Stokes Parameters Research Articles

A White‐Box Digital Twin for Real‐Time Polarization Tracking

AbstractTracking polarization in real‐time is a long‐term challenge. The conventional heuristic and gradient‐descent‐based algorithms for polarization tracking lack efficiency and interpretability. To resolve the problem, a white‐box digital twin modeling the entire polarization tracking system is derived by calculating with Stokes vectors and Mueller matrices. Moreover, the real‐time polarization tracking enabled by the white‐box digital twin is experimentally demonstrated, which is over 7 times faster than the commonly used stochastic parallel gradient descent (SPGD) on average. The adoption of digital twin allows the algorithm to bypass the loop of perturbation, sampling, and adjusting over the real system, thereby significantly reducing the sample times and recovery time. The proposed white‐box digital‐twin‐based algorithm has strong interpretability and high efficiency, which has substantial potential to become a standard approach to achieve real‐time polarization tracking.

Wide-angle metalens array with quadratic phase for terahertz polarization detection

Abstract With the advances of micro/nano fabrication technology, metasurface has become an alternative to design functional devices for manipulating electromagnetic wave. Metalens is one of the basic electromagnetic functional devices that can be applied in various fields. Currently, polarization measurement based on metalens arrays has been widely investigated, but most of them can only work for normal incident wave due to the limited field-of-view of metalens. Herein, a dielectric wide-angle metalens array (WMA) for the terahertz polarization detection is presented. The WMA is composed of three wide-angle metalenses, each wide-angle metalens is constructed by utilizing quadratic phase profile. The angle tolerance of meta-atoms which constitute the wide-angle metalens is elucidated in detail. The WMA can decompose incident terahertz wave into four channels, and the full Stokes parameters of incident wave is determined by intensities in these four channels. Simulated results show that the WMA proposed here has excellent performance for the polarization detection within incident angle of ±40°. In addition, this WMA can also be used to detect the phase gradient of incident terahertz wave, the detection error is less than 1.1%. This WMA is promising in the fields of terahertz polarization generation, detection and imaging.

Matrix-based integral transformations for Stokes imaging with partially polarized and partially coherent light

With the aid of the matrix-based integral transforms called matrix convolution and matrix direct correlation, we provide a simplified expression for the space- and frequency-domain calculations of polarization imaging with partially polarized and partially coherent light. As an example of practical interest, a formula for Stokes imaging, based on the generalized Stokes parameters, is presented, in which a hypermatrix-based transmission cross-coefficient matrix is introduced to represent the combined effects of diffraction and aberrations of a polarization-dependent imaging system and a partially polarized, partially coherent illumination system. The coherent and incoherent limits in Stokes imaging are discussed with the optical transfer matrix, along with its frequency response for a diffraction-limited incoherent polarization imaging system. A generalized concept of the apparent transfer matrix is introduced to deal with the nonlinearity inherent in the polarization imaging system under partially coherent illumination.

Combining magneto-hydrostatic constraints with Stokes profile inversions. IV. Imposing divB =0 condition

Inferences of the magnetic field in the solar atmosphere by means of spectropolarimetric inversions (i.e., Stokes inversion codes) yield magnetic fields that are non-solenoidal ($ B 0$). Because of this, results obtained by such methods are sometimes put into question. We aim to develop and implement a new technique that, in conjunction with Stokes inversion codes, can retrieve magnetic fields that are simultaneously consistent with observed polarization signals and with the null divergence condition. The method used in this work strictly imposes $ B =0$ by determining the vertical component of the magnetic field ($B_ z $) from the horizontal ones ($B_ x B_ y $). We implement this technique, which we refer to as solenoidal inversion, into the FIRTEZ Stokes inversion code and apply it to spectropolarimetric observations of a sunspot observed with the Hinode/SP instrument. We show that the solenoidal inversion retrieves a vertical component of the magnetic field that is consistent in 80<!PCT!> of the analyzed three-dimensional $(x,y,z )$ domain, with the vertical component of the magnetic field inferred from the non-solenoidal inversion. We demonstrate that the solenoidal inversion is capable of a better overall fitting to the observed Stokes vector than the non-solenoidal inversion. In fact, the solenoidal magnetic field fits Stokes $V$ worse, but this is compensated by a better fit to Stokes $I$. We find a direct correlation between the worsening in the fit to the circular polarization profiles by the solenoidal inversion and the deviations in the inferred $B_ z $ with respect to the non-solenoidal inversion. Finally, we also show that the spatial distribution of the electric currents given by $ B $ does not change significantly after imposing the null divergence condition. In spite of being physically preferable, solenoidal magnetic fields are topologically very similar in 80<!PCT!> of the analyzed three-dimensional domain to the non-solenoidal fields obtained from spectropolarimetric inversions. These results support the idea that common Stokes inversion techniques fail to reproduce $ B =0$ mainly as a consequence of the uncertainties in the determination of the individual components of the magnetic field. In the remaining 20<!PCT!> of the analyzed domain, where the $B_ z $ inferred by the solenoidal and non-solenoidal inversions disagree, it remains to be proven that the solenoidal inversion is to be preferred because even though the overall fit to the Stokes parameters improves, the fit to Stokes $V$ worsens. It is in these regions where the application of the Stokes inversion constrained by the null divergence condition can yield new insights about the topology of the magnetic field in the solar photosphere.

