%0 Journal Article %T Generalizing the exact multipole expansion: density of multipole modes in complex photonic nanostructures %+ Centre d'élaboration de matériaux et d'études structurales (CEMES) %+ Airbus Defence and Space [Toulouse] %+ Équipe Matériaux et Procédés pour la Nanoélectronique (LAAS-MPN) %+ Laboratoire de physique et chimie des nano-objets (LPCNO) %A Majorel, Clément %A Patoux, Adelin %A Estrada-Real, Ana %A Urbaszek, Bernhard %A Girard, Christian %A Arbouet, Arnaud %A Wiecha, Peter %Z HPC CALMIP de Toulouse (subvention p20010) %Z 13 pages, 6 figures. Includes a supporting information pdf and python examples %< avec comité de lecture %Z Rapport LAAS n° 22377 %@ 2192-8614 %J Nanophotonics %I De Gruyter %V 11 %N 16 %P 3663-3678 %8 2022-08-17 %D 2022 %Z 2204.13402 %R 10.1515/nanoph-2022-0308 %Z Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] %Z Physics [physics]/Physics [physics]/Optics [physics.optics] %Z Physics [physics]/Condensed Matter [cond-mat] %Z Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall]Journal articles %X 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. %G English %L hal-03800162 %U https://hal.laas.fr/hal-03800162 %~ UNIV-TLSE2 %~ UNIV-TLSE3 %~ CNRS %~ INSA-TOULOUSE %~ LAAS %~ UT1-CAPITOLE %~ LAAS-MPN %~ LAAS-MICRO-NANO-BIO-TECHNOLOGIES %~ INC-CNRS %~ CEMES %~ LPCNO %~ INSA-GROUPE %~ FERMI %~ TOULOUSE-INP %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP %~ TEST2-HALCNRS