Parametric dependence of bound states in the continuum in periodic structures: vectorial cases

Abstract

A periodic structure sandwiched between two homogeneous media can support bound states in the continuum (BICs) that are valuable for many applications. It is known that generic BICs in periodic structures with an up-down mirror symmetry and an in-plane inversion symmetry are robust with respect to structural perturbations that preserve these two symmetries. For two-dimensional (2D) structures with one periodic direction and the up-down mirror symmetry (without the in-plane inversion symmetry), it was recently established that some scalar BICs can be found by tuning a single structural parameter. In this paper, we analyze vectorial BICs in such 2D structures, and show that a typical vectorial BIC with nonzero wavenumbers in both the invariant and the periodic directions can only be found by tuning two structural parameters. Using an all-order perturbation method, we prove that such a vectorial BIC exists as a curve in the 3D space of three generic parameters. Our theory is validated by numerical examples involving periodic arrays of dielectric cylinders. The numerical results also illustrate the conservation of topological charge when structural parameters are varied, if both BICs and circularly polarized states (CPSs) are included. Our study reveals a fundamental property of BICs in periodic structure and provides a systematically approach for finding BICs in structures with less symmetry.

11 pages, 8 figures

References in corpus (20)

• Asymmetric metasurfaces with high-$Q$ resonances governed by bound states in the continuum
• Resonantly Trapped Bound State in the Continuum Laser
• Topological nature of bound states in the radiation continuum
• Individual nanoantennas empowered by bound states in the continuum for nonlinear photonics
• Topologically Enabled Ultra-high-Q Guided Resonances Robust to Out-of-plane Scattering
• High-Q supercavity modes in subwavelength dielectric resonators
• Nonradiating Photonics with Resonant Dielectric Nanostructures
• Circularly polarized states spawning from bound states in the continuum
• Analytical Perspective for Photonic Bound States in the Continuum in Photonic Crystal Slabs
• Generation and Annihilation of Topologically-Protected Bound States in the Continuum and Circularly-Polarized States by Symmetry Breaking
• Anisotropy-induced photonic bound states in the continuum
• Bloch bound states in the radiation continuum in a periodic array of dielectric rods
• Quasi Bound States in the Continuum with Few Unit Cells of Photonic Crystal Slab
• Bound States in the Continuum on Periodic Structures: Perturbation Theory and Robustness
• Bound states in the continuum on periodic structures surrounded by strong resonances
• Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures
• Resonant field enhancement near bound states in the continuum on periodic structures
• Conditional robustness of propagating bound states in the continuum on biperiodic structures
• Bound states with complex frequencies near the continuum on lossy periodic structures
• Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

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• Parametric dependence of bound states in the continuum: a general theory
• Approximating transmission and reflection spectra near isolated nondegenerate resonances
• How many parameters do we need to obtain a BIC in symmetric and asymmetric structures?
• Frequency perturbation theory of bound states in the continuum in a periodic waveguide