Table Of ContentMODERN LENS
ANTENNAS FOR
COMMUNICATIONS
ENGINEERING
John Thornton
Kao-Cheng Huang
IEEE PRESS
Copyright © 2013 by Institute of Electrical and Electronics Engineers
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
Library of Congress Cataloging-in-Publication Data is available.
ISBN: 978-1-118-01065-5
Printed in the United States of America.
CONTENTS
Preface ix
1
INTRODUCTION 1
John Thornton and Kao-Cheng Huang
1.1 Lens Antennas: An Overview 2
1.1.1 The Microwave Lens 2
1.1.2 Advantages of Lens Antennas 4
1.1.3 Materials for Lenses 5
1.1.4 Synthesis 6
1.2 Feeds for Lens Antennas 8
1.2.1 Microstrip Feeds 8
1.2.2 Horn Feeds 9
1.3 Luneburg and Spherical Lenses 10
1.4 Quasi Optics and Lens Antennas 14
1.5 Lens Antenna Design 18
1.6 Metamaterial Lens 26
1.7 Planar Lens or Phase-Shifting Surface 30
1.7.1 Reflect Array 31
1.7.2 Planar Lens or Lens Array 33
1.8 Applications 36
1.9 Antenna Measurements 37
1.9.1 Radiation Pattern Measurement 37
1.9.2 Gain Measurement 38
1.9.3 Polarization Measurement 38
1.9.4 Anechoic Chambers and Ranges 38
v
2
REVIEW OF ELECTROMAGNETIC WAVES 49
Kao-Cheng Huang
2.1 Maxwell’s Equations 49
2.1.1 Boundary Conditions 53
2.1.2 Equivalence Theorem 55
2.2 Antenna Parameters 56
2.2.1 Beam Solid Angle and Antenna
Temperature 56
2.2.2 Directivity and Gain 58
2.2.3 Antenna Beamwidth 60
2.2.4 Aperture of a Lens 62
2.2.5 Phase Center 63
2.3 Polarization 64
2.4 Wave Propagation in Metamaterials 71
3
POLYROD ANTENNAS 77
Kao-Cheng Huang
3.1 Polyrods as Resonators 78
3.2 The Polyrod as a Radiator 83
3.2.1 Tapered Polyrod Antenna 85
3.3 Patch-Fed Circular Polyrod 90
3.4 Array of Polyrods 97
3.5 Multibeam Polyrod Array 105
4
MILLIMETER WAVE LENS ANTENNAS 113
Kao-Cheng Huang
4.1 Millimeter Wave Characteristics 114
4.1.1 Millimeter Wave Loss Factors 114
4.1.2 Ray-Tracing Propagation 117
4.2 Millimeter Wave Substrate Lens for Imaging 121
4.3 Millimeter Wave and Submillimeter Wave Lens 126
4.3.1 Extended Hemispherical Lens 128
4.3.2 Off-Axis Extended Hemispherical Lens 133
4.3.3 Submillimeter Wave Lens Antennas
for Communications 136
4.4 Analysis of Millimeter Wave Spherical Lens 139
4.5 Waveguide-Fed Millimeter Wave Integrated Lens 141
5
LENS ANTENNAS FOR COMMUNICATIONS FROM
HIGH-ALTITUDE PLATFORMS 147
John Thornton
5.1 Introduction 147
5.2 The High-Altitude Platform Concept 148
5.2.1 Spectrum Reuse Using HAPs 150
5.2.2 Example Results: Cell Power and Interference 155
5.3 Advantages of Lenses over Reflector Antennas 159
5.3.1 Reflectors 160
5.3.2 Lenses 161
5.3.3 Commercial Lens Antennas 162
5.4 Development of a Shaped Beam Low-Sidelobe Lens Antenna with
Asymmetric Pattern 164
5.4.1 Primary Feed 165
5.4.2 Symmetric 5° Beamwidth Antenna 166
5.4.3 Asymmetric Beam 166
5.4.4 Measurements 174
5.5 Lens Antenna Payload Model 177
5.6 Multifeed Lens 178
5.7 Multiple Beam Spherical Lens Antennas for HAP Payload 181
6
SPHERICAL LENS ANTENNAS 187
John Thornton
6.1 Introduction 187
6.2 Spherical Lens Overview 192
6.3 Analytical Methods 195
6.3.1 Ray Tracing 195
6.3.2 SWE 197
6.3.3 Computational Method and Results 202
6.3.4 Generic Feed Pattern 206
6.3.5 Commercial Solvers 208
6.4 Spherical Lens Materials and Fabrication Methods 210
6.4.1 Machined Polymers 210
6.4.2 Molding 212
6.4.3 Polymer Foams 212
6.4.4 PU Dielectric Loss 214
6.4.5 Artificial Dielectrics 215
6.5 Revisiting the Constant-Index Lens 215
6.5.1 A Practical, Patch-Fed Hemispherical Constant-Index Lens 219
6.5.2 Off-Axis Array-Fed Spherical Lens 219
6.6 Cross-Polarization Properties of Spherical Lenses 221
7
HEMISPHERICAL LENS-REFLECTOR SCANNING ANTENNAS 225
John Thornton
7.1 Introduction 225
7.2 Candidate Scanning Antenna Technologies 226
7.3 Spherical and Hemispherical Lens Antenna 228
7.4 Hemispherical Lens Prototype 229
7.5 Evolution of a Two-Layer Stepped-Index Polymer Lens 232
7.6 A Hemispherical Lens-Reflector Antenna for Satellite
Communications 238
7.6.1 Requirements 239
7.6.2 Lens Analysis 240
7.6.3 Three-Layer Lens Geometry 240
7.6.4 Lens Fabrication and Performance 243
7.6.5 Mechanical Tracking System 245
7.6.6 Ground Plane Effects 249
7.6.7 Aperture Blockage in Scanning Lens Reflector 251
7.7 A Low-Index Lens Reflector for Aircraft Communications
(Contribution by D. Gray) 252
Index 268
PREFACE
The aim of this book is to present the modern design principles and analyses of lens
