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

TL;DR

This paper introduces a formalism called generalized polarizabilities that enables instant, exact multipole decomposition for any illumination in nano-photonics, allowing calculation of the total density of multipole modes regardless of specific excitation.

Contribution

The authors develop a novel formalism combining exact multipole decomposition with generalized field propagators, enabling illumination-independent analysis of multipole mode densities in complex nanostructures.

Findings

Allows instant computation of multipole decomposition for any illumination after initial setup.

Enables calculation of total multipole mode density independent of specific excitation.

Provides a tool for optimized illumination field design to target specific modes.

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 only gives access to the modes that are excited by a specific illumination. In particular the study of various illuminations requires multiple, costly numerical simulations. Here we present a formalism we call "generalized polarizabilities", in which we combine the recently developed exact multipole decomposition [Alaee et al., Opt. Comms. 407, 17-21 (2018)] with the concept of a generalized field propagator. After an initial computation step, our approach allows to instantaneously obtain the exact multipole decomposition for any illumination. Most importantly, since all possible illuminations are included in the generalized polarizabilities, our formalism allows to calculate the total density of multipole modes, regardless of a specific illumination, which is not possible with the conventional multipole expansion. Finally, our approach directly provides the optimum illumination field distributions that maximally couple to specific multipole modes. 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.