Multipurpose S-shaped solvable profiles of the refractive index: application to modeling of antireflection layers and quasi-crystals

TL;DR

This paper introduces a class of exact, elementary, S-shaped refractive index profiles derived via the Property & Field Darboux Transformation method, useful for modeling light propagation in photonic devices like antireflection layers and quasicrystals.

Contribution

It provides a comprehensive set of tools for implementing S-shaped solvable refractive index profiles, enabling advanced modeling of photonic structures with smooth, sigmoidal index variations.

Findings

Profiles are highly flexible and analytically solvable.

Applications demonstrated for antireflection layers and 1D quasicrystals.

Profiles approximate cosine functions for small index modulations.

Abstract

A class of four-parameter solvable profiles of the electromagnetic admittance has recently been discovered by applying the newly developed Property & Field Darboux Transformation method (PROFIDT). These profiles are highly flexible. In addition, the related electromagnetic-field solutions are exact, in closed-form and involve only elementary functions. In this paper, we focus on those who are S-shaped and we provide all the tools needed for easy implementation. These analytical bricks can be used for high-level modeling of lightwave propagation in photonic devices presenting a piecewise-sigmoidal refractive-index profile such as, for example, antireflection layers, rugate filters, chirped filters and photonic crystals. For small amplitude of the index modulation, these elementary profiles are very close to a cosine profile. They can therefore be considered as valuable surrogates for computing the scattering properties of components like Bragg filters and reflectors as well. In this paper we present an application for antireflection layers and another for 1D quasicrystals (QC). The proposed S-shaped profiles can be easily manipulated for exploring the optical properties of smooth QC, a class of photonic devices that adds to the classical binary-level QC.