Polarization Matrices Research Articles

Cocrystalline Matrices for Hyperpolarization at Room Temperature Using Photoexcited Electrons.

We propose using cocrystals as effective polarization matrices for triplet dynamic nuclear polarization (DNP) at room temperature. The polarization source can be uniformly doped into cocrystals formed through acid-acid, amide-amide, and acid-amide synthons. The dense-packing crystal structures, facilitated by multiple hydrogen bonding and π-π interactions, result in extended T1 relaxation times, enabling efficient polarization diffusion within the crystals. Our study demonstrates the successful polarization of a DNP-magnetic resonance imaging molecular probe, such as urea, within a cocrystal matrix at room temperature using triplet-DNP.

Multi-fold binary Darboux transformation and mixed solitons of a three-component Gross-Pitaevskii system in the spinor Bose-Einstein condensate

The Bose-Einstein-condensation applications give rise to the superfluidity in the liquid helium and superconductivity in the metals. In this paper, we work on a three-component Gross-Pitaevskii system, which describes the matter waves in an spin-1 spinor Bose-Einstein condensate. We construct a multi-fold binary Darboux transformation with the zero seed solutions to describe the three vertical spin projection of the spin-1 spinor BEC, which is different from all the existing Darboux-type ones for the same system, and derive three types of the exponential-and-rational mixed soliton solutions associated with two conjugate complex eigenvalues. For such mixed solitons, we give their asymptotic expressions, indicating that they consist of the Ieda-Miyakawa-Wadati (IMW)-polar-state or IMW-ferromagnetic solitons but possess the time-dependent velocities. Asymptotically and graphically, interaction mechanisms between the mixed and exponential solitons are classified in six cases, and we exhibit the inelastic and elastic interactions through calculating the modifications of the polarization matrices and phase shifts for the two interacting solitons. We find that both the IMW-polar-state solitons, including the mixed and exponential solitons, can not alter the other soliton’s intensity distribution during the interaction, while the mixed or exponential soliton in the IMW-ferromagnetic state does.

Dryland Crop Classification Combining Multitype Features and Multitemporal Quad-Polarimetric RADARSAT-2 Imagery in Hebei Plain, China.

The accuracy of dryland crop classification using satellite-based synthetic aperture radar (SAR) data is often unsatisfactory owing to the similar dielectric properties that exist between the crops and their surroundings. The main objective of this study was to improve the accuracy of dryland crop (maize and cotton) classification by combining multitype features and multitemporal polarimetric SAR (PolSAR) images in Hebei plain, China. Three quad-polarimetric RADARSAT-2 scenes were acquired between July and September 2018, from which 117 features were extracted using the Cloude–Pottier, Freeman–Durden, Yamaguchi, and multiple-component polarization decomposition methods, together with two polarization matrices (i.e., the coherency matrix and the covariance matrix). Random forest (RF) and support vector machine (SVM) algorithms were used for classification of dryland crops and other land-cover types in this study. The accuracy of dryland crop classification using various single features and their combinations was compared for different imagery acquisition dates, and the performance of the two algorithms was evaluated quantitatively. The importance of all investigated features was assessed using the RF algorithm to optimize the features used and the imagery acquisition date for dryland crop classification. Results showed that the accuracy of dryland crop classification increases with evolution of the phenological period. In comparison with SVM, the RF algorithm showed better performance for dryland crop classification when using full polarimetric RADARSAT-2 data. Dryland crop classification accuracy was not improved substantially when using only backscattering intensity features or polarization decomposition parameters extracted from a single-date image. Satisfactory classification accuracy was achieved using 11 optimized features (derived from the Cloude–Pottier decomposition and the coherency matrix) from 2 RADARSAT-2 images (acquisition dates corresponding to the middle and late stages of dryland crop growth). This study provides an important reference for timely and accurate classification of dryland crop in Hebei plain, China.

