# Electromagnetic Wave Theory by Jin Au Kong PDF: An Essential Resource for Electromagnetic Wave Theory and Applications

## Electromagnetic Wave Theory by Jin Au Kong: A Comprehensive Textbook for Students and Researchers

Electromagnetic wave theory is a branch of physics that studies the propagation, interaction, and application of electromagnetic waves in various media. Electromagnetic waves are oscillating electric and magnetic fields that can travel through space or matter. They include visible light, radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. Electromagnetic wave theory has many applications in engineering, communication, radar, remote sensing, imaging, optics, biomedicine, and more.

## electromagnetic wave theory kong pdf download

One of the most influential and authoritative textbooks on electromagnetic wave theory is Electromagnetic Wave Theory by Jin Au Kong. Jin Au Kong was a professor of electrical engineering at MIT and a pioneer in electromagnetic scattering, diffraction, inverse problems, metamaterials, and biophotonics. He published over 500 papers and 10 books on these topics. He also founded the Research Laboratory of Electronics at MIT and served as its director for many years.

In this article, we will introduce you to Electromagnetic Wave Theory by Jin Au Kong and show you how to download the PDF version of this book for free. We will also give you an overview of the book's contents, features, and benefits. Finally, we will highlight some of the key concepts and problems from each chapter and provide you with some references and resources for further reading.

## Overview of the Book

Electromagnetic Wave Theory by Jin Au Kong was first published in 1986 by Wiley. It has since been revised and updated several times. The latest edition was published in 2008 by EMW Publishing. The book consists of 18 chapters and covers a wide range of topics in electromagnetic wave theory. The book is suitable for advanced undergraduate and graduate students as well as researchers and practitioners in the field.

The book has several features and benefits that make it a valuable resource for learning and research. Some of them are:

The book provides a rigorous mathematical treatment of electromagnetic wave theory using vector analysis, complex variables, integral equations, Green's functions, Fourier transforms, dyadic tensors, spectral domain methods, variational principles, perturbation techniques, asymptotic methods, etc.

The book covers both classical and modern topics in electromagnetic wave theory such as plane waves, spherical waves, cylindrical waves, waveguides, resonators, antennas, scattering, diffraction, inverse problems, metamaterials, biophotonics, etc.

The book includes numerous examples, figures, tables, diagrams, graphs, and illustrations to help explain the concepts and applications.

The book contains over 1000 problems and exercises at the end of each chapter to test your understanding and reinforce your learning.

The book provides detailed solutions to selected problems and exercises in the appendix.

The book offers a comprehensive bibliography and index to help you find relevant information and references.

To use the book effectively for learning and research, you should have a solid background in calculus, linear algebra, differential equations, and basic electromagnetics. You should also be familiar with some numerical methods and computational tools for solving electromagnetic problems. You should read the book carefully and follow the derivations and proofs. You should also try to solve as many problems and exercises as possible and compare your answers with the solutions provided. You should also consult the references and resources for further reading to deepen your knowledge and broaden your perspective.

## Chapter Highlights

In this section, we will give you a brief summary of each chapter and its main concepts. We will also provide you with some examples of problems and exercises from each chapter. We will not go into too much detail or technicality, but rather give you a general overview and a taste of what the book has to offer.

### Chapter 1: Introduction

This chapter introduces the basic concepts and principles of electromagnetic wave theory. It reviews the Maxwell's equations, the constitutive relations, the boundary conditions, the Poynting theorem, the wave equation, the polarization, the dispersion, the attenuation, the reflection, the refraction, the Snell's law, the Fresnel's formulas, the Brewster's angle, the total internal reflection, the evanescent waves, etc. It also discusses some applications of electromagnetic waves in communication, radar, remote sensing, imaging, optics, biomedicine, etc.

Some examples of problems and exercises from this chapter are:

Derive the wave equation for a homogeneous isotropic medium from Maxwell's equations.

Show that a linearly polarized plane wave can be expressed as a superposition of two circularly polarized plane waves with opposite handedness.

Calculate the reflection and transmission coefficients for a plane wave incident on a dielectric slab at normal incidence.

Explain why metals are good reflectors and poor transmitters of electromagnetic waves.

Describe how a prism can be used to separate white light into its constituent colors.

### Chapter 2: Vector Analysis

This chapter reviews some essential tools and techniques of vector analysis that are frequently used in electromagnetic wave theory. It covers topics such as vector algebra, vector calculus, coordinate systems, gradient, divergence, curl, Laplacian, divergence theorem, Stokes' theorem, Helmholtz's theorem, etc. It also introduces some special functions such as delta function, Heaviside function, step function, ramp function, signum function, etc.

