Brewster angle for anisotropic materials from the extinction theorem

By the extinction theorem we explore the Brewster effect in the external and internal reflections of electromagnetic wave associated with an anisotropic material that is both dielectric and magnetic, including metamaterials. We obtain Fresnel's coefficients and the condition of Brewster's angle, and give microscopic explanations from the view point of molecular optics. The Brewster angle is the incidence of angle at which the contribution of all electric and magnetic dipoles in the anisotropic material to the reflection field becomes zero. Distinct from isotropic media, the anisotropic material can exhibit Brewster angle for both TE and TM waves due to the anisotropy of the material.