Optical Ray Tracing Based on Dijkstra Algorithm in Inhomogeneous Medium

This paper is concerned with proposing a numerical method to predict the wave front movement of optical rays based on the Dijkstra algorithm. Data for refractive index of the medium through which optical rays propagate are assigned to all nodes of rectangular meshes and its values apart from the mesh nodes can be approximated in terms of linear interpolation. The velocity of the wave front of an optical ray can be calculated by the refractive index assigned to each node and it varies from one node to another due to the medium in homogeneity. Since the wave front movement of any waves is governed by the Fermat principle, it can be easily estimated based on the Dijkstra algorithm. In this paper we discuss the Dijkstra algorithm relevant to optical rays propagating through the inhomogeneous media such as Luneburg lens and Maxwell´s fish-eye lens. We also show some numerical examples to demonstrate the effectiveness of the proposed method for analyzing ray front movement and ray tracing.