A Supersymmetric Approach to the Problem of Micro-bending Attenuation in Optical Waveguides

TL;DR

This paper applies supersymmetric quantum mechanics techniques to model and optimize refractive index profiles in optical waveguides, aiming to reduce micro-bending losses by transforming initial profiles into less lossy configurations.

Contribution

It introduces a novel formalism combining supersymmetric quantum mechanics with Fokker-Planck equations to derive index profiles that minimize micro-bending attenuation.

Findings

Existence of index profile transformations that reduce loss.

Explicit example with monomial profiles showing reduced loss.

Range of parameters where supersymmetric transformations are beneficial.

Abstract

Micro-bending is a well-known source of loss in optical waveguides. By treating the micro-bending as a stochastic process, the problem of loss mitigation can be modeled in terms of a Fokker-Planck equation. Given an initial refractive index profile, and taking micro-bending into account, we develop a formalism to derive a new refractive index profile which potentially results in less loss. Our formalism is based on applying the techniques of Supersymmetric Quantum Mechanics to a Fokker-Planck equation that is associated with a particular refractive index profile. We derive a non-linear differential equation, whose solutions determine whether an index profile can undergo a supersymmetric transformation that results in less loss. As an explicit example, we consider a monomial index profile. We show that there exists a range of values for the monomial exponent which results in the new index profile having less loss.