antennas. It gives graduates and RF/microwave professionals the design insights in
order to make full use of lens antennas. The reader might ask: Why is such a book
considered necessary and timely? The reply we would bring to such an inquiry is that
the topic has not been thoroughly publicized recently and so its importance has become
somewhat underestimated. Furthermore, the work has brought about an opportunity to
gather together the authors’ contributions to several areas of research where lens anten-
nas have been promoted. Foremost among these are communications applications,
where of course antennas play a key role and where we will show why certain advan-
tages accrue from the particular characteristics of lens antennas.
The major advantages of lens antennas are narrow beamwidth, high gain, low
sidelobes and low noise temperature. Their structures can be more compact and weigh
less than horn antennas and parabolic reflector antennas. Lens antennas, with their
quasi-optical characteristics, also have low loss, particularly at near millimeter and
submillimeter wavelengths where they have particular advantages. Beam shaping can
be achieved by controlling the phase distribution across the lens aperture in a manner
that can be more accurate and less costly than would be the case for a reflector. Such
a shaped dielectric lens can be more economical to produce in small- to medium-scale
production runs than other antenna types where certain niche applications are consid-
ered. In addition, spherical lens antennas have the benefit of no scan loss and wide
bandwidth, with the option for multiple beams from a common aperture.
Modern Lens Antennas for Communications Engineering serves as an excellent
tool for RF/microwave professionals (engineers, designers, and developers) and indus-
tries with microwave and millimeter wave research projects. For university students,
this book requires a prerequisite course on antennas and electromagnetic waves, which
covers propagation, reflection, and transmission of waves, waveguides, transmission
lines, and some other antenna fundamental concepts. Such a course is usually followed
by design projects. This book can be used as further study material in such design
projects. Advanced students and researchers working in the field of modern communi-
cations will also find this book of interest. Included is a bibliography of current research
literature and patents in this area.
Based on these credentials, this book systematically conducts advanced and up-to-
date treatment of lens antennas. It does not purport to present a far-reaching treatise on
every aspect of lens antennas, but rather, following the introductory chapters, the
emphasis of the work is taken from the authors’ own research of recent years. Example
designs are presented and the analysis of their performance detailed.
A summary of each chapter is as follows.
Chapter 1 gives an overview of different types of lens antennas and their history.
It discusses basic principles of delay lenses (in which the electrical path length is
increased by the lens medium), fast lenses (in which the electrical path length is
decreased by the lens medium), materials for lenses, and applications for lens antennas.
It attempts a fairly broad review of some quite disparate antenna types that are never-
theless classed as “lenses” such as the planar or frequency selective surface type and
also the Fresnel zone variants of dielectric lenses. Antenna measurement techniques are
also summarized.
Chapter 2 reviews important wave propagations and antenna parameters, for the
purpose of consistency in notation and easy referencing. The material progresses
from uniform plane waves in various media, such as lossless and lossy dielectrics, to
all important antenna parameters.
Chapter 3 focuses on low-cost yet high-directivity dielectric polyrod antennas.
Different feeding methods, maximum gain, and beam tilting are discussed in detail. A
multibeam polyrod array is presented where this increases radiation coverage, and
phase compensation is introduced to adjust beam direction.
Chapter 4 tackles millimeter wave issues such as high path loss and high power
consumption. It then explores the variety of millimeter wave lens antennas and novel
design methods. Quasi-optical characteristics of lens antennas are identified for aiding
design at millimeter and submillimeter wavelengths.
