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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., Comment: 13 pages, 6 figures. Includes a supporting information pdf and python examples

Using Localized Surface Plasmon Resonance (LSPR) as an optical probe we demonstrate the presence of free carriers in phosphorus doped silicon nanocrystals (SiNCs) embedded in a silica matrix. In small SiNCs, with radius ranging from 2.6 to 5.5 nm, the infrared spectroscopy study coupled to numerical simulations allows us to determine the number of electrically active phosphorus atoms with a precision of a few atoms. We demonstrate that LSP resonances can be supported with only about 10 free electrons per nanocrystal, confirming theoretical predictions and probing the limit of the collective nature of plasmons. We reveal a phenomenon, unique to embedded nanocrystals, with the appearance of an avoided crossing behavior linked to the hybridization between the localized surface plasmon in the doped nanocrystals and the silica matrix phonon modes. Finally, a careful analysis of the scattering time dependence versus carrier density in the small size regime allows us to detect the appearance of a new scattering process at high dopant concentration.

Optical interactions have an important impact on the optical response of nanostructures in complex environments. Accounting for interactions in large ensembles of structures requires computationally demanding numerical calculations. In particular if no periodicity can be exploited, full field simulations can become prohibitively expensive. Here we propose a method for the numerical description of aperiodic assemblies of plasmonic nanostructures. Our approach is based on dressed polarizabilities, which are conventionally very expensive to calculate, a problem which we alleviate using a deep convolutional neural network as surrogate model. We demonstrate that the method offers high accuracy with errors in the order of a percent. In cases where the interactions are predominantly short-range, e.g. for out-of-plane illumination of planar metasurfaces, it can be used to describe aperiodic metasurfaces of basically unlimited size, containing many thousands of unordered plasmonic nanostructures. We furthermore show that the model is capable to spectrally resolve coupling effects. The approach is therefore of highest interest for the field of metasurfaces. It provides significant advantages in applications like homogenization of large aperiodic planar metastructures or the design of sophisticated wavefronts at the micrometer scale, where optical interactions play a crucial role., Comment: 13 pages, 8 figures + supporting informations pdf

pyGDM is a python toolkit for electro-dynamical simulations of individual nano-structures, based on the Green Dyadic Method (GDM). pyGDM uses the concept of a generalized propagator, which allows to solve cost-efficiently monochromatic problems with a large number of varying illumination conditions such as incident angle scans or focused beam raster-scan simulations. We provide an overview of new features added since the initial publication [Wiecha, Computer Physics Communications 233, pp.167-192 (2018)]. The updated version of pyGDM is implemented in pure python, removing the former dependency on fortran-based binaries. In the course of this re-write, the toolkit's internal architecture has been completely redesigned to offer a much wider range of possibilities to the user such as the choice of the dyadic Green's functions describing the environment. A new class of dyads allows to perform 2D simulations of infinitely long nanostructures. While the Green's dyads in pyGDM are based on a quasistatic description for interfaces, we also provide as new external python package pyGDM2_retard a module with retarded Green's tensors for an environment with two interfaces. We have furthermore added functionalities for simulations using fast-electron excitation, namely electron energy loss spectroscopy and cathodoluminescence. Along with several further new tools and improvements, the update includes also the possibility to calculate the magnetic field and the magnetic LDOS inside nanostructures, field-gradients in- and outside a nanoparticle, optical forces or the chirality of nearfields. All new functionalities remain compatible with the evolutionary optimization module of pyGDM for nano-photonics inverse design., Comment: 29 pages, 20 figures

Deep learning in the context of nano-photonics is mostly discussed in terms of its potential for inverse design of photonic devices or nanostructures. Many of the recent works on machine-learning inverse design are highly specific, and the drawbacks of the respective approaches are often not immediately clear. In this review we want therefore to provide a critical review on the capabilities of deep learning for inverse design and the progress which has been made so far. We classify the different deep learning-based inverse design approaches at a higher level as well as by the context of their respective applications and critically discuss their strengths and weaknesses. While a significant part of the community's attention lies on nano-photonic inverse design, deep learning has evolved as a tool for a large variety of applications. The second part of the review will focus therefore on machine learning research in nano-photonics "beyond inverse design". This spans from physics informed neural networks for tremendous acceleration of photonics simulations, over sparse data reconstruction, imaging and "knowledge discovery" to experimental applications., Comment: Review article of 18 pages, 7 figures, 4 info-boxes

We present the experimental realization of ordered arrays of hyper-doped silicon nanodisks, which exhibit a localized surface plasmon resonance. The plasmon is widely tunable in a spectral window between 2 and 5 $\mu$m by adjusting the free carrier concentration between 10$^{20}$ and 10$^{21}$ cm$^{-3}$. We show that strong infrared light absorption can be achieved with all-silicon plasmonic metasurfaces employing nano-structures with dimensions as low as 100\,nm in diameter and 23 nm in height. Our numerical simulations show an excellent agreement with the experimental data and provide physical insights on the impact of the nanostructure shape as well as of near-field effects on the optical properties of the metasurface. Our results open highly promising perspectives for integrated all-silicon-based plasmonic devices for instance for chemical or biological sensing or for thermal imaging., Comment: 6 pages, 4 figures

