Stokes Parameters Research Articles

Revealing the Electric and Magnetic Nature of the Scattered Light.

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 of the expansion. However, the experimental determination of 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 . Thus, our Stokes polarimetry method allows us to capture and separately, a distinction that can not be achieved by measuring the total energy of the scattered field via an integrating sphere. Moreover, the determination of enables us to infer the amplitude of the scattered field at all points of the radiation zone, including the amplitude of the near-field distribution generated by the objects. 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.

Snapshot Multi-Wavelength Birefringence Imaging.

A snapshot multi-wavelength birefringence imaging measurement method was proposed in this study. The RGB-LEDs at wavelengths 463 nm, 533 nm, and 629 nm were illuminated with circularly polarized light after passing through a circular polarizer. The transmitted light through the birefringent sample was captured by a color polarization camera. A single imaging process captured light intensity in four polarization directions (0°, 45°, 90°, and 135°) for each of the three RGB spectral wavelength channels, and subsequently measured the first three elements of Stokes vectors (S0, S1, and S2) after the sample. The birefringence retardance and fast-axis azimuthal angle were determined simultaneously. An experimental setup was constructed, and polarization response matrices were calibrated for each spectral wavelength channel to ensure the accurate detection of Stokes vectors. A polymer true zero-order quarter-wave plate was employed to validate measurement accuracy and repeatability. Additionally, stress-induced birefringence in a PMMA arch-shaped workpiece was measured both before and after the application of force. Experimental results revealed that the repeatability of birefringence retardance and fast-axis azimuthal angle was better than 0.67 nm and 0.08°, respectively. This approach enables multispectral wavelength, high-speed, high-precision, and high-repeatability birefringence imaging measurements through a single imaging session.

Realization of spinful metaphotonic stokes skyrmions

Abstract Topologically protected skyrmion textures of light have garnered significant attention due to their potential applications in next-generation high-density data storage and logic devices. However, achieving compact and tunable on-chip skyrmion modes remains a formidable challenge. In this work, we present a novel approach empowered by birefringent metasurfaces to generate and manipulate spin-multiplexed photonic skyrmion textures. By encoding independent phase profiles onto orthogonal spin states, we observe the emergence of anti-skyrmions and skyrmioniums via Stokes parameter measurements, elucidating their distinct topological characteristics. This spin-multiplexed metasurface platform not only facilitates high-dimensional multiplexing but also enables the miniaturization of topological quasi-particles, offering promising prospects for applications in optical memory, information processing, and communications.

The Depth Distribution Law of the Polarization of the Vector Acoustic Field in the Ocean Waveguide

The polarization of the acoustic field in the ocean waveguide environment is a unique property that can provide new ideas for locating and detecting the underwater target, so it is interesting to study the polarization. This paper extends the Stokes parameters to a broadband form, and uses the non-stationary phase approximation method to simplify the expressions, reducing the complexity of theoretical derivation. A physical phenomenon is observed where polarization exhibits significant variations concerning the sea surface, seafloor, source depth, and the source symmetrical depth. Simulation results demonstrate that the simplified equations using the non-stationary phase approximation are effective. Additionally, by normalizing the broadband Stokes parameters, the effects of horizontal range on the depth distribution law of polarization can be eliminated. Subsequently, using the normalized broadband Stokes parameters, the influence of environmental and source parameters on the depth distribution law of polarization is analyzed. The effectiveness of the non-stationary phase approximation and the range-independence property of the normalized broadband Stokes parameters are verified by processing RHUM-RUM experimental data. Based on the conclusions of this paper, it is expected that the polarization can be used for target depth estimation.

Mapping structured Laguerre–Gaussian beam states onto the orbital Poincaré sphere in the form of controllable spatial trajectories

