Part II: Electromagnetic Waves
Maxwell's equations unify electricity, magnetism, and optics into a single elegant framework. The prediction and subsequent discovery of electromagnetic waves stands as one of the greatest triumphs of theoretical physics, revealing that light itself is an electromagnetic phenomenon.
Part Overview
Starting from Maxwell's equations, we derive the electromagnetic wave equation and explore the rich physics of wave propagation in different media. Topics include the Poynting vector for energy transport, Snell's law from boundary conditions, impedance matching, and the phenomenon of dispersion where different frequencies travel at different speeds.
Key Topics
- \(\bullet\) Maxwell's equations in differential and integral form
- \(\bullet\) Derivation of the EM wave equation and the speed of light \(c = 1/\sqrt{\mu_0\epsilon_0}\)
- \(\bullet\) Energy density and the Poynting vector \(\vec{S} = \vec{E} \times \vec{H}\)
- \(\bullet\) Reflection, refraction, and Snell's law from boundary conditions
- \(\bullet\) Impedance matching and transmission line theory
- \(\bullet\) Phase velocity, group velocity, and dispersion relations
- \(\bullet\) Kramers-Kronig relations and anomalous dispersion
3 chapters | From Maxwell to light | Foundation for optics
Chapters
Chapter 4: Maxwell's Equations & the Wave Equation
The four Maxwell equations, displacement current, derivation of the wave equation, the speed of light, electromagnetic energy, and the Poynting vector.
Chapter 5: Wave Propagation
Reflection and refraction at interfaces, Snell's law, Fresnel equations, total internal reflection, impedance matching, and waveguide modes.
Chapter 6: Dispersion
Phase and group velocity, dispersion relations, Kramers-Kronig relations, anomalous dispersion, and pulse broadening in dispersive media.