Theory of Electromagnetic Waves, Radiation, and Scattering

Graduate / Professional

This is a graduate-level course on electromagnetic theory, focusing on electromagnetic wave phenomena in a variety of contexts. Electrostatics and magnetostatics are reviewed briefly and then the full time-dependent Maxwell equations are studied to derive the fundamentals of wave propagation, the wave equation, plane waves, polarization, energy and momentum flow in EM waves, conservation laws, gauge transformation, and Green functions for the wave equations. Dielectric media and Fresnel reflection and refraction, total internal reflection, group velocity, wave packets and dispersion. Beam propagation and gaussian optics, optical birefringence. Waves in confined structures, waveguides, optical fibers, resonant cavities. Radiating sources, electric and magnetic dipolar radiation, multipolar radiation, near and far-field solutions, radiating antennas. Scattering theory, scalar and vector diffraction, Rayleigh scattering, scattering matrix and temporal coupled mode theory, scattering resonances, multiple scattering, systems with gain and lasing. Time permitting: relativistic kinematics, covariance of Maxwell's equations, Lorentz transformation of electric and magnetic fields, relativistic mechanics of charged particles. Prerequisites: an undergraduate course on electricity and magnetism and graduate-level vector calculus and differential equations. TTh 1:05pm-2:20pm