Scanning near-field optical imaging (SNOM) using local active probes provides in general images of the electric part of the photonic local density of states. However, certain atomic clusters can supply more information by simultaneously revealing both the magnetic (m-LDOS) and the electric (e-LDOS) local density of states in the optical range. For example, nanoparticles doped with rare-earth elements like europium or terbium provide both electric dipolar (ED) and magnetic dipolar (MD) transitions. In this theoretical article, we develop a quantum description of active systems (rare earth ions) coupled to a photonic nanostructure, by solving the optical Bloch equations together with Maxwell's equations. This allows us to access the population of the emitting energy levels for all atoms excited by the incident light, degenerated at the extremity of the tip of a near-field optical microscope. We show that it is possible to describe the collected light intensity due to ED and MD transitions in a scanning configuration. By carrying out simulations on different experimentally interesting systems, we demonstrate that our formalism can be of great value for the interpretation of experimental configurations including various external parameters (laser intensity, polarization and wavelength, the SNOM probe size, the nature of the sample ...)., Comment: 10 pages, 8 figures

When the sizes of photonic nanoparticles are much smaller than the excitation wavelength, their optical response can be efficiently described with a series of polarizability tensors. Here, we propose a universal method to extract the different components of the response tensors associated with small plasmonic or dielectric particles. We demonstrate that the optical response can be faithfully approximated, as long as the effective dipole is not induced by retardation effects, hence do not depend on the phase of the illumination. We show that the conventional approximation breaks down for a phase-driven dipolar response, such as optical magnetic resonances in dielectric nanostructures. To describe such retardation induced dipole resonances in intermediate-size dielectric nanostructures, we introduce "pseudo-polarizabilities" including first-order phase effects, which we demonstrate at the example of magnetic dipole resonances in dielectric spheres and ellipsoids. Our method paves the way for fast simulations of large and inhomogeneous meta-surfaces., Comment: 13 pages, 11 figures

We demonstrate inverse design of plasmonic nanoantennas for directional light scattering. Our method is based on a combination of full-field electrodynamical simulations via the Green dyadic method and evolutionary optimization (EO). Without any initial bias, we find that the geometries reproducibly found by EO, work on the same principles as radio-frequency antennas. We demonstrate the versatility of our approach by designing various directional optical antennas for different scattering problems. EO based nanoantenna design has tremendous potential for a multitude of applications like nano-scale information routing and processing or single-molecule spectroscopy. Furthermore, EO can help to derive general design rules and to identify inherent physical limitations for photonic nanoparticles and metasurfaces., Comment: 13 pages, 9 figures

We propose a simple experimental technique to separately map the emission from electric and magnetic dipole transitions close to single dielectric nanostructures, using a few nanometer thin film of rare-earth ion doped clusters. Rare-earth ions provide electric and magnetic dipole transitions of similar magnitude. By recording the photoluminescence from the deposited layer excited by a focused laser beam, we are able to simultaneously map the electric and magnetic emission enhancement on individual nanostructures. In spite of being a diffraction-limited far-field method with a spatial resolution of a few hundred nanometers, our approach appeals by its simplicity and high signal-to-noise ratio. We demonstrate our technique at the example of single silicon nanorods and dimers, in which we find a significant separation of electric and magnetic near-field contributions. Our method paves the way towards the efficient and rapid characterization of the electric and magnetic optical response of complex photonic nanostructures., Comment: 10 pages and 7 figures

On-chip optoelectronic and all-optical information processing paradigms require compact implementation of signal transfer for which nanoscale surface plasmons circuitry offers relevant solutions. This work demonstrates the directional signal transmittance mediated by 2D plasmonic eigenmodes supported by crystalline cavities. Channel devices comprising two mesoscopic triangular input and output ports and sustaining delocalized, higher-order plasmon resonances in the visible to infra-red range are shown to enable the controllable transmittance between two confined entry and exit ports coupled over a distance exceeding 2 $\mu$m. The transmittance is attenuated by > 20dB upon rotating the incident linear polarization, thus offering a convenient switching mechanism. The optimal transmittance for a given operating wavelength depends on the geometrical design of the device that sets the spatial and spectral characteristic of the supporting delocalized mode. Our approach is highly versatile and opens the way to more complex information processing using pure plasmonic or hybrid nanophotonic architectures.

