Extinction theorem and propagation of electromagnetic waves between two anisotropic materials

We systematically investigate the reflection and refraction of an electromagnetic wave between two semi-infinite anisotropic magnetoelectric materials. Using the integral formulation of Hertz vectors and the principle of superposition, we generalize the extinction theorem and derive the propagation characteristics of wave. Applying the results obtained, we find a general origin of Brewster effect. We also show that, through choosing appropriate material parameters, oblique or omnidirectional total transmission can occur to TE and TM waves. Compared to the traditional method, the method used here discloses the underlying mechanism of wave propagation between two arbitrary anisotropic materials and can be applied to other problems of propagation.