  The interaction of electromagnetic waves with metallic nanostructures
generates resonant oscillations of the conduction-band electrons at the metal
surface. These resonances can lead to large enhancements of the incident field
and to the confinement of light to small regions, typically several orders of
magnitude smaller than the incident wavelength. The accurate prediction of
these resonances entails several challenges. Small geometric variations in the
plasmonic structure may lead to large variations in the electromagnetic field
responses. Furthermore, the material parameters that characterize the optical
behavior of metals at the nanoscale need to be determined experimentally and
are consequently subject to measurement errors. It then becomes essential that
any predictive tool for the simulation and design of plasmonic structures
accounts for fabrication tolerances and measurement uncertainties.
  In this paper, we develop a reduced order modeling framework that is capable
of real-time accurate electromagnetic responses of plasmonic nanogap structures
for a wide range of geometry and material parameters. The main ingredients of
the proposed method are: (i) the hybridizable discontinuous Galerkin method to
numerically solve the equations governing electromagnetic wave propagation in
dielectric and metallic media, (ii) a reference domain formulation of the
time-harmonic Maxwell's equations to account for geometry variations; and (iii)
proper orthogonal decomposition and empirical interpolation techniques to
construct an efficient reduced model. To demonstrate effectiveness of the
models developed, we analyze geometry sensitivities and explore optimal designs
of a 3D periodic annular nanogap structure.