The structured Laguerre–Gaussian (LG) beam is a two-parameter superposition of 2n+ℓ+1 Hermite–Gaussian modes (where n and ℓ are a radial number and a topological charge of the initial LG beam) whose orbital angular momentum oscillations are controlled by phases and amplitude parameters. But we succeeded in reducing its representation to a simple sum of a standard LG mode and a hybrid Hermite–Laguerre–Gaussian (HLG) beam that is a key point in understanding a hidden geometry of the structured LG (sLG) beams and implementations of its unique prosperities. In assents, the hybrid HLG beam is mapped onto the orbital Poincaré sphere in the form of a plane trajectory along a main meridian of the sphere. However, the most intriguing thing is as follows. First, once we slightly perturb the HLG beam with a single LG mode, the flat trajectory turns into a complex multi-petalled tracery with multiple self-intersections due to cyclic variation of the phase parameter of the sLG beam. Moreover, the shape of the tracery as well as the birth and destruction of the self-intersection points can be controlled with the amplitude parameter. However, it is worth noting that when changing the beam parameters cyclically, the area outlined by the trajectory on the sphere is directly related to the geometric phase acquired by the sLG beam that can be treated as an additional degree of freedom for transmitting big data. In the article, we study the sLG beam properties and its mapping onto the orbital Poincarè sphere in the framework of a symplectic 4×4 matrix formalism while the orbital Stokes parameters are experimentally measured, and we have found good agreement between theory and experiment.

Uncertainties in radiometric measurements of the ocean surface from above water and helicopter hyperspectral and polarimetric observations

A new system was assembled with a snapshot hyperspectral imager and a polarimetric camera for quantifying uncertainties in aquatic remote sensing applications. The hyperspectral imager measures radiances from a field-of-view (FOV) creating imagery for each of its spectral bands. The polarimetric camera measures the Stokes vector components of the radiance. A combination of polarimetric and hyperspectral measurements provides data about the wind-roughened surface in various water and sky conditions. Uncertainties in the total radiance L t in unpolarized and polarized modes are estimated by observations from the ships in two ocean cruises, from a nearshore platform, and a helicopter in the Chesapeake Bay showing that uncertainties are a combination of the effects of the reflected sky from the surface (ρL s ), water leaving radiance (L w ), and Rayleigh scattering; the impact of the latter increases with the height.

Joint optimization of coded aperture metasurface and residual self-attention network for snapshot full-Stokes imaging

Traditional full-Stokes polarization imaging typically relies on the movements or segmentation of imaging systems, often accompanied by sacrifices in temporal or spatial resolution. Therefore, simultaneous encoding of full-Stokes vectors at the pixel scale is of great significance. Benefiting from the multi-dimensional light field control capability of metasurfaces, a coded aperture metasurface for polarization imaging is proposed in this paper, which can achieve pixel-level encoding of four Stokes vectors in a single imaging session. In addition, a Stokes residual self-attention network is designed to restore the encoded image, where the introduction of a channel-wise self-attention mechanism can effectively address the impact of intensity differences between Stokes vectors. Since the control of polarization states by metasurfaces is a differentiable physical process, the front-end metasurface encoding and back-end recovery network parameters can be jointly optimized, and this work achieves high-quality polarization imaging via such co-optimization methods. The proposed work demonstrates the flexibility and designability of metasurfaces in compact computational full-Stokes imaging systems.

Diagnostics of Magnetohydrodynamic Modes in the Interstellar Medium through Synchrotron Polarization Statistics

One of the biggest challenges in understanding magnetohydrodynamic (MHD) turbulence is identifying the plasma mode components from observational data. Previous studies on synchrotron polarization from the interstellar medium (ISM) suggest that the dominant MHD modes can be identified via statistics of Stokes parameters, which would be crucial for studying various ISM processes such as the scattering and acceleration of cosmic rays, star formation, and dynamo. In this paper, we present a numerical study of the synchrotron polarization analysis (SPA) method through systematic investigation of the statistical properties of the Stokes parameters. We derive the theoretical basis for our method from the fundamental statistics of MHD turbulence, recognizing that the projection of the MHD modes allows us to identify the modes dominating the energy fraction from synchrotron observations. Based on the discovery, we revise the SPA method using synthetic synchrotron polarization observations obtained from 3D ideal MHD simulations with a wide range of plasma parameters and driving mechanisms, and present a modified recipe for mode identification. We propose a classification criterion based on a new SPA+ fitting procedure, which allows us to distinguish between Alfvén mode and compressible/slow mode dominated turbulence. We further propose a new method to identify fast modes by analyzing the asymmetry of the SPA+ signature and establish a new asymmetry parameter to detect the presence of fast mode turbulence. Additionally, we confirm through numerical tests that the identification of the compressible and fast modes is not affected by Faraday rotation in both the emitting plasma and the foreground.

