Laser propagation in Rindler accelerated reference frame based on matrix optics

TL;DR

This paper investigates laser beam propagation in Rindler accelerated frames using matrix optics, revealing unique optical effects and linking geometry, gravity, and refractive index influences, with implications for beam uncertainty and quantization.

Contribution

It introduces a novel method combining covariant wave equations and ABCD matrix optics to analyze laser propagation in Rindler spacetime, highlighting differences from flat spacetime.

Findings

Propagation characteristics differ significantly from flat spacetime.

Analytical description of hollow beam propagation in Rindler spacetime.

Position-momentum uncertainty relation aligns with quantization principles.

Abstract

The Rindler spacetime describing a series of accelerating observers is Ricci flat, but it still has novel optical effects. In the case of WKB approximation, we derive the light geodesics in the Rindler frame based on the covariant wave equation and geodesic equations. Then, we use ABCD matrix optics method to explore the propagation characteristics of Rindler frame, thus link three different optical transformation scenes (geometry, gravity and vacuum refractive index) together. Moreover, the propagation characteristics of hollow beam in Rindler spacetime are described analytically. Those characteristics are quite different from the ones in the flat spacetime. Based on these calculations, we simply demonstrate the position uncertain relationship between the transverse beam size and the momentum, which surprisingly coincides with the derivation of quantization. We hope that we can provide one simple method to analyze the beam propagation in the accelerated frame.