New Analytical Approach for Computation of Band Structure in One-dimensional Periodic Media

TL;DR

This paper introduces a novel analytical method based on the differential transfer matrix approach for precisely computing the band structure of one-dimensional periodic media, accommodating arbitrary refractive index profiles.

Contribution

The paper develops a closed-form dispersion equation for 1D periodic media using DTMM, applicable to arbitrary refractive index profiles and simplifying under specific symmetry and incidence conditions.

Findings

Derived a closed-form dispersion relation for 1D periodic media.

Validated the approach with numerical test cases.

Showed TE and TM modes share the same band structure at normal incidence.

Abstract

In this paper, we present a new approach for the exact calculation of band structure in one-dimensional periodic media, such as photonic crystals and superlattices, based on the recently reported differential transfer matrix method (DTMM). The media analyzed in this paper can have arbitrary profile of refractive index. We derive a closed form dispersion equation using differential transfer matrix formalism, and simplify it under the assumptions of even symmetry and real-valued wavenumber. We also show that under normal incidence both TE and TM modes must have the same band structure. Several numerical test cases are also studied and discussed.