Propagation of light in linear and quadratic GRIN media: The Bohm potential

TL;DR

This paper demonstrates that light propagation in linear and quadratic GRIN media follows similar rules to free space, explained through the Bohm potential which modifies the dynamics based on initial conditions.

Contribution

It introduces the Bohm potential to explain the propagation behavior in GRIN media, showing the mathematical equivalence to free space propagation under certain conditions.

Findings

Propagation in GRIN media can be modeled similarly to free space.

The Bohm potential explains the modified dynamics in these media.

Different initial conditions affect the propagation behavior.

Abstract

It is shown that field propagation in linear and quadratic gradient-index (GRIN) media obeys the same rules of free propagation in the sense that a field propagating in free space has a (mathematical) form that may be {\it exported} to those particular GRIN media. The Bohm potential is introduced in order to explain the reason of such behavior: it changes the dynamics by modifying the original potential. The concrete cases of two different initials conditions for each potential are analyzed.