Wave equations for one-dimensional inhomogenous anisotropic dielectric structures

In general, Maxwell equations are coupled when governing light propagation through one-dimensional inhomogeneous anisotropic dielectric structures. However, for on-axis propagation in one-dimensional inhomogeneous uniaxially anisotropic dielectric structures with any orientation of the optic axis, and biaxially anisotropic structures with certain orientations of principal axes, we show that the equations can be decoupled into two wave equations satisfied by the two independent polarizations of light. Furthermore, the dielectric tensor in the original Maxwell equations is replaced with effective dielectric constants for each polarization of the light. We also give specialized results for anisotropic multilayer dielectric structures and one-dimensional anisotropic photonic crystals.