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SUMMARY:Geometric spectral properties of electromagnetic waveguides - Mich
 ele Zaccaron (ENSTA ParisTech)
DTSTART:20260206T114500Z
DTEND:20260206T121500Z
UID:TALK239854@talks.cam.ac.uk
DESCRIPTION:Consider a reference homogeneous and isotropic electromagnetic
  waveguide with a simply connected cross-section embedded in a perfect con
 ductor. In this setting\, when the waveguide is straight\, the spectrum of
  the associated self-adjoint Maxwell operator with a constant twist lies o
 n the real line\, is symmetric with respect to zero and exhibits a spectra
 l gap around the origin. Moreover\, the spectrum is purely essential\, and
  contains 0 which is an eigenvalue of infinite multiplicity.\nIn this talk
 \, we present new results on the effects of geometric deformations of bend
 ing and twisting on the spectrum of the Maxwell operator. More precisely\,
  we provide\, on the one hand\, sufficient conditions on the asymptotic be
 haviour of curvature and twist ensuring the preservation of the essential 
 spectrum of the reference waveguide. Our approach relies on a Birman-Schwi
 nger-type principle which has an interest of its own. On the other hand\, 
 we give sufficient conditions\, involving in particular the shape of the c
 rosssection of the waveguide\, so that the geometrical deformation creates
  discrete spectrum within the gap of the essential spectrum. In addition\,
  we give some results on the possible localization of these discrete eigen
 values. Finally\, we show some theoretical and numerical results further i
 nvestigating the sufficient condition involving the geometry of the cross-
 section.\nThis is a joint work in collaboration with P. Briet\, M. Cassier
  and T. Ourmi&egrave\;res-Bonafos.
LOCATION:Seminar Room 1\, Newton Institute
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