ВИЗНАЧЕННЯ ЗНАКУ МІРИ ОБЕРТАННЯ ПРИ РЕЄСТРАЦІЇ ОДНІЄЇ ЛІНІЙНОЇ ПОЛЯРИЗАЦІЇ РАДІОВИПРОМІНЮВАННЯ ПУЛЬСАРІВ

Purpose: The studies of pulsars allow enriching our knowledge in determination of parameters of both the exotic electron-positron plasma in the pulsar magnetosphere with strong magnetic field and the ordinary ion-electron plasma of the interstellar medium, which exists in a weak magnetic field. To determine the parameters of the both plasma types it is reasonable to use polarization characteristics of a pulsed radio emission of pulsars. An accurate determination of these characteristics is quite a complex problem. For its solving, primarily we have to determine two parameters of the propagation medium – its dispersion and rotation measures. Their absolute values can be determined with the relative precision of 10-4, but the problem of rotation measure value sign determination arises. This sign depends on the interstellar magnetic field direction along the line of sight. Hear, a new method of rotation measure value sign determination is proposed. Design/methodology/approach: Muller polarization matrices are usually used for determination of such a propagation parameter as the rotation measure absolute value. When only one linear polarization is received, using of these matrices allows quite accurate determining the absolute value of the rotation measure, but not the sign of this parameter due to a certain symmetry of these matrices with respect to the direction of the linear polarization rotation plane. If we complement the system of equations, which determines the rotation measure value, with some new additional components, which take into account the contributions of the Earth ionosphere and magnetosphere to the rotation measure value, one can notice that this contribution is always positive in the Southern magnetic hemisphere (the majority of the Northern geographical hemisphere) and is always negative in the Northern magnetic hemisphere (the majority of the Southern geographical hemisphere). Moreover, the absolute value of this contribution is maximal at noon and minimal at midnight, when the concentration of ions in the Earth ionosphere is maximal and minimal, respectively. Accounting for these regularities allows to determine not only the absolute value of the rotation measure, but also its sign by means of two independent time-shifted estimations of the observed absolute value of this parameter for various ionization degrees of the Earth ionosphere. Findings: We show that using of additional equations, which take into account the contribution of the Earth ionosphere and magnetosphere to the value of the rotation measure parameter, allows full determination of this parameter accounting for the sign of this value even for the antennas, which can record a single linear polarization only. This approach allows to determine all polarization parameters of the pulsar radio emission as well as of the pulsed or continuum polarized radio emission of other cosmic sources. Conclusions: The paper presents the results of measurement of the rotation measure for the two closest to the Earth pulsars, namely J0814+7429 (B0809+74), J0953+0755 (B0950+08), and the comparison of the proposed technique for this parameter determination with other existing techniques. Key words: pulse, dispersion measure, rotation measure, plasma, polarization, pulsar, radio telescope

Soliton interactions in certain square matrix nonlinear Schrödinger systems

This work deals with a class of square matrix nonlinear Schrodinger (MNLS) systems whose reductions include two equations that model hyperfine spin $$F = 1$$ spinor Bose–Einstein condensates in the focusing and defocusing dispersion regimes, and two novel (mixed sign) equations that were recently shown to be integrable. Our main goal is to discuss the bright soliton solutions and their interactions for the focusing MNLS and for the two mixed sign systems within the framework of the inverse scattering transform. The nature of the solitons and their interactions depend on whether the associated norming constants (polarization matrices) are rank-one matrices (giving rise to ferromagnetic solitons) or full rank (corresponding to polar solitons). By computing the long-time asymptotics of the 2-soliton solutions, we determine how the polarization matrix of each soliton changes because of the interaction. Explicit formulas for the soliton interactions are given for all possible types of interacting solitons, namely ferromagnetic–ferromagnetic, polar–polar, and polar–ferromagnetic soliton interactions, and for all three inequivalent reductions of the MNLS systems that admit regular bright soliton solutions. We also present bound states, representing 2 solitons travelling with the same velocity, for all three systems.

