Real transmission and reflection zeros of periodic structures with a bound state in the continuum

TL;DR

This paper introduces a new, simple, and complete theory explaining the existence of real transmission and reflection zeros in lossless periodic structures with symmetry and bound states in the continuum, validated by numerical examples.

Contribution

The paper develops a novel, accessible theory for real zeros in spectra of symmetric periodic structures with BICs, filling gaps in existing incomplete theories.

Findings

The theory accurately predicts zero dips in spectra.

Numerical examples confirm the theory's validity.

The approach simplifies analysis of spectral zeros.

Abstract

For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks and dips that are truly $100\%$ and $0\%$, respectively. The full peaks and zero dips typically appear near resonant frequencies, and they are robust with respect to structural perturbations that preserve the required symmetry. However, current theories on the existence of full peaks and zero dips are incomplete and difficult to use. For periodic structures with a bound state in the continuum (BIC), we present a new theory on the existence of real transmission and reflection zeros that correspond to the zero dips in the transmission and reflection spectra. Our theory is relatively simple, complete, and easy to use. Numerical examples are presented to validate the new theory.