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SUMMARY:Trapped modes in electromagnetic waveguides - Anne-Sophie Bonnet-B
 en Dhia (ENSTA ParisTech)
DTSTART:20260415T104500Z
DTEND:20260415T114500Z
UID:TALK244012@talks.cam.ac.uk
DESCRIPTION:This is a common work with Lucas Chesnel and Sonia Fliss. We c
 onsider the Maxwell&rsquo\;sequations with perfect electric conductor boun
 dary conditions in three-dimensional unbounded domainswhich are the union 
 of a bounded resonator and one or several semi-infinite waveguides. We are
 interested in the existence of electromagnetic trapped modes\, that is L2 
 solutions of the problemwithout source term. These trapped modes are assoc
 iated to eigenvalues of the Maxwell&rsquo\;s operator\,that can be either 
 below the continuous spectrum or embedded in it. First for homogeneous wav
 eguides\,we present different families of geometries for which we can prov
 e the existence of eigenvalues. Thenwe show that certain non homogeneous w
 aveguides with local perturbations of the dielectric constantscan support 
 trapped modes. Let us mention that certain mechanisms we propose are very 
 specific toMaxwell&rsquo\;s equations and have no equivalent in the classi
 cal proofs of existence of trapped modes forthe scalar Dirichlet or Neuman
 n Laplacians.
LOCATION:Seminar Room 1\, Newton Institute
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