The use of the stationary phase method as a mathematical tool to determine the path of optical beams

TL;DR

This paper applies the stationary phase method to analyze optical beam paths in dielectric media, accurately predicting geometrical paths and phenomena like the Goos-Haenchen shift, enhancing understanding of beam propagation.

Contribution

It demonstrates the effectiveness of the stationary phase method in deriving optical beam paths and predicting shifts beyond classical laws like Snell's law.

Findings

Accurately predicts beam paths in dielectric blocks.

Recovers Snell's law in partial internal reflection.

Predicts the Goos-Haenchen shift in total internal reflection.

Abstract

We use the stationary phase method to determine the path of optical beams which propagate through a dielectric block. In the presence of partial internal reflection, we recover the geometrical result obtained by using the Snell law. For total internal reflection, the stationary phase method overreaches the Snell law predicting the Goos-Haenchen shift.