Laser propagation in a Rindler accelerated reference frame based on matrix optics.

Abstract

The Rindler space-time describing a series of accelerating observers is Ricci flat, but it still has novel optical effects. In the case of Wenzel, Kramers, and Brillouin (WKB) approximation, we derive the light paths 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 space-time are described analytically. In the longitudinal direction, we demonstrate the shift and stretch effects of the dark spot of a beam, while the transverse spot size is proved to be convergence in the accelerated system, and the wavefront curvature can tend a constant twice the acceleration at the far field. Those characteristics are quite different from the ones in the flat space-time. 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.