Fourier spectral simulations and Gegenbauer reconstructions for electromagnetic waves in the presence of a metal nanoparticle

We describe Fourier pseudospectral time-domain simulations, carried out in order to study light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to accurately predict the electromagnetic scattering in such problems arises from the discontinuity in the dielectric function along the surface of the metallic object. Standard Fourier methods lead to oscillatory behavior in approximating solutions that are nonsmooth or that have steep gradients. By applying the Gegenbauer reconstruction technique as a postprocessing method to the Fourier pseudospectral solution, we successfully reduce the oscillations after postprocessing. Our computational results, including comparison with finite-difference time-domain simulations, demonstrate the efficiency and accuracy of the method.