2018/01/26 by Anne-Sophie Bonnet-Ben Dhia, Dhia, Anne-Sophie Bonnet-Ben, Lucas Chesnel +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Numerical Analysis (math.NA) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1801.08703
openalex publication_date 2018/01/26 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28
We consider the reflection-transmission problem in a waveguide with obstacle.\nAt certain frequencies, for some incident waves, intensity is perfectly\ntransmitted and the reflected field decays exponentially at infinity. In this\nwork, we show that such reflectionless modes can be characterized as\neigenfunctions of an original non-selfadjoint spectral problem. In order to\nselect ingoing waves on one side of the obstacle and outgoing waves on the\nother side, we use complex scalings (or Perfectly Matched Layers) with\nimaginary parts of different signs. We prove that the real eigenvalues of the\nobtained spectrum correspond either to trapped modes (or bound states in the\ncontinuum) or to reflectionless modes. Interestingly, complex eigenvalues also\ncontain useful information on weak reflection cases. When the geometry has\ncertain symmetries, the new spectral problem enters the class of\n\PT-symmetric problems.\n