Time-domain mapping of electromagnetic ray movement inside 2D anisotropic region

The paper presents the extension of the time-domain mapping method applied to 2D billiard problem inside an anisotropic region bounded by ellipse [1]. In this paper, it has been considered the ray movement inside 2D anisotropic region bounded by arbitrary differentiable curve. It has been proved that the problem can be one-to-one mapped onto 2D mathemeatical billiard problem inside the region possessing isotropic properties by linear transformation of group velocity hodograph and boundary with the same coefficient, which is equal to anisotropy of the ray group velocity, simultaneously. The main features of the ray movement inside 2D anistropic region are discussed.