Theory of electromagnetic pulses
Electromagnetic pulse
IOP Publishing
2018
EISBN 9781643270227
1. Fundamentals.
1.1. Introduction.
1.2. Universal properties of electromagnetic pulses.
1.3. Conservation laws.
1.4. Energy-momentum inequality.
1.5. 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 z - ct and z + ct space-time dependence.
2.4. Solutions in cylindrical coordinates.
2.5. Bateman's integral solution.
2.6. Pulses as superpositions of beams, casual waveforms.
Appendix A. Cylindrical integrals related to spherical sums.
Appendix B. Two-parameter causal wavefunctions.
Appendix C. The causal wavefunction [psi]â‚€ 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 Ziolowski, Hellwarth-Nouchi pulse.
3.6. The Feng, Winful and Hellwarth pulse.
3.7. Oscillatory pulses.
3.8. Causal TE and TM pulses.
Appendix A. Energy of a TE+iTM pulse.
Appendix B. Chirality measures of electromagnetic fields
4. Angular momentum.
4.1. Intrinsic angular momentum, polarization.
4.2. A TE+iTM self-dual pulse.
4.3. Two self-dual 'CP' pulses.
4.4. Pulses based on wavefunctions with azimuthal dependence.
4.5. Causal TE+iTM pulses.
4.6. Causal self-dual 'CP' pulses.
Appendix A. Evaluation of Jz 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.
This book 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. 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.
1.1. Introduction.
1.2. Universal properties of electromagnetic pulses.
1.3. Conservation laws.
1.4. Energy-momentum inequality.
1.5. 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 z - ct and z + ct space-time dependence.
2.4. Solutions in cylindrical coordinates.
2.5. Bateman's integral solution.
2.6. Pulses as superpositions of beams, casual waveforms.
Appendix A. Cylindrical integrals related to spherical sums.
Appendix B. Two-parameter causal wavefunctions.
Appendix C. The causal wavefunction [psi]â‚€ 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 Ziolowski, Hellwarth-Nouchi pulse.
3.6. The Feng, Winful and Hellwarth pulse.
3.7. Oscillatory pulses.
3.8. Causal TE and TM pulses.
Appendix A. Energy of a TE+iTM pulse.
Appendix B. Chirality measures of electromagnetic fields
4. Angular momentum.
4.1. Intrinsic angular momentum, polarization.
4.2. A TE+iTM self-dual pulse.
4.3. Two self-dual 'CP' pulses.
4.4. Pulses based on wavefunctions with azimuthal dependence.
4.5. Causal TE+iTM pulses.
4.6. Causal self-dual 'CP' pulses.
Appendix A. Evaluation of Jz 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.
This book 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. 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.
