General solution of EM wave propagation in anisotropic media

When anisotropy is involved, the wave equation becomes simultaneous partial differential equations that are not easily solved. Moreover, when the anisotropy occurs due to both permittivity and permeability, these equations are insolvable without a numerical or an approximate method. The problem is essentially due to the fact neither ε nor μ can be extracted from the curl term, when they are in it. The terms curl(E) (or H) and curl(εE) (or μH) are practically independent variables, and E and H are coupled to each other. However, if Maxwell's equations are manipulated in a different way, new wave equations are obtained. The obtained equations can be applied in anisotropic, as well as isotropic, cases. In addition, E and H are decoupled in the new equations, so the equations can be solved analytically by using tensor Green's functions.