics to cavity height H 54

Fig 4.3 Antenna characteristics with respect to W side variations for three

different cavity sizes A: (a) 500 µm, (b) 1000 µm, and (c) 1500 µm 56

Fig 4.4 Radiation pattern comparison with the fixed bulk GaAs substrate size

W bulk of 4000 µm for three different cavity sizes A (a) x–z plane, (b)

y–z plane plotted at the resonance frequency of 1.05 THz 57

Fig 4.5 The relationship of antenna characteristics to membrane thickness t 59

Fig 4.6 Antenna characteristics according to diameter of the ground-plane

hole d 60

Fig 4.7 Full-wavelength dipole antenna with a PBG bias line structure 61

Fig 4.8 Input resistance and radiation efficiency as a function of (a) the

distance between the first PBG cell and the full-wavelength dipole,

(b) the gap between the high-impedance lines 62

Fig 4.9 (a) Input resistance and (b) radiation efficiency of the optimized

antenna with and without the PBG bias line structure 63

Fig 4.10 Radiation patterns of the optimized antenna structure with PBG bias

line structure at frequencies of 1.03 THz, 1.05 THz, and 1.07 THz 63

Fig 5.1 Geometry of the proposed antenna: (a) front view and (b) top view 71

Fig 5.2 Antenna characteristics according to the length of the bend, L bend,

(without a hemispherical lens) 74

Fig 5.3 Antenna characteristics with respect to the change of the connection

position, D connect (without a hemispherical lens) 75

Fig 5.4 Simulation results for the antenna with the modified PBG bias line

but without a hemispherical lens: (a) input resistance (compared with

the straight case) and (b) radiation patterns 77

Fig 5.5 Antenna characteristics with variations in the size of the bulk GaAs

substrate W bulk in the presence of the hemispherical lens: (a) antenna

efficiency and (b) antenna directivity 79

Fig 5.6 Antenna efficiency and directivity with respect to the depth of the

trench, t support, in the extension layer of the hemispherical lens 82

Fig 5.7 Antenna efficiency and directivity with respect to the width of the

trench, A2, in the extension layer of the hemisphere lens 82

Fig 5.8 Efficiency and directivity of the antenna on a lens with variations in

the T/R ratio (extension layer thickness to the radius of hemisphere) 82

Fig 5.9 (a) Input resistances and (b) radiation patterns of the optimized

antenna structure 84

Fig 6.1 Antenna geometry with (a) front view, (b) top view of the FSS layer,

(c) top view of the GaAs membrane substrate, and (d) top view of

Fig 6.2 (a) Input resistance and radiation efficiency and (b) directivity of the

antenna with respect to the changes of the cavity size (A) 94

Fig 6.3 Current distribution induced on the FSS for two different cavity sizes;

(a) A = 1000 μm and (b) A = 2000 μm 94

Fig 6.4 (a) Input resistance, (b) radiation efficiency, and (c) directivity of the

antenna with respect to the changes of the number of holes in the

FSS for different cavity sizes (A) 96

Fig 6.5 Radiation patterns in (a) the x-z plane and (b) the y-z plane of the

antenna with different numbers of holes in the array where A = 2000

μm 98

Fig 6.6 Resonance frequency with respect to the position of the quartz

substrate 98

Fig 6.7 (a) Efficiency and (b) directivity of the antenna with respect to the

quartz substrate thickness variation 100

Fig 6.8 Simulated results of the optimized antenna (a) input resistance and

radiation efficiency, (b) directivity, and (c) radiation patterns at the

resonance frequency of 1.03 THz 101

Fig 7.1 Photoconductive antenna structure 108

Fig 7.2 Input impedance characteristics of the antenna (L d = 40 μm) with

respect to the change in the bias line length L b : (a) L b = 50 μm, (b) L b

= 100 μm, (c) L b = 150 μm, and (d) L b = 200 μm 110

Fig 7.3 Input impedance characteristics of the antenna (L d = 40 μm) with

respect to the change in the bias line length L b : (a) L b = 2000 μm, (b)

