Resonant transmission near nonrobust periodic slab modes (original) (raw)

EXISTENCE OF GUIDED MODES ON PERIODIC SLABS

We prove the existence of bound guided modes for the Helmholtz equa- tion on lossless penetrable periodic slabs. We handle both robust modes, for which no Bragg harmonics propagate away from slab, as well as nonrobust standing modes, which exist in the presence of propagating Bragg harmonics. The latter are made possible by symmetries of the slab structure, which prevent coupling of energy to the propagating harmonics. These modes are isolated in wavevector-frequency space, as they disappear under a perturbation of the wavevector. The main tool is a volumetric integral equation of Lippmann-Schwinger type that has a self-adjoint kernel. 1. Introduction. In this work, we prove the existence of bound guided acoustic and electromagnetic modes in periodic slab structures. These are material slabs that are infinitely periodic in two spatial directions and finite in the other. Such a structure can be thought of as an acoustic or photonic crystal slab if it arises from an infinite periodic ...

Fano-Type Resonance of Waves in Periodic Slabs

We investigate Fano-type anomalous transmission of energy of plane waves across lossless slab scatterers with periodic structure in the presence of non-robust guided modes. Our approach is based on rigorous analytic perturbation of the scattering problem near a guided mode and applies to very general structures, continuous and discrete.

Bloch Waves in High Contrast Electromagnetic Crystals

2021

Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the identification and utilization of a resonance spectrum for quasiperiodic source-free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. A convergent power series for the Bloch wave spectrum is recovered from the representation formulas. Explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum.