Bound states in the continuum on periodic structures surrounded by strong resonances

Yuan, Lijun; Lu, Ya Yan

doi:10.1103/physreva.97.043828

Cited by 50 publications

(39 citation statements)

References 52 publications

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“…It is well known that the Q-factors of these resonant modes tend to infinity as the wave vector tends to that of the BIC. For 2D periodic structures, we show that if an ASW satisfies a condition first derived in [45], the Qfactors of nearby resonant modes are O(1/β 6 ), where β is the Bloch wavenumber. These theoretical results can be useful for practical applications where high-Q resonances are needed.…”

Section: Discussionmentioning

confidence: 73%

“…A BIC can be considered as a resonant mode with an infinite Q-factor. This implies that resonant modes with extremely large Q-factors can be created by perturbing the structure or varying a physical parameter slightly [43][44][45][46][47]. Since many applications of the BICs are related to the high-Q resonances, it is of significant importance to understand how the Q-factors depend on the structural or parametric perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…We also consider the perturbation with respect to the Bloch wavenumber. It is known that for any BIC (with Bloch wavenumber β * ) satisfying a special condition [45], the Qfactors of nearby resonant modes (with Bloch wavenumber β) are O(1/|β − β * | 4 ) in general. We show that if the BIC is an ASW, then the Q-factors are in fact O(1/β 6 ).…”

Section: Introductionmentioning

confidence: 99%

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

Yuan

2020

Phys. Rev. A

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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.

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Section: Discussionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Yuan

2020

Phys. Rev. A

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“…Importantly, a BIC can be regarded as a resonant mode (or resonant state) with an infinite quality factor (Qfactor). This implies that resonant modes with arbi- * Corresponding author: mayylu@cityu.edu.hk trarily high Q-factors can be created by modifying the structure [40] or varying a physical parameter such as a component of the Bloch wavevector [41,42]. Applications of optical BICs include lasing [43], sensing [45], filtering [46,47], switching [48], nonlinear optics [41,49], etc.…”

Section: Introductionmentioning

confidence: 99%

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

Zhen

Yuan

2020

Phys. Rev. A

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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.

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“…The BICs are observed from the dispersion of the leaky-zone Q-factor as the points where the Q-factor diverges to infinity. This implies that spectrally any BIC is surrounded by a family by high-Q leaky modes [28,29] with the Q-factort infinitely increasing as β is tuned to the BIC point.…”

Section: Introductuionmentioning

confidence: 99%

Optical response induced by bound states in the continuum in arrays of dielectric spheres

Bulgakov

Максимов

2018

J. Opt. Soc. Am. B

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We consider optical response induced by bound states in the continuum (BICs) in arrays of dielectric spheres. By combining quasi-mode expansion technique with coupled mode theory (CMT) we put forward a theory of the optical response by high-Q resonance surrounding BICs in momentum space. The central result are analytical expressions for the CMT parameters, which can be easily calculated from the eigenfrequencies and eigenvectors of the interaction matrix of the scattering systems. The results obtained are verified in comparison against exact numerical solutions to demonstrate that the CMT approximation is capable of reproducing Fano features in the spectral vicinity of the BIC. Based on the quasi-mode expansion technique we derived the asymptotic scaling law for the CMT parameters in the vicinity of the Γpoint. It is rigourously demonstrated that the line width in the CMT approximation exhibits different asymptotic behavior depending on the symmetry of the BIC.

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Bound states in the continuum on periodic structures surrounded by strong resonances

Cited by 50 publications

References 52 publications

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

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

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

Optical response induced by bound states in the continuum in arrays of dielectric spheres

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