A handheld polarimetric imaging device and calibration technique for accurate mapping of terahertz Stokes vectors

In recent years, handheld and portable terahertz instruments have been in rapid development for various applications ranging from non-destructive testing to biomedical imaging and sensing. For instance, we have deployed our Portable Handheld Spectral Reflection (PHASR) Scanners for in vivo full-spectroscopic imaging of skin burns in large animal models in operating room settings. In this paper, we debut the polarimetric version of the PHASR Scanner, and describe a generalized calibration technique to map the spatial and spectral dependence of the Jones matrix of an imaging scanner across its field of view. Our design is based on placement of two orthogonal photoconductive antenna (PCA) detectors separated by a polarizing beam splitter in the PHASR Scanner housing. We show that as few as three independent measurements of a well-characterized polarimetric calibration target are sufficient to determine the polarization state of the incident beam at the sample location, as well as to extract the Jones propagation matrix from the sample location to the detectors. We have tested the accuracy of our scanner by validating polarimetric measurements obtained from a birefringent crystal rotated to various angles, as compared to the theoretically predicted response of the sample. This new version of our PHASR scanner can be used for high-speed imaging and investigation of heterogeneity of polarization-sensitive samples in the field.

SuperSynthIA: Physics-ready Full-disk Vector Magnetograms from HMI, Hinode, and Machine Learning

Vector magnetograms of the Sun’s photosphere are cornerstones for much of solar physics research. These data are often produced by data-analysis pipelines combining per-pixel Stokes polarization vector inversion with a disambiguation that resolves an intrinsic 180° ambiguity. We introduce a learning-based method, SuperSynthIA, that produces full-disk vector magnetograms from Stokes vector observations. As input, SuperSynthIA uses Stokes polarization images from Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI). As output, SuperSynthIA simultaneously emulates the inversion and disambiguation outputs from the Hinode/Solar Optical Telescope-Spectro-Polarimeter (SOT-SP) pipeline. Our method extends our previous approach SynthIA with heliographic outputs as well as using an improved data set and inference method. SuperSynthIA provides a new tool for improved magnetic fields from full-disk SDO/HMI observations using information derived from the enhanced capabilities of Hinode/SOT-SP. Compared to our previous SynthIA, SuperSynthIA provides physics-ready vector magnetograms and mitigates unphysical angle preferences and banding artifacts in SynthIA. SuperSynthIA data are substantially more temporally consistent than those from the SDO/HMI pipeline, most notably seen in, e.g., evolving active regions. SuperSynthIA substantially reduces noise in low-signal areas, resulting in less center-to-limb bias outside of strong-signal areas. We show that outputs from SuperSynthIA track the SDO/HMI-recorded evolution of the magnetic field. We discuss the limitations of SuperSynthIA that the user must understand, and we demonstrate a broad set of evaluations to test SuperSynthIA and discuss remaining known artifacts. Our tests provide both methodology and evidence that SuperSynthIA outputs are ready for use by the community, and that learning-based approaches are suitable for physics-ready magnetograms.

Demonstration of extrinsic chirality in self-assembled asymmetric plasmonic metasurfaces and nanohole arrays

Chirality, the lack of mirror symmetry, can be mimicked in nanophotonics and plasmonics by breaking the symmetry in light-nanostructure interaction. Here we report on versatile use of nanosphere lithography for the fabrication of low-cost metasurfaces, which exhibit broadband handedness- and angle-dependent extinction in the near-infrared range, thus offering extrinsic chiro-optical behavior. We measure wavelength and angle dependence of the extinction for four samples. Two samples are made of polystyrene nanospheres asymmetrically covered by silver and gold in one case and silver only in the other case, with a nanohole array at the bottom. The other two samples are nanohole arrays, obtained after the nanosphere removal from the first two samples. Rich extrinsic chiral features are governed by different chiro-optical mechanisms in the three-dimensional plasmonic semi-shells and planar nanohole arrays. We also measure Stokes parameters in the same wavelength and incidence angle range and show that the transmitted fields follow the extrinsic chirality features of the extinction dissymmetry. We further study the influences of the nanostructured shapes and in-plane orientations on the intrinsic vs extrinsic chirality. The nanoholes are modelled as oval shapes in metal, showing good agreement with the experiments. We thus confirm that nanosphere lithography can provide different geometries for chiral light manipulation at the nanoscale, with the possibility to extend functionalities with optimized oval shapes and combination of constituent metals.

