Bound States in Continuum via Singular Transfer Matrices

TL;DR

This paper introduces an analytical approach using transfer matrices to better understand and design bound states in continuum in photonic devices, bridging exact formulas with numerical data.

Contribution

It presents a novel method that combines exact analytical transfer matrix formulas with numerical data to analyze BICs in non-homogeneous thin laminae devices.

Findings

Bound states in continuum are linked to the null space of the transfer matrix.

Analytical formulas help identify geometric parameters and frequency bands for BICs.

The approach enhances understanding of BIC origins and supports practical device design.

Abstract

In recent years, bound states in continuum (BICs) have gained significant value for practitioners in both theoretical and applied photonics. This paper focuses on devices that utilize non-homogeneous thin patterned laminae. The properties, design principles, and behavior of BICs for this class of devices are frequently explained through a variety of models, ranging from numerical or semi-analytical solutions for the Maxwell equations to heuristic approaches that rely on fitting functions to provide phenomenological descriptions. The field of devices under study has given less attention to approaches that integrate exact analytical solutions of the transfer matrix with numerical data. In this vein, this paper aims to adopt an approach where exact analytical formulas, detailed in our previous manuscript arXiv:2303.06765 (2023), are translated into equations to explore the origins and properties of the bound states in continuum, as well as their practical implementation. The geometric parameters of the device and its operating frequency band emerge from the null space of the transfer matrix.