1st Edition

# Electromagnetic Waves, Materials, and Computation with MATLAB®

**Also available as eBook on:**

Readily available commercial software enables engineers and students to perform routine calculations and design without necessarily having a sufficient conceptual understanding of the anticipated solution. The software is so user-friendly that it usually produces a beautiful colored visualization of that solution, often camouflaging the fact that the program is executing the wrong simulation of the physical problem.

**Electromagnetic Waves, Materials, and Computation with MATLAB ^{®}** takes an integrative modern approach to the subject of electromagnetic analysis by supplementing quintessential "old school" information and methods with instruction in the use of newer commercial software such as MATLAB and methods including FDTD. Delving into the electromagnetics of bounded simple media, equations of complex media, and computation, this text includes:

- Appendices that cover a wide range of associated issues and techniques
- A concluding section containing an array of problems, quizzes, and examinations
- A downloadable component for instructors including PowerPoint™ slides, solutions to problems, and more

Striking a balance between theoretical and practical aspects, internationally recognized expert Dikshitulu Kalluri clearly illustrates how intuitive approximate solutions are derived. Providing case studies and practical examples throughout, he examines the role of commercial software in this process, also covering interpretation of findings. Kalluri’s extensive experience teaching this subject enables him to streamline and convey material in a way that helps readers master conceptual mathematical aspects. This gives them confidence in their ability to use high-level software to write code, but it also ensures that they will never be solely dependent on such programs.

*Part I: Electromagnetics of Bounded Simple Media*

**Electromagnetics of Simple Media**

Introduction

Simple Medium

Time-Domain Electromagnetics

Time-Harmonic Fields

Quasistatic and Static Approximations

Electromagnetics of Simple Media: One-Dimensional Solution

Uniform Plane Waves in Sourceless Medium (ρV = 0, Jsource = 0)

Good Conductor Approximation

Uniform Plane Wave in a Good Conductor: Skin Effect

Boundary Conditions at the Interface of a Perfect Electric Conductor with a Dielectric

