Link between the laws of geometrical optics and the radiative transfer equation in media with a spatially varying refractive index

TL;DR

This paper demonstrates that a modified radiative transfer equation accurately models radiative transfer in media with spatially varying refractive index in the non-absorbing, non-scattering limit, addressing previous debates on its validity.

Contribution

It confirms the validity of a previously proposed modified radiative transfer equation in specific media conditions, clarifying misconceptions about its implications.

Findings

The equation works in the non-absorbing, non-scattering limit.

It refutes the claim that the equation implies zero divergence of rays.

Addresses and clarifies previous criticisms of the model.

Abstract

We proposed in a previous paper [Opt. Commun. 228, 33 (2003)] a modified radiative transfer equation to describe radiative transfer in a medium with a spatially varying refractive index. The present paper is devoted to the demonstration that this equation perfectly works in the non-absorbing / non-scattering limit, what was contested by L. Mart\'i-L\'opez and coworkers [Opt. Commun. 266, 44 (2006)]. The assertion that this equation would imply a zero divergence of the rays is also commented.