M. Fabbrichesi , SISSA

Maxwell equations in the absence of sources

In this lecture it is shown how the Maxwell equations in the absence of sources lead to wave equations for the electric and magnetic fields (Helmholtz equations). Moreover these fields are mutually orthogonal and propagate at the speed of light. Definitions of linear, circular and elliptic polarization are given. The Poynting vector of electromagnetic waves is shown to be along the direction of propagation and its modulus is proportional to the energy density. Refraction and reflection of electromagnetic waves at the interface between two media (e.g water/air) is then discussed. Fresnel equations and Snell's law are derived by exploiting Maxwell's equations. Next, non-dispersive and dispersive media are introduced and definitions of group velocity and phase velocity are given.