An Ensemble Learning Method for Detection of Head and Neck Squamous Cell Carcinoma Using Polarized Hyperspectral Microscopic Imaging.

Head and neck squamous cell carcinoma (HNSCC) has a high mortality rate. In this study, we developed a Stokes-vector-derived polarized hyperspectral imaging (PHSI) system for H&E-stained pathological slides with HNSCC and built a dataset to develop a deep learning classification method based on convolutional neural networks (CNN). We use our polarized hyperspectral microscope to collect the four Stokes parameter hypercubes (S0, S1, S2, and S3) from 56 patients and synthesize pseudo-RGB images using a transformation function that approximates the human eye's spectral response to visual stimuli. Each image is divided into patches. Data augmentation is applied using rotations and flipping. We create a four-branch model architecture where each branch is trained on one Stokes parameter individually, then we freeze the branches and fine-tune the top layers of our model to generate final predictions. Our results show high accuracy, sensitivity, and specificity, indicating that our model performed well on our dataset. Future works can improve upon these results by training on more varied data, classifying tumors based on their grade, and introducing more recent architectural techniques.

Effect of instrumental polarization with a half-wave plate on the B-mode signal: prediction and correction

We study the effect of incident unpolarized signal converted to polarized light produced by a realistic half-wave plate (HWP) and evaluate the impact of the effect in the measurement of Cosmic Microwave Background (CMB) B-mode polarization signal targeting to probe the tensor-to-scalar ratio r. The HWP is modeled with the Mueller formalism, and coefficients are decomposed for any incident angle into harmonics of the HWP rotation frequency due to azimuthal angle dependence. Although we use a general formalism, band-averaged matrix coefficients are calculated as an example for a 9-layer sapphire HWP using EM propagation simulations. We perform simulations of multi-detector observations in a band centered at 140 GHz using LiteBIRD instrumental configuration. We show both theoretically and with the simulations that most of the artefacts on Stokes parameter maps are produced by the dipole leakage on B-modes induced by the fourth harmonics MQI (4f) and MUI (4f). The resulting effect is strongly linked to the spin-2 focal plane scanning cross linking parameters. We develop a maximum likelihood-based method to correct the IP leakage by joint fitting of the Mueller matrix coefficients as well as the Stokes parameter maps. We show that the residual leakage after correction leads to an additional noise limited uncertainty on r of the order of 10-7, independently of the value of the Mueller matrix coefficients. We discuss the impact of the monopole signal and the potential coupling with other systematic effects such as gain variations and detector nonlinearities.

Stokes vector characterization by strongly measuring weak values.

We report the implementation of a non-standard procedure to perform Stokes polarimetry, which was recently proposed by considering weak value measurements. Our procedure is not restricted to weak measurements but applies for both weak and strong couplings between the observable being measured; the polarization (spin) vector; and the measuring device, the "pointer." In optics, the polarization-pointer coupling is usually implemented with a birefringent crystal. This applies in the weak coupling regime. We overcame this limitation by using an alternative setup in which one can go from weak to strong couplings by tuning a moveable mirror. We carried out our proof-of-concept experiments with a laser beam, the image of which was recorded and processed on a charge-coupled device. Our results illustrate that some concepts, originally introduced in a quantum context, in fact refer to properties that are common to both quantum and classical phenomena.

