Bound states with complex frequencies near the continuum on lossy periodic structures

Abstract

On a lossless periodic dielectric structure sandwiched between two homogeneous media, bound states in the continuum (BICs) with real frequencies and real Bloch wavevectors may exist, and they decay exponentially in the surrounding homogeneous media and do not couple with propagating plane waves with the same frequencies and wavevectors. The BICs are of significant current interest, because they give rise to high-Q resonances when the structure or the Bloch wavevector is slightly perturbed. In this paper, the effect of a small material loss on the BICs is analyzed by a perturbation method and illustrated by numerical results. It is shown that bound states with complex frequencies near the continuum appear, but they behave differently depending on whether the BIC is symmetryprotected or not. The Bloch wavevector of a bound state with a complex frequency can be real if the original BIC is symmetry-protected, and it is usually complex if the original BIC is not symmetryprotected. Our study improves the theoretical understanding on BICs and provides useful insight for their practical applications.

Conditional robustness of propagating bound states in the continuum on biperiodic structures

“…It is obvious that a lossy biperiodic structure cannot have a BIC with a real frequency and a real Bloch wavenumber. It turns out that it usually cannot even have a bound state with a complex frequency and a real non-zero Bloch wavevector [52]. In other words, if the original lossless structure has a propagating BIC and the perturbation profile s(x) represents material loss and satisfies the symmetry condition (2), then a propagating BIC is usually destroyed by the perturbation.…”

Frequency perturbation theory of bound states in the continuum in a periodic waveguide

“…For a structure with at least one open spatial direction, a photonic BIC is an eigenmode of the governing Maxwell's equations satisfying two conditions: (1) it decays rapidly in the open spatial direction, and (2) at the same frequency as the BIC, there exist waves that propagate to or from infinity in the open spatial direction. For a periodic structure sandwiched between two homogeneous media, such as a photonic crystal slab [5][6][7][8][9][10][11][12][13][14] or a periodic array of cylinders [15][16][17][18][19][20][21][22], a BIC is characterized by its frequency and Bloch wavevector, the direction perpendicular to the periodic layer is the open spatial direction, and propagating diffraction orders compatible with the BIC frequency and wavevector are the waves that propagate to or from infinity.…”

Resonant field enhancement in lossy periodic structures supporting complex bound states in the continuum

“…If the real part of its complex frequency lies in the radiation continuum, the bound state will be referred to as a complex BIC (cBIC) in this paper. For periodic structures with an in-plane inversion symmetry, symmetry-protected cBICs are easy to find [29]. A resonant mode is an eigenmode that radiates out power in the surrounding media.…”