From zero transmission to trapped modes in waveguides

Abstract

We consider the time-harmonic scattering wave problem in a 2D waveguide at wavenumber $k$ such that one mode is propagating in the far field. In a first step, for a given $k$, playing with one scattering branch of finite length, we demonstrate how to construct geometries with zero transmission. The main novelty in this result is that the symmetry of the geometry is not needed: the proof relies on the unitary structure of the scattering matrix. Then, in a second step, from a waveguide with zero transmission, we show how to build geometries supporting trapped modes associated with eigenvalues embedded in the continuous spectrum. For this second construction, using the augmented scattering matrix and its unitarity, we play both with the geometry and the wavenumber. Finally, the mathematical analysis is supplemented by numerical illustrations of the results.

References in corpus (8)

• Fano resonances in nanoscale structures
• Topological nature of bound states in the radiation continuum
• Anisotropy-induced photonic bound states in the continuum
• Bound states in continuum in an electron waveguide
• Bound states in the continuum in graphene quantum dot structures
• Resonant electromagnetic scattering in anisotropic layered media
• Symmetry and resonant modes in platonic grating stacks
• Bound States in the Continuum in Two-Dimensional Serial Structures

Cited by in corpus (2)

• Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
• Acoustic passive cloaking using thin outer resonators