Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers

TL;DR

This paper derives exact analytic expressions for electromagnetic propagation in finite 1D periodic multilayers and applies them to model second harmonic generation, providing a precise modal approach for complex layered structures.

Contribution

It introduces a closed-form solution for electric fields in finite 1D periodic structures and extends it to nonlinear SHG analysis, enhancing modeling accuracy.

Findings

Exact analytic expressions for linear propagation

Closed-form electric field formulas in multilayers

Application to second harmonic generation

Abstract

Translation Matrix Formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional (1D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to Second Harmonic Generation (SHG) in the undepleted pump regime.