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Maxwell's equations are solved when the amplitude and phase of the electromagnetic field are determined at all points in space. Generally, the Stokes parameters can only capture the amplitude and polarization state of the electromagnetic field in the radiation (far) zone. Therefore, the measurement of the Stokes parameters is, in general, insufficient to solve Maxwell's equations. In this Letter, we solve Maxwell's equations for a set of objects widely used in Nanophotonics using the Stokes parameters alone. Our method for solving Maxwell's equations endows the Stokes parameters an even more fundamental role in the electromagnetic scattering theory.

The multipolar expansion of the electromagnetic field plays a key role in the study of light-matter interactions. All the information about the radiation and coupling between the incident wavefield and the object is embodied in the electric and magnetic scattering coefficients $\{a_{\ell m}, b_{\ell m} \}$ of the expansion. However, the experimental determination of $\{a_{\ell m}, b_{\ell m} \}$ requires measuring the components of the scattered field in all directions, something that is exceptionally challenging. Here, we demonstrate that a single measurement of the Stokes vector unlocks access to the quadrivector $ \mathbf{D}_{\ell m} = \left[|a_{\ell m}|^2, |b_{\ell m}|^2, \Re \{ a_{\ell m} b^*_{\ell m} \}, \Im \{ a_{\ell m} b^*_{\ell m} \} \right]$. Thus, our Stokes polarimetry method allows us to capture $|a_{\ell m}|^2$ and $|b_{\ell m}|^2$ separately, a distinction that can not be achieved by measuring the total energy of the scattered field via an integrating sphere. Importantly, we demonstrate the robustness of our Stokes polarimetry method, showing its fidelity with just two measurements of the Stokes vector at different scattering angles. Our findings, supported by analytical theory and exact numerical simulations, can find applications in Nanophotonics and greatly facilitate routine light-scattering measurements in optical laboratories.

Researchers routinely characterize optical samples by computing the scattering cross-section. However, the experimental determination of this magnitude requires the measurement and integration of the components of the scattered field in all directions. Here, we propose a method to determine the scattering cross-section and global polarization state of radiation through measurements of two Stokes parameters at an angle of choice in far-field. The method applies to cylindrically symmetric samples whose optical response is well-described by a single multipolar order j. Moreover, the formalism is applicable for a wide range of different illuminations, and it only requires the use of a single camera and conventional wave plates. Our findings significantly reduce the complexity of routine characterization measurements for cylindrical samples in optical laboratories.

The search for objects that yield maximum electromagnetic chirality in their emitted wavefield has garnered significant attention in recent years. However, achieving such maximum chirality is challenging, as it typically requires complex chiral metamaterials. Here we demonstrate that chiral spheres can yield maximum chirality in their emitted wavefield. Specifically, we analytically find the spectral trajectories at which chiral spheres become optically transparent to a given helicity of the incident field, while for its opposite helicity, they behave as dual objects, i.e., on scattering, they preserve helicity. Since chiral spheres behave as dual objects at the first Kerker condition of zero backscattering, we significantly simplify this condition in terms of a Riccati-Bessel function. Importantly, all our results are exact and applicable regardless of the multipolar order, refractive index contrast, optical size, and intrinsic chirality of the chiral sphere. Thus, our exact findings can serve as building blocks for designing novel metasurfaces or metamaterials with maximum electromagnetic chirality properties.

Dual scatterers preserve the helicity of an incident field, whereas antidual scatterers flip it completely. In this setting of linear electromagnetic scattering theory, we provide a completely general proof on the non-existence of passive antidual scatterers. However, we show that scatterers fulfilling the refractive index matching condition flip the helicity of the fields very efficiently without being in contradiction with the law of energy conservation. Moreover, we find that this condition is paired with the impedance matching condition in several contexts of electromagnetism and, in particular, within Fresnel's and Mie's scattering problems. Finally, we show that index-matched media induce a resonant helicity mixing on the propagating electromagnetic waves. We reach to this conclusion by identifying that the refractive index matching condition leads to the phenomenon of avoided level-crossing. Our contribution not only closes a historical discussion within the Nanophotonics community, but also opens up new possibilities in the fields of Metamaterials and Particle Physics.