L b = 4000 μm, (c) L b = 6000 μm, and (d) L b = 8000 μm The insets

show zoomed-in views at low frequencies 112

Fig 7.4 Current distribution along the bias lines (L b = 8000 μm) of the

antenna (L d = 40 μm) calculated at different frequencies 113

Fig 7.5 Radiation patterns at various frequencies of the antenna (L d = 40 μm)

with a bias line length of L b = 8000 μm xz-plane

yz-plane 114

Fig 7.6 Gain (checked at θ = 180°) and efficiency of the antenna (L d = 40 μm)

with (a) L b = 2000 μm and (b) L b = 8000 μm 116

Fig 7.7 Input impedance of the antenna with different center dipole lengths

(L b = 8000 μm) 118

Fig 7.8 (a) Gain and (b) efficiency of the antennas with different center

dipole lengths (L b = 8000 μm) 118

LIST OF TABLES

Page

Table 1.1 Different THz sources with output power levels 3

Table 2.1  Comparison of characteristics of the four antennas on the extended

hemispherical lens with radius of R = 4.5 λ (λ = 300 μm) 30

Table 5.1 Design parameters of the optimized antenna design with a lens

substrate for a maximum directivity and maximum total efficiency 85

Table 6.1 Design parameters for maximum total efficiency and directivity at

1.03 THz of the proposed antenna 103

Chapter 1 Introduction

1.1 Terahertz radiation and sources

The terahertz (THz) range, which is with wavelengths between 3000-30μm (0.1-10 THz), bridges the gap between microwave and infrared frequencies, has long been known as the THz gap and being until recently one of the least explored regions of the electromagnetic spectrum, see Fig 1.1 The primary reason is due to the lack of suitable and efficient signal sources and detectors and this limits applications to a number of areas that demand highly reliable performance, ranging from molecular spectroscopy to astronomy, environment monitoring, bio-imaging, and security screening [1-5], see Table 1.1 Nevertheless, several efforts have been still conducted because of the unique characteristics of THz radiation related to wavelength, photon energy, spectral fingerprint, and time-domain spectroscopy For example, THz wave can be used to see through the internal structure of opaque objects,

to analyze a molecule-level mechanism, to transmit radio signal from space, or to provide much higher data transmission rates [6-8] Despite of that, there exist some fundamental concerns causing problem for future development of THz application; high attenuation as propagating in air, weak signal as passing a thick sample, and low efficiency of the present THz sources

To date, both pulsed and continuous-wave (CW) THz sources have been realized

in two different schemes either using non-linear optical media or accelerating electrons

Several methods to generate THz radiation have been developed and can be classified into two classes illustrated in Fig 1.2: broadband (pulse) and narrow band (CW) sources Most broadband THz sources are based on the generation of pulsed THz radiation by exciting material with ultrashort laser pulses, using mechanisms such as carrier acceleration in photoconductive antenna [9], optical rectification in non-linear media [10], and surface current at semiconductors [11] The pulsed THz sources enable broadband THz spectroscopy but giving a low spectral resolution of only several tens of GHz In comparison with pulsed THz sources, CW THz sources provide a narrow line-width in THz spectrum but with a higher spectral THz power Such CW THz sources are significant for high-resolution THz spectroscopy, THz sensing, and broadband THz communication There are several means to generate CW THz radiation such as Gunn diodes, backward oscillator, CO2-laser pump gas laser, non-linear difference frequency generation, optical parametric oscillators, free-electron lasers, quantum cascade lasers and photomixers At the same time, various coherent detection techniques have been created for detecting pulsed and CW radiation Electro-optic sampling have been chosen for pulsed THz radiation detection while photomixing and heterodyne have been primarily used for detecting CW THz radiation

1.2 THz photoconductive antenna

Antenna is designed on the surface of the semiconductor substrate for efficient coupling of the generated THz radiation from substrate into free space The photoconducting antenna

z sources with

ctor bulk matsed onto the

or material Tnerate a THzich are phot

d THz systems

h output powe

terial with twgap betweenThese carrier

z wave Figutoconductive s)

er levels

wo metal elect

n the two ele

rs are then acure 1.2 showswitch (bro

trodes on top.ectrodes, freeccelerated by

ws two mainoadband THz

Fig 1.2 (a) Photoconductive switch for broadband THz systems and (b) photomixer for

narrow band THz systems

The typical substrate used for THz photoconductive antenna is low-temperature grown (LTG) GaAs substrate which processing several advantages of short carrier life time (less than 0.25 ps), high electrical breakdown field (greater than 5 x 105 V/cm), and high carrier mobility (greater than 200 cm2 V-1s-1) Among the many previously mentioned THz sources, photomixers are considers one of the most promising techniques owning to their compactness, widely tunable frequency range, and operability at room temperature [12-16] The THz frequency range of the THz photomixer can be tuned by varying the difference frequency of the two laser beams The stability of THz radiation is linked to the stability of the optical beat signals

