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 versatile tool to interpret optical effects in nano-optics, but it only gives access the modes that are excited by specific illumination. In particular study various illuminations requires multiple, costly numerical simulations. Here we present formalism call “generalized polarizabilities”, which combine recently developed exact decomposition [Alaee et al., Opt. Comms. 407, 17–21 (2018)] with concept generalized field propagator. After an initial computation step, our approach allows instantaneously obtain for any Most importantly, since all possible included polarizabilities, calculate total density modes, regardless illumination, not conventional expansion. Finally, directly provides optimum illumination distributions maximally couple modes. will be very useful applications nano-optics like illumination-field engineering, or meta-atom design e.g. Huygens metasurfaces. We provide open source implementation compatible pyGDM python package.