Mathematical aspects of nanophotonics

https://icms-org-uk.zoom.us/j/89672877164?pwd=bC9UanpZOEl4dGxHVkdpelF5cW...
Passcode: Euler05772, Meeting ID: 896 7287 7164

n the last couple of decades, the field of nanophotonics, i.e. the study of light-matter interactions at the nanoscale, has gained enormous importance in different disciplines of science and engineering. A large portion of this field concerns the study of electromagnetic resonances in nanoparticles which are, in turn, the building blocks of many applications in energy, healthcare, material science, to name a few.

The description of these resonances relies on interesting math problems with strong connections to PDE spectral problems, both self-adjoint and non-self-adjoint. As such, there is a growing interest from the math world in tackling some of the mathematical issues arising in nanophotonics. For instance, a canonical problem is the Laplace transmission problem showing a sign-change in the PDE coefficients, whose solutions can be understood in terms of the spectral properties of the Neumann-Poincare operator (and/or the so-called plasmonic eigenvalue problem).

In this applied analysis talk I will introduce some of the mathematically interesting problems arising in nanophotonics and discuss recent analytical results in the analysis of resonances in metallic nanoparticles (also known as plasmonic resonances), which include the use of layer potential techniques and asymptotic analysis.