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 relies 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.