Molecular Circular dichroism (CD) spectroscopy faces significant limitations due to the inherent weakness of chiroptical light-matter interactions. In this view, resonant optical antennas constitute a promising solution to this problem since they can be tuned to increase the CD enhancement factor, fCD, a magnitude describing the electromagnetic near-field enhancement of scatterers associated with a given helicity. Here, we derive an exact multipolar expansion of fCD, which is valid to deduce the integrated near-field CD enhancements of chiral molecules in the presence of scatterers of any size and shape under general illumination conditions. Based on our analytical findings, we show that the near-field fCD factor can be related to magnitudes that can be computed in the far-field, i.e., the scattering cross-section and the helicity expectation value. Moreover, we show that in the case of lossless cylindrically symmetric samples, the near-field fCD factor can be inferred experimentally only from two far-field measurements at specific scattering angles. Our contribution paves the way for the experimental characterization of devices capable of enhancing molecular CD spectroscopy.

Spin-orbit interactions of light are ubiquitous in multiple branches of nanophotonics, including optical wave localization. In that framework, it is widely accepted that circularly polarized beams lead to spin-dependent apparent shifts of dipolar targets commonly referred to as optical mirages. In contrast, these optical mirages vanish when the illumination comes from a spinless beam such as a linearly polarized wave. Here we show that optical localization errors emerge for particles sustaining electric and magnetic dipolar response under the illumination of spinless beams. As an example, we calculate the optical mirage for the scattering by a high refractive index nanosphere under the illumination of a linearly polarized plane wave carrying null spin, orbital, and total angular momentum. Our results point to an overlooked interference between the electric and magnetic dipoles rather than the spin-orbit interactions of light as the origin for the tilted position of the nanosphere.

The study of helicity in the context of light-matter interactions is an increasing area of research. However, some fundamental aspects of the helicity content of light fields inside scatterers have been overlooked. In this work, we demonstrate that the helicity of light fields inside lossless spherical cavities cannot be either conserved or sign-flipped as a result of a scattering event. The underlying reason is that the internal electric and magnetic Mie coefficients cannot simultaneously oscillate with equal amplitude and equal/opposite phase. Our analytical demonstration is fulfilled regardless of the refractive index, sphere size, and multipolar order. In addition, we show that the helicity of light fields inside lossy spheres can be conserved. This fact is in striking contrast to the behavior of the scattered field, whose helicity content cannot be conserved precisely when the sphere has losses. Finally, we show that the helicity content of internal fields can be flipped for materials with gain.

Bound states in the continuum (BICs) have been thoroughly investigated due to their formally divergent Q-factor, especially those emerging in all-dielectric, nanostructured metasurfaces from symmetry protection at the $\Gamma$ point (in-plane wavevector $k_{||}=0$). Less attention has been paid to accidental BICs that may appear at any other $k_{||}\not =0$ in the band structure of supported modes, being in turn difficult to predict. Here we make use of a coupled electric/magnetic dipole model to determine analytical conditions for the emergence of accidental BICs, valid for any planar array of meta-atoms that can be described by dipolar resonances, which is the case of many nanostructures in the optical domain. This is explored for all-dielectric nanospheres through explicit analytical conditions that allow us in turn to predict accidental BIC positions in the parameter space $(\omega,\bf{k_{||}}$). Finally, such conditions are exploited to determine not only single, but also double (for both linear polarizations) accidental BICs occurring at the same position in the dispersion relation $\omega-\bf{k_{||}}$ for realistic semiconductor nanodisk meta-atoms. This might pave the way to a variety of BIC-enhanced light-matter interaction phenomena at the nanoscale such as lasing or non-linear conversion, that benefit from emerging at wavevectors away from the $\Gamma$ point (off-normal incidence) overlapping for both linear polarizations., Comment: 18 pages, 7 figures

Helicity preserving nanostructures and metasurfaces have been recently proposed as suitable candidates to enhance spectroscopic features of chiral matter. With this in mind, we highlight that losses in the constituent nonmagnetic materials dramatically affect the possibility of constructing structures which conserve helicity. We first present a general procedure that permits the evaluation of the normalized helicity expectation value, $\langle\hat{\Lambda}\rangle$, i.e. the observable that permits the identification of helicity preserving scatterers. We then apply this procedure to the case of a chiral sphere, which in an orientation averaged picture can capture the optical response of chiral inorganic nanostructures, obtaining a widely applicable analytical expression of $\langle\hat{\Lambda}\rangle$ for this type of objects. Finally, we numerically show that optical losses impose an upper bound to the helicity expectation value on nonmagnetic core-shells and chiral spheres.