Sub-micron pixel polarization-sensitive photodetector based on silicon nanowire

Silicon nanowire is a potential candidate to be used as polarization-sensitive material, but the relative mechanism of polarization response must be carried out. Herein, a sub-micron metal-single silicon nanowire-metal photodetector exhibits polarization-sensitive characteristics with an anisotropic photocurrent ratio of 1.59 at 780 nm, an excellent responsivity of 24.58 mA/W, and a high detectivity of 8.88 × 109 Jones at 980 nm. The underlying principle of optical anisotropy in silicon nanowire is attributed to resonance enhancement verified by polarizing light microscopy and simulation. Furthermore, Stokes parameter measurements and imaging are all demonstrated by detecting the characteristics of linearly polarized light and imaging the polarizer array, respectively. Given the maturity of silicon processing, the sub-micron linearly polarized light detection proposed in this study lays the groundwork for achieving highly integrated, simplified processes, and cost-effective on-chip polarization-sensitive optical chips in the future.

Wave-optics limit of the stochastic gravitational wave background

The stochastic gravitational wave background (SGWB) is a rich resource of cosmological information, encoded both in its source statistics and anisotropies induced by propagation effects. We provide a theoretical description of it, without employing tools which rely on the geometric optics assumption. Our formalism is based on the so-called classical matter approximation and it is able to capture wave-optics effects, such as interference and diffraction. We show that the interaction between the gravitational waves and the cosmic structures along the line-of-sight produce observable scalar and vector polarization modes, on top of modulating the tensorial ones. We build the two point correlation function describing the statistics of the SGWB, and introduce the intensity and gravitational Stokes parameters for all its components. In the case of an unpolarized, Gaussian and statistically homogeneous SGWB, we show that the interaction with matter modulates its intensity and does not generate a net difference between left- and right-helicity tensor and vector modes, as expected. We demonstrate that, in order to produce QT- and UT-tensor polarization modes the background must possess a hexadecapole anisotropy, while a quadrupole anisotropy can source the vector QV- and UV-Stokes parameters.

Dirac equation for photons in a fibre: Origin of polarisation

Spin is a fundamental degree of freedom, which was discovered by Dirac for an electron in his relativistic quantum mechanics, known as the Dirac equation. The origin of spin for a photon is unclear because Maxwell's equations in a vacuum are Lorentz invariant without introducing the concept of spin. Here, the propagation of coherent rays of photons in a graded-index optical fibre is considered to discuss the origin of polarisation for photons using exact solutions of the Laguerre-Gauss and Hermite-Gauss modes. The energy spectrum is massive, and the effective mass is a function of the confinement and orbital angular momentum. The propagation is described by the one-dimensional (1D) non-relativistic Schrödinger equation, which is equivalent to the 2D space-time Klein-Gordon equation by a unitary transformation. The probabilistic interpretation and the conservation law require the factorisation of the Klein-Gordon equation, leading to the 2D Dirac equation with spin. The spin expectation values of photons correspond to the polarisation state on the Poincaré sphere. As an application of the theory, a polarisation interferometer is proposed, whose energy spectrum shows a Dirac cone in the Stokes parameter space.

Polarization Property Associated with Surface Plasmon Resonance in a Palladium Thin-Film Coated Aluminum Grating in a Conical Mounting and Its Application to Hydrogen Gas Detection.

We have investigated a polarization property of the (specularly) reflected light from an aluminum grating, coated with a palladium (Pd) thin-film on its surface. The polarization property, which is associated with surface plasmon resonance (SPR), and occurs in the Pd thin-film on the aluminum grating in a conical mounting, is observed as a rapid change in the normalized Stokes parameter s3, around the resonance angle, θsp, at which point, SPR occurs. The sensing technique used the rapid change in s3 to allow us to successfully detect a small change in the complex refractive index of the Pd thin-film layer upon exposure to hydrogen gas, with a concentration near the lower explosion level. Experimental results showed that the sensing technique provided a sensitive and stable response when the Pd thin-film layer was exposed to gas mixtures containing hydrogen at concentrations of 1 to 4% (by volume) in nitrogen.

