Poincare Sphere Research Articles

Robust Symbol Detection Based on Quaternion Neural Networks in Wireless Polarization-Shift-Keying Communications.

Quaternion neural networks (QNNs) form a class of neural networks constructed with quaternion numbers. They are suitable for processing 3-D features with fewer trainable free parameters than real-valued neural networks (RVNNs). This article proposes symbol detection in wireless polarization-shift-keying (PolSK) communications by employing QNNs. We demonstrate that quaternion plays a crucial role in the symbol detection of PolSK signals. Existing artificial-intelligence communication studies mainly focus on RVNN-based symbol detection in digital modulations having constellations in complex plane. However, in PolSK, information symbols are represented as the state of polarization, which can be mapped on the Poincare sphere and thus its symbols have a 3-D data structure. Quaternion algebra offers a unified representation to process 3-D data with rotational invariance and, therefore, it keeps the internal relationship among three components of a PolSK symbol. Hence, we can expect that QNNs learn the distribution of received symbols on the Poincare sphere with higher consistency to detect the transmitted symbols more efficiently than RVNNs. We compare PolSK symbol detection accuracy of two types of QNNs, RVNN, existing methods such as least-square and minimum-mean-square-error channel estimations, as well as detection knowing perfect channel state information (CSI). Simulation results including symbol error rate show that the proposed QNNs outperform the existing estimation methods and that they reach better results with two to three times fewer free parameters than the RVNN. We find that QNN processing will bring practical use of PolSK communications.

Simulating polarization characteristics of arbitrary-layer target systems’ infrared radiation by photon tracing strategy

It remains a big challenge to simulate and perceive polarization characteristics of coated targets’ infrared radiations, especially for the targets coated with several layers. In this paper, an arbitrary-layer radiational target system model (ARTSmodel) is constructed based on photon trace strategy (PTS) and Monte Carlo algorithm (MCA) to resolve this problem by continually tracing the evolution of the radiating photons’ state of polarization (SoP). In the proposed ARTSmodel, multiple scattering events among different coat layers are well represented, and the wide-band property of the radiations is accounted as well. Additionally, the infrared radiations are regarded as photon packages, and continually traced until they leave the topmost layer and get captured by the sensors bestrewing the entirely upper hemisphere space, whose values will form an upper-hemisphere-space polarization data (UPD) distribution. The UPD is compared with the analytic method and empirical data, and the consistency of results evidences the effectiveness and reliability of the proposed model. Moreover, the UPD and its representation in the Poincare sphere demonstrate that the proposed model provides a new and practicable way to coated target identification and analysis.

Upper limit on the polarization-assisted amplitude modulation capability of cascaded single-cell wave-plate-like metasurfaces.

The Jones matrix method offers a robust framework for designing polarization multiplexed metasurfaces (PMMs). Traditional PMMs design involves initially defining functions and working channels, then mapping feature functions to adjustable parameters of metasurfaces. However, this approach makes it difficult to predict how working channels affect metasurface features. Here, we employ the generalized Malus law and Rodriguez rotation matrix on the Poincare Sphere to analyze diverse working channels' impact on PMMs' amplitude modulation capacity. For single-celled waveplate-like PMMs, up to three distinct images can be displayed. We demonstrate this in both theoretic method and numerical simulations. Our study establishes a framework for multi-channel amplitude modulation design of metasurfaces, applicable in information encryption, optical computation, diffraction neural networks, etc.

Spatial Varying Vectorial Holography and Polarization Encryption Based on Birefringent Metasurface

AbstractVectorial holography technology plays a fundamental role by exploring the vectorial nature of light and enriches disruptive applications in optical encryption, display, and manipulation. With its flexible control methods and high‐precision subwavelength design, metasurface possesses rich modulation flexibility that surpasses traditional optical modulation devices. Here, a vectorial holographic design is implemented that can cover various polarization information by using a birefringent metasurface. The design adopts a gradient descent optimization method to jointly optimize the phase information of the orthogonal polarization channels with the birefringent metasurface, for continuous variation of polarization information in the entire vector space on the Poincare Sphere with efficient information integration. Based on the detailed depiction of full vector space polarization texture, such efficient vectorial holographic optimization methods can expand the encryption channels and achieve high spatial resolution allowing large capacity multiplexing, data storage, pattern recognition, etc.

Pseudo coherent-perfect-absorption approach toward perfect polarization conversion

Polarization is one of the essential properties of light. Thereby, its manipulation is important for numerous applications. When employing a resonance in a mirror-symmetry system to manipulate polarization, non-zero residual light in the excited polarization channel leads to the shrink in the scope of the polarization manipulation, and a perfect polarization conversion cannot occur. In this work we show that the concept of coherent perfect absorption can be applied to perfect polarization conversion for circular polarization states. We find that the only requirement to achieve a perfect polarization conversion is that the working frequency is the resonant one. More importantly, the range of the output polarization states can be efficiently enlarged, and can span the entire Poincare sphere by combining the momentum dependent radiative coupling rate driven by the bound states in the continuum (BIC) and the phase delay. When applied to realistic design, we adopt a guided mode resonance driven from the symmetry protected BICs in a dielectric photonic crystal slab. Numerical results are in good agreements with our theoretical predictions. We believe this work can deliver important benefits for a variety of applications based on the efficiently light polarization control and management.

