# Infinite-Space Dyadic Green Functions in Electromagnetism

- Muhammad Faryad, Akhlesh Lakhtakia

- August 2018

### Description

In any linear system the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in spacetime, the corresponding output is an entity called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. Numerous research papers have been written on dyadic Green functions when both the input and the output are time harmonic and a linear homogeneous medium occupies all space. This book provides a self-contained survey of the state-of-the-art knowledge of infinite-space dyadic Green functions.### About Editors

Muhammad Faryad is an assistant professor of physics at the Lahore University of Management Sciences and he is a section editor of*Optik: International Journal for Light and Electron Optics*. His current research interests include electromagnetics of complex mediums, surface electromagnetic waves, photonic crystals, and solar cells.

Akhlesh Lakhtakia is the Charles Godfrey Binder (endowed) professor of engineering science and mechanics at Pennsylvania State University and an adjunct professor of electrical engineering at the Indian Institute of Technology Kanpur. He was the editor-in-chief of the

*Journal of Nanophotonics*from its inception in 2007 until 2013.

### Table of Contents

Dedication

Preface

Acknowledgements

1 Introduction

1.1 Concept of infinite-space dyadic Green functions

1.2 Examples of linear operators

1.2.1 RL circuit

1.2.2 Sound wave

1.2.3 Plate vibration

1.2.4 Helmholtz operator

1.3 Linear electromagnetism

1.3.1 Dyadic Green functions for field phasors

1.3.2 Dyadic Green functions for vector potential phasors

1.4 Solution approaches

1.4.1 Spatial-Fourier-transform approach

1.4.2 Direct approach

1.4.3 Eigenfunction-expansion approach

1.4.4 Scalarization approach

1.5 Organization of the monograph

2 Isotropic and Biisotropic Mediums

2.1 Isotropic dielectric-magnetic medium

2.1.1 Dyadic Green functions

2.1.2 Radiation from point-electric dipole

2.1.3 Radiation from point-magnetic dipole

2.1.4 Radiation from electrically small electric-current loop

2.2 Isotropic chiral medium

2.2.1 Dyadic Green functions

2.2.2 Radiation from point-electric dipole

2.2.3 Radiation from point-magnetic dipole

2.2.4 Radiation from an electrically small electric-current loop

2.3 Lorentz-nonreciprocal biisotropy

3 Anisotropic and Bianisotropic Mediums

3.1 Symmetry and antisymmetry

3.2 Uniaxial mediums

3.3 Uniaxial dielectric medium

3.3.1 Dyadic Green functions

3.3.2 Radiation from point-electric dipole

3.3.3 Radiation from point-magnetic dipole

3.4 Uniaxial magnetic medium

3.5 Uniaxial dielectric-magnetic medium

3.5.1 Dyadic Green functions

3.5.2 Radiation from point-electric dipole

3.5.3 Radiation from point-magnetic dipole

3.6 Axially uniaxial reciprocal medium

3.7 Axially uniaxial nonreciprocal medium

3.8 Anisotropic chiral reciprocal medium

3.9 Cross-handed gyrotropy

3.10 General self-dual bianisotropic medium

3.11 A special gyrotropic bianisotropic medium

3.12 General uniaxial bianisotropic medium

3.12.1 Non-gyrotropic medium

3.12.2 Gyrotropic medium

3.13 Transformable medium

3.13.1 Dyadic Green functions

3.13.2 Extensions

3.13.3 Pathologically unirefringent uniaxial dielectric-magnetic medium

3.13.4 Medium inspired by general relativity

3.13.5 Orthorhombic dielectric-magnetic medium with gyrotropic magnetoelectric properties

4 Bilinear Expansions

4.1 Isotropic dielectric-magnetic medium

4.1.1 Cartesian coordinate system

4.1.2 Cylindrical coordinate system

4.1.3 Spherical coordinate system

4.2 Isotropic chiral medium

4.2.1 Cartesian coordinate system

4.2.2 Cylindrical coordinate system

4.2.3 Spherical coordinate system

4.3 Orthorhombic dielectric-magnetic medium

4.3.1 Special case: x = y =

5 Applications of Dyadic Green Functions

5.1 The Ewald{Oseen extinction theorem

5.1.1 Constitutive relations

5.1.2 Dyadic Green functions

5.1.3 Huygens principle

5.1.4 Ewald{Oseen extinction theorem

5.1.5 Surface integral equations for scattering

5.2 Fields in the source region

5.2.1 Depolarization dyadic

5.2.2 Depolarization dyadics for bianisotropic mediums

5.3 Volume integral equations for scattering

5.3.1 Formulation

5.3.2 Method of moments

5.3.3 Polarizability-density dyadics

5.3.4 Coupled-dipole method

5.4 Homogenization

A Dyadics and Dyads

A.1 Matrix representation

A.2 Useful identities

About the authors

### Bibliographic

Paperback ISBN: 9780750329309

Ebook ISBN: 9781681745589

DOI: 10.1088/978-1-6817-4557-2

Publisher: Morgan & Claypool Publishers