Fractional Schr\"odinger equation in gravitational optics

TL;DR

This paper explores fractional quantum mechanics within gravitational optics, analyzing light propagation, beam acceleration, and fractal photonics, emphasizing the role of fractional Laplacian and fractional-time derivatives in curved space geometries.

Contribution

It introduces the application of fractional Schrödinger equations to gravitational optics, highlighting new effects of fractional derivatives on optical phenomena in curved geometries.

Findings

Fractional Laplacian influences light propagation and beam acceleration.

Fractional-time derivatives affect optical effects in curved space.

Application of fractional quantum mechanics models in gravitational optics.

Abstract

This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so called gravitational optics. Besides Schr\"odinger Newton equation, we have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics, related to nonlinear Schr\"odinger equation, where impact of the fractional Laplacian is discussed. Another important feature of the gravitational optics' implementation is its geometry with the paraxial approximation, when quantum mechanics, in particular, fractional quantum mechanics, is an effective description of optical effects. In this case, fractional-time differentiation reflexes this geometry effect as well.