Optimization of resonant effects in nanostructures via Weierstrass factorization

Extensive numerical computations are often required to optimize the optical properties of nanostructures. Here, we use the Weierstrass factorization theorem to express the scattering matrix in terms of spectral singularities. We show that the location of poles and zeros of the scattering matrix fully determines all scattering properties, and that the scattering spectra of nanostructures can be decomposed into Lorentzian resonances over an arbitrary range of frequencies. This technique is applied to design nanoshell particles with enhanced absorption.