Title Theory of electromagnetic beams / John Lekner

Published Cham, Switzerland : Springer, [2020]

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Description 1 online resource (185 pages) : illustrations Series Synthesis Lectures on Engineering, Science, and Technology ; lecture #39 Synthesis lectures on engineering, science, and technology. Contents Intro -- Preface -- Acknowledgments -- Fundamentals -- Introduction -- Maxwell Equations, Vector and Scalar Potentials -- Conservation Laws, Beam Invariants -- Energy-Momentum Inequality -- Non-Existence Theorems -- Zeros of the Beam Wavefunction in the Focal Region -- References -- Beam-Like Solutions of the Helmholtz Equation -- Introduction -- Paraxial Approximation of the Helmholtz Equation -- Solutions in Cylindrical Coordinates -- Bateman's Integral Solution -- Exact Beam Wavefunctions -- Properties of _b(, z) -- Focal Region Extent, Local Wavelength Beam Wavefunctions Derived from _0(, z) -- Appendix: Cylindrical Integrals Related to Spherical Sums -- Appendix: Properties of the Proto-Beam Wavefunction -- References -- Electromagnetic Beams -- E and B from Solutions of the Wave Equation -- TM and TE Beams -- Invariant Quantities of TM and TE Beams -- TM and TE beams based on _0 -- TM and TE Beams Based on _1 -- Self-Dual Electromagnetic Beams -- TM+iTE Electromagnetic Beams -- TM+iTE Beams-Based on _0 and _1 -- Appendix: Two Singular Integrals over Products of Bessel Functions Appendix: Comparison of TM or TE Beam energy and Momentum Densities with Those of a TM+iTE Beam -- References -- Polarization -- Polarization of Electromagnetic Fields -- Polarization Properties of TM and TE Beams -- Polarization in Self-Dual TM+iTE Beams -- ̀Circularly Polarized' Beams -- Self-Dual ̀CP' Beam Derived from _0(, z) -- Self-Dual ̀CP' Beam Derived from _1(, z) -- ̀Linearly Polarized' Beams -- ̀Linearly Polarized' Beam Derived from _0 -- ̀Linearly Polarized' Beam Derived from _1 -- Appendix: Non-Existence Theorems Appendix: Energy, Momentum, and Angular Momentum per Unit Length of ̀CP' Beams -- Cited References -- Chirality -- Introduction -- Properties of the Chirality Measures of Electromagnetic Fields -- Chirality of TM and TE Beams -- Chiral Properties of ̀Linearly Polarized' Beams -- Chiral Properties of Self-Dual Monochromatic Beams -- Appendix: Chiral Content of ̀LP' Beams -- Cited References -- Additional References (Chronological Order) -- Comparison of Electromagnetic Beams -- Energy, Momentum and Angular Momentum per Unit Length of Beams -- Tightly-Focused Beams Compared Variable Tightness of Focus -- Cited References -- Additional References (Chronological Order) -- Sound Beams and Particle Beams -- Part A: Acoustic Beams -- References for Part A -- Part B: Particle Beams -- References for Part B -- Measures of Focal Extent -- Introduction -- Andrejic Measure of Focal Plane Intensity -- Andrejic Measure of Longitudinal Extent -- Comparison of the Focal Extent Measures -- Appendix: A(s) and L(s) for the Proto-Beam -- Appendix: Focal Region Extent of the _b Family -- Appendix: Focal Region Extent of the Carter Beam Family -- Cited References Summary The theory of electromagnetic beams is presented in a simple and physical way, with all necessary mathematics explained in the text. The topics covered are in free-space classical electrodynamics, but contact is made with quantum theory in proofs that causal beams of various kinds can be viewed as superpositions of photons. This follows from explicit expressions for the energy, momentum and angular momentum per unit length for each type of beam. The properties of beams in the focal region, of special experimental and theoretical interest, are discussed in detail. There are eight chapters: on Fundamentals, Beam-like solutions of the Helmholtz equation, Electromagnetic beams, Polarization, Chirality, Comparison of electromagnetic beams, a chapter on Sound beams and particle beams (to show the similarities to and differences from the vector electromagnetic beams), and a final chapter on Measures of focal extent. Ten Appendices cover mathematical or associated physical topics Bibliography Includes bibliographical references Notes Online resource; title from digital title page (viewed on October 29, 2020) Subject Electromagnetic theory -- Mathematics Electron beams. Electromagnetic theory -- Mathematics Electron beams Form Electronic book ISBN 1681737698 9781681737690 9783031020827 3031020820

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