Periodic Structures E-Book

Ruey-Bing Hwang

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 349

Veröffentlichungsjahr: 2012

Beschreibung

PERIODIC STRUCTURES

Mode-Matching Approach and Applications in Electromagnetic Engineering

In Periodic Structures, Hwang gives readers a comprehensive understanding of the underlying physics in meta-materials made of periodic structures, providing a rigorous and firm mathematical framework for analyzing their electromagnetic properties. The book presents scattering and guiding characteristics of periodic structures using the mode-matching approach and their applications in electromagnetic engineering.

• Provides an analytic approach to describing the wave propagation phenomena in photonic crystals and related periodic structures
• Covers guided and leaky mode propagation in periodic surroundings, from fundamentals to practical device applications
• Demonstrates formulation of the periodic system and applications to practical electromagnetic / optical devices, even further to artificial dielectrics
• Introduces the evolution of periodic structures and their applications in microwave, millimeter wave and THz
• Written by a high-impact author in electromagnetics and optics
• Contains mathematical derivations which can be applied directly to MATLAB® programs
• Solution Manual and MATLAB® computer codes available on Wiley Companion Website

The book is primarily intended for graduate students in electronic engineering, optics, physics, and applied physics, or researchers working with periodic structures. Advanced undergraduates in EE, optics, applied physics applied math, and materials science who are interested in the underlying physics of meta-materials, will also be interested in this text.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