1.3 THz photomixer and antenna

A typical THz photomixer system is implemented by integrating photomixer elements with

a compact planar antenna on a dielectric lens to achieve efficiency coupling of the THz

radiation to free space The planar antenna can be considered as a THz photomixer antenna which consists of an antenna for radiating THz waves into free space and a bias stripline for applying DC bias to the photomixer element Though owning several advantages, a THz photomixer system produces a low output power, on the order of few microwatts, and this drawback is caused by two THz photomixing mechanisms One is the low conversion efficiency of the photomixer from the incident laser to the THz photocurrent This is related to the transit time and photocarrier lifetime, and it can be overcome by an improvement in the photoconductor [17-18] and the design of the photomixer structure [19] The other drawback is the low total efficiency of the antenna from the THz photocurrent to the THz wave, which can be overcome by the design of the antenna structure The total efficiency in a THz antenna design is the product of the internal

efficiency (or laser-to-electrical power-conversion efficiency) ε LE,the radiation efficiency

ε radiation , and the impedance matching efficiency ε match [20] and can be expressed as:

In this expression, the impedance-matching efficiency is calculated from

2

* antenna photomixer match

* antenna photomixer

Fig 1.3 Equivalent circuit of the photomixer integrated with a THz antenna

depends on factors such as the photoconductive material, excitation power, and bias conditions This efficiency is very small, resulting in an extremely low total photomixer efficiency Clearly, improving the laser-to-electrical power-conversion efficiency, matching efficiency, and radiation efficiency of the antenna would significantly improve the total efficiency of a THz photomixer design

Figure 1.3 shows an equivalent circuit of a photomixer integrated with a THz antenna The photomixer can be represented as a shunt circuit of a photoconductance and a

capacitance G P (ω) is the photoconductance of the photomixer, and C elect is the capacitance

due to the accumulated charge between the electrodes of the photomixer Y a (ω) is a shunt

admittance of the antenna, and Y b (ω) is a shunt admittance of the bias line Both the

antenna and the bias line can be represented by an equivalent shunt circuit with the photomixer Since the bias line functions as a part of the antenna, the equivalent

admittance of Y a (ω) and Y b (ω) can be represented as Y L (ω), the total admittance of the

antenna From the equivalent circuit, the THz output power can be calculated

as follows [21]:

2 0

) ( )

( ) (

) ( 1

2 )

P

L L

B C G

G

G I

where P L (ω) is the output power of the antenna, τ is a photocarrier recombination lifetime,

and G L (ω) and B L (ω) are the conductance and susceptance of the antenna, respectively

Since the imaginary part becomes zero at resonance, we have Celect BL(  )  0 Therefore, the power transferred to the antenna is expressed as follows:

2 0

) ( ) (

) ( 1

2 )

L L

G G

G I

) ( ) (

) ( ) ( 1

2 ) (

) (

L P

L

L

G G

G G

I G

P , the maximum power is transferred to

the antenna Therefore, when the input resistance of the antenna and the photomixer are equal, the THz output power is maximized Thus, the impedance matching between photomixer and antenna is one of the key factors in improving the efficiency of the THz photomixer system The input resistance of the photomixer is typically above 10 kΩ when photomixing with two incident continuous wave (CW) lasers, whereas that of the antenna

is generally low This causes quite low mismatch efficiency between photomixer and

(a) (b)

Fig 1.4 Antenna on (a) a substrate lens and on (b) a thin membrane

particularly important due to the resonance effects of the antenna structure and the reduced conductivity of metals at THz frequencies Therefore, an antenna structure with high input resistance and high radiation efficiency would yield a significantly improved total efficiency for the antenna in converting the THz photocurrent into the THz wave

