Goos-H\"{a}nchen Shifts of Partially Coherent Light Fields

TL;DR

This paper analyzes how the spatial coherence of partially coherent light fields influences the Goos-H"{a}nchen} shift, deriving a formal expression and demonstrating the dependence on coherence and beam width, especially near critical angles.

Contribution

It introduces a formal expression for GH shifts of partially coherent fields using Mercer's expansion, highlighting the dependence on spatial coherence and beam width.

Findings

GH shifts depend on spatial coherence and beam width.

Near critical angles, coherence significantly affects GH shifts.

Derived a formal expression for GH shifts in PCFs.

Abstract

We investigate the Goos-H\"{a}nchen (GH) shifts of partially coherent fields (PCFs) by using the theory of coherence. We derive a formal expression for the GH shifts of PCFs in terms of Mercer's expansion, and then clearly demonstrate the dependence of the GH shift of each mode of PCFs on spatial coherence and beam width. We discuss the effect of spatial coherence on the resultant GH shifts, especially for the cases near the critical angles, such as totally reflection angle.