1D Photonic Crystals with a Sawtooth Refractive Index

TL;DR

This paper derives exact analytical solutions for the optical properties of one-dimensional photonic crystals with a sawtooth refractive index profile, expanding the set of solvable models in photonics.

Contribution

It provides the first exact analytical expressions for bandgaps, reflectance, and transmittance in these structures, including asymptotic approximations.

Findings

Exact solutions in terms of Bessel functions for bandgaps, reflectance, and transmittance.

Extension of solvable models of periodic refractive indices.

Asymptotic approximations of the exact results.

Abstract

Exact analytical results (in terms of Bessel functions) for the bandgaps, reflectance, and transmittance of one-dimensional photonic crystals with a sawtooth refractive index profile on the period are derived for the first time. This extends a group of exactly solvable models of periodic refractive indices. The asymptotic approximations of the above exact results have been also obtained.