1.4 Substrate for THz antenna design

There are two main schemes for using a substrate in a THz photoconductive antenna which are a thick substrate of lens and a thin substrate of membrane Generally, electromagnetic waves that radiate from an antenna on the dielectric substrate penetrate the substrate side in

a ratio of εr3/2:1 Each substrate scheme, shown in Fig, 1.4, generally has their own advantages and disadvantages The substrate lenses produce high directivity antenna pattern, allow IC technique compatibility, mechanical rigidity, thermal stability, multi-beam formation capability, and to be capable of suppressing surface-wave losses However,

their overall dimension is big with several wavelengths even at centimeter size Particularly, the antenna on a substrate lens have been suffered an inherent obstacle of the input impedance reduction caused by the high permittivity lens substrate The thin substrate with membrane structure allows to maintain antenna impedance, integrated subsystem possibility, simple transmission measurements, reduction of loss and dispersion effects, suppression of unwanted substrate modes, and increased directivity by a ground plane However, the antennas on such substrate structures are difficult to fabricate and typically exhibit moderate directivity In general, the substrate for THz photoconductive antenna has to be considered in particular in one hand for the overall antenna performance and in another hand for the device realization

1.5 Thesis organization

The thesis is organized in seven chapters as follow:

Chapter 2 and Chapter 3: These two chapters cover the study of antenna on a substrate

lens The resonant type and the self-complementary type with different antenna geometries are chosen for individual examination The overall performance of the antennas is also compared

Chapter 4: A full-wavelength dipole antenna was designed on a GaAs membrane substrate

for an improved input impedance The input impedance and the radiation efficiency are optimized with respect to the membrane geometry Also, the back excitation configuration

is also considered

Chapter 5: A substrate lens is designed for the antenna in Chapter 4 The substrate lens is

with a non-contact configuration with the main radiator so that the impedance affected by the high permittivity lens is minimized The antenna shape and size is also studied and optimized to obtain a maximum antenna directivity

Chapter 6: A frequency-selective surface (FSS) is designed for the antenna in Chapter 4

The effects of number of holes, size of the cavity in the GaAs membrane substrate, also the substrate supporting FSS layer are investigated The maximum directivity of the antenna can be obtained with a careful design FSS layer

Chapter 7: This chapter considers a photoconductive H-shaped dipole antenna by

investigating the antenna response itself The effects of antenna design parameters, i.e., the bias line and the center dipole, on the impedance and radiation characteristics of the antenna are investigated Some interesting phenomenon are drawn and evaluated in the antenna perspective

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Chapter 2 Terahertz Resonant Antennas on Semi-Infinite

and Lens Substrate

This chapter is concerned with four different types of resonant antennas on semi-infinite and lens substrates made of high-permittivity dielectric materials at terahertz frequency Full-wavelength single-dipole, full-wavelength dual-dipole, half-wavelength single-slot, and full-wavelength four-leaf-clover-shaped dipole antennas are studied at a frequency of around 1.0 THz The resonance characteristics of the four antennas are first investigated on

a semi-infinite substrate, using the moment simulator FEKO Based on these characteristics, the antennas are placed on an extended hemispherical lens to examine and compare the radiation effects of a substrate lens on each antenna, using the finite-integration time-domain simulator CST Microwave Studio The shape of an extended hemispherical lens with optimum thickness and quarter-wavelength matching layer plays

an important role in maximizing the directivity, while the radiation efficiency is generally affected by the antenna structure

2.1 Introduction

The idea of using a planar antenna that has been lithographically integrated on the surface

of a dielectric lens to couple electromagnetic radiation to active semiconductor devices is attractive because of its potential for eliminating substrate modes and increasing the

Gaussian coupling efficiency (Gaussicity) In addition, the fabrication procedures are well suited to monolithic or hybrid integrated circuit technology, and offer greater dimensional accuracy and durability, and reduced cost Since the lens is electrically large compared to the antenna, the antenna elements act as if they are at the interface of an air–dielectric half-space Moreover, aside from the radiation patterns, an antenna exhibits similar resonant characteristics on both a lens substrate and a semi-infinite substrate [1] Hence, an antenna designed on a semi-infinite substrate can be used in the initial investigation of its resonant characteristics, which saves a significant amount of computational time

A comparison of dipole, bow-tie, spiral, and log-periodic antennas on a thin substrate at infrared frequencies has recently been reported [2] However, planar antennas built on a substrate are quite different from ordinary antennas in free space or on a thin substrate, primarily because antennas tend to radiate most of their energy on the substrate side, especially on high-permittivity substrates at high frequencies The properties of antennas on semi-infinite substrates have been studied extensively for many years, from substrates made of lossy dielectrics (such as water or earth) [3-5] to substrates made of lossless dielectrics (such as GaAs or silicon) [1, 5–9] However, there have been no detailed studies comparing several types of resonant antenna on lossless semi-infinite and lens substrates made of high-permittivity materials at terahertz (THz) frequency

