Light Propagation in a Medium with Transverse Refractive Index Gradient

Within the framework of geometric optics, we obtain an analytical description of light propagation in media with a transverse variation in the refractive index. For a plane wave normally incident on a medium with a smooth monotonic step-like refractive-index profile, we show that strong wave distortion and the formation of a cusp caustic are generic features. Analytical expressions are derived for the ray trajectories, ray-crossing coordinates, caustic structure, and beam evolution. The physical mechanisms responsible for these phenomena are elucidated. Possible realizations based on electro-optic effects are discussed, and quantitative estimates relevant to potential applications are presented.