AC Resistance

AC Resistance of Round Wires

Voltage and Current Harmonic Waves: Transmission Lines

Bounded Transmission Line

Electromagnetic Wave Polarization

Arbitrary Direction of Propagation

Wave Reflection

Incidence of p Wave: Parallel-Polarized

Incidence of s Wave: Perpendicular-Polarized

Critical Angle and Surface Wave

One-Dimensional Cylindrical Wave and Bessel Functions

Two-Dimensional Problems and Waveguides

Two-Dimensional Solutions in Cartesian Coordinates

TM*mn* Modes in a Rectangular Waveguide

TE*mn* Modes in a Rectangular Waveguide

Dominant Mode in a Rectangular Waveguide: TE10 Mode

Power Flow in a Waveguide: TE10 Mode

Attenuation of TE10 Mode due to Imperfect Conductors and Dielectric Medium

Cylindrical Waveguide: TM Modes

Cylindrical Waveguide: TE Modes

Sector Waveguide

Dielectric Cylindrical Waveguide—Optical Fiber

**Three-Dimensional Solutions**

Rectangular Cavity with PEC Boundaries: TM Modes

Rectangular Cavity with PEC Boundaries: TE Modes

Q of a Cavity

**Spherical Waves and Applications**

Half-Integral Bessel Functions

Solutions of Scalar Helmholtz Equation

Vector Helmholtz Equation

TMr Modes

TEr Modes

Spherical Cavity

**Laplace Equation: Static and Low-Frequency Approximations**

One-Dimensional Solutions

Two-Dimensional Solutions

Three-Dimensional Solution

Miscellaneous Topics on Waves

Group Velocity vg

Green’s Function

Network Formulation

Stop Bands of a Periodic Media

Radiation

Scattering

Diffraction

*Part II: Electromagnetic Equations of Complex Media*

**Electromagnetic Modeling of Complex Materials**

Volume of Electric Dipoles

Frequency-Dependent Dielectric Constant

Modeling of Metals

Plasma Medium

Polarizability of Dielectrics

Mixing Formula

Good Conductors and Semiconductors

Perfect Conductors and Superconductors

Magnetic Materials

Artificial Electromagnetic Materials

Artificial Dielectrics and Plasma Simulation

Left-Handed Materials

Chiral Medium

**Waves in Isotropic Cold Plasma: Dispersive Medium**

Basic Equations

Dielectric–Dielectric Spatial Boundary

Reflection by a Plasma Half-Space

Reflection by a Plasma Slab

Tunneling of Power through a Plasma Slab

Inhomogeneous Slab Problem

Periodic Layers of Plasma

Surface Waves

Transient Response of a Plasma Half-Space

Solitons

**Spatial Dispersion and Warm Plasma**

Waves in a Compressible Gas

Waves in Warm Plasma

Constitutive Relation for a Lossy Warm Plasma

Dielectric Model of Warm Loss-Free Plasma

Conductor Model of Warm Lossy Plasma

Spatial Dispersion and Nonlocal Metal Optics

Technical Definition of Plasma State

**Wave in Anisotropic Media and Magnetoplasma**

Introduction

Basic Field Equations for a Cold Anisotropic Plasma Medium

One-Dimensional Equations: Longitudinal Propagation and L and R Waves

One-Dimensional Equations: Transverse Propagation: O Wave

One-Dimensional Solution: Transverse Propagation: X Wave

Dielectric Tensor of a Lossy Magnetoplasma Medium

Periodic Layers of Magnetoplasma

Surface Magnetoplasmons

Surface Magnetoplasmons in Periodic Media

Permeability Tensor

**Optical Waves in Anisotropic Crystals**

Wave Propagation in a Biaxial Crystal along the Principal Axes

Propagation in an Arbitrary Direction

Propagation in an Arbitrary Direction: Uniaxial Crystal

k-Surface

Group Velocity as a Function of Polar Angle

Reflection by an Anisotropic Half-Space

**Electromagnetics of Moving Media**

Introduction

Snell’s Law

Galilean Transformation

Lorentz Transformation

Lorentz Scalars, Vectors, and Tensors

Electromagnetic Equations in Four-Dimensional Space

Lorentz Transformation of the Electromagnetic Fields

Frequency Transformation and Phase Invariance

Reflection from a Moving Mirror

Constitutive Relations for a Moving Dielectric

Relativistic Particle Dynamics

Transformation of Plasma Parameters

Reflection by a Moving Plasma Slab

Brewster Angle and Critical Angle for Moving Plasma Medium

Bounded Plasmas Moving Perpendicular to the Plane of Incidence

Waveguide Modes of Moving Plasmas

Impulse Response of a Moving Plasma Medium

*Part III: Electromagnetic Computation*

**Introduction and One-Dimensional Problems**

Electromagnetic Field Problem: Formulation as Differential and Integral Equations

Discretization and Algebraic Equations

One-Dimensional Problems

**Two-Dimensional Problem**

Finite-Difference Method

Iterative Solution

Finite-Element Method

FEM for Poisson’s Equation in Two Dimensions

FEM for Homogeneous Waveguide Problem

Characteristic Impedance of a Transmission Line: FEM

Moment Method: Two-Dimensional Problems

Moment Method: Scattering Problem

**Advanced Topics on Finite-Element Method**

Node- and Edge-Based FEM

Weak Formulation and Weighted Residual Method

Inhomogeneous Waveguide Problem

Open Boundary, Absorbing Boundary, Conditions, and Scattering Problem

The 3D Problem

Case Study Ridged Waveguide with Many Elements

Homogenous Ridged Waveguide

Inhomogeneous Waveguide

Finite-Difference Time-Domain Method

Air-Transmission Line

Finite-Difference Time-Domain Solution

Numerical Dispersion

Waves in Inhomogeneous, Nondispersive Media: FDTD Solution

Waves in Inhomogeneous, Dispersive Media

Waves in Debye Material: FDTD Solution

Stability Limit and Courant Condition

Open Boundaries

Source Excitation

Frequency Response

Finite-Difference Time-Domain Method Simulation of Electromagnetic Pulse Interaction with a Switched Plasma Slab

