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SUMMARY:Trapped modes in electromagnetic waveguides - Lucas  Chesnel  (INR
 IA Saclay - Île-de-France)
DTSTART:20260415T091500Z
DTEND:20260415T101500Z
UID:TALK244009@talks.cam.ac.uk
DESCRIPTION:We consider the Maxwell's equations with perfect electric cond
 uctor boundary conditions in three-dimensional unbounded domains which are
  the union of a bounded resonator and one or several semi-infinite wavegui
 des. We are interested in the existence of electromagnetic trapped modes\,
  that is L2 non zero solutions of the problem without source term. These t
 rapped modes are associated to eigenvalues of the Maxwell's operator\, tha
 t can be either below the continuous spectrum or embedded in it. First for
  homogeneous waveguides\, we will present different families of geometries
  for which we can prove the existence of eigenvalues. Then we will show th
 at certain non homogeneous waveguides with local perturbations of the diel
 ectric constants can support trapped modes. Let us mention that certain me
 chanisms we will describe are very specific to Maxwell's equations and hav
 e no equivalent in the classical proofs of existence of trapped modes for 
 the scalar Dirichlet or Neumann Laplacians. \nThis is a joint work with A.
 -S. Bonnet-BenDhia and S. Fliss.
LOCATION:Seminar Room 1\, Newton Institute
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