On the equations of diffracted geodesics

TL;DR

This paper derives explicit geodesic equations for diffracted light rays, incorporating effects from the ambient metric, refractive index, and diffraction, advancing theoretical understanding in optical physics.

Contribution

It provides a new explicit formulation of geodesic equations that include diffraction effects, combining geometric and optical factors.

Findings

Derived explicit geodesic equations for diffracted light

Identified the Levi-Civita connection as a sum of contributions

Discussed the challenges in obtaining diffraction corrections

Abstract

An explicit form for the geodesic equations that would describe diffracted light rays is obtained and the Levi-Civita connection that enters into it is shown to be a sum of contributions from the metric of the ambient space, the index of refraction of the optical medium, and diffraction effects. The nature of the problem of obtaining explicit forms for the diffraction correction in various problems of interest to optics is discussed briefly.