Ray tracing method beyond idealized gradient-index lenses

In recent decades, ray tracing methods in gradient-index (GRIN) lenses have gained significant attention due to their diverse applications. However, most of these methods have been developed for idealized lenses—namely, normalized, symmetric, and centered configurations in which the isoindicial surfaces (surfaces of constant refractive index) are concentric. This limits their applicability to more complex lens geometries. In this work, we present a ray tracing method suitable for both idealized and non-idealized GRIN lenses, which rely on a fixed optical path length step size, thereby eliminating the need to discretize the medium in advance. Its simple implementation and versatility make it a valuable tool for modeling light propagation in arbitrary GRIN media, offering strong numerical stability and high accuracy.