Introduction

Development of FDTD equations

Interaction of a Continuous Wave with a Switched Plasma Slab

Interaction of a Pulsed Wave with a Switched Plasma Slab

Approximate Analytical Methods Based on Perturbation and Variational Techniques

Perturbation of a Cavity

Variational Techniques and Stationary Formulas

*Part IV: Appendices*

Appendix 1A: Vector Formulas and Coordinate Systems

Appendix 1B: Retarded Potentials and Review of Potentials for the Static Cases

Appendix 1C: Poynting Theorem

Appendix 1D: Low-Frequency Approximation of Maxwell’s Equations R, L, C, and Memristor M

Appendix 2A: AC Resistance of a Round Wire when the Skin Depth δ is Comparable to the Radius a of the Wire

Appendix 2B: Transmission Lines: Power Calculation

Appendix 2C: Introduction to the Smith Chart

Appendix 2D: Non-uniform Transmission lines

Appendix 4A: Calculation of Losses in a Good Conductor at High Frequencies: Surface Resistance RS

Appendix 6A: On Restricted Fourier Series Expansion

Appendix 7A: Two- and Three-Dimensional Green’s Functions

Appendix 9A: Experimental Simulation of a Warm-Plasma Medium

Appendix 9B: Wave Propagation in Chiral Media

Appendix 10A: Backscatter from a Plasma Plume due to Excitation of Surface Waves

Appendix 10B: Classical Photon Theory of Electromagnetic Radiation

Appendix 10C: Photon Acceleration in a Time-Varying Medium

Appendix 11A: Thin Film Reflection Properties of a Warm Isotropic Plasma Slab Between Two Half-Space Dielectric Media

Appendix 11B: The First-Order Coupled Differential Equations for Waves

in Inhomogeneous Warm Magnetoplasmas

Appendix 11C: Waveguide Modes of a Warm Drifting Uniaxial Electron Plasma

Appendix 12A: Faraday Rotation versus Natural Rotation

Appendix 12B: Ferrites and Permeability Tensor

Appendix 14A: Electromagnetic Wave Interaction with Moving Bounded Plasmas

Appendix 14B: Radiation Pressure Due to Plane Electromagnetic Waves Obliquely Incident on Moving Media

Appendix 14C: Reflection and Transmission of Electromagnetic Waves

Obliquely Incident on a Relativistically Moving Uniaxial Plasma Slab

Appendix 14D: Brewster Angle for a Plasma Medium Moving at a Relativistic Speed

Appendix 14E: On Total Reflection of Electromagnetic Waves from Moving Plasmas

Appendix 14F: Interaction of Electromagnetic Waves with Bounded Plasmas

Moving Perpendicular to the Plane of Incidence

Appendix 16A: MATLAB® Programs

Appendix 16B: Cotangent Formula

Appendix 16C: Neumann Boundary Conditions: FEM Method

Appendix 16D: Standard Area Integral

Appendix 16E: Numerical Techniques in the Solution of Field Problems

Appendix 17A: The Problem of Field Singularities

Appendix 18A: Input Data

Appendix 18B: Main Programs

Appendix 18C: Function Programs

Appendix 21A: Complex Poynting Theorem

*Part V: Problems*

### Biography

Internationally recognized expert **Dikshitulu Kalluri** is professor of electrical and computer engineering at the University of Massachusetts-Lowell, where he is coordinator of the doctoral program and co-director of the Center for Electromagnetic Materials and Optical Systems (CEMOS). Dr. Kalluri has collaborated with research groups at the Lawrence Berkeley Laboratory, UCLA, the University of Southern California, and the University of Tennessee. He has also served as a faculty research associate at Air Force Laboratories.

"… a required reference in the library of anyone doing research or development in plasma physics or engineering."

—Igor Alexeff, Electrical Engineering Department, University of Tennessee"Most appropriate for advanced engineering students. Comprehensive, yet ‘eases’ into difficult matters."

—Andrew M. Sessler, Lawrence Berkeley National Laboratory"... a meticulously written and extremely useful book for both students and professionals...The approach is especially directed toward electrical engineers whose deeper appreciation of circuits is exploited to help their concept building, [as applied in] transmission line analogies."

"…brings together many increasingly important concepts from previously somewhat separate areas of electromagnetics into one clear and coherent tome."

—Michael A. Fiddy, University of North Carolina at Charlotte