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

Yuan, Lijun; Lu, Ya Yan

doi:10.48550/arxiv.2001.00832

Cited by 3 publications

(9 citation statements)

References 51 publications

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“…It is known that the existence and robustness of BICs, including the propagating BICs in periodic structures, depend crucially on symmetry [11,34]. More precisely, it has been proved that some propagating BICs are robust with respect to structural perturbations that preserve the in-plane inversion symmetry and the up-down reflection symmetry, even though these BICs do not have a symmetry mismatch with compatible radiating waves [35,36].…”

Section: Discussionmentioning

confidence: 99%

“…In periodic structures sandwiched between two homogeneous media, there are also BICs with a nonzero Bloch wavevector, and they * Corresponding author: mabdrabou2-c@my.cityu.edu.hk propagate in the periodic directions [9-12, 29, 32, 33]. Such a propagating BIC is not protected by symmetry in the usual sense, but can also be robust with respect to symmetry-preserving perturbations [34][35][36]. More precisely, in a periodic structure with an up-down mirror symmetry and an in-plane inversion symmetry, a generic low-frequency propagating BIC (with only one radiation channel) continues its existence if the structure is perturbed by a perturbation preserving these two symmetries [35,36].…”

Section: Introductionmentioning

confidence: 99%

“…Such a propagating BIC is not protected by symmetry in the usual sense, but can also be robust with respect to symmetry-preserving perturbations [34][35][36]. More precisely, in a periodic structure with an up-down mirror symmetry and an in-plane inversion symmetry, a generic low-frequency propagating BIC (with only one radiation channel) continues its existence if the structure is perturbed by a perturbation preserving these two symmetries [35,36].…”

Section: Introductionmentioning

confidence: 99%

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Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

Abdrabou,

2021

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Bound states in the continuum (BICs) in a periodic structure sandwiched between two homogeneous media have interesting properties and useful applications in photonics. The topological nature of BICs was previously revealed based on a topological charge related to the far-field polarization vector of the surrounding resonant states. Recently, it was established that when a symmetryprotected BIC (with a nonzero topological charge) is destroyed by a generic symmetry-breaking perturbation, a pair of circularly polarized resonant states (CPSs) emerge and the net topological charge is conserved. A periodic structure can also support propagating BICs with a nonzero wavevector. These BICs are not protected by symmetry in the sense of symmetry mismatch, but they need symmetry for their robust existence. Based on a highly accurate computational method for a periodic array of slightly noncircular cylinders, we show that a propagating BIC is typically destroyed by a structural perturbation that breaks only the in-plane inversion symmetry, and when this happens, a pair of CPSs of opposite handedness emerge so that the net topological charge is conserved. We also study the generation and annihilation of CPSs when a structural parameter is varied. It is shown that two CPSs with opposite topological charge and same handedness, connected to two BICs or in a continuous branch from one BIC, may collapse and become a CPS with a zero charge. Our study clarifies the important connection between symmetry and topological charge conservation.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

Abdrabou,

2021

Preprint

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“…In this section, we study the robustness of BICs in optical waveguides based on an all-order perturbation method developed in our previous works [30,32]. The robustness refers to the continual existence of a BIC under small structural perturbations.…”

Section: Robustness Of Bicsmentioning

confidence: 99%

“…If a BIC is protected by a symmetry, i.e., there is a symmetry mismatch between the BIC and the radiation modes, it is typically robust with respect to symmetry-preserving perturbations. For periodic structures with the in-plane inversion symmetry and the up-down mirror symmetry, some BICs unprotected by symmetry are also robust with respect to perturbations preserving these two symmetries [28][29][30][31][32]. An optical waveguide may have a lateral leakage channel, if the structure away from the waveguide core has guided modes that can propagate in the lateral direction.…”

Section: Introductionmentioning

confidence: 99%

On the robustness of bound states in the continuum in waveguides with lateral leakage channels

Yuan,

2020

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Bound states in the continuum (BICs) are trapped or guided modes with frequencies in radiation continua. They are associated with high-quality-factor resonances that give rise to strong local field enhancement and rapid variations in scattering spectra, and have found many valuable applications. A guided mode of an optical waveguide can also be a BIC, if there is a lateral structure supporting compatible waves propagating in the lateral direction, i.e., there is a channel for lateral leakage. A BIC is typically destroyed (becomes a resonant or a leaky mode) if the structure is slightly perturbed, but some BICs are robust with respect to a large family of perturbations. In this paper, we show (analytically and numerically) that a typical BIC in optical waveguides with a left-right mirror symmetry and a single lateral leakage channel is robust with respect to any structural perturbation that preserves the left-right mirror symmetry. Our study improves the theoretical understanding on BICs and can be useful when applications of BICs in optical waveguides are explored.

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Parametric Dependence of Bound States in the Continuum on Periodic Structures

Yuan,

2020

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Bound states in the continuum (BICs) have some unusual properties and important applications in photonics. A periodic structure sandwiched between two homogeneous media is the most popular platform for observing BICs and realizing their applications. Existing studies on BICs assume the periodic structure has a C2 rotational symmetry about the axis perpendicular to the periodic layer. It is known that all BICs turn to resonant states with finite quality factors if the periodic structure is perturbed by a generic perturbation breaking the C2 symmetry, and a typical BIC continues to exist if the perturbation keeps the C2 symmetry. We study how typical BICs depend on generic structural parameters. For a class of BICs with one opening radiation channel, we show that in the plane of two generic parameters, the BICs exist continuously as a curve. Consequently, BICs can exist on periodic structures without the C2 symmetry, and they can be found by tuning a single structural parameter. The result is established analytically by a perturbation theory with two independent perturbations and validated by numerical examples. Our study reveals a much larger family for BICs on periodic structures, and provides new opportunities for future applications.

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

Cited by 3 publications

References 51 publications

Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

On the robustness of bound states in the continuum in waveguides with lateral leakage channels

Parametric Dependence of Bound States in the Continuum on Periodic Structures

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