Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures

Abstract

On dielectric periodic structures with a reflection symmetry in a periodic direction, there can be antisymmetric standing waves (ASWs) that are symmetry-protected bound states in the continuum (BICs). The BICs have found many applications, mainly because they give rise to resonant modes of extremely large quality-factors (Q-factors). The ASWs are robust to symmetric perturbations of the structure, but they become resonant modes if the perturbation is non-symmetric. The Q-factor of a resonant mode on a perturbed structure is typically O(1/δ 2 ) where δ is the amplitude of the perturbation, but special perturbations can produce resonant modes with larger Q-factors. For twodimensional (2D) periodic structures with a 1D periodicity, we derive conditions on the perturbation profile such that the Q-factors are O(1/δ 4 ) or O(1/δ 6 ). For the unperturbed structure, an ASW is surrounded by resonant modes with a nonzero Bloch wave vector. For 2D periodic structures, the Q-factors of nearby resonant modes are typically O(1/β 2 ), where β is the Bloch wavenumber. We show that the Q-factors can be O(1/β 6 ) if the ASW satisfies a simple condition.

Acoustics of a partially partitioned narrow slit connected to a half-plane: case study for exponential quasi-bound states in the continuum and their resonant excitation

“…Notably, the latter constitutes a singular asymptotic limit, in which, for example, the quality factor diverges. To date, the asymptotic approach of quasi-BIC to BIC has been theoretically studied mainly in the context of embedded guided modes in periodic structures [7][8][9][10][11][12][13][14][15][16][17], in which case perturbation theory [18][19][20][21][22] reveals algebraically singular quality factors scaling like 1/ǫ s , where s is a positive integer (typically s = 2, 4 or 6) and ǫ represents the perturbation of the Bloch wavenumber from its value at which an embedded guided mode exists.…”

Parametric dependence of bound states in the continuum on periodic structures

“…( 14), Φ 1 also can be scaled to satisfies Eq. (14). For any j ≥ 2, if α m , k m , η m are real, β m = 0 and Φ m satisfies Eq.…”

“…If C 1 = e 2iϕ for a real ϕ, we can replace E by e iϕ E, then the new E satisfies E(r) =Ê(r). (14) This implies that E y and E z are real and E x is pure imaginary. Similarly, the diffraction solutions E (s) 1 and E (s) 2 can also be scaled to satisfy condition (14).…”

“…Due to their intriguing properties and valuable applications, photonic bound state in the continuum (BICs) have been extensively studied in recent years [1][2][3]. In a lossless structure that is invariant or periodic in one or two spatial directions, a BIC is a special resonant state with an infinite quality factor (Q factor) [4][5][6][7][8][9][10][11], and it gives high-Q resonances when the structure or the wavevector is perturbed [12][13][14][15][16][17][18][19][20]. The BICs have found important applications include lasing [21], sensing [22], harmonic generation [23], low-refractive-index light guiding [10,24], etc.…”

“…Although a BIC typically becomes a high-Q resonance when the structure is perturbed [12][13][14], it may persist if the perturbation satisfies certain conditions. If a BIC is protected by a symmetry [4,[30][31][32][33][34], it naturally continues to exist when the perturbation preserves the symmetry.…”