Planck data revisited: Low-noise synchrotron polarization maps from the WMAP and Planck space missions

Observations of cosmic microwave background (CMB) polarization, essential for probing a potential phase of inflation in the early Universe, suffer from contamination by polarized emission from the Galactic interstellar medium. This work combines existing observations from the WMAP and space missions to make a low-noise map of polarized synchrotron emission that can be used to clean forthcoming CMB observations. We combine DR5 K, Ka and Q WMAP maps with PR4 30 GHz and 44 GHz LFI maps and WMAP K, Ka and Q maps with LFI 30 GHz and 44 GHz maps, using weights that near-optimally combine the observations as a function of sky direction, angular scale, and polarization orientation. We publish well-characterized maps of synchrotron $Q$ and $U$ Stokes parameters at $ = 30$ GHz and an angular resolution of 1 degree. A statistical description of uncertainties is provided with Monte-Carlo simulations of additive and multiplicative errors. Our maps are the most sensitive full-sky maps of synchrotron polarization to date, and are made available to the scientific community on a dedicated website.

Spin-Weighted Spherical Harmonics for Polarized Light Transport

The objective of polarization rendering is to simulate the interaction of light with materials exhibiting polarization-dependent behavior. However, integrating polarization into rendering is challenging and increases computational costs significantly. The primary difficulty lies in efficiently modeling and computing the complex reflection phenomena associated with polarized light. Specifically, frequency-domain analysis, essential for efficient environment lighting and storage of complex light interactions, is lacking. To efficiently simulate and reproduce polarized light interactions using frequency-domain techniques, we address the challenge of maintaining continuity in polarized light transport represented by Stokes vectors within angular domains. The conventional spherical harmonics method cannot effectively handle continuity and rotation invariance for Stokes vectors. To overcome this, we develop a new method called polarized spherical harmonics (PSH) based on the spin-weighted spherical harmonics theory. Our method provides a rotation-invariant representation of Stokes vector fields. Furthermore, we introduce frequency domain formulations of polarized rendering equations and spherical convolution based on PSH. We first define spherical convolution on Stokes vector fields in the angular domain, and it also provides efficient computation of polarized light transport, nearly on an entry-wise product in the frequency domain. Our frequency domain formulation, including spherical convolution, led to the development of the first real-time polarization rendering technique under polarized environmental illumination, named precomputed polarized radiance transfer, using our polarized spherical harmonics. Results demonstrate that our method can effectively and accurately simulate and reproduce polarized light interactions in complex reflection phenomena, including polarized environmental illumination and soft shadows.

Manipulation of Helicity-Dependent Photocurrent and Stokes Parameter Detection in Topological Insulator Bi2Te3 Nanowires.

Helicity-dependent photocurrent (HDPC) and its modulation in topological insulator Bi2Te3 nanowires have been investigated. It is revealed that when the incident plane of a laser is perpendicular to the nanowire, the HDPC is an odd function of the incident angle, which is mainly contributed by the circular photogalvanic effect originating from the surface states of Bi2Te3 nanowire. When the incident plane of a laser is parallel to the nanowire, the HDPC is approximately an even function of the incident angle, which is due to the circular photon drag effect coming from the surface states. It is found that the HDPC can be effectively tuned by the back gate and the ionic liquid top gate. By analyzing the substrate dependence of the HDPC, we find that the HDPC of the Bi2Te3 nanowire on the Si substrate is an order of magnitude larger than that on SiO2, which may be due to the spin injection from the Si substrate to the Bi2Te3 nanowire. In addition, by applying different biases, the Stokes parameters of a polarized light can be extracted by arithmetic operation of the photocurrents measured in the Bi2Te3 nanowire. This work suggests that topological insulator Bi2Te3 nanowires may provide a good platform for opto-spintronic devices, especially in chirality and polarimtry detection.

Characteristic parameters of an optically equivalent model based on measured Stokes parameters

This study presents an approach to determine the characteristic parameters of an optically equivalent model consisting of a linear retarder and a rotator. These parameters—retardance, orientation of the linear retarder, and rotation—are determined by using linearly polarized incident light and measuring the first three Stokes parameters of the outgoing light. With the help of Mueller calculus, the retardation can be determined up to π rad. The position of the refractive index axes can be specified; however, it is not possible to differentiate between fast and slow axis. The rotation can be determined over the full measurement range of π rad. To measure retardations larger than π rad, an adapted RGB method is presented that directly uses the retardations resulting from the Mueller calculus instead of light intensity measurements. Synthetic examples demonstrate the application of the methods presented.

