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SUMMARY:Black-hole waves at a conical tip of negative material - Anne-Soph
 ie Bonnet-Ben Dhia (ENSTA ParisTech)
DTSTART:20230210T094500Z
DTEND:20230210T103000Z
UID:TALK196861@talks.cam.ac.uk
DESCRIPTION:This is a work in collaboration with Mahran Rihani and Lucas C
 hesnel. We are interested in time-harmonic electromagnetic waves in a medi
 um where the dielectric permittivity is supposed to be real-valued and pie
 cewise constant\, with both positive and negative values. Such model is re
 levant for instance when considering&nbsp\; metal-dielectric interfaces at
  optical frequencies. Due to the sign change of the permittivity\, so-call
 ed plasmonic waves can travel at the surface of the metal. More specifical
 ly\, this talk concerns configurations where the surface of the metal has 
 a geometric singularity which coincides locally with a conical tip (not ne
 cessarily circular). Then a very strange phenomenon occurs. Some plasmonic
  waves travel towards the tip\, slowing down more and more\, so that they 
 never reach the tip. These so-called black-hole waves result in a hyper-os
 cillating behavior of the electric field which is non longer square-integr
 able\, because of the energy accumulated in the vicinity of the tip. Black
 -hole waves are linked to the solutions of a transmission problem for the 
 Laplace equation for the infinite conical tip\, with sign-changing coeffic
 ients. After a separation of variables\, one has to study an eigenvalue pr
 oblem set on the sphere. The difficulty comes from the sign-change of the 
 coefficients which makes it non-selfadjoint. During the talk\, we will giv
 e a survey of the theoretical\, analytical and numerical results that have
  been proved for this unusual spectrum.
LOCATION:Seminar Room 1\, Newton Institute
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