Spatial-polarization diversity HAP-MIMO transmission system for emergency high-capacity mobile communications

The deployment of high-altitude platforms (HAPs) as an emergency communication system is a cost-effective method to deal with the decrease in channel capacity caused by shadows or multipath fading at low elevation angles. This study proposes a 4 × 4 multiple-input multiple-output (MIMO) scheme that employs spatial and polarization diversity to improve the channel capacity for HAP communication systems. This scheme utilizes the advantages of HAP size to install two pairs of dual-polarized antennas between HAP and mobile terminals to form a 4 × 4 spatial-polarized diversity MIMO system to counteract shadows and multipath fading. The polarization and spatial correlation matrices are obtained through the reasonable expansion of a 2 × 2 polarized parametric or spatial geometry MIMO channel model. Simulation results show that the proposed 4 × 4 MIMO transmission scheme can effectively improve the channel capacity by 1.5 times compared with the existing satellite 2 × 2 dual-polarization MIMO system at low elevation angles under typical scenarios.

Mag2Pol: a program for the analysis of spherical neutron polarimetry, flipping ratio and integrated intensity data

Mag2Pol is a graphical user interface program which is devoted to the treatment of data from polarized neutron diffractometers with spherical polarization analysis. Nuclear and magnetic structure models can be introduced using space-group symbols and individual symmetry operators, respectively, and viewed in an OpenGL widget. The program calculates nuclear/magnetic structure factors, flipping ratios and polarization matrices for magnetic Bragg reflections, taking into account structural twins and magnetic domains. Spherical neutron polarimetry data can be analyzed by refining a magnetic structure model including magnetic domain populations in a least-squares fit and can also be correlated with an integrated intensity data set in a joint refinement. Further features are the simultaneous refinement of nuclear and magnetic structures with integrated intensity data and the analysis of flipping ratios either with tabulated magnetic form factors or using a multipole expansion of the magnetization density.

Topological derivative for the nonlinear magnetostatic problem

The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical engineering, we derive the topological derivative for an optimization problem which is constrained by the quasilinear equation of two-dimensional magnetostatics. Here, the main ingredient is to establish a sufficiently fast decay of the variation of the direct state at scale 1 as $|x|\rightarrow \infty$. In order to apply the method in a bi-directional topology optimization algorithm, we derive both the sensitivity for introducing air inside ferromagnetic material and the sensitivity for introducing material inside an air region. We explicitly compute the arising polarization matrices and introduce a way to efficiently evaluate the obtained formulas. Finally, we employ the derived formulas in a level-set based topology optimization algorithm and apply it to the design optimization of an electric motor.

Magnetic structure of the swedenborgiteCaBa(Co3Fe)O7derived by unpolarized neutron diffraction and spherical neutron polarimetry

We present a study that combines polarized and unpolarized neutrons to derive the magnetic structure of the swedenborgite compound $\mathrm{CaBa}({\mathrm{Co}}_{3}\mathrm{Fe}){\mathrm{O}}_{7}$. Integrated intensities from a standard neutron diffraction experiment and polarization matrices from spherical neutron polarimetry have been simultaneously analyzed revealing a complex order, which differs from the usual spin configurations on a kagome lattice. We find that the magnetic structure is well described by a combination of two one-dimensional representations corresponding to the magnetic superspace symmetry $P{2}_{1}^{\ensuremath{'}}$, and it consists of spins rotating around an axis close to the [110] direction. Due to the propagation vector $\mathbf{q}=(\frac{1}{3}00)$, this modulation has cycloidal and helicoidal character rendering this system a potential multiferroic. The resulting spin configuration can be mapped onto the classical $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structure of a kagome lattice, and it indicates an important interplay between the kagome and the triangular layers of the crystal structure.

Polarization monotones of two-dimensional and three-dimensional random electromagnetic fields

We propose a formal resource-theoretic approach to quantify the degree of polarization of two and three-dimensional random electromagnetic fields. This endows the space of spectral polarization matrices with the orders induced by majorization or convex mixing that naturally recover the best-known polarization measures.

Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo2(AsO4)2 frustrated honeycomb-lattice magnet

The magnetic properties of the cobaltite BaCo2(AsO4)2, a good realization of the quasi two-dimensional frustrated honeycomb-lattice system with strong planar anisotropy, have been reinvestigated by means of spherical neutron polarimetry with CRYOPAD. From accurate measurements of polarization matrices both on elastic and inelastic contributions as a function of the scattering vector Q, we have been able to determine the low-temperature magnetic structure of BaCo2(AsO4)2 and reveal its puzzling in-plane spin dynamics. Surprisingly, the ground-state structure (described by an incommensurate propagation vector k1=(kx,0,kz), with kx=0.270±0.005 and kz≈−1.31) appears to be a quasi-collinear structure, and not a simple helix, as previously determined. In addition, our results have revealed the existence of a non-negligible out-of-plane moment component ≈0.25μB/Co2+, representing about 10% of the in-plane component, as demonstrated by the presence of finite off-diagonal elements Pyz and Pzy of the polarization matrix, both on elastic and inelastic magnetic contributions. Despite a clear evidence of the existence of a slightly inelastic contribution of structural origin superimposed to the magnetic excitations at the scattering vectors Q=(0.27,0,3.1) and Q=(0.73,0,0.8) (energy transfer ΔE≈2.3 meV), no strong inelastic nuclear-magnetic interference terms could be detected so far, meaning that the nuclear and magnetic degrees of freedom have very weak cross-correlations. The strong inelastic Pyz and Pzy matrix elements can be understood by assuming that the magnetic excitations in BaCo2(AsO4)2 are spin waves associated with trivial anisotropic precessions of the magnetic moments involved in the canted incommensurate structure.

Frozen Acrylamide Gels as Dynamic Nuclear Polarization Matrices

AbstractAqueous acrylamide gels can be used to provide dynamic nuclear polarization (DNP) NMR signal enhancements of around 200 at 9.4 T and 100 K. The enhancements are shown to increase with crosslinker concentration and low concentrations of the AMUPol biradical. This DNP matrix can be used in situations where conventional incipient wetness methods fail, such as to obtain DNP surface enhanced NMR spectra from inorganic nanoparticles. In particular, we obtain 113Cd spectra from CdTe‐COOH NPs in minutes. The spectra clearly indicate a highly disordered cadmium‐rich surface.

Frozen Acrylamide Gels as Dynamic Nuclear Polarization Matrices.

Aqueous acrylamide gels can be used to provide dynamic nuclear polarization (DNP) NMR signal enhancements of around 200 at 9.4 T and 100 K. The enhancements are shown to increase with crosslinker concentration and low concentrations of the AMUPol biradical. This DNP matrix can be used in situations where conventional incipient wetness methods fail, such as to obtain DNP surface enhanced NMR spectra from inorganic nanoparticles. In particular, we obtain 113 Cd spectra from CdTe-COOH NPs in minutes. The spectra clearly indicate a highly disordered cadmium-rich surface.

Structure of polarimetric purity of three-dimensional polarization states

It has recently been demonstrated that a general three-dimensional (3D) polarization state cannot be considered an incoherent superposition of (1) a pure state, (2) a two-dimensional unpolarized state, and (3) a 3D unpolarized state [J. J. Gil, Phys. Rev. A 90, 043858 (2014)]. This fact is intimately linked to the existence of 3D polarization states with fluctuating directions of propagation, but whose associated polarization matrices R satisfy rank $\mathbf{R}=2$. In this work, such peculiar states are analyzed and characterized, leading to a meaningful general classification and interpretation of 3D polarization states. Within this theoretical framework, the interrelations among the more significant polarization descriptors presented in the literature, as well as their respective physical interpretations, are studied and illustrated with examples, providing a better understanding of the structure of polarimetric purity of any kind of polarization state.