Chapter 1: Introduction

1.1 Historical Perspective on the Research in Periodic Structures

1.2 From 1D Periodic Stratified Medium to 3D Photonic Crystals: An Overview of this Book

References

Further Readings

Chapter 2: Wave Propagation in Multiple Dielectric Layers

2.1 Plane-Wave Solutions in a Uniform Dielectric Medium

2.2 Transmission-Line Network Representation of a Dielectric Layer of Finite Thickness

2.3 Scattering Characteristics of Plane Wave by Multiple Dielectric Layers

2.4 Transverse Resonance Technique for Determining the Guiding Characteristics of Waves in Multiple Dielectric Layers

Appendix: Dyadic Definition and Properties

References

Further Reading

Chapter 3: One-Dimensional Periodic Medium

3.1 Bloch–Floquet Theorem

3.2 Eigenwave in a 1D Holographic Grating

3.3 Eigenwave in 1D Dielectric Gratings: Modal Transmission-Line Approach

3.4 Eigenwave in a 1D Metallic Periodic Medium

3.5 Hybrid-Mode Analysis of a 1D Dielectric Grating: Fourier-Modal Approach

3.6 Input–Output Relation of a 1D Periodic Medium of Finite Thickness

3.7 Scattering Characteristics of a Grating Consisting of Multiple 1D Periodic Layers

3.8 Guiding Characteristics of Waveguides Consisting of Multiple 1D Periodic Layers

References

Further Readings

Chapter 4: Two- and Three-Dimensional Periodic Structures

4.1 Modal Transmission-Line Approach for a 2D Periodic Metallic Medium: In-Plane Propagation

4.2 Modal Transmission Line Approach for a 2D Periodic Dielectric Medium: In-Plane Propagation

4.3 Double Fourier-Modal Approach for a 2D Dielectric Periodic Structure: Out-of-Plane Propagation

4.4 Three-Dimensional Periodic Structures

Appendix: Closed-Form Solution of εpq,mn and μpq,mn

References

Chapter 5: Introducing Defects into Periodic Structures

5.1 A Parallel-Plane Waveguide having a Pair of 1D Semi-Infinite Periodic Structures as its Side Walls

5.2 Dispersion Relation of a Parallel-Plane Waveguide with Semi-Infinite 1D Periodic Structures as Waveguide Side Walls

5.3 A Parallel-Plane Waveguide with 2D Dielectric Periodic Structures as its Side Walls

5.4 Scattering Characteristics of a Periodic Structure with Defects

5.5 A Parallel-Plane Waveguide with 2D Metallic Periodic Structures as its Side Walls

5.6 Other Applications in Microwave Engineering

References

Chapter 6: Periodic Impedance Surface

6.1 Scattering Characteristics of Plane Wave by a 1D Periodic Structure Consisting of a Cavities Array

6.2 Periodic Impedance Surface Approach (PISA)

6.3 Scattering of Plane Wave by 1D Periodic Impedance Surface: Non-Principal Plane Propagation

6.4 Scattering of Plane Wave by a Dyadic 2D Periodic Impedance Surface

References

Chapter 7: Exotic Dielectrics Made of Periodic Structures

7.1 Synthetic Dielectrics Using a 2D Dielectric Columns Array

7.2 Refractive Index of a 2D Periodic Medium

7.3 An Artificial Dielectric Made of 1D Periodic Dielectric Layers

7.4 Conclusion

References

Index

This edition first published 2013

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Library of Congress Cataloging-in-Publication Data

Hwang, Ruey-Bing.

Periodic structures: mode-matching approach and applications in electromagnetic engineering / Ruey-Bing (Raybeam) Hwang.

pages cm

Includes bibliographical references and index.

ISBN 978-1-118-18803-3 (hardback)

1. Electric filters. 2. Optoelectronic devices. 3. Wave guides. 4. Antennas (Electronics) 5. Photonic crystals. 6. Crystal lattices–Electric properties. 7. Electromagnetic waves. I. Title.

TK7872.F5H93 2013

621.3–dc23

2012027877

A catalogue record for this book is available from the Library of Congress.

ISBN: 9781118188033

Preface

My objective in writing this book is twofold. The first objective is to build up a firm and rigorous mathematical framework, namely a mode-matching approach and transmission-line network representation, for analyzing the typical problem of wave processes involved in periodic structures ranging from the one-dimensional to the three-dimensional. The second objective is to allow the reader to understand that most of the interesting phenomena occurring in contemporary periodic structures can be clarified using existing classical electromagnetism, such as coupled-mode theory, phase-matching condition, and so on. I believe that some people will question the mode-matching method in handling periodic structures in regard to two disadvantages: the slow convergence rate for metallic structures and the infinite structure under consideration. I confess that how to solve the electromagnetic fields in a finite periodic structure is not my major concern in this book; after all, there are many well-developed commercial software packages available nowadays based on several numerical methods (e.g., the finite-difference time (frequency) domain, the finite-element method, the integral equation with moment method, the finite-integration method) for dealing with real-world electromagnetic problems in the microwave and optical communities. As to the convergence problem, the modal transmission-line approach to be elucidated in this book can tackle the task. The mode-matching method has its own advantages in facilitating the understanding of electromagnetic fields using the concept of the modal solution; for example, the eigenwave solution in a periodic medium can reveal information concerning the mode phase-and dispersion-relation; the mode dispersion relation in a gratings-assisted waveguide can be directly determined by solving the generalized eigenvalue equation rather than by extracting from electromagnetic fields.

Some of the subject matter in this book has been presented for several years as a one-semester course in the Graduate School of National Chiao-Tung University, Hsinchu, Taiwan. The prerequisites for the course are a knowledge of linear algebra and electromagnetic theory. I have not attempted the task of referring to all relevant publications. The lists of books and journal and conference articles in the reference sections at the ends of each chapter are representative, but are by no means exhaustive.

I would like to thank Professor Song-Tsuen Peng (Professor Emeritus at National Chiao-Tung University) who guided me to this exciting field during my PhD study. I appreciate Prof. Fung-Yuel Chang for polishing my English writing and encouraging me to pursue independent research when he was a visiting Professor in National Chiao-Tung University.

I wish to acknowledge with thanks the consistent encouragement and support I received from Professor Jan-Dong Tseng (National Chin-Yi University of Technology).

