A cornerstone of topological electrodynamics is the bulk-boundary (or bulk-edge) correspondence principle (BBCP): the number of topologically protected interface modes between two periodic heterostructures depends on discrete invariants (Zak phases in 1D and Chern numbers in higher dimensions) of the respective Bloch bands.

In physics literature, analyses are typically performed only for Bloch modes in the bulk. Thus, conclusions about the boundary behavior of fields are reached after ignoring this behavior in the first place; this needs to be explained. Moreover, a puzzling feature of the BBCP is that the properties of evanescent modes in a band gap somehow depend on the properties of propagating modes at completely different frequencies.

The talk includes a complete analysis and results for problems in 1D and “1.5D” (two-component fields but material parameters depending on one coordinate only); mathematical considerations and numerical evidence are presented for the 2D case. Notably, for materials with frequency-dependent parameters, the BBCP turns out to be closely connected to the positivity of electromagnetic energy density.
 

Biosketch

Igor Tsukerman is Professor of Electrical and Computer Engineering at the University of Akron, Ohio, USA, where he has been a faculty member since 1995. His research is focused on the simulation of nanoscale systems, applied electromagnetics and photonics. He teaches a variety of undergraduate and graduate courses (Circuits, Electromagnetic Fields, Programming for Engineers, Signals & Systems, Digital Signal Processing, Random Signal Analysis, Simulation of Nanoscale Systems, and others). Tsukerman has over 200 refereed publications. He has authored the monograph Computational Methods for Nanoscale Applications: Particles, Plasmons and Waves (Springer 2008, 2020), co-edited another book, Plasmonics and Plasmonic Metamaterials (World Scientific 2011), and acted as Editor-in-Chief of a five-volume reference set on electromagnetic analysis and simulation (World Scientific, 2020). He is also working on a 3^rd edition of Computational Methods for Nanoscale Applications.

Before coming to the University of Akron, Tsukerman worked at the Department of Electrical & Computer Engineering, the University of Toronto (1990–1995). His academic degrees are from St. Petersburg Polytechnic in Russia: a BSc/MSc degree with honors in Control Systems (1982) and a PhD in Electrical Engineering (1988).

Please contact phweb@ust.hk should you have questions about the talk.