Resonant-state expansion for planar photonic-crystal structures

TL;DR

This paper introduces the resonant-state expansion (RSE) as a new method for accurately analyzing optical resonances in planar photonic-crystal structures, enhancing understanding and computational efficiency.

Contribution

The paper applies the RSE to planar photonic crystals, providing a novel, efficient, and precise tool for calculating resonant states in these structures.

Findings

RSE achieves unprecedented accuracy and convergence in calculating resonant states.

Numerical verification confirms the effectiveness of the RSE approach.

Mode evolution analysis reveals the role of guided modes in bound states formation.

Abstract

We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in photonic-crystal structures in terms of the analytic resonant states of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the resonant states of a photonic-crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of the present approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound states in the continuum.