The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The multipole moments of the source. These numbers are frequently computed with expressions obtained after the long-wavelength approximation. Here, we derive exact expressions for the multipole moments of dynamic sources that resemble in their simplicity their approximate counterparts. We validate our new expressions against analytical results for a spherical source, and then use them to calculate the induced moments for some selected sources with a nontrivial shape. The comparison of the results to those obtained with approximate expressions shows a considerable disagreement even for sources of subwavelength size. Our expressions are relevant for any scientific area dealing with the interaction between the electromagnetic field and material systems.PACS numbers: 78.67. Pt, 13.40.Em,78.67.Bf, 03.50.De The multipolar decomposition of a given chargecurrent distribution is taught in every undergraduate course in physics. The resulting set of numbers are called the multipolar moments. They are classified according to their order, i.e. dipoles, quadrupoles etc... For each order, there are electric and magnetic multipolar moments. Each multipolar moment is uniquely connected to a corresponding multipolar field. Their importance stems from the fact that the multipolar moments of a charge-current distribution completely characterize both the radiation of electromagnetic fields by the source, and the coupling of external fields onto it. The multipolar decomposition is important in any scientific area dealing with the interaction between the electromagnetic field and material systems. In particle physics, the multipole moments of the nuclei provide information on the distribution of charges inside the nucleus. In chemistry, the dipole and quadrupolar polarizabilities of a molecule determine most of its properties. In electrical engineering, the multipole expansion is used to quantify the radiation from antennas. And the list goes on.In this Letter, we present new exact expressions for the multipolar decomposition of an electric charge-current distribution. They provide a straightforward path for upgrading analytical and numerical models currently using the long-wavelength approximation. After the upgrade, the models become exact. The expressions that we provide are directly applicable to the many areas where the multipole decomposition of electrical current density distributions is used. For the sake of concreteness, in this article we apply them to a specific field: Nanophotonics.In nanophotonics, one purpose is to control and manipulate light on the nanoscale. Plasmonic or highindex dielectric nanoparticles are frequently used for this purpose 1,2 . The multipole expansion provides insight into several optical phenomena, such as Fano resonances 3,4 , electromagnetically-induced-transparen...

In this Letter, we show that the electromagnetic duality symmetry, broken in the microscopic Maxwell's equations by the presence of charges, can be restored for the macroscopic Maxwell's equations. The restoration of this symmetry is shown to be independent of the geometry of the problem. These results provide a tool for the study of light-matter interactions within the framework of symmetries and conservation laws. We illustrate its use by determining the helicity content of the natural modes of structures possessing spatial inversion symmetries and by elucidating the root causes for some surprising effects in the scattering off magnetic spheres.

We introduce a definition of the electromagnetic chirality of an object and show that it has an upper bound. Reciprocal objects attain the upper bound if and only if they are transparent for all the fields of one polarization handedness (helicity). Additionally, electromagnetic duality symmetry, i.e. helicity preservation upon interaction, turns out to be a necessary condition for reciprocal objects to attain the upper bound. We use these results to provide requirements for the design of such extremal objects. The requirements can be formulated as constraints on the polarizability tensors for dipolar objects or on the material constitutive relations for continuous media. We also outline two applications for objects of maximum electromagnetic chirality: A twofold resonantly enhanced and background free circular dichroism measurement setup, and angle independent helicity filtering glasses. Finally, we use the theoretically obtained requirements to guide the design of a specific structure, which we then analyze numerically and discuss its performance with respect to maximal electromagnetic chirality.

We propose a new theoretical and practical framework for the study of light-matter interactions and the angular momentum of light. Our proposal is based on helicity, total angular momentum, and the use of symmetries. We compare the new framework to the current treatment, which is based on separately considering spin angular momentum and orbital angular momentum and using the transfer between the two in physical explanations. In our proposal, the fundamental problem of spin and orbital angular momentum separability is avoided, predictions are made based on the symmetries of the systems, and the practical application of the concepts is straightforward. Finally, the framework is used to show that the concept of spin to orbit transfer applied to focusing and scattering is masking two completely different physical phenomena related to the breaking of different fundamental symmetries: transverse translational symmetry in focusing and electromagnetic duality symmetry in scattering.

We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored.

The multipolar decomposition of electromagnetic sources is an important tool for the study of light–matter interactions in general, and optical materials in particular. Here, a report is given on recent progress in the multipolar decomposition of electromagnetic sources. First, the exact and simple expressions for the multipolar moments of electric current density distributions are reviewed, and then, the results are extended to multipolar moments of magnetization current density distributions due to intrinsic spin. The consideration of both electric and magnetic sources allows to establish the conditions for sources of pure handedness. Scripts are provided that facilitate the computation of multipolar moments of arbitrary order. The work and the included examples of use are placed in the context of nanophotonics and metamaterials, and an outlook for applications in these and other fields is provided.

We design a planar array of connected silicon disks for improved molecular circular dichroism measurements in the near infrared. Full wave simulations demonstrate a volume averaged five-fold enhancement of the circular dichroism signal under normal illumination at the operating frequency. The enhancement is achieved by optimizing the disks according to three design requirements: Helicity preservation to obtain nearfields of pure handedness, spatial inversion symmetries to avoid introducing biases, and a resonant response to obtain large near-field amplitudes. The understanding and formalization of the requirements, and the analysis and optimization of the structures is facilitated by the Riemann-Silberstein representation of electromagnetic fields.Chiral objects are omnipresent in and all around us. Ranging from the double-helical structure of our DNA, extending over our hands -that originally lent the property its name -up to the spiral galaxies in the sky. Chiral objects, which are not super-imposable onto their mirror images by any translation or rotation, play a fundamental role in modern science as well as life itself. The reason for which living nature tends to have a bias for molecules and macroscopic structures of a certain handedness, is still one of its greatest secrets. 1 Apart from the fundamental questions arising due to the violation of mirror symmetry in the laws of our universe, we often deal with more pragmatic problems. Enantiomers, being pairs of mirror-image chiral molecules, often react differently in biological organisms due to the chiral specifications of the cells' receptors. As a result, drugs consisting of chiral molecules can have profoundly different therapeutic and/or toxicological properties. 2 Sharing the same atomic composition, pairs of enantiomers are indistinguishable when measuring their scalar physical properties. It is only in the interaction with other chiral objects, that they unveil their chiral nature. In optics, the most common chiral object that is dealt with is circularly polarized light (CPL). Upon interaction with light, a chiral molecule exhibits a preferential absorption for either left or right circular polarization, measured by means of circular dichroism (CD) spectroscopy. In a traditional CD setup, the molecular solution is sequentially illuminated by propagating beams of different polarization handedness, and the total outgoing power is recorded in each case. The CD signal is the difference between the two power measurements. Chiral light-matter interactions, however, are typically of small magnitude compared to the achiral interactions. For samples of low molecular concentration, the impossibility of indefinitely increasing the illumination power leads to long measurement times, often of several hours cite**, that are needed in order to elevate the CD signal over the noise. Moreover, some envisioned applications e.g. in the context of lab-on-a-chip, require the testing of minute quantities of analytes in small volumes that are not easily accessed by a focused...

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.