Chapter 5 discusses the properties of antennas which would be required for com-
munications from high-altitude platforms. As such, it presents a case study where lens
antennas were identified as being a potential solution for this niche area. Beginning
with a system-level analysis of a cellular architecture employing spectrum reuse through
multiple spot beams, the chapter goes on to show how a type of lens antenna, with
shaped beam and low sidelobes, directly controls cochannel interference. A practical
design and results are reported.
Chapter 6 presents a summary of the properties of spherical lens antennas including
the Luneburg lens and its relatives. Analytical techniques are discussed, beginning with
ray tracing but then leading to the much more powerful spherical wave expansion
technique. Lens construction problems are addressed, and then the properties of
constant-index spherical lenses are summarized.
Chapter 7 follows on from Chapter 6 and reports from several programs where
hemispherical lens-reflector antennas were developed in practice. Here, a hemisphere
with ground plane recovers the equivalent aperture of a spherical lens but in half the
height—a profound advantage where a low profile is required. A dual-beam lens
antenna for satellite communications is reported, as is a constant-index lens reflector
partially developed for aircraft-to-ground links.
John Thornton
Kao-Cheng Huang
1
INTRODUCTION
John Thornton and Kao-Cheng Huang
The topic of lens antennas was widely investigated during the early development of
microwave antennas and was influenced by the extensive body of existing work from
optics. Subsequently, interest declined somewhat as lens antennas were overtaken by
reflectors for high efficiency, large aperture antennas; and by arrays for shaped-beam,
multi-beam, and scanning antennas. Quite recently, as research interest has expanded
into the use of millimeter wave and sub-millimeter wave frequency bands, lens antennas
have again attracted developers’ attention.
This chapter is organized as nine sections to introduce the basics of lens antennas.
Section 1.1 gives an overview of lens antennas, including its advantages, disadvantages,
and the materials encountered. This is followed by a discussion of antenna feeds at
Section 1.2. Then Section 1.3 introduces the fundamentals of the Luneburg lens (a
topic to which Chapters 6 and 7 are dedicated). Section 1.4 introduces quasi-optics and
Section 1.5 treats design rules. A discussion of metamaterials for lens antennas makes
up Section 1.6 and then the planar lens array, which is a relative of the reflect-array
antenna, follows in Section 1.7. Applications are proposed in Section 1.8 and measure-
ment techniques and anechoic chambers discussed in the final section.
2 INTRODUCTION
1.1 LENS ANTENNAS: AN OVERVIEW
The use of dielectric lenses in microwave applications seems to date back to the early
days of experiments associated with the verification of the optical properties of elec-
tromagnetic waves at 60 GHz [1]. However, it was not until World War II that lenses
gained interest as antenna elements. Even then they were not widely used because of
their bulky size at rather low frequencies.
Nowadays there is a renewed interest in dielectric lenses, not least because of the
rapidly growing number of applications for millimeter waves where lens physical
dimensions have acceptable sizes. Besides, very low loss dielectric materials are avail-
able, and present-day numerically controlled machines enable low-cost fabrication of
quite sophisticated lenses made with very good tolerances.
In one of the earliest dielectric lens antenna applications, a homogeneous lens was
designed to produce a wide-angle scanning lobe [2]. Also, homogeneous lenses have
been used as phase front correctors for horns. The lens is often mounted as a cap on a
hollow metallic horn [3]. In this configuration the lens surfaces on both sides can be
used to design for two simultaneous conditions. In addition, lenses may be designed to
further control the taper of the field distribution at the lens aperture [4] or to shape the
amplitude of the output beam in special applications [5].
The aperture of a solid dielectric horn can be shaped into a lens to modify or
improve some radiation characteristics [6]. For instance, the aperture efficiency of a
solid dielectric horn may be improved by correcting the aperture phase error. Alterna-
tively we may use a lens to shape the amplitude of the output beam or to improve the
cross-polarization performance, but because there is only the one lens surface to be
varied, only one of these design targets might be made optimum.
1.1.1 The Microwave Lens
In optics, a lens refracts light while a mirror reflects light. Concave mirrors cause light
to reflect and create a focal point. In contrast, lenses work the opposite way: convex
lenses focus the light by refraction. When light hits a convex lens, this results in focus-
ing since the light is all refracted toward a line running through the center of the lens
(i.e., the optical axis). Save for this difference, convex lens antennas work in an analo-
gous fashion to concave reflector antennas. All rays between wavefronts (or phase
fronts) have equal optical path lengths when traveling through a lens. Fresnel’s equa-
tions, which are based on Snell’s law with some additional polarization effects, can be
applied to the lens surfaces.
In general, lenses collimate incident divergent energy to prevent it from spreading
in undesired directions. On the other hand, lenses collimate a spherical or cylindrical
wavefront produced respectively by a point or line source feed into an outgoing planar
or linear wavefront. In practice, however, complex feeds or a multiplicity of feeds can
be accommodated since performance does not deteriorate too rapidly with small off-
axis feed displacement.
