Flaw of photonic band structure and its implication for photonic bound state in the continuum

TL;DR

This paper identifies a flaw in the traditional photonic band structure concept, proposes a corrected continuous-folded band structure, and clarifies the true nature of bound states in the continuum in photonic systems.

Contribution

It introduces a continuous-folded band structure to rectify the flawed understanding of photonic band structures and accurately describes bound states in the continuum.

Findings

The traditional band structure has a fundamental flaw affecting BIC understanding.

The proposed continuous-folded band structure correctly predicts BIC positions.

Verification with photonic crystal slabs confirms the validity of the new model.

Abstract

We show a flaw in the photonic band structure which forms the basis of our understanding of crystal momentum in photonic systems. We investigate the origin of this flaw and propose a continuous-folded band structure as the rectification. Based on the proposed continuous-folded photonic band structure, a bound state in the continuum (BIC) is actually below the light line, similar to the conventional guided modes. We present the condition for the boundedness of photonic modes and verify the effectiveness of our condition via two photonic crystal slabs with resonance-trapped BIC and symmetry-protected BIC, respectively. In the second case, our condition of boundedness correctly indicates a radiative mode, which satisfies the condition of symmetry-protected BIC.