Phenylazide Hybrid‐Silica – Polarization Platform for Dynamic Nuclear Polarization at Cryogenic Temperatures

Hyperpolarization of NMR‐active nuclei is key to gather high quality spectra of rare species and insensitive isotopes. We have recently established that silica‐based materials containing regularly distributed nitroxyl radicals connected to the silica matrix by flexible linkers can serve as promising polarization matrices for dynamic nuclear polarization (DNP). Here we investigate the influence of the linker on the efficiency of the polarization. The materials were fully characterized and exhibit high surface areas and narrow pore size distributions with a tunable amount of phenyl azide groups over a broad range of concentrations. The phenyl azide groups can be easily functionalized via a two‐step procedure with 4‐carboxy‐2,2,6,6‐tetramethyl‐1‐oxylpiperidine (TEMPO) to give polarizing matrices with controllable radical content. The DNP efficiency was found to be similar as in materials with flexible linkers, both for magic angle spinning at 105 K and dissolution DNP at 4 K.

Silica materials with wall-embedded nitroxides provide efficient polarization matrices for dynamic nuclear polarization NMR.

Hybrid mesoporous silica materials with wall-embedded nitroxides are shown to efficiently polarize impregnated substrates in high-field dynamic nuclear polarization magic-angle spinning solid-state NMR experiments.

Empirical Stochastic Modeling of Multipath Polarizations in Indoor Propagation Scenarios

In this contribution, a stochastic modeling approach is proposed for characterizing the polarization status of multipath components (MPCs) in propagation channels. The $2 \times 2$ polarization matrix of each MPC is represented by the geometrical parameters of two ellipses, i.e., the ovality, tilt angle, and size of each ellipse, as well as the rotating direction of electric field intensity along the ellipse. The statistics of these parameters including correlation behaviors among them extracted from measurement data constitute the stochastic polarization model for the propagation scenario of interest. Analytical expressions are presented for the transformation from the ellipse parameters to the $2 \times 2$ polarization matrix, and vice versa. Comparing with conventional polarization models addressing merely the cross-polarization ratios, the new model provides a more complete description for the per-path polarizations in terms of the power imbalance, tilting, and polarization spread. Furthermore, based on multiple-input multiple-output channel measurement data collected with 100-MHz bandwidth and at the center frequency of 5.25 GHz, stochastic polarization models of the proposed structure are extracted for five indoor scenarios. These models are complementary to the existing geometry-based stochastic channel models for generating realistic polarization matrices for MPCs.

The Eshelby Theorem and its Variants for Piezoelectric Media

We prove the Eshelby theorem for an ellipsoidal piezoelectric inclusion in an infinite piezoelectric material. Explicit formulas for the link and polarization matrices are derived. Passing to the limits with respect to parameters in the corresponding equations, the result is extended to cases when either the inclusion or the surrounding material is purely elastic.

Partial polarization theory of pulsed optical beams

We introduce a consistent matrix formalism for the characterization of partial polarization and coherence of random, nonstationary electromagnetic beams in time and frequency domains. We derive the temporal and spectral degrees of polarization and the Stokes parameters in terms of the time-domain and frequency-domain polarization matrices. The connections between temporal polarization and spectral coherence on the one hand and spectral polarization and temporal coherence on the other hand are discussed. Additionally, we establish equivalence theorems for fields with different temporal coherence properties to have the same spectral polarization states and for fields with different spectral coherence properties to possess identical temporal polarization. The theory is illustrated by analyzing specific examples of time-domain and frequency-domain electromagnetic Gaussian Schell-model pulsed beams.

Phase calculation for image rotation in a nonplanar polarization nulling interferometer

We propose a new matrix method for calculating geometric image rotation, taking into account the effects of the geometric and dynamic phases in a nonplanar optical layout. In order to describe the propagation of light in this system, the algebra of two-dimensional Jones polarization vectors and matrices in two-dimensional space is extended to three-dimensional space. We give practical examples of nonplanar layouts of polarization nulling interferometers for application in astronomy and precision wavefront analysis.