Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders

Abstract

Electromagnetic bound states in the radiation continuum are studied for periodic double arrays of subwavelength dielectric cylinders in TM polarization. They are similar to localized waveguide mode solutions of Maxwell's equations for metal cavities or defects of photonic crystals, but, in contrast to the latter, their spectrum lies in the radiation continuum. The phenomenon is identical to the existence of bound sates in the radiation continuum in quantum mechanics, discovered by von Neumann and Wigner. In the formal scattering theory, these states appear as resonances with the vanishing width. For the system studied, the bound states are shown to exist at specific distances between the arrays in the spectral region where one or two diffraction channels are open. Analytic solutions are obtained for all bound states (below the radiation continuum and in it) in the limit of thin cylinders (the cylinder radius is much smaller than the wavelength). The existence of bound states is also established in the spectral region where three and more diffraction channels are open, provided the cylinders' dielectric constant and radius are fine-tuned. The near field and scattering resonances of the structure are investigated when the distance between the arrays varies in the neighborhood of its critical values at which the bound states are formed. In particular, it is shown that the near field in the scattering process becomes significantly amplified in specific regions of the array as the distance approaches its critical values. The effect may be used to control optical non-linear effects by varying the distance between the arrays near its critical values.

Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in (J. Math. Phys. 51, 102901 (2010)) and may be found at (http://link.aip.org/link/?JMP/51/102901)

Cited by in corpus (23)

• Asymmetric metasurfaces with high-$Q$ resonances governed by bound states in the continuum
• Bound states in the continuum and Fano resonances in the strong mode coupling regime
• Multipolar origin of bound states in the continuum
• Interference traps waves in open system: Bound states in the continuum
• Bloch bound states in the radiation continuum in a periodic array of dielectric rods
• Enhanced Light-Matter Interactions in Dielectric Nanostructures via Machine Learning Approach
• Bound states in the continuum in photonic structures
• Light trapping above the light cone in one-dimensional array of dielectric spheres
• Propagating bound states in the continuum in dielectric gratings
• Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity
• Robust bound states in the continuum in Kerr microcavity embedded in photonic crystal waveguide
• Bound States in the Continuum on Periodic Structures: Perturbation Theory and Robustness
• Bound states in the continuum on periodic structures surrounded by strong resonances
• Accidental and symmetry-protected bound states in the continuum in planar photonic-crystal structures, studied by the resonant-state expansion
• Light guiding above the light line in arrays of dielectric nanospheres
• Fabry-Perot Bound States in the Continuum in an Anisotropic Photonic Crystal
• Near-bound states in the radiation continuum in circular array of dielectric rods
• Resonant properties of composite structures consisting of several resonant diffraction gratings
• Desktop laboratory of bound states in the continuum in metallic waveguide with dielectric cavities
• Bound states in the continuum in a two-channel Fano-Anderson model
• Robustness of Bound States in the Continuum in Bilayer Structures against Symmetry Breaking
• Experimental Study of Fabry-Perot BICs in a Microwave Waveguide
• Singular value decomposition to describe bound states in the continuum in periodic metasurfaces