Vortex retarder-based Stokes polarimeters: optimal data processing and autocalibration capability.

We present a full Stokes polarimeter that utilizes a vortex retarder (VR) in conjunction with a polarization camera. We demonstrate its capability to estimate the full Stokes vector in a single shot with optimal precision and to autocalibrate the VR retardance, ensuring precise measurements even in dynamic environments where retardance is variable.

Distributed optical fiber magnetic field sensor based on polarization-sensitive OFDR.

A distributed optical fiber magnetic field sensor based on a polarization-sensitive optical frequency domain reflectometer (POFDR) is proposed. It extracts the accumulated Faraday rotation by combining the Stokes vectors and the backward Mueller matrices from the measured states of polarization (SOPs) and obtains the magnetic field component. This method avoids adjusting the input polarization during the magnetic field sensing process. It overcomes the drawback of the conventional POFDR scheme, which requires at least two sets of different input SOPs for each sensing. Finally, the aforementioned effectiveness has been experimentally verified by using a single-mode sensing fiber. The results show that the sensor has good repeatability and linearity. The measurement error of the magnetic field sensor is 19.4 mT. The measured magnetic field variations agree with the applied ones with similarities higher than 0.98.

Time-varying optical spin-orbit Hall effect in tightly focused femtosecond optical field.

The spin-orbit Hall effect (HE) is dominated by the law of conservation of angular momentum of a beam and is highly significant in light-matter interactions. The electromagnetic field, phase, topological structure, and spin-orbit HE of an azimuthally polarized vortex pulse beam in a tightly focused system are studied theoretically here. Calculations show that the focal field has ultrafast bright-dark alternating characteristics and a distorted phase distribution. Furthermore, the time evolution of the polarization singularity in the focused light field is explained using Stokes parameters. Importantly, the spin-orbit HE of the pulsed beam is shown to be time-varying in a tightly focused system. This time-varying spin-orbit HE is particularly sensitive to the pulse width and central wavelength. Our method has important applications in particle manipulation.

Polarized Hyperspectral Microscopic Imaging for Zebrafish.

Zebrafish is a well-established animal model for developmental and disease studies. Its optical transparency at early developmental stages is ideal for tissue visualization. Interaction of light with zebrafish tissues provides information on their structure and properties. In this study, we developed a microscopic imaging system for improving the visualization of unstained zebrafish tissues on tissue slides, with two different setups: polarized light imaging and polarized hyperspectral imaging. Based on the polarized light imaging setup, we collected the RGB images of Stokes vector parameters (S0, S1, S2, and S3), and calculated the Stokes vector derived parameters: the degree of polarization (DOP), the degree of linear polarization (DOLP)). We also calculated Stokes vector data based on the polarized hyperspectral imaging setup. The preliminary results demonstrate that Stokes vector data in two imaging setups (polarized light imaging and polarized hyperspectral imaging) are capable of improving the visualization of different types of zebrafish tissues (brain, muscle, skin cells, blood vessels, and yolk). Using the images collected from larval zebrafish samples by polarized light imaging, we found that DOP and DOLP could show clearer structural information of the brain and of skin cells, muscle and blood vessels in the tail. Furthermore, DOP and DOLP parameters derived from images collected by polarized hyperspectral imaging could show clearer structural information of skin cells developing around yolk as well as the surrounding blood vessel network. In addition, polarized hyperspectral imaging could provide complementary spectral information to the spatial information on Stokes vector data of zebrafish tissues. The polarized light imaging & polarized hyperspectral imaging systems provide a better insight into the microstructures of zebrafish tissues.

Scattering of partially coherent electromagnetic beams by a sphere.

We examine the scattering of a partially coherent, partially polarized electromagnetic beam by a homogeneous sphere (Mie scattering). The degree of polarization and the Stokes parameters in the far zone are found to be strongly dependent on the state of coherence and polarization of the incident beam. In particular, we demonstrate the emergence of polarization singularities and show that partial spatial coherence gives rise to significant depolarization effects. In addition we explore the symmetry properties of the scattered field.