Optimized configuration for liquid crystal Stokes polarimeters in the presence of fast-axis orientation errors.

We present an optimal configuration for Stokes polarimeters based on liquid crystal variable retarders, with the minimum number of measurements. Due to the inherent variations of the director orientation of the liquid crystal molecules, we propose a configuration that minimizes the sensibility of the polarimeter to fast-axis variations. For the optimization we consider a scheme that maximizes the volume of a tetrahedron inscribed in the Poincare sphere, to address additive and Poisson noise, with one of the vertices invariant to changes in the axis positions. We provide numerical simulations, considering misalignment errors, to analyze the robustness of the configuration. The results show that the proposed configuration helps to maintain the volume enclosed by the tetrahedron with high tolerance to fast-axis orientation errors. The condition number will remain below 3.07 for common misalignment errors and below 1.88 for more controlled liquid crystals. This optimization will improve the performance of liquid crystals polarimeters, with a more robust configuration that also considers misalignment errors, beyond additive and Poisson noise.

Full characterization of vector eigenstates in symmetrically confined systems with photonic spin-orbit coupling.

The photonic spin-orbit (SO) coupling is a widely investigated effect in optical microcavities leading to various interesting physical phenomena and potential applications. We report the full sets of eigenenergies and eigenstates in a symmetrically confined potential under the effect of SO coupling induced by the transverse-electric transverse-magnetic (TE-TM) splitting, which are derived analytically via the degenerate perturbation theory. We obtained the eigenenergies and the eigenstates from the 1st to the 6th orders of excited manifold, and demonstrate unambiguously that universal rules governing the mode formation exist in such complicated photonic systems, making the modes exhibiting the features of solid and hollow skyrmions as well as spin vortices. We show that these eigenstates can be described by the SO coupled hyperspheres that can be decomposed into a series of higher-order Poincare spheres. Our results significantly extend the area of microcavity spin-optronics to the general theory of eigenvalues in confined systems, and provide an efficient theoretical frame for the information processing using microcavity-based high-dimensional vector states.

Interaction of four level closed loop atomic systems in the presence of two vector beams

In this manuscript, we have theoretically studied the four level closed loop atomic systems in the presence of two vector beams. A spatially dependent transparency for the probe vector beam is obtained based on the semiclassical model. We have explicitly shown that the number of petals formed for probe absorption depends on the value of orbital angular momentum (OAM) of the constituting beams. A detailed study for absorption and dispersion of right circularly polarized (RCP) and left circularly polarized (LCP) components of the probe beam is carried out and the importance of the polarization state of the beams on Higher Order Poincare Sphere (HOPS) is highlighted. An explicit effect of the interferometer phase of the vector beam which is geometric in nature, is shown for probe beam response. Three types of four level closed loop atomic system is studied with particular emphasis given for double Λ and Diamond atomic system. A dark state analysis of the atomic system is carried out which facilitate a physical understanding of the obtained results. Our study has explored the effects of inhomogeneity in both polarization and intensity for probe and coupling beam in a closed loop atomic system which is phase dependent.

Arbitrary Achromatic Polarization Control with Reconfigurable Metasurface Systems

AbstractDynamic control over the polarization state of light is foundational for many scientific and technological applications, yet it remains a challenge to dynamically tailor responses with arbitrary polarization bases over a broad bandwidth. Broadband metasurface systems that utilize microscale displacements between two metasurfaces to enable reconfigurable polarization responses within a predefined polarization basis are reported. The metasurface pairs form an interferometer, and the lateral displacements produce detour phase shifts within the interferometer beam paths that mediate polarization state tuning. It is shown how the metasurface systems can be designed using freeform topology optimization to enable tailorable elliptical birefringence responses over a large bandwidth and how cascaded metasurface systems can enable the mapping of input and output polarization states between any two points on the Poincare sphere. It is anticipated that these concepts will have utility in imaging, display, communications, and metrology applications in classical and quantum optical domains.

Full Stokes polarimetry using a monolithic off-axis polarizing interferometer and a 2D array sensor.

This paper describes a full Stokes polarimeter employing a monolithic off-axis polarizing interferometric module and a 2D array sensor. The proposed passive polarimeter provides a dynamic full Stokes vector measurement capability of around 30Hz. As the proposed polarimeter employs no active devices and is operated by employing an imaging sensor, it has significant potential to become a highly compact polarization sensor for smartphone applications. To show the