Field, Force, Energy and Momentum in Classical Electrodynamics

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Field, Force, Energy and Momentum in Classical Electrodynamics

Dedication

Contents

Preface

Keywords

CHAPTER 1  Scalar and Vector Fields
     1.1. Introduction
     1.2. Space and time
     1.3. Scalar and vector fields
     1.4. Gradient of a scalar field
     1.5. Integration of fields over time and/or space.
     1.6. Divergence of a vector field
     1.7. Theorem of Gauss.
     1.8. Curl of a vector field.
     1.9. Theorem of Stokes
     1.10. Longitudinal and transverse vector plane-waves.
     General References
     Problems

CHAPTER 2  Foundations of the Classical Maxwell-Lorentz Theory of Electrodynamics
     2.1. Introduction
     2.2. Definition: Permittivity eo of free-space
     2.3. Definition: Permeability µ o of free space
     2.4. Speed of light c and impedance of free space Zo:
     2.5. Sources of electromagnetic fields
     2.6. Electric field E and magnetic field H
     2.7. Electric displacement D and magnetic induction B.
     2.8. Rules of the game
     2.9. Rule 1: Maxwell’s first equation
     2.10. Rule 2: Maxwell’s second equation
     2.11. Continuity equation of charge and current
     2.12. Rule 3: Maxwell’s third equation
     2.13. Rule 4: Maxwell’s fourth equation
     2.14. Macroscopic versus microscopic equations
     2.15. Bound charge and bound current associated with polarization and magnetization.
     2.16. Magnetic bound charge and bound current
     2.17. Maxwell’s boundary conditions.
     2.18. Rule 5: Energy in electromagnetic systems.
     2.19. Rule 6: Momentum density of the electromagnetic field
     2.20. The Einstein-box gedanken experiment
     2.21. The thought experiment of Balazs
     2.22. Rule 7: Angular momentum density of the electromagnetic field.
     2.23. Rule 8: Force density exerted by electromagnetic fields on material media
     2.24. Conservation of linear momentum
     2.25. Rule 9: Torque density exerted by electromagnetic fields on material media
     2.26. Conservation of angular momentum
     General References
     Problems

CHAPTER 3  Mathematical Preliminaries
     3.1. Introduction
     3.2. Elementary special functions
     3.3. The Fourier transform operator
     3.4. The Fourier theorem.
     3.5. Fourier transformation in higher dimensions
     3.6. Bessel functions and their properties
     General References
     Problems

CHAPTER 4  Solving Maxwell’s Equations
     4.1. Introduction
     4.2. Plane-wave solutions of Maxwell’s equations
     4.3. Electric field produced by a stationary point-charge (electrostatics).
     4.4. Electric field of a line-charge (electrostatics).
     4.5. Electric field of a uniformly-charged plate (electrostatics)
     4.6. Magnetic field of a long, thin wire carrying a constant current (magnetostatics).
     4.7. Magnetic field of a hollow cylinder carrying a constant current (magnetostatics).
     4.8. Electric field produced by a point-dipole (electrostatics).
     4.9. Fields radiated by an oscillating point-dipole (electrodynamics).
     4.10. Radiation by an oscillating current sheet (electrodynamics).
     4.11. Radiation by an oscillating line-current (electrodynamics).
     4.12. Radiation by a hollow cylinder carrying an oscillating current (electrodynamics).
     General References
     Problems

CHAPTER 5  Solving Maxwell’s Equations in Space-time: The Wave Equation
     5.1. Introduction
     5.2. Scalar potential . (r,t) as the solution of a 2nd-order partial differential equation.
     5.3. Vector potential A(r,t) as the solution of a 2nd-order partial differential equation
     5.4. Meaning of the Laplacian operator acting on a vector field
     5.5. Relating scalar and vector potentials to their sources in the space-time domain
          5.5.1. Example: Oscillating point-dipole
          5.5.2. Example: Infinitely-long, thin, current-carrying wire radiating cylindrical waves
          5.5.3. Example: Infinite sheet of oscillating current radiating plane-waves
     General References
     Problems

