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SUMMARY:Surface Plasmon Problem: Spectral Analysis and Existence of Nonlin
 ear Polychromatic Solutions [Oberseminar Mathematical Physics]
DTSTART:20241125T131500Z
DTEND:20241125T141500Z
DTSTAMP:20260308T034600Z
UID:indico-event-102@math-events.uni-bonn.de
DESCRIPTION:Speakers: Tomáš Dohnal (Martin-Luther-Universität Halle-Wit
 tenberg)\n\nThe study of time harmonic electromagnetic waves at a flat int
 erface of dispersive (i.e. frequency dependent) media leads to a non-self-
 adjoint Maxwell operator pencil. A classical application is to surface pla
 smon polaritons at the interface of a dielectric and a metal. We assume th
 at the interface is flat and the media in the two half spaces are spatiall
 y homogenous and unbounded. The dependence of the permittivity on the spec
 tral parameter (frequency) is generally nonlinear. The whole spectrum cons
 ists of eigenvalues and the essential spectrum\, but the various standard 
 types of essential spectra do not coincide in all cases. The functional se
 tting is such that the operator domain is not a subset of the range which 
 brings about a difficulty in defining the discrete spectrum. The spectral 
 analysis is complete in one and two dimensions\; in collaboration with Mal
 colm Brown (Cardiff)\, Michael Plum (Karlsruhe)\, and Ian Wood (Canterbury
 ). In the case of cubically (Kerr) nonlinear materials monochromatic solut
 ions do not exist. In the one dimensional case we find polychromatic solut
 ions in the form of an infinite series of odd harmonics with the frequency
  of the leading order term being a complex eigenvalue of the linear proble
 m. This work is in collaboration with Max Hanisch (Halle) and Runan He (Ma
 drid).\n\nhttps://math-events.uni-bonn.de/event/102/
LOCATION:R. 0.006 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/102/
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