  In this paper we consider scattering resonance computations in optics when
the resonators consist of frequency dependent and lossy materials, such as
metals at optical frequencies. The proposed computational approach combines a
novel $hp$-FEM strategy, based on dispersion analysis for complex frequencies,
with a fast implementation of the nonlinear eigenvalue solver NLEIGS. Numerical
computations illustrate that the pre-asymptotic phase is significantly reduced
compared to standard uniform $h$ and $p$ strategies. Moreover, the efficiency
grows with the refractive index contrast, which makes the new strategy highly
attractive for metal-dielectric structures. The $hp$-refinement strategy
together with the efficient parallel code result in highly accurate
approximations and short runtimes on multi processor platforms.
