Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

TL;DR

This paper develops a hydrodynamic analogy for nonlinear light diffraction in photorefractive media with an embedded reflecting wire, revealing the formation of Mach cones, dark solitons, and ship waves, with stability analysis of the solitons.

Contribution

It introduces a novel hydrodynamic framework for understanding nonlinear light diffraction and derives analytical solutions for dark solitons and ship waves in this context.

Findings

Mach cone separates regions with dark solitons and ship waves

Dark solitons are stable at high Mach numbers

Analytical solutions for ship waves and dark solitons are obtained

Abstract

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ``equation of state'' of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ``Mach number'' is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ``ship waves'' is situated. Analytical theory of ``ship waves'' is developed and two-dimensional dark soliton solutions of the equation describing the beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.