A New Matrix Formulation of Classical Electrodynamics. Part 2. Wave Propagation in Optical Materials of Infinite Extent

Presented in this document is the development of a new matrix description of electromagnetic wave propagation in optical media of infinite extent. This material will interest individuals desiring a description of electromagnetic wave propagation that deviates from the traditional vector calculus approach. Our starting point will be with the fundamental equations of classical electrodynamics, namely the Maxwell field equations. From the vector form of Maxwell's equations, and 8-by-8 differential matrix operator formulation of Maxwell's equations will be developed. The matrix form of the Maxwell field equations allows for simple and direct derivation of matrix representations of the electromagnetic wave and charge continuity equations, the Lorentz conditions and definition of the electromagnetic potentials, the electromagnetic potential wave equations, and Poynting's conservation of energy theorem. The matrix form of the Maxwell field equations and the electromagnetic wave and continuity equations will be used to solve a variety of wave-propagation problems dealing with linear, homogeneous, anisotropic optical media of infinite extent in the presence of monochromatic plane-wave electromagnetic fields. The indices of refraction as well as corresponding states of polarization, associated with wave propagation in crystalline, optically active, and electrooptical media, will be determined by using these matrix representations.