Polarization upgrade of specMACS: calibration and characterization of the 2D RGB polarization-resolving cameras

Abstract. The spectrometer of the Munich Aerosol Cloud Scanner (specMACS) is a high-spatial-resolution hyperspectral and polarized imaging system. It is operated from a nadir-looking perspective aboard the German High Altitude and LOng range (HALO) research aircraft and is mainly used for the remote sensing of clouds. In 2019, its two hyperspectral line cameras, which are sensitive to the wavelength range between 400 and 2500 nm, were complemented by two 2D RGB polarization-resolving cameras. The polarization-resolving cameras have a large field of view and allow for multi-angle polarimetric imaging with high angular and spatial resolution. This paper introduces the polarization-resolving cameras and provides a full characterization and calibration of them. We performed a geometric calibration and georeferencing of the two cameras. In addition, a radiometric calibration using laboratory calibration measurements was carried out. The radiometric calibration includes the characterization of the dark signal, linearity, and noise as well as the measurement of the spectral response functions, a polarization calibration, vignetting correction, and absolute radiometric calibration. With the calibration, georeferenced, absolute calibrated Stokes vectors rotated into the scattering plane can be computed from raw data. We validated the calibration results by comparing observations of the sunglint, which is a known target, with radiative transfer simulations of the sunglint.

Full-Stokes metasurface polarimetry requiring only a single measurement

Polarization is crucial in various fields such as imaging, sensing, and substance detection. A compact, fast, and accurate polarization detection device is vital for these applications. Herein, we demonstrate a multifocus metalens for terahertz polarization detection that requires only a single measurement to obtain complete polarization parameters and reconstruct the polarization state of the incident field. The individual subarrays of this metalens convert each of the six polarized components into the same polarization, which in turn links the Stokes parameters to these six foci. The incident linear polarizations and elliptical polarizations are characterized by Stokes parameters and polarization ellipses. Simulations and experimental results show that the scheme can accurately detect the incident polarization with a single measurement. The proposed metasurface polarimetry may find applications in the fields of real-time terahertz detection and integrated optics.

Pulse Jitter and Single-pulse Variability in Millisecond Pulsars

Understanding the jitter noise resulting from single-pulse phase and shape variations is important for the detection of gravitational waves using pulsar timing arrays. We present measurements of the jitter noise and single-pulse variability of 12 millisecond pulsars that are part of the International Pulsar Timing Array sample using the Five-hundred-meter Aperture Spherical radio Telescope. We find that the levels of jitter noise can vary dramatically among pulsars. A moderate correlation with a correlation coefficient of 0.57 between jitter noise and pulse width is detected. To mitigate jitter noise, we perform matrix template matching using all four Stokes parameters. Our results reveal a reduction in jitter noise ranging from 6.7% to 39.6%. By performing longitude-resolved fluctuation spectrum analysis, we identify periodic intensity modulations in 10 pulsars. In PSR J0030+0451, we detect single pulses with energies more than 10 times the average pulse energy, suggesting the presence of giant pulses. We also observe a periodic mode-changing phenomenon in PSR J0030+0451. We examine the achievable timing precision by selecting a subset of pulses with a specific range of peak intensity, but no significant improvement in timing precision is achievable.

Realizing Minimally Perturbed, Nonlocal Chiral Metasurfaces for Direct Stokes Parameter Detection.

Recent development in nonlocal resonance based chiral metasurfaces draws great attention due to their abilities to strongly interact with circularly polarized light at a relatively narrow spectral bandwidth. However, there still remain challenges in realizing effective nonlocal chiral metasurfaces in optical frequency due to demanding fabrications such as 3D-multilayered or nanoscaled chiral geometry, which, in particular, limit their applications to polarimetric detection with high-Q spectra. Here, we study the underlying working principles and reveal the important role of the interaction between high-Q nonlocal resonance and low-Q localized Mie resonance in realizing effective nonlocal chiral metasurfaces. Based on the working principles, we demonstrate one of the simplest types of nonlocal chiral metasurfaces which directly detects a set of Stokes parameters without the numerical combination of transmitted values presented from typical Stokes metasurfaces. This is achieved by minimally altering the geometry and filling ratio of every constituent nanostructure in a unit cell, facilitating consistent-sized nanolithography for all samples experimentally at a targeted wavelength with relatively high-Q spectra. This work provides an alternative design rule to realizing effective polarimetric metasurfaces and the potential applications of nonlocal Stokes parameters detection.