We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid variation for real frequencies in a vicinity of a complex resonance located close to the real axis. This is the so-called Fano resonance phenomenon. And when the geometry presents certain properties of symmetry, there are two different real frequencies such that we have either R= 0 or T= 0 , where R and T denote the reflection and transmission coefficients. In this work, we prove that without the assumption of symmetry of the geometry, quite surprisingly, there is always one real frequency for which we have T= 0. In this situation, all the energy sent in the waveguide is backscattered. However in general, we do not have R= 0 in the process. We provide numerical results to illustrate our theorems.

Original languageEnglish
Article number82
Number of pages13
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume71
Issue number3
DOIs
StatePublished - 4 May 2020

    Research areas

  • Fano resonance, Scattering matrix, Waveguides, Zero transmission, TRAPPED MODES, EIGENVALUE, REFLECTION, COMPLEX RESONANCES, ENFORCED STABILITY, CONTINUOUS-SPECTRUM

    Scopus subject areas

  • Physics and Astronomy(all)
  • Applied Mathematics
  • Mathematics(all)

ID: 60873423