# Theory of Electromagnetic Pulses

- John Lekner

- July 2018

### Description

This short monograph presents the theory of electromagnetic pulses in a simple and physical way. All pulses discussed are exact solutions of the Maxwell equations, and have finite energy, momentum and angular momentum. There are five chapters: Fundamentals, Solutions of the wave equation, Electromagnetic pulses, Angular momentum, and Lorentz transformations. Nine appendices cover mathematical or associated aspects, such as chiral measures of electromagnetic fields. The subject matter is restricted to free-space classical electrodynamics, but contact is made with quantum theory in proofs that causal pulses are equivalent to superpositions of photons.### About Editors

John Lekner is an Emeritus Professor of theoretical physics at Victoria University of Wellington, New Zealand. After an MSc at the University of Auckland and PhD at the University of Chicago, he taught at the Cavendish Laboratory, Cambridge, where he was also Fellow and tutor in physics at Emmanuel College. He has worked in statistical physics, electromagnetism, quantum theory and theory of fluids. He is the author of 150 papers and of the book*Theory of Reflection*.

### Table of Contents

- 1 Fundamentals
- 1-1 Introduction
- 1-2 Universal properties of electromagnetic pulses
- 1-3 Conservation laws
- 1-4 Energy-momentum inequality
- 1-4 Lorentz invariants
- Appendix A. Radiation of electromagnetic pulses
- Appendix B. Particle wavepackets

- 2 Solutions of the wave equation
- 2-1 Vector and scalar potentials
- 2-2 General solutions of the wave equation
- 2-3 Solutions with both ๐ง๐งโ๐๐๐๐ and ๐ง๐ง+๐๐๐๐ space-time dependence
- 2-4 Solutions in cylindrical coordinates
- 2-5 Bateman's integral solution
- 2-6 Pulses as superpositions of beams
- Appendix A. Cylindrical integrals related to spherical sums
- Appendix B. Two-parameter causal wavefunctions
- Appendix C. The causal wavefunction ๐๐0 in 'spheroidal' coordinates

- 3 Electromagnetic pulses
- 3-1 E and B from solutions of the wave equation
- 3-2 TE and TM pulses
- 3-3 Self-dual complex fields, TE+iTM pulses
- 3-4 A particular TE+iTM pulse
- 3-5 The Ziolkowski, Hellwarth and Nouchi pulse
- 3-6 The Feng, Winful and Hellwarth pulse
- 3-7 Oscillatory pulses
- 3-8 Causal TE and TM pulses
- Appendix A. Energy and momentum of a TE+iTM pulse
- Appendix B. Chirality measures of electromagnetic fields

- 4 Angular momentum
- 4-1 Intrinsic angular momentum, polarization
- 4-2 The TE+iTM self-dual pulse
- 4-3 Two 'CP' self-dual pulses
- 4-4 Pulses based wavefunctions with azimuthal dependence
- 4-5 Causal TE+iTM pulses
- 4-6 Causal self-dual 'CP' pulses
- Appendix A. Evaluation of ๐ฝ๐ฝ๐ง๐ง for a TE+iTM pulse
- Appendix B. Singular integrals over products of Bessel functions

- 5 Lorentz transformation of pulses
- 5-1 Lorentz transformation of scalar pulses
- 5-2 Transformation of electromagnetic pulses
- 5-3 A TE+iTM pulse in its zero-momentum frame
- 5-4 A self-dual 'CP' pulse in its zero-momentum frame
- 5-5 A causal TE+iTM pulse in its zero-momentum frame

### Bibliographic

Paperback ISBN: 9780750329279

Ebook ISBN: 9781643270210

DOI: 10.1088/978-1-6432-7022-7

Publisher: Morgan & Claypool Publishers