Some examples of problems and exercises from this chapter are:

Prove that the divergence of a curl is zero using vector identities.

Convert the following vector field from Cartesian coordinates to cylindrical coordinates: $\vecF = x\hatx + y\haty + z\hatz$.

Evaluate the following surface integral using divergence theorem: $\int_S \vecF \cdot d\vecS$ where $\vecF = x^2\hatx + y^2\haty + z^2\hatz$ and $S$ is the surface of a sphere of radius $a$ centered at the origin.

Show that $\nabla \times (\nabla \times \vecF) = \nabla (\nabla \cdot \vecF) - \nabla^2 \vecF$ using vector identities.

Express $\vecF = x\hatx + y\haty + z\hatz$ as a sum of an irrotational vector and a solenoidal vector using Helmholtz's theorem.

### Chapter 3: Complex Variables

This chapter reviews some essential tools and techniques of complex variables that are frequently used in electromagnetic wave theory. It covers topics such as complex numbers, complex functions, analytic functions, Cauchy-Riemann equations, harmonic functions, conformal mapping, complex integration, Cauchy's integral theorem, Cauchy's integral formula, residue theorem, Laurent series, singularities, poles, zeros, branch points, branch cuts, etc. It also introduces some special functions such as Bessel functions, Hankel functions, Legendre functions, Laguerre functions, Hermite functions, etc.

Some examples of problems and exercises from this chapter are:

### Chapter 4: Integral Equations

This chapter introduces some essential tools and techniques of integral equations that are frequently used in electromagnetic wave theory. It covers topics such as integral operators, kernels, Fredholm equations, Volterra equations, Green's functions, boundary value problems, method of moments, etc. It also discusses some applications of integral equations in electromagnetic scattering, diffraction, inverse problems, etc.

Some examples of problems and exercises from this chapter are:

Solve the following Fredholm equation of the second kind using the method of successive approximations: $f(x) = \lambda \int_0^1 K(x,y) f(y) dy + g(x)$ where $K(x,y) = x^2 + y^2$ and $g(x) = e^x$.

Find the Green's function for the following boundary value problem: $\nabla^2 u(x,y) = 0$ in the region $0 < x < a$, $0 < y < b$ with the boundary conditions $u(0,y) = u(a,y) = 0$ and $u(x,0) = f(x)$, $u(x,b) = g(x)$.

Derive the integral equation for the electric field scattered by a dielectric sphere of radius $a$ and relative permittivity $\epsilon_r$ when illuminated by a plane wave of frequency $\omega$ and polarization $\hatp$.

Solve the integral equation for the electric current induced on a thin wire antenna of length $L$ and radius $a$ when excited by a voltage source of frequency $\omega$ and impedance $Z_s$ at one end using the method of moments.

Explain how the inverse scattering problem can be formulated as an integral equation and how it can be solved using iterative methods.

### Chapter 5: Green's Functions

This chapter reviews some essential properties and applications of Green's functions in electromagnetic wave theory. It covers topics such as definition and interpretation of Green's functions, Green's functions for various coordinate systems and boundary conditions, Green's theorem, dyadic Green's functions, vector potentials, Hertz potentials, etc. It also discusses some applications of Green's functions in electromagnetic radiation, scattering, diffraction, inverse problems, etc.

Some examples of problems and exercises from this chapter are:

Show that the scalar Green's function for free space satisfies the following equation: $\nabla^2 G(\vecr,\vecr') + k^2 G(\vecr,\vecr') = -\delta(\vecr - \vecr')$ where $k = \omega \sqrt\mu \epsilon$ is the wavenumber.

Find the scalar Green's function for a rectangular cavity of dimensions $a$, $b$, and $c$ with perfectly conducting walls using the method of separation of variables.

Show that the dyadic Green's function for free space can be expressed as: $\overline\overlineG(\vecr,\vecr') = \frace^ikR4\pi R \left[ \left( 1 + \frac1ikR - \frac1k^2 R^2 \right) \overline\overlineI + \left( -1 - \frac3ikR + \frac3k^2 R^2 \right) \hatR \hatR \right]$ where $\overline\overlineI$ is the identity dyadic and $\hatR = (\vecr - \vecr')/R$.

Find the vector potential $\vecA$ for a magnetic dipole moment $\vecm$ located at the origin using the dyadic Green's function for free space.