For terahertz receivers, planar integrated quasi-optical technology, implemented by mounting a planar antenna on a substrate lens, is expected to be a preferable alternative to waveguide-based front ends Recent progress in nano-structuring and micro-machining

enables reliable production and alignment of planar antenna structures on dielectric lenses with sufficient accuracy for high-frequency operation Furthermore, it has been shown that this type of integrated lens antenna makes a THz heterodyne receiver perform better when combined with a hot electron bolometer (HEB) [10–12] Therefore, a planar integrated lens antenna with optimum substrate and antenna structure plays a critical role in optimizing an output power design Single- and dual-antenna elements, such as dipoles and slots, have been successfully used on quartz and silicon dielectric lenses at millimeter-wave and terahertz-regime frequencies [13–17] The conventional design technique for a planar integrated lens antenna is generally based on the hybrid complementation of geometrical optics (GO) inside the lens and physical optics (PO) outside the lens to characterize the field irradiated by the feeds and the Gaussian coupling efficiency However, there remains

a need for full characterization and comparison of several types of resonant antennas, particularly at THz frequencies

In this chapter, we examine and compare the overall performance of several types of resonant antenna in terms of input impedance, radiation patterns, and radiation efficiency The four antenna types selected for this research are full-wavelength single-dipole, full-wavelength dual-dipole, half-wavelength single-slot, and full-wavelength four-leaf-clover-shaped dipole, all designed to resonate at around 1.0 THz Two radiation environments are

used to investigate the characteristics of each antenna: a semi-infinite Si substrate (ε r = 11.7) and an extended hemispherical lens made entirely of Si This study should be very helpful to optimize several types of resonant antenna on a substrate lens for THz

photomixer designs

2.2 Antennas and substrate geometries

Figure 2.1 shows the four types of antenna under consideration The antennas were all designed to resonate at around 1.0 THz for the sake of comparison The metal layer had a conductivity of 1.6  107 S/m and a thickness of 0.35 μm The single-dipole, dual-dipole, and four-leaf-clover-shaped antennas all had a total length of approximately 1 λ at about 1.0 THz on the Si substrate, in order to provide maximum input resistance However, the single-slot antenna provided maximum input resistance at a total length of approximately λ/2, since a slot antenna is complementary to a dipole antenna (in accordance with Babinet's principle) Accordingly, these four resonant antennas exhibited high input resistance characteristics suitable for THz photomixer designs The initial dimensions of

the antennas were as follows: L D = 94 μm and w D = 3 μm for the single-dipole antenna [Fig

2.1(a)]; A = 70 μm, B = 49 μm, C = 3 μm, D = 1 μm, and E = 5 μm for the dual-dipole antenna [Fig 2.1(b)]; L S = 46 μm and w S = 3 μm for the single-slot antenna [Fig 2.1(c)];

D x = D y = 37 μm, G x = G y = 2 μm, and w = 3 μm for the four-leaf-clover-shaped antenna

[Fig 2.1(d)] Note that the right and left halves of the four-leaf-clover-shaped antenna each

formed a full-wavelength dipole with a total length of approximately 2[(Dx + Dy)  (Gx +

Gy) – 1.5w], corresponding to 1 λ at about 1.0 THz on the Si substrate [18] Figure 2.2 (a)

and (b) show prototypes of an antenna on a semi-infinite Si substrate (ε r, sub = 11.7) and an

extended hemispherical Si lens (ε r, ext = ε r, lens = 11.7), respectively The extension layer and

(a) (b) (c) (d)

Fig 2.1 Geometries of the four resonant antennas: (a) full-wavelength single-dipole, (b)

wavelength dual-dipole, (c) half-wavelength single-slot, and (d) wavelength four-leaf-clover-shaped antennas

Fig 2.2 (a) Antenna on a semi-infinite substrate; (b) antenna on an extended

hemispherical lens substrate structure

radius of the lens are denoted by T and R, respectively A λ/4-thick matching layer, made of plexiglass (ε r = 3.4), was used to suppress reflected waves from the internal lens surface

