Extended Energy Approach to Propagation Problems in General Anisotropic Media

In this article, a new general approach has been presented for exact and efficient extraction of eigenpolarizations in anisotropic electromagnetic media with arbitrary constitutive relations. It is shown that the plane wave propagation eigenpolarizations in a linear homogeneous time-independent anisotropic media without free sources, can be obtained through extremizing the difference between stored electric and magnetic energies as a variational functional. It is demonstrated that at these stationary points the wave equation is satisfied by showing that each of the Maxwell curl equations may be obtained by using the other equation as a constraint. Furthermore, it is proven that the theorem holds for extrema of the stored electric energy independently, when the medium is magnetically isotropic. It is concluded that when at least one of the permittivity and permeability tensors are scalar, both the total of and the difference between electric and magnetic energies are extremized simultaneously. As an example, the eigenpolarizations in a non-magnetic anisotropic medium with optical activity are obtained.