Explain how the Hertz potentials can be used to generate solutions for electromagnetic fields in terms of scalar and vector potentials.

### Chapter 6: Fourier Transforms

### Chapter 7: Spectral Domain Methods

This chapter introduces some essential tools and techniques of spectral domain methods in electromagnetic wave theory. It covers topics such as definition and interpretation of spectral domain methods, plane wave spectrum, angular spectrum, Fourier-Bessel series, Fourier-Legendre series, Fourier-Hankel transform, etc. It also discusses some applications of spectral domain methods in electromagnetic radiation, scattering, diffraction, waveguides, resonators, antennas, etc.

Some examples of problems and exercises from this chapter are:

Show that the plane wave spectrum of a scalar function $f(x,y)$ is given by: $F(k_x,k_y) = \int_-\infty^\infty \int_-\infty^\infty f(x,y) e^-j(k_x x + k_y y) dx dy$ where $k_x$ and $k_y$ are the components of the wave vector $\veck$ in the $x$ and $y$ directions.

Find the angular spectrum of a circular aperture of radius $a$ illuminated by a plane wave of amplitude $E_0$ and wavenumber $k$ using the Fourier-Bessel series.

Find the Fourier-Legendre series of a function defined on the interval $[-1,1]$ as: $f(x) = \begincases 1 & x \leq 1/2 \\ 0 & x > 1/2 \endcases$.

Find the Fourier-Hankel transform of a Bessel function of the first kind of order zero: $J_0(x)$.

Explain how the spectral domain methods can be used to analyze electromagnetic fields in cylindrical and spherical coordinates.

### Chapter 8: Variational Principles

This chapter introduces some essential tools and techniques of variational principles in electromagnetic wave theory. It covers topics such as definition and interpretation of variational principles, Rayleigh-Ritz method, principle of minimum potential energy, principle of minimum complementary energy, principle of stationary action, Lagrangian and Hamiltonian formulations, etc. It also discusses some applications of variational principles in electromagnetic radiation, scattering, diffraction, waveguides, resonators, antennas, etc.

Some examples of problems and exercises from this chapter are:

Show that the Rayleigh-Ritz method can be used to find an approximate solution to an eigenvalue problem by minimizing a functional.

Use the principle of minimum potential energy to find the natural frequencies and modes of vibration of a string fixed at both ends and subject to a tension force.

Use the principle of minimum complementary energy to find the stress and strain distributions in a beam subjected to a bending moment.

Use the principle of stationary action to derive the Euler-Lagrange equation for a system with one degree of freedom.

Use the Lagrangian and Hamiltonian formulations to analyze the motion of a charged particle in an electromagnetic field.

### Chapter 9: Perturbation Techniques

### Chapter 10: Asymptotic Methods

This chapter introduces some essential tools and techniques of asymptotic methods in electromagnetic wave theory. It covers topics such as definition and interpretation of asymptotic methods, regular and singular perturbations, boundary layer theory, matched asymptotic expansions, WKB method, method of steepest descent, method of stationary phase, geometrical optics, physical optics, etc. It also discusses some applications of asymptotic methods in electromagnetic radiation, scattering, diffraction, waveguides, resonators, antennas, etc.

Some examples of problems and exercises from this chapter are:

Show that the solution of the following differential equation can be obtained by using regular perturbation: $y'' + y = \epsilon \sin x$ where $\epsilon$ is a small parameter.

Show that the solution of the following differential equation can be obtained by using singular perturbation: $y'' + \epsilon y' + y = 0$ where $\epsilon$ is a small parameter.

Use the boundary layer theory to analyze the flow of a viscous fluid over a flat plate.

Use the matched asymptotic expansions to find the solution of the following boundary value problem: $y'' + y = 0$ in $0 < x < 1$ with the boundary conditions $y(0) = 0$ and $y(1) = \epsilon$ where $\epsilon$ is a small parameter.

Use the WKB method to find an approximate solution to the following differential equation: $y'' + (k^2 - x^2) y = 0$ where $k$ is a large parameter.

Use the method of steepest descent to evaluate the following integral: $I(\lambda) = \int_-\infty^\infty e^-\lambda x^2 dx$ where $\lambda$ is a large parameter.

Use the method of stationary phase to evaluate the following integral: $I(\omega) = \int_-\infty^\infty f(x) e^j\omega g(x) dx$ where $\omega$ is a large parameter.

Use the geometrical optics to find the ray paths and phase fronts of electromagnetic waves propagating in a graded-index medium.

