Robustness of perfect transmission resonances to asymmetric perturbation

TL;DR

This paper explores how asymmetric perturbations affect perfect transmission resonances in one-dimensional periodic systems, revealing conditions under which PTRs remain robust due to underlying symmetries, with implications for optical device design.

Contribution

It demonstrates that PTRs can persist under asymmetric perturbations if the unperturbed system has mirror symmetry, linking PTR preservation to the system's symmetry properties.

Findings

PTRs can survive asymmetric perturbations with mirror symmetry.

A dual PTR exists if one PTR is preserved, due to symmetry.

Insights enable robust optical device design.

Abstract

We investigate the impact of asymmetric perturbations on the perfect transmission resonances (PTRs) of one-dimensional finite periodic systems. With no perturbations, the scattering region consists of $N$ identical cells, and the transmission spectrum exhibits at least $N-1$ PTRs in each pass band of the Bloch dispersion of the unit cell. By introducing a perturbation, the periodic structure is broken, which \textit{a priori} results in the elimination of all PTRs. However, we demonstrate that PTRs can still arise under asymmetric perturbations when the unperturbed system possesses mirror symmetry, utilizing the $\mathcal{PT}$ symmetry of the unperturbed reflectionless eigenvalue problem. We also reveal an intriguing connection between two seemingly independent PTRs that lies in the symmetry of the unperturbed unit cell: If one PTR is preserved, then a dual one is necessarily also preserved. Our findings offer insights for the design of, for example, a robust antireflection setup at multiple wavelengths or all-optical diode devices.