While colloidal chemistry provides ways to obtain a great variety of nanoparticles, with different shapes, sizes, material composition, and surface functions, their controlled deposition and combination on arbitrary positions of substrates remains a considerable challenge. Over the last ten years, optical printing arose as a versatile method to achieve this purpose for different kinds of nanoparticles. In this article we review the state of the art of optical printing of single nanoparticles, and discuss its strengths, limitations, and future perspectives, by focusing on four main challenges: printing accuracy, resolution, selectivity, and nanoparticles photostability., Comment: The following article has been submitted to The Journal of Chemical Physics. After it is published, it will be found at https://aip.scitation.org/journal/jcp

High refractive index dielectric spheres present remarkable light-scattering properties in the spectral range dominated by dipolar modes. However, most of these properties are absent for larger spheres under plane wave illumination. Here, we propose to unravel dipolar regimes regardless of the sphere size and refractive index by illuminating with a pure dipolar field. This type of illumination ensures that the scattering response of the sphere is purely dipolar. In this scenario, we show that Kerker conditions are not only related to duality symmetry and a strong backward-to-forward asymmetric light-scattering, but also to the appearance of non-radiating sources: the so-called hybrid anapoles. Finally, we show that all the abovementioned scattering features under dipolar illumination are reproducible with an experimentally accessible tightly-focused Gaussian beam.

Silicon nanoparticles possess unique size-dependent optical properties due to their strong electric and magnetic resonances in the visible range. However, their widespread application has been limited, in comparison to other (e.g. metallic) nanoparticles, because their preparation on monodisperse colloids remains challenging. Exploiting the unique properties of Si nanoparticles in nano- and micro-devices calls for methods able to sort and organize them from a colloidal suspension onto specific positions of solid substrates with nanometric precision. Here, we demonstrate that surfactant-free Silicon nanoparticles of a predefined and narrow ($\sigma$ < 10 nm) size range can be selectively immobilized on a substrate by optical printing from a polydisperse colloidal suspension. The size selectivity is based on differential optical forces that can be applied on nanoparticles of different sizes by tuning the light wavelength to the size-dependent magnetic dipolar resonance of the nanoparticles.

The optical properties of infinite planar array of scattering particles, metasurfaces and metagratings, are attracting special attention lately for their rich phenomenology, including both plasmonic and high-refractive-index dielectric meta-atoms with a variety of electric and magnetic resonant responses. Herein we derive a coupled electric and magnetic dipole (CEMD) analytical formulation to describe the reflection and transmission of such periodic arrays, including specular and diffractive orders, valid in the spectral regimes where only dipolar multipoles are needed. Electric and/or magnetic dipoles with all three orientations arising in turn from a single or various meta-atoms per unit cell are considered. The 2D lattice Green function is rewritten in terms of a 1D (chain) version that fully converges and can be easily calculated. Modes emerging as poles of such lattice Green function can be extracted. This formulation can be applied to investigate a wealth of plasmonic, all-dielectric, and hybrid metasurfaces/metagratings of interest throughout the electromagnetic spectrum., Comment: 8 pages, 4 figures

The directionality and polarization of light show peculiar properties when the scattering by a dielectric sphere can be described exclusively by electric and magnetic dipolar modes. Particularly, when these modes oscillate in-phase with equal amplitude, at the so-called first Kerker condition, the zero optical backscattering condition emerges for non-dissipating spheres. However, the role of absorption and optical gain in the first Kerker condition remains unexplored. In this work, we demonstrate that either absorption or optical gain precludes the first Kerker condition and, hence, the absence of backscattered radiation light, regardless of the size of the particle, incident wavelength, and incoming polarization. Finally, we derive the necessary prerequisites of the second Kerker condition of the zero forward light scattering, finding that optical gain is a compulsory requirement.