Snapshot spectropolarimeter based on a six-fold separating prism operating from 360 nm to 1 µm

We describe a new type of spectropolarimeter in which light is separated to simultaneously measure six spectra carrying polarimetric information on a 2D CMOS camera. The polarization separation along one of the camera axes was obtained using a novel prism, and the spectral dispersion along the other camera axis was obtained using an imaging spectrometer. An ideal version of the six-fold separating prism is first described, in which polarimetric separation is performed along the canonical polarization states used to define the Stokes vector, and it can be explained without any math. The real version is then presented, with math that is simple for those familiar with polarization. The operation of the spectropolarimeter is described. Experimental results show that the polarimetric accuracy is a few 10−3, and noise (mainly due to shot noise) is in the same range for a single acquisition. The spectral resolution depends on the entrance pinhole width and can be as low as 2 nm. Several examples are presented that feature how informative snapshots, high spectral resolution, spectropolarimetric measurements can be. The anticipated applications of this spectropolarimeter and, more broadly, for this novel polarization-separating prism are discussed. Technical details, such as the calibration procedure, noise levels, and consistency checks, are presented as supplementary material.

Analysis of Stokes singularities using a lateral shear interferometer

Polarization and Poincaré singularities in the optical fields can be studied by analyzing the phase singularities of mathematically constructed Stokes vector fields. The wider applicability of the Stokes construction is found by exploring the generation and detection methods for various types of Stokes singularities and their analysis. Here, we detect and analyze all forms of the Stokes singularities through lateral shear interferometry. Specifically, the projections of a Stokes singularity on three pairs of orthogonal polarization basis states, defined by the eigen polarization states of Pauli’s matrices, are analyzed through unique fork patterns in the shearogram pairs. These interference patterns also provide the topological indices of the singularities. Such a self-referencing interferometric method also helps to remove the degeneracy in the Stokes index and polarization. Through both, simulations and experiments, we have analyzed specific beams represented by higher order Poincaré sphere and hybrid order Poincaré sphere topological constructs.

Design of an aperiodic Cr/C reflective multilayer quarter-wave plate at the carbon K-edge

An aperiodic Cr/C reflective multilayer quarter-wave plate is designed and optimized at the carbon K-edge, by implementing both the genetic algorithm (GA) and the non-dominated sorting genetic algorithm II (NSGA-II). The performance is demonstrated using test free electron laser (FEL) pulses simulated by GENESIS to convert the imperfect linearly polarized light to circular polarization; the characteristics are verified by a numerical analysis of the Stokes parameter of the FEL pulses before and after penetration through the multilayer.

Solving Maxwell's Equations Using Polarimetry Alone.

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. These objects are lossless, axially symmetric, and well described by a single multipolar order. Our method for solving Maxwell's equations endows the Stokes parameters an even more fundamental role in the electromagnetic scattering theory.

Multiwavelength Emission of the Gamma-Ray Burst Prompt Phase. I. Time-resolved and Time-integrated Polarizations

The time-integrated polarization degree (PD) in the prompt optical band of a gamma-ray burst (GRB) was predicted to be less than 20%, while the time-resolved one can reach as high as 75% in the photosphere model. Polarizations in the optical band during the GRB prompt phase have not previously been studied in the framework of the magnetic reconnection model. Here, a three-segment power law of the energy spectrum is used to reconstruct the Stokes parameters of the magnetic reconnection model. Multiwavelength light curves and polarization curves from the optical band to MeV gamma rays in the GRB prompt phase are studied. We found that, depending mainly on the jet dynamics, there is a long-lasting high-PD phase in all calculated energy bands for the typical parameter sets. The time-resolved PD could be as high as 50%, while the time-integrated one is roughly 17% in the optical band. The time-resolved PD in X-rays can reach 60% and the time-integrated one is around 30%–40%. The evolution of polarization angle (PA) is random in both optical and gamma-ray bands for the photosphere model, while it is roughly constant in the synchrotron models. Therefore, future time-resolved PA observations in the prompt optical or gamma-ray band could distinguish between the photosphere and synchrotron models.