Frank-Condon principle and adjustment of optical waveguides with nonhomogeneous refractive indices

TL;DR

This paper explores the adjustment of optical waveguides with nonhomogeneous refractive indices using exact mode-connection formulas and the Frank-Condon principle, linking optical and quantum state analysis.

Contribution

It introduces a novel application of the Frank-Condon principle to optical waveguide adjustment and provides exact formulas for mode-connection coefficients using Hermite polynomials.

Findings

Exact formulas for mode-connection coefficients derived

Illustrative plots for various refractive-index profiles presented

Connection established between optical waveguides and quantum state tomography

Abstract

The adjustment of two different selfocs is considered using both exact formulas for the mode-connection coefficients expressed in terms of Hermite polynomials of several variables and a qualitative approach based on the Frank-Condon principle. Several examples of the refractive-index dependence are studied and illustrative plots for these examples are presented. The connection with the tomographic approach to quantum states of a two-dimensional oscillator and the Frank-Condon factors is established.