A new computational method for plasmon resonances of nanoparticles and for wave propagation

Numerical simulation of electromagnetic wave propagation and scattering in nanoscale applications, and in particular photonic crystals and plasmon resonances, faces serious challenges. This paper addresses one of the computational difficulties: the treatment of material interface boundaries. Flexible local approximation methods (FLAME) employ any desired local approximating functions that are seamlessly built into the difference scheme. In particular, this new finite-difference calculus provides an accurate representation of material interfaces on geometrically nonconforming simple Cartesian grids. For instance, in the vicinity of cylindrical or spherical dielectric particles the field can be approximated by cylindrical or spherical harmonics. The new approach achieves the same level of accuracy as the finite element method with two orders of magnitude fewer unknowns.