In this article, we propose a concise theoretical framework based on mixed field-susceptibilities to describe the decay of magnetic dipoles induced by non--magnetic nanostructures. This approach is first illustrated in simple cases in which analytical expressions of the decay rate can be obtained. We then show that a more refined numerical implementation of this formalism involving a volume discretization and the computation of a generalized propagator can predict the dynamics of magnetic dipoles in the vicinity of nanostructures of arbitrary geometries. We finally demonstrate the versatility of this numerical method by coupling it to an evolutionary optimization algorithm. In this way we predict a structure geometry which maximally promotes the decay of magnetic transitions with respect to electric emitters., Comment: 8 pages, 5 figures. Separate supporting informations of 12 pages and 13 figures

It has been experimentally demonstrated only recently that a simultaneous excitation of interfering electric and magnetic resonances can lead to uni-directional scattering of visible light in zero-dimensional dielectric nanoparticles. We show both theoretically and experimentally, that strongly anisotropic scattering also occurs in individual dielectric nanowires. The effect occurs even under either pure transverse electric or pure transverse magnetic polarized normal illumination. This allows for instance to toggle the scattering direction by a simple rotation of the incident polarization. Finally, we demonstrate that directional scattering is not limited to cylindrical cross-sections, but can be further tailored by varying the shape of the nanowires., Comment: 12 pages, 6 figures + supporting informations of 12 pages, 19 figures

The rational design of photonic nanostructures consists in anticipating their optical response from simple models or as variations of reference systems. This strategy is limited when different objectives are simultaneously targeted. Inspired from biology, evolutionary approaches drive the morphology of a nano-object towards an optimum through several cycles of selection, mutation and cross-over, mimicking the process of natural selection. However, their extension to scenarii with multiple objectives demands efficient computational schemes. We present a numerical technique to design photonic nanostructures with optical properties optimized along several arbitrary objectives. This combination of evolutionary multi-objective algorithms with frequency-domain electro-dynamical simulations is used to design silicon nanostructures resonant at user-defined, polarization-dependent wavelengths. The spectra of pixels fabricated by electron beam lithography following the optimized design show excellent agreement with the targeted objectives. The method is self-adaptive to arbitrary constraints, and therefore particularly interesting for the design of complex structures within technological limits., Comment: 10 pages, 6 figures + 10 pages of supporting informations including 17 additional figures

We investigate Second Harmonic Generation from individual silicon nanowires and study the influence of resonant optical modes on the far-field nonlinear emission. We find that the polarization of the Second Harmonic has a size-dependent behavior and explain this phenomenon by a combination of different surface and bulk nonlinear susceptibility contributions. We show that the Second Harmonic Generation has an entirely different origin, depending on whether the incident illumination is polarized parallel or perpendicularly to the nanowire axis. The results open perspectives for further geometry-based studies on the origin of Second Harmonic Generation in nanostructures of high-index centrosymmetric semiconductors., Comment: 7 Pages, 4 Figures + 3 Pages, 6 Figures in Appendix

Antibodies are affinity proteins with a wide spectrum of applications in analytical and therapeutic biology. Proteins showing specific recognition for a chosen molecular target can be isolated and their encoding sequence identified in vitro from a large and diverse library by phage display selection. In this work, we show that this standard biochemical technique rapidly yields a collection of antibody protein binders for an inorganic target of major technological importance: crystalline metallic gold surfaces. 21 distinct anti-gold antibody proteins emerged from a large random library of antibodies and were sequenced. The systematic statistical analysis of all the protein sequences reveals a strong occurrence of arginine in anti-gold antibodies, which corroborates recent molecular dynamics predictions on the crucial role of arginine in protein/gold interactions. Once tethered to small gold nanoparticles using histidine tag chemistry, the selected antibodies could drive the self-assembly of the colloids onto the surface of single crystalline gold platelets as a first step towards programmable protein-driven construction of complex plasmonic architectures. Electrodynamic simulations based on the Green Dyadic Method suggest that the antibody-driven assembly demonstrated here could be exploited to significantly modify the plasmonic modal properties of the gold platelets. Our work shows that molecular biology tools can be used to design the interaction between fully folded proteins and inorganic surfaces with potential applications in the bottom-up construction of plasmonic hybrid nanomaterials., Comment: 34 pages, 6 figures, 1 table

Self-assembled Plasmonic Nanoparticle Networks (PNN) composed of chains of 12-nm diameter crystalline gold nanoparticles exhibit a longitudinally coupled plasmon mode cen- tered at 700 nm. We have exploited this longitudinal absorption band to efficiently confine light fields and concentrate heat sources in the close vicinity of these plasmonic chain net- works. The mapping of the two phenomena on the same superstructures was performed by combining two-photon luminescence (TPL) and fluorescence polarization anisotropy (FPA) imaging techniques. Besides the light and heat concentration, we show experimentally that the planar spatial distribution of optical field intensity can be simply modulated by controlling the linear polarization of the incident optical excitation. On the contrary, the heat production, which is obtained here by exciting the structures within the optically transparent window of biological tissues, is evenly spread over the entire PNN. This contrasts with the usual case of localized heating in continuous nanowires, thus opening opportunities for these networks in light-induced hyperthermia applications. Furthermore, we propose a unified theoretical framework to account for both the non-linear optical and thermal near-fields around PNN. The associated numerical simulations, based on a Green s function formalism, are in excellent agreement with the experimental images. This formalism therefore provides a versatile tool for the accurate engineering of optical and thermodynamical properties of complex plasmonic colloidal architectures.