Isotropically polarized speckle patterns

Dielectric metamaterials with effective self-duality and full-polarization omnidirectional brewster effect

Conventional dielectric solid materials, both natural and artificial, lack electromagnetic self-duality and thus require additional coatings to achieve impedance matching with free space. Here, we present a class of dielectric metamaterials that are effectively self-dual and vacuum-like, thereby exhibiting full-polarization omnidirectional impedance matching as an unusual Brewster effect extended across all incident angles and polarizations. With both birefringence and reflection eliminated regardless of wavefront and polarization, such anisotropic metamaterials could establish the electromagnetic equivalence with "stretched free space" in transformation optics, as substantiated through full-wave simulations and microwave experiments. Our findings open a practical pathway for realizing unprecedented polarization-independence and omnidirectional impedance-matching characteristics in pure dielectric solids.

Statistical insights of polarization speckle via von Mises-Fisher distribution on the Poincaré sphere

Polarization speckles generated via random scattering of light are ubiquitous in natural and engineered systems. They not only manifest intensity fluctuations but also reveal a spatially fluctuating, random polarization distribution. The precise morphology of the polarization speckle pattern serves as a deterministic signature of the light's state of polarization fluctuation within a scattering medium. Given the inherent randomness of polarization speckle patterns, a statistical approach emerges as the most pragmatic method for their analysis. Stokes parameters, implemented as temporal or spatial averages, are utilized for this purpose. However, within a polarization speckle field featuring a specific spatial average of Stokes parameters, the polarization state exhibits spatial variations across the speckle pattern. These random polarization fluctuations can be effectively modeled using a particular probability density function (PDF), visually represented on the Poincaré sphere. In this work, von Mises-Fisher (vMF) distribution on the Poincaré sphere is extended and applied to demonstrate a statistical insight of polarization speckle fields. A complete theoretical basis is established to investigate the spatial fluctuation of the state of polarization in the polarization speckle using vMF distribution on the Poincaré sphere, including the spatial mean direction, and spatial concentration parameter. Behavior of the marginal vMF distribution on the axes of the Poincaré sphere and its association with the probability density function of the normalized at-the-point Stokes parameters for three different polarization speckles are examined by experiment and simulation. The experimental results are in good agreement with the simulation results and confirm the usefulness of the established theoretical framework for the analysis of the polarization speckles. Characterization of spatial polarization fluctuation offers significant applications, such as in polarimetric analysis and optical sensing, and the same analogy can be used in quantum optics.

Multidimensional joint statistics of the Stokes parameters in a polarization speckle

A model of multivariate Gaussian statistics has been applied to study the higher-order statistics of the polarization speckle at two spatial or temporal points. Based on the Gaussian assumption for the random electric field, the joint probability density functions of the Stokes parameters and the parameters characterizing the polarization ellipse for the produced random polarization fields at two points are obtained. Subsequently, the corresponding statistics of an isotropic polarization speckle at two points have been investigated to obtain the joint and conditional probability densities of these random variables.

Statistics of polarization speckle produced by a constant polarization phasor plus a random polarization phasor sum

The statistical properties of the polarization speckle produced by a random polarization phasor sum plus a constant polarization phasor are studied. Based on the Gaussian assumption for the random electric field, the three-dimensional joint probability density functions of the Stokes parameters and the parameters characterizing the polarization ellipse for the produced random polarization fields are obtained. Subsequently, the statistics of an isotropic polarization speckle with a coherent polarization background have been investigated. The joint and marginal probability densities of these random variables are given to study the effect of the constant polarization background on the statistics of random polarization fields.

Colloidal Solutions of Silicon Nanospheres toward All-Dielectric Optical Metafluids

A colloidal solution of nanophotonic structures exhibiting optical magnetism is dubbed a liquid-phase metamaterial or an optical metafluid. Over the decades, plasmonic nanoclusters have been explored as constituents of a metafluid. However, optical magnetism of plasmonic nanoclusters is usually much weaker than the electric responses; the highest reported intensity ratio of the magnetic-to-electric responses so far is 0.28. Here, we propose an all-dielectric metafluid composed of crystalline silicon nanospheres. First, we address the advantages of silicon as a constituent material of a metafluid among major dielectrics. Next, we experimentally demonstrate for the first time that a silicon nanosphere metafluid exhibits strong electric and magnetic dipolar Mie responses across the visible to near-infrared spectral range. The intensity ratio of the magnetic-to-electric responses reaches unity. Finally, we discuss the perspective to achieve unnaturally high (>3), low, and even near-zero (<1) refractive index in the metafluid.

Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter

The inherently weak nature of chiral light–matter interactions can be enhanced by orders of magnitude utilizing artificially-engineered nanophotonic structures. These structures enable high spatial concentration of electromagnetic fields with controlled helicity and chirality. However, the effective design and optimization of nanostructures requires defining physical observables which quantify the degree of electromagnetic helicity and chirality. In this perspective, we discuss optical helicity, optical chirality, and their related conservation laws, describing situations in which each provides the most meaningful physical information in free space and in the context of chiral light–matter interactions. First, an instructive comparison is drawn to the concepts of momentum, force, and energy in classical mechanics. In free space, optical helicity closely parallels momentum, whereas optical chirality parallels force. In the presence of macroscopic matter, the optical helicity finds its optimal physical application in the case of lossless, dual-symmetric media, while, in contrast, the optical chirality provides physically observable information in the presence of lossy, dispersive media. Finally, based on numerical simulations of a gold and silicon nanosphere, we discuss how metallic and dielectric nanostructures can generate chiral electromagnetic fields upon interaction with chiral light, offering guidelines for the rational design of nanostructure-enhanced electromagnetic chirality.

Tailoring the chirality of light emission with spherical Si-based antennas

Chirality of light is of fundamental importance in several enabling technologies with growing applications in life sciences, chemistry and photodetection. Recently, some attention has been focused on chiral quantum emitters. Consequently, optical antennas which are able to tailor the chirality of light emission are needed. Spherical nanoresonators such as colloids are of particular interest to design optical antennas since they can be synthesized at a large scale and they exhibit good optical properties. Here, we show that these colloids can be used to tailor the chirality of a chiral emitter. To this purpose, we derive an analytic formalism to model the interaction between a chiral emitter and a spherical resonator. We then compare the performances of metallic and dielectric spherical antennas to tailor the chirality of light emission. It is seen that, due to their strong electric dipolar response, metallic spherical nanoparticles spoil the chirality of light emission by yielding achiral fields. In contrast, thanks to the combined excitation of electric and magnetic modes, dielectric Si-based particles feature the ability to inhibit or to boost the chirality of light emission. Finally, it is shown that dual modes in dielectric antennas preserve the chirality of light emission.

Far-field measurements of vortex beams interacting with nanoholes

We measure the far-field intensity of vortex beams going through nanoholes. The process is analyzed in terms of helicity and total angular momentum. It is seen that the total angular momentum is preserved in the process, and helicity is not. We compute the ratio between the two transmitted helicity components, γ_m,p. We observe that this ratio is highly dependent on the helicity (p) and the angular momentum (m) of the incident vortex beam in consideration. Due to the mirror symmetry of the nanoholes, we are able to relate the transmission properties of vortex beams with a certain helicity and angular momentum, with the ones with opposite helicity and angular momentum. Interestingly, vortex beams enhance the γ_m,p ratio as compared to those obtained by Gaussian beams.

Exact dipolar moments of a localized electric current distribution

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.

Antenna resonances in low aspect ratio semiconductor nanowires

We present numerical simulations of low aspect ratio gallium phosphide nanowires under plane wave illumination, which reveal the interplay between transverse and longitudinal antenna-like resonances. A comparison to the limiting case of the semiconducting sphere shows a gradual, continuous transition of resonant electric and magnetic spherical Mie modes into Fabry-Pérot cavity modes with mixed electric and magnetic characteristics. As the length of the nanowires further increases, these finite-wire modes converge towards the leaky-mode resonances of an infinite cylindrical wire. Furthermore, we report a large and selective enhancement or suppression of electric and magnetic field in structures comprising two semiconducting nanowires. For an interparticle separation of 20 nm, we observe up to 300-fold enhancement in the electric field intensity and an almost complete quenching of the magnetic field in specific mode configurations. Angle-dependent extinction spectra highlight the importance of symmetry and phase matching in the excitation of cavity modes and show the limited validity of the infinite wire approximation for describing the response of finite length nanowires toward glancing angles.