Controlling the electromagnetic helicity and directionality of the light scattered by dielectric particles is paramount to a variety of phenomenology of interest in all-dielectric optics and photonics. In this Letter, we show that the conservation of the electromagnetic helicity in the scattering by high-index dielectric Mie spheres can be used as a probe of pure-multipolar spectral regions, particularly, of dipolar nature, beyond its presumed spectral interval. This finding reveals that the dipolar behavior is not necessarily limited to small particles, in striking contrast to the current state of the art. Interestingly, we demonstrate that the optimum forward light scattering condition, predicted for a particular nano-sphere in the limit of small particle, is fulfilled in fact at a fixed x size parameter for an infinite number of refractive indexes

The nearly zero optical forward scattering and anti-dual conditions are usually associated to the so-called second Kerker condition, at which the electric and magnetic responses are phase-shifted by {\pi}. However, as we show, this condition is insufficient to both give rise to the nearly zero optical forward scattering and the anti-duality symmetry, in striking contrast to the actual view of the problem. Interestingly, we demonstrate that near the electric and magnetic dipolar resonances, the energy radiation pattern in the far-field limit resembles to the one arising from the first Kerker condition, with nearly-zero backscattering.

We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hemispherical illumination, we show that the only possible propagating multipole beams are `sectoral' multipoles. The sectoral dipole beam is shown to be equivalent to the non-singular time-reversed field of an electric and a magnetic point dipole Huygens' source located at the beam focus. Higher order multipolar beams are vortex beams vanishing on the propagation axis. The simple analytical expressions of the electric field of sectoral multipole beams, exact solutions of Maxwell's equations, and the peculiar behaviour of the Poynting vector and spin and orbital angular momenta in the focal volume could help to understand and model light-matter interactions under strongly focused beams., Comment: 16 pages, 5 figures

The conservation of the photon total angular momentum in the incident direction in an axially symmetric scattering process is a very well known fact. Nonetheless, the re-distribution of this conserved magnitude into its spin and orbital components, an effect known as the spin-orbit interaction (SOI) of light, is still a matter of active research. Here, we discuss the effect of the absorption on the SOI in the scattering of a sub-wavelength Silicon particle. Describing the scattering process of a electric and magnetic dipole, we show via the asymmetry parameter that the SOI of light in the scattering of high refractive index nanoparticles endures in the presence of optical losses. This effect results in optical mirages whose maximum values surpass those of an electric dipolar scatterer.

Light scattering and spin-orbit angular momentum coupling phenomena from subwavelength objects, with electric and magnetic dipolar responses, are receiving an increasing interest. Under illumination by circularly polarized light, spin-orbit coupling effects have been shown to lead to significant shifts between the measured and actual position of particles. Here we show that the remarkable angular dependence of these "optical mirages" and those of the intensity, degree of circular polarization (DoCP), and spin and orbital angular momentum of scattered photons, are all linked and fully determined by the dimensionless "asymmetry parameter" g, being independent of the specific optical properties of the scatterer. Interestingly, for g different from 0, the maxima of the optical mirage and angular momentum exchange take place at different scattering angles. In addition we show that the g parameter is exactly half of the DoCP at a right-angle scattering. This finding opens the possibility to infer the whole angular properties of the scattered fields by a single far-field polarization measurement., Comment: 5 pages, 3 figures

Spin-orbit interaction of light can lead to the so-called optical mirages, i.e. a perceived displacement in the position of a particle due to the spiraling structure of the scattered light. In electric dipoles, the maximum displacement is subwavelength and does not depend on the optical properties of the scatterer. Here we will show that the optical mirage in high refractive index dielectric nanoparticles depends strongly on the ratio between electric and magnetic dipolar responses. When the dual symmetry is satisfied (at the first Kerker condition), there is a considerable enhancement (far above the wavelength) of the spin-orbit optical mirage which can be related to the emergence of an optical vortex in the backscattering direction., Comment: 5 pages, 4 figures