Path Integral for Non-Paraxial Optics

TL;DR

This paper develops a path integral approach for non-paraxial optics by leveraging an analogy with deformed Schrödinger equations, revealing potential applications in quantum gravity analogs and optical phenomena.

Contribution

It introduces a novel path integral formulation for non-paraxial optics based on a minimal length analogy, expanding the theoretical tools available in optical physics.

Findings

Derived instanton solutions for non-paraxial optical systems.

Analyzed the Berry phase in the context of minimal length optics.

Proposed optical systems as analogs for quantum gravity phenomena.

Abstract

In this paper, we have constructed the Feynman path integral method for non-paraxial optics. This is done by using the mathematical analogy between a non-paraxial optical system and the generalized Schr\"odinger equation deformed by the existence a minimal measurable length. Using this analogy, we investigated the consequences of a minimal length in this optical system. This path integral has been used to obtain instanton solution for such a optical systems. Moreover, the Berry phase of this optical system has been investigated. These results may disclose a new way to use the path integral approach in optics. Furthermore, as such system with an intrinsic minimal length have been studied in quantum gravity, the ultra-focused optical pluses can be used as an optical analog of quantum gravity.