일시 : 5월 26일(금) 15:00 - 16:00
장소 : 아산이학관 525호
연사 : Matias Ruiz (University of Edinburgh)
제목 : Spectral analysis of the eigen-permittivity modes for the Helmholtz equation
초록 :
In this talk I will present recent progress on the study of a spectral problem defined by an unforced Helmholtz equation when using the permittivity as the eigenvalue. The eigensolutions of such problems are useful for modal expanding electromagnetic scattering fields by resonant nanocavities in nanophotonic systems. Owing to radiation conditions, this linear spectral problem is non-self-adjoint, which is at the source of numerical and theoretical difficulties. Furthermore, the problem is non-standard in that its eigenvalues both diverge and accumulate at finite points. Our main result is the completeness of the (generalised) eigenfunctions in a pertinent energy functional space for generic cavities. We further show that they form a Riesz basis in some particular configurations.