2.3 Antenna characteristics

2.3.1 Semi-infinite Si substrate

The four antennas were simulated via the FEKO software package featuring the method of moments (MoM), the Si substrate being approximated with a semi-infinite Green's function layer The single-slot antenna was fed by a wire port, while the single-dipole, dual-dipole, and four-leaf-clover-shaped antennas were all fed by an edge port with the same voltage source (of magnitude 1 V) The single-slot antenna was oriented in the x-direction, whereas the other three antennas were oriented in the y-direction, in order to provide a clear comparison of the antenna radiation patterns

The input impedance characteristics of the single-dipole, dual-dipole, single-slot, and four-leaf-clover-shaped antennas are shown in Fig 2.3 (a–d), respectively The single- and dual-dipole antennas resonated at around 1.0 THz, and had input resistances of 302 Ω and 220 Ω, respectively The single-slot antenna exhibited a slightly lower input resistance than the two dipole antennas, and had an input resistance of 170 Ω at the resonant frequency of 1.0 THz The highly resonant four-leaf-clover-shaped antenna had a high input resistance of about 1800 Ω at the resonant frequency of 1.0 THz The high input resistance of this antenna was due to the high Q and narrow band characteristics of the design

Figure 2.4 (a–d) shows the radiation patterns of the four antennas plotted in the E- and H-planes, which respectively correspond to the yz- and xz-planes of the antennas’

orientation As the figure indicates, all of the antennas exhibited radiation patterns with a

(a) (b)

Fig 2.3 Input impedance of the (a) single-dipole, (b) dual-dipole, (c) single-slot, and (d)

four-leaf-clover-shaped antennas on a semi-infinite Si substrate

minimum in the E-plane and a maximum in the H-plane at the critical angle θ c = π – sin1

[(ε r) 1/2] on the dielectric side, which is about 163 for the Si substrate (εr = 11.7) Both the E- and H-plane patterns of the four antennas had a null value at the air–dielectric interface

For the single-dipole antenna, the E-plane beam pattern was narrower than the H-plane

beam pattern due to the nature of current distribution on the dipole However, for the

dual-dipole antenna, the E-plane beam pattern was wider than the H-plane beam pattern because

of the array effect Hence, a small side lobe appeared near the interface in the H-plane pattern of the dual-dipole antenna For the four-leaf-clover-shaped antenna, the E-plane and H-plane patterns were almost identical to those of the single-dipole antenna, but the E- plane beam pattern was wider than the H-plane pattern This beam angle behavior was

similar to that of the dual-dipole antenna The radiation patterns on the air sides of the single-dipole, dual-dipole, and four-leaf-clover-shaped antennas were almost identical

However, the E-plane and H-plane radiation patterns of the single-slot antenna were quite

different from those of the other three antennas, as can be seen in Fig 2.4(c) Since the patch was modeled to be infinite in extent, the two media (air and dielectric) were effectively isolated Minimum and maximum values did not occur at the critical angle for

the single-slot antenna The E-plane had no null value at the air–dielectric interface, but the

H-plane did, as noted in [5]

From the radiation efficiency and directivity perspectives, the four antennas behaved differently The radiation efficiencies of the single-dipole, dual-dipole, and four-leaf-clover-shaped antennas were 95%, 82.5%, and 51%, respectively The maximum directivities at the critical angle were 9.9, 9.8, and 8.9 dBi for the single-dipole, dual-

dipole, and four-leaf-clover-shaped antennas, respectively The directivities at θ = 180

were 7.7, 8.7, and 7.9 dBi, corresponding to directivity differences (compared to the maximum values at the critical angles) of 2.2, 1.1, and 1.0 dBi for the single-dipole, dual-dipole, and four-leaf-clover-shaped antennas, respectively For the single slot antenna, the

radiation efficiency was 78.8% and the directivity at θ = 180 was only 1.2 dBi This

behavior variation was also noted in [5], in which it was reported that the radiation of a slot

in an infinite ground does not concentrate in a cone, as with a current dipole

2.3.2 Extended hemispherical Si lens substrate

The four antennas were simulated on a substrate lens using the commercially available electromagnetic simulator CST Microwave Studio, which is based on the finite-integration time-domain technique Except for the radiation patterns, antennas exhibit similar resonant characteristics on either a lens substrate or a semi-infinite substrate [1] Accordingly, we investigated the radiation of the four antennas in general, and the directivity of the main