I would like to express my gratitude to Professor Chang-Yu Wu, Professor Ching-Wen Hsue at National Taiwan University of Science and Technology, and Professor Raj Mittra at Pennsylvania State University for their constructive suggestions. The following warrant particular mention: Dr. Cheng-Chi Hsiao, Professors T. Tamir and K. M. Leung at Polytechnic University, Brooklyn, New York, my colleagues at National Chiao-Tung University, Professor Sin-Horng Chen (Dean), Professor Li-Chun Wang (Chairman), Professor Jen-Tsai Kuo, Professor Lin-Kun Wu, Professor Kuan-Kin Chan, Professor Yu-De Lin, Professor Shyh-Jong Chung, Professor Yi-Chiu, Professor Malcolm Ng, and Professor Edward-Yi Chang (Dean of Office of Research and Development, NCTU), Professor Ching-Cheng Tien at Chung Hua University, Professor Chien-Jen Wang at National University of Tainan, Professor Chih-Wen Kuo and Professor Ken-Huang Lin at National Sun Yat-Sen University, and Professor Kitazawa Toshihide at Ritsumeikan University, Professors Ming-Shing Lin and Chung-I G. Hsu at National Yunlin University of Science and Technology, Professor Shyue-Win Wei at National Chi-Nan University, Professor Dau-Chyrh Chang at Oriental Institute of Technology.

I would convey special acknowledgement to James Murphy (Publisher at John Wiley & Sons) for his full and consistent support.

Last but not the least, a special word of thanks is also due my wife, Belinda, who took care of everything, including me, during the writing and preparation of this book.

Ruey-Bing (Raybeam) HwangHsinchu, TaiwanMarch 2012

Chapter 1

Introduction

1.1 Historical Perspective on the Research in Periodic Structures

The class of periodic structures has been a subject of continuing interest in the literature. The main effort in the past has been on the scattering and guiding of waves by one-dimensional (1D) periodic structures. In particular, the microwave field has employed periodic structures in many different applications, of which a few examples are linear accelerators, slow-wave structures in microwave tubes, filters, artificial dielectrics, slot arrays, phase-array antennas, frequency-selective structures, leaky-wave antennas, and so on. On the other hand, the 1D periodic structure also has its own applications in optical engineering; for example, in dielectric gratings used in integrated-optics applications (Tamir 1975, 1979) (diffraction gratings for beam splitting, grating couplers, and leaky-wave structures).

In recent years, considerable attention has been focused on the numerical and experimental studies of wave phenomena associated with two-dimensional (2D) and three-dimensional (3D) structures, and many applications have been demonstrated. Most of the potential applications were found and developed in the optics community, such as the photonic crystal. A photonic crystal contains dielectric or metallic inclusions periodically arranged in a 2D or 3D lattice pattern; these mimic a natural crystal with a small and basic building block of atoms or molecules repeated in space. The periodic nature of the dielectric function results in the simultaneous reflection of waves from each period, producing a stop-band where the wave propagation is forbidden. Such behavior is analogous with the electronic band gap in electronic materials, which is caused by introducing a gap into the energy band structure of a crystal so that electrons are forbidden to propagate with a certain energy in a certain direction (Kittle 1986). A semiconductor is the best representative having a complete band gap between the valence and conduction energy bands. Therefore, engineering an artificial crystal with a complete stop-band, which can extend its gap to all possible directions, becomes a hot spot of research interest. With the complete stop-band (or photonic band gap), we may design a photonic crystal waveguide to guide light in a channel surrounded by photonic crystals, which are operated in the stop-band or below-cutoff condition, even in a tight corner (Joannopoulos et al. 1995). Additionally, the complete stop-band can also be employed to design a planar and linear defect. By tailoring the size of defect in a photonic crystal, the single mode can be pinned to the defect, producing the so-called photonic crystal microcavities (Joannopoulos et al. 1995; Soukoulis 2001).

More recently, researchers found that through engineering the commonly used dielectric materials –for example, constructing resonators and wire arrays (with sub-wavelength period) made of metallic strip lines printed on a dielectric substrate (Shelby et al. 2001; Smith et al. 2000) – one may obtain artificial materials that have properties that may not be found in nature, such as having simultaneously negative εeff(ω) and μeff(ω) in a certain frequency band. Such an artificial material is called a metamaterial, which gains its electromagnetic properties from the structure instead of the chemical composition. Interestingly, the “unusual” electromagnetic property of negative refraction (negative refractive index) caused by the simultaneous existence of negative permittivity and permeability were demonstrated numerically (Engheta and Ziolkowski 1964) or experimentally (Eleftheriades and Balmain 2005).