## Mathematical Physics and Harmonic Analysis Seminar

**Date: ** September 22, 2023

**Time: ** 1:50PM - 2:50PM

**Location: ** BLOC 302

**Speaker: **Matthias Maier, Texas A&M University

**Title: *** Lorentz Resonance in the Homogenization of Plasmonic Crystals*

**Abstract: ** We explain the Lorentz resonances in plasmonic crystals that consist
of 2D nano dielectric inclusions as the interaction between resonant
material properties and subwavelength geometric resonances of
electrostatic nature. One example of such plasmonic crystals is
graphene nanosheets that are periodically arranged within a
non-magnetic bulk dielectric.

We identify local geometric resonances on the length scale of the
small scale period. From a materials perspective, the graphene surface
exhibits a dispersive surface conductance captured by the Drude
model. Together these phenomena conspire to generate Lorentz
resonances at frequencies controlled by the surface geometry and the
surface conductance.

The Lorentz resonances found in the frequency response of the
effective dielectric tensor of the bulk metamaterial is shown to be
given by an explicit formula, in which material properties and
geometric resonances are decoupled.

Joint work with Wei Li (DePaul University) and Robert Lipton
(Louisiana State University)