beam on the z-axis in particular (θ = 180), by varying the ratio of the extension layer thickness to the radius of the hemisphere (T/R) The results are shown in Fig 2.5 (a–d) We

used hemisphere radii of 2.5, 3.5, and 4.5 λ at a resonant wavelength of 300 μm in free

space The ratio T/R was varied from 0.25 to 0.5 for each value of the hemisphere radius,

and the results were plotted separately for each antenna It should be noted that all directivities and radiation efficiencies shown in the figure were deduced from the radiation patterns of the antennas at the resonant frequency of around 1.0 THz In general, higher directivity of the main beam was achieved with a larger hemisphere radius for all four antennas In addition, the extension layer thickness for maximum directivity became more distinct as the radius of the hemisphere increased

(a) (b)

Fig 2.4 Radiation patterns of the antennas on a semi-infinite Si substrate: (a)

single-dipole, (b) dual-single-dipole, (c) single-slot, and (d) four-leaf-clover-shaped antennas

at the resonant frequency of around 1.0 THz

For the single-dipole antenna [Fig 2.5(a)], the maximum directivity of the radiation

pattern was 24.0 dBi at a ratio of T/R = 0.36, 26.8 dBi at T/R = 0.37, and 28.4 dBi at T/R =

0.35 for hemisphere radii of 2.5, 3.5, and 4.5 λ, respectively Beam-splitting phenomena

(i.e., maximum not at θ = 180) occurred at ratios of T/R = 0.41, 0.44, and 0.46 for

hemisphere radii of 2.5, 3.5, and 4.5 λ, respectively For the dual-dipole antenna [Fig

2.5(b)], the maximum directivity of the radiation pattern was 23.6 dBi at a ratio of T/R = 0.36, 26.0 dBi at T/R = 0.37, and 28.0 dBi at T/R = 0.36 for hemisphere radii of 2.5, 3.5,

and 4.5 λ, respectively Beam-splitting phenomena also occurred in this case, at ratios of

T/R = 0.42, 0.44, and 0.45 for hemisphere radii of 2.5, 3.5, and 4.5 λ, respectively, but with

a degree of suffering far less than that of the single-dipole antenna For the single-slot antenna [Fig 2.5(c)], the maximum directivity of the radiation pattern was 24.0 dBi at a

ratio of T/R = 0.38, 26.6 dBi at T/R = 0.37, and 28.5 dBi at T/R = 0.37 for hemisphere radii

of 2.5, 3.5, and 4.5 λ, respectively The directivity was almost constant in the range of T/R

values from 0.35 to 0.43 for the small radius case R = 2.5 λ For the larger hemisphere

radii, main-beam splitting occurred (at ratios of T/R = 0.45 and 0.43 for hemisphere radii

of R = 3.5 and 4.5 λ, respectively) For the four-leaf-clover-shaped antenna [Fig 2.5(d)], the maximum directivity of the radiation pattern was 24.6 dBi at a ratio of T/R = 0.38, 27.3 dBi at T/R = 0.37, and 29.3 dBi at T/R = 0.37 for hemisphere radii of 2.5, 3.5, and 4.5 λ, respectively Beam-splitting phenomena occurred at ratios of T/R = 0.48, 0.45, and 0.44 for

hemisphere radii which main-beam splitting occurred increased slightly with the hemisphere radius, resulting in broad, gently sloping directivity curves In contrast, the directivity curves for the single-slot and four-leaf-clover-shaped antennas became progressively sharper with increasing hemisphere radius, since the ratio at which main-beam splitting occurred decreased Generally speaking, the four antennas exhibited almost

(a) (b)

Fig 2.5 Directivities of the (a) single-dipole, (b) dual-dipole, (c) single-slot, and (d)

four-leaf-clover-shaped antennas on a lens at the resonant frequency of around 1.0 THz, for varying values of the ratio of the extension layer thickness to the radius

of the hemisphere (T/R)

the same maximum directivity for the same hemispherical lens substrate structure, but the optimum extension layer thicknesses varied according to antenna type

In Fig 2.6, the variation in radiation efficiency of each of the four antennas is

plotted as a function of the ratio T/R for hemisphere radii of 2.5, 3.5, and 4.5 λ For the