High order and Multi-physics Numerical Methods for surface plasmon polaritons

Wei Cai
University of North Carolina Charlotte

Surface plasmon polariton (SPP) is an electronic excitation at a metal surface which involves
collective motions of electron gas in a metallic material. Understanding and simulation of SPP is
important for the calculation of optical properties of metallic materials to external electromagnetic fields
for applications such as surface enhanced Raman scattering and near field optics and optical circuits.
In this talk, we will first review the basic physical concept of SPPs and some classical models. Then, we will
present two numerical methods for simulating plasmons: (1) A dispersive high order
discontinuous Galerkin (DG) method, (2) A density functional theory-Maxwell equation coupling method.
The dispersive DG methods will be used to simulate the plasmon resonant phenomena of coupled silver
nanowires for optical circuit applications. The multi-physics method coupling the density functional theory
and Maxwell equations will be used to study the many body quantum effects in the optical responses of
SPPs. Under the Thomas-Fermi DFT model, we will derive the Hamilton-Jacobi equations for the electron density
and hydrodynamic velocity potential coupled with the Maxwell equations. Numerical issues and boundary
conditions are then discussed. In addition to linear analysis of the multi-physics coupling model,
numerical simulation of SPPs on a periodic grating will show the improvement over classical models.

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