报告题目：Spectral analysis of the material-independent modes for the Helmholtz equation

报 告 人： Dr. Matias Ruiz  (University of Leicester)

报告时间：2024年4月20日（星期六） 9:00-10:00

报告地点：数学楼114（小报告厅）

校内联系人：张旭平 副教授         联系电话：84708351-8025

报告摘要：In this talk I will discuss the spectral analysis of a family of non-self-adjoint spectral problems defined by a homogeneous Helmholtz equation when using the permittivity/permeability as the eigenvalue. The study of such problems is motivated by the modal decomposition approach in computational electromagnetism, wherein the  electromagnetic field scattered by a nanocavity subject to radiation losses (i.e. in an open system), can be described as an infinite sum using as basis functions the eigenfunctions of a spectral problem defined by the unforced Maxwell's equations. Owing to radiation conditions, this linear spectral problem is non-self-adjoint, which is the source of numerical and theoretical difficulties. Furthermore, the problem is non-standard in that its eigenvalues both diverge and accumulate at multiple finite points. I will present a rigorous spectral analysis of these modes and show their completeness in H^1(D), where D is the domain occupied by the resonant nanocavity. I will also show that they define a Riesz basis in some particular geometric configurations.

报告人简介： Dr. Matias Ruiz is working at the School of Computing and Mathematical Sciences, University of Leicester, UK. His research is in applied analysis. In particular, He is interested in the study of wave propagation in complex media with applications to nanophotonics, metamaterials, and related topics. He is also interested in the computational side of these problems.