CHAPTER 6  The Lorentz Oscillator Model
     6.1. Introduction
     6.2. Mass-and-spring model of an atomic dipole
     6.3. Generalization to the case of multi-electron atoms and molecules
     6.4. Drude model of the conduction electrons
     6.5. The Clausius-Mossotti relation
     6.6. Dependence of the real and imaginary parts of C(. ) on frequency.
     6.7. Phase and group velocities
     6.8. Step-response and Impulse-response
     6.9. The Kramers-Kronig relations
     General References
     Problems
    
CHAPTER 7  Plane Electromagnetic Waves in Isotropic, Homogeneous, Linear Media
     7.1. Introduction
     7.2. Complex vector algebra of the electromagnetic field.
     7.3. Plane electromagnetic waves and their properties
     7.4. Plane-waves in isotropic, homogeneous, linear media
     7.5. Energy flux and the Poynting vector
     7.6. Reflection and transmission of plane-waves at a flat interface between adjacent media.
          7.6.1. Case of TM or p-polarized incident plane-wave at a flat interface located at z=0
          7.6.2. Case of TE or s-polarized incident plane-wave at a flat interface located at z=0
     7.7. Fresnel reflection and transmission coefficients in several cases of practical interest.
          7.7.1. Special Case 1: normal incidence
          7.7.2. Special Case 2: Brewster’s angle
          7.7.3. Special Case 3: total internal reflection
     7.8. Concluding remarks
     General References
     Problems

CHAPTER 8  Simple Applications Involving Plane Electromagnetic Waves
     8.1. Introduction
     8.2. Transmission through a multilayer stack
     8.3. Reflection and transmission coefficients of a non-absorbing slab
     8.4. Optical characteristics of a parallel-plate slab
     8.5. Reflection and transmission properties of bilayer slab
     8.6. Compound dielectric slab
     8.7. Optical cavity resonator
     8.8. Perfectly matched layer
     References
     Problems

CHAPTER 9  Maxwell’s Equations in Cylindrical Coordinates
     9.1. Introduction
     9.2. Solving Maxwell’s equations in linear, isotropic, homogeneous, circularly symmetric media
     9.3. Bessel function Jm(·) as superposition of plane-waves
     9.4. Hankel functions Hm(1,, 2)(. ) as superpositions of plane-waves
     9.5. Guided modes and surface-plasmon-polaritons in systems of cylindrical symmetry
     9.6. Energy flux and the Poynting vector
     General References
     Problems

CHAPTER 10  Electromagnetic Momentum, Angular Momentum, Force and Torque
     10.1. Introduction
     10.2. Brief review of classical mechanics
     10.3. Pulse of light incident on a reflecting surface
     10.4. Continuous wave (cw) beam incident on a reflecting surface
     10.5. Continuous wave (cw) beam incident on a transparent or semi-transparent slab.
     10.6. Transparent prism illuminated at Brewster’s angle
     10.7. Transparent parallel-plate slab illuminated at Brewster’s angle
     10.8. Laser beam focused onto a spherical glass bead
     10.9. Angular momentum of an optical vortex
     10.10. Angular momentum of a circularly-polarized plane-wave
     General References
     Problems

CHAPTER 11  Plane-wave Propagation in Linear, Homogeneous, Isotropic Media Exhibiting Temporal as well as Spatial Dispersion
     11.1. Introduction
     11.2. Mass-and-spring model of polarization exhibiting spatial dispersion
     11.3. Dispersion relations
     11.4. Case of s-polarized incident plane-wave.
     11.5. Case of p-polarized incident plane-wave
     11.6. Mechanical energy density
     General References

CHAPTER 12  The Reciprocity Theorem
     12.1. Introduction
     12.2. Electromagnetic field radiated by an oscillating electric dipole
     12.3. Electromagnetic field radiated by an oscillating magnetic dipole
     12.4. Reciprocity in a system containing electrically-polarizable media
     12.5. Reciprocity in systems containing both electric and magnetic media
     12.6. Reciprocity in the presence of spatial dispersion.
     12.7. Comparison with standard proofs of reciprocity
     12.8. Summary and Concluding Remarks
     References
     Problems

Solutions to Selected Problems

Appendix A  Vector Identities
Appendix B  Vector Operations in Cartesian, Cylindrical, and Spherical Coordinates
Appendix C  Useful Integrals and Identities

Index