Generalizing the exact multipole expansion: Density of multipole modes in complex photonic nanostructures

Abstract

The multipole expansion of a nano-photonic structure's electromagnetic response is a versatile tool to interpret optical effects in nano-optics, but it requires knowledge of the internal field distribution, for which in general expensive full-field simulations are necessary. We present a generalized polarizability model based on the Green's Dyadic Method (GDM), capable to describe resonant nanostructures, supporting both electric and magnetic dipole and quadrupole modes. Our formalism combines the recently developed exact multipole decomposition [Alaee et al., Opt. Comms. 407, 17-21 (2018)] with the concept of a generalized field propagator. It reproduces the exact multipole moments for any particle size and for arbitrary, inhomogeneous illumination fields such as focused vector beams or local light sources. After an initial computation step, our approach allows to instantaneously obtain the exact multipole decomposition for any possible illumination, and it allows to calculate spectra of the total density of multipole modes. Furthermore, the technique can be used to visualize spatial zones inside a nanostructure, where an external illumination couples strongly to a specific multipole moment. The formalism will be very useful for various applications in nano-optics like illumination-field engineering, or meta-atom design e.g. for Huygens metasurfaces. We provide a numerical open source implementation compatible with the pyGDM python package.