A contour integral-based method for nonlinear eigenvalue problems for semi-infinite photonic crystals


Speaker: Professor Li Tiexiang

Topic: A contour integral-based method for nonlinear eigenvalue problems for semi-infinite photonic crystals

Date: June 26th, 2024 (Wednesday)

Time: 3.00 p.m.

Venue: Academic Lecture Hall 203, Jingyuan Building

Sponsors: School of Mathematics and Statistics, Institute of Mathematics, Institute of Science and Technology


Li Tiexiang is a professor of mathematics at Southeast University. She is a doctoral supervisor, an assistant director of the Shing-Tung Yau Center of Southeast University, and the assistant director of the Nanjing Center for Applied Mathematics. She is mainly engaged in researches of large-scale matrix computing, electromagnetic computing, computational geometry, etc. Professor Li presides over 4 projects that are supported by National Natural Science Foundation. In 2014, she was elected as the academic leader for young researchers of QingLan Project in Jiangsu province. She has published more than 60 academic papers in journals such as SISC, SIIMS, SIMAX, ACMTOMS, JCP, and Inverse Problems. Also, she has won the third prize of Jiangsu Science and Technology in 2013 (ranked fifth), the 2017 and 2019 ICCM Best Paper Award by International Consortium Chinese Mathematician, and the Youth Award of Jiangsu Society for Industrial and Applied Mathematics in 2020.


In this study, we introduce an efficient algorithm for determining the isolated singular point of semi-infinite photonic crystals with perfect electric conductor and quasi-periodic mixed boundary conditions. This specific problem can be modelled by a Helmholtz equation, which becomes an eigenvalue problem of an infinite-dimensional Toeplitz matrix after discretization. Through ingenious matrix transformations, our computational goal is to obtain the closest eigenvalue to a given value and its corresponding eigenvector of a nonlinear eigenvalue problem. The contour integration method can be used elegantly for this purpose. Moreover, this particular eigenpair holds significant importance in the examination of edge states in photonic crystals.