# Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders - Mathematical Physics

Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Electromagnetic bound states in the radiation continuum are studied forperiodic double arrays of subwavelength dielectric cylinders in TMpolarization. They are similar to localized waveguide mode solutions ofMaxwell-s equations for metal cavities or defects of photonic crystals, but, incontrast to the latter, their spectrum lies in the radiation continuum. Thephenomenon is identical to the existence of bound sates in the radiationcontinuum in quantum mechanics, discovered by von Neumann and Wigner. In theformal scattering theory, these states appear as resonances with the vanishingwidth. For the system studied, the bound states are shown to exist at specificdistances between the arrays in the spectral region where one or twodiffraction channels are open. Analytic solutions are obtained for all boundstates below the radiation continuum and in it in the limit of thin cylindersthe cylinder radius is much smaller than the wavelength. The existence ofbound states is also established in the spectral region where three and morediffraction channels are open, provided the cylinders- dielectric constant andradius are fine-tuned. The near field and scattering resonances of thestructure are investigated when the distance between the arrays varies in theneighborhood of its critical values at which the bound states are formed. Inparticular, it is shown that the near field in the scattering process becomessignificantly amplified in specific regions of the array as the distanceapproaches its critical values. The effect may be used to control opticalnon-linear effects by varying the distance between the arrays near its criticalvalues.

Author: ** Friends R. Ndangali, Sergei V. Shabanov**

Source: https://arxiv.org/