Electromagnetic and Optical Pulse Propagation 1

Spectral Representations in Temporally Dispersive Media

• Introduction
• Microscopic Electromagnetics
  • The Microscopic Maxwell–Lorentz Theory
    • Differential Form of the Microscopic Maxwell Equations
    • Integral Form of the Microscopic Maxwell Equations
  • Invariance of the Maxwell–Lorentz Equations
    • Transformation Laws in Special Relativity
    • Transformation of Dynamical Quantities
    • Interdependence of Electric and Magnetic Fields
    • Transformation Relations for Electric and Magnetic Fields
    • Invariance of Maxwell’s Equations
  • Conservation Laws for the Microscopic Electromagnetic Field
    • Conservation of Energy and Poynting’s Theorem
    • Conservation of Linear Momentum
    • Conservation of Angular Momentum
  • Uniqueness of Solution
• Microscopic Potentials and Radiation
  • The Microscopic Electromagnetic Potentials
    • The Lorenz Condition and the Lorenz Gauge
    • The Coulomb Gauge
    • The Retarded Potentials
  • The Hertz Potential and Elemental Dipole Radiation
    • The Hertz Potential
    • Radiation from an Elemental Hertzian Dipole
  • Li’enard–Wiechert Potentials
    • The Liénard–Wiechert Potentials
    • The Field Produced by a Moving Charged Particle
    • Radiated Energy from a Moving Charged Particle
  • The Radiation Field Produced by a General Dipole Oscillator
    • The Field Vectors Produced by a General Dipole Oscillator
    • The Electric Dipole Approximation
    • The Field Produced by a Monochromatic Dipole
    • Oscillator in the Electric Dipole Approximation
  • The Complex Potential and the Scalar Optical Field
    • The Wave Equation for the Complex Potential
    • Electromagnetic Energy and Momentum Densities
    • A Scalar Representation of the Optical Field
• Macroscopic Electromagnetics
• Fundamental Field Equations in a Temporally Dispersive Medium
• The Angular Spectrum Representation of the Pulsed Radiation Field
• The Angular Spectrum Representation of Pulsed
• Electromagnetic and Optical Beam Fields in Temporally Dispersive Media
• Free Fields in Temporally Dispersive Media
• A – Helmholtz’ Theorem
• B – The Dirac Delta Function
• C – The Fourier–Laplace Transform
• D – The Effective Local Field
• E – Magnetic Field Contribution to the Classical Lorentz Model of Resonance Polarization