Use the physical optics to find the diffraction pattern of electromagnetic waves passing through a circular aperture.

### Chapter 11: Plane Waves

### Chapter 12: Spherical Waves

This chapter reviews some essential properties and applications of spherical waves in electromagnetic wave theory. It covers topics such as definition and interpretation of spherical waves, spherical harmonics, multipole expansion, vector spherical harmonics, vector multipole expansion, Hertz potentials, radiation fields, radiation patterns, directivity, gain, beamwidth, etc. It also discusses some applications of spherical waves in electromagnetic radiation, scattering, diffraction, antennas, etc.

Some examples of problems and exercises from this chapter are:

Show that the scalar spherical harmonics $Y_lm(\theta,\phi)$ satisfy the following equation: $\nabla^2 Y_lm(\theta,\phi) + l(l+1) Y_lm(\theta,\phi) = 0$ where $l$ and $m$ are integers.

Find the multipole expansion of a scalar potential $\phi(r,\theta,\phi) = \frac1r^2 \cos \theta$ using the spherical harmonics.

Show that the vector spherical harmonics $\vecM_lm$ and $\vecN_lm$ satisfy the following equations: $\nabla \times \vecM_lm = k \vecN_lm$ and $\nabla \times \vecN_lm = -k \vecM_lm$ where $k$ is the wavenumber.

Find the vector multipole expansion of a vector potential $\vecA(r,\theta,\phi) = \frac\mu_0 I4\pi r^2 \sin \theta \hat\phi$ using the vector spherical harmonics.

Use the Hertz potentials to find the electric and magnetic fields of a magnetic dipole moment $\vecm$ located at the origin.

Find the radiation fields of a small loop antenna of radius $a$ carrying a sinusoidal current $I_0 e^j\omega t$ using the vector multipole expansion.

Find the radiation pattern, directivity, gain, and beamwidth of a short dipole antenna of length $l$ carrying a sinusoidal current $I_0 e^j\omega t$ using the far-field approximation.

### Chapter 13: Cylindrical Waves

### Chapter 14: Waveguides

This chapter reviews some essential properties and applications of waveguides in electromagnetic wave theory. It covers topics such as definition and interpretation of waveguides, modes, cutoff frequencies, propagation constants, attenuation constants, phase velocities, group velocities, power flow, impedance matching, etc. It also discusses some types of waveguides such as rectangular waveguides, circular waveguides, coaxial cables, optical fibers, etc.

Some examples of problems and exercises from this chapter are:

Show that the modes of a rectangular waveguide of dimensions $a$ and $b$ are given by: $E_mn = E_0 \cos \fracm\pi xa \cos \fracn\pi yb e^-j\beta z$ and $H_mn = H_0 \sin \fracm\pi xa \sin \fracn\pi yb e^-j\beta z$ where $m$ and $n$ are integers and $\beta = \sqrtk^2 - (\fracm\pia)^2 - (\fracn\pib)^2$ is the propagation constant.

Find the cutoff frequency, propagation constant, phase velocity, group velocity, power flow, and characteristic impedance of the TE$_10$ mode of a rectangular waveguide of dimensions $a = 5$ cm and $b = 2.5$ cm operating at a frequency of 10 GHz.

Show that the modes of a circular waveguide of radius $a$ are given by: $E_mn = E_0 J_m (k_\rho \rho) \cos (m\phi) e^-j\beta z$ and $H_mn = H_0 J_m (k_\rho \rho) \sin (m\phi) e^-j\beta z$ where $m$ and $n$ are integers, $J_m$ is the Bessel function of the first kind of order $m$, $k_\rho$ is the transverse wavenumber, and $\beta = \sqrtk^2 - k_\rho^2$ is the propagation constant.

Find the cutoff frequency, propagation constant, phase velocity, group velocity, power flow, and characteristic impedance of the TM$_01$ mode of a circular waveguide of radius $a = 2.5$ cm operating at a frequency of 10 GHz.

Show that the modes of a coaxial cable of inner radius $a$ and outer radius $b$ are given by: $E_mn = E_0 J_m (k_\rho \rho) \cos (m\phi) e^-j\beta z$ and $H_mn = H_0 J_m (k_\rho \rho) \sin (m\phi) e^-j\beta z$ where $m$ and $n$ are integers, $J_m$ is the Bessel function of the first kind of order $m$, $k_\rho$ is the transverse wavenumber, and $\beta = \sqrtk^2 - k_\rho^2$ is the propagation constant.

### Chapter 15: Resonators

This chapter reviews some ess