Mie-resonant high-index dielectric nanoparticles and metasurfaces have been suggested as a viable platform for enhancing both electric and magnetic dipole transitions of fluorescent emitters. While the enhancement of the electric dipole transitions by such dielectric nanoparticles has been demonstrated experimentally, the case of magneticdipole transitions remains largely unexplored. Here, we study the enhancement of spontaneous emission of Eu 3+ ions, featuring both electric and magnetic-dominated dipole transitions, by dielectric metasurfaces composed of Mie-resonant silicon nanocylinders.By coating the metasurfaces with a layer of an Eu 3+ doped polymer, we observe an enhancement of the Eu 3+ emission associated with the electric (at 610 nm) and magneticdominated (at 590 nm) dipole transitions. The enhancement factor depends systematically on the spectral proximity of the atomic transitions to the Mie resonances as well as their multipolar order, which is controlled by the nanocylinder radius. Importantly, the branching ratio of emission via the electric or magnetic transition channel can be modified by carefully designing the metasurface, where the magnetic dipole transition is enhanced more than the electric transition for cylinders with radii of about 130 nm.We confirm our observations by numerical simulations based on the reciprocity principle. Our results open new opportunities for bright nanoscale light sources based on magnetic transitions.

lithography, provide great flexibility but are slow and expensive, and are therefore not feasible. Conventional scalable techniques, for instance random etching processes such as chemical wet etching [3,4] or plasma dry etching, [5,6] operate in a small window of parameters, thus offering only limited freedom of design and the statistics of fabricated disordered interfaces is more or less fixed. Bottom up, self-organized colloid deposition is a promising candidate for scalable interface texturing. [7][8][9] There are a number of both theoretical and experimental studies on how structures fabricated by colloid deposition can be used for light management in photo nic devices such as solar cells. [10][11][12][13][14][15] Colloid-defined samples are mostly used to produce strictly periodic structures, such as hexagonal photonic crystals and nanoparticle arrays. [7][8][9] However, partly ordered and disordered structures have been shown to possibly perform significantly better than perfectly ordered structures in recent studies. [15][16][17][18][19][20] Nevertheless, a colloid-based deposition technique to prepare disordered structures with the ability to tailor its topographical statistics, and thus a tailored optical response, is still missing.In this work, we investigate the scalable deposition of disordered arrangements of colloidal nanoparticles that selforganize on a substrate to create disordered topographies of defined statistics. The fabricated substrates may serve as templates in a subsequent fabrication process, e.g., etching, nanosphere lithography, or overcoating with optical materials such as absorber layers for solar cells or light generation layers for solid-state lighting. Irregular deposition of colloids is often governed by unwanted effects, such as ordering into regular periodic patterns, autostratification, or separation of particle sizes due to surface tension or depletion forces. [9,[21][22][23][24] Here, we introduce a self-stabilized particle deposition process to overcome these effects. The process allows us to control lateral and vertical structure dimensions by setting size distribution and interparticle spacing of a sub-monolayer of particles through experimentally easy-to-access parameters. By understanding the deposition process and the resulting statistics, we can predict the topography and thereby enable optimization of these structures for a specific application without the need for laborious trial-and-error experiments.The pattern structure of the substrates fabricated by our procedure is of correlated disorder and reveals features that resemble hyperuniformity. [25,26] Like glasses, disorderd Disordered optical substrates play a key role in photonic applications. Furthermore, structures of correlated, in particular hyperuniform, disorder are an emerging new class of photonic material enabling new ways of k-space engineering. Yet, there are little to no feasible technologies that allow fabrication of tailored disordered structures to facilitate a tailored optical response. This work ...

Abstract:The multipolar decomposition of current distributions is used in many branches of physics. Here, we obtain new exact expressions for the dipolar moments of a localized electric current distribution. The typical integrals for the dipole moments of electromagnetically small sources are recovered as the lowest order terms of the new expressions in a series expansion with respect to the size of the source. All the higher order terms can be easily obtained. We also provide exact and approximated expressions for dipoles that radiate a definite polarization handedness (helicity). Formally, the new exact expressions are only marginally more complex than their lowest order approximations.

We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts causes the appearance of non-radiative components in each of the two parts. These non-radiative components, which cancel each other when both parts are summed, preclude the separate determination of each part by means of measurements of the radiation from the source or of its coupling to external electromagnetic waves. In other words, there is no toroidal radiation or independent toroidal electromagnetic coupling. The formal meaning of the toroidal multipoles is clear in our derivations. They are the higher order terms of an expansion of the multipolar coefficients of electric parity with respect to the electromagnetic size of the source.

Two-dimensional transition-metal dichalcogenides such as WSe 2 show great promise as versatile atomic-scale light sources for on-chip applications due to their advanced optoelectronic properties and compatibility with a silicon photonics platform. However, the sub-nanometer thickness of such active materials limits their emission efficiency. Hence, new approaches to simultaneously enhance the emission and control its directionality are required. Here, we demonstrate enhanced and directional emission from a WSe 2 monolayer integrated onto a silicon photonic structure. This is achieved by coupling of the WSe 2 layer to a multiresonant silicon grating-waveguide structure. The interaction with the multiple resonant modes supported by the structure provides simultaneous excitation and emission enhancement, while the dispersion of the modes further routes the emission into specified directions. In addition, our hybrid structure offers the opportunity for ultrafast emission modulation, owing to the reduced emission lifetime of WSe 2 . Such a silicon-based hybrid platform is fully scalable and promising as efficient chip-integrated and spatially multiplexed light sources.