Transverse relativistic effects in paraxial wave interference

TL;DR

This paper explores how relativistic effects cause observable deformations in paraxial wave interference patterns, including fringe distortions and phase delays, at non-relativistic velocities.

Contribution

It introduces the concept of relativistic deformations in paraxial wave interference, highlighting effects like fringe distortion and phase delay due to superluminal phase velocities.

Findings

Interference patterns deform into fork-like fringes (relativistic Hall effect).

Relativistic motion causes fringe counter-rotation at non-relativistic speeds.

Deformations are linked to superluminal transverse phase velocities.

Abstract

We consider relativistic deformations of interfering paraxial waves moving in the transverse direction. Owing to superluminal transverse phase velocities, noticeable deformations of the interference patterns arise when the waves move with respect to each other with non-relativistic velocities. Similar distortions also appear on a mutual tilt of the interfering waves, which causes a phase delay analogous to the relativistic time delay. We illustrate these observations by the interference between a vortex wave beam and a plane wave, which exhibits a pronounced deformation of the radial fringes into a fork-like pattern (relativistic Hall effect). Furthermore, we describe an additional relativistic motion of the interference fringes (a counter-rotation in the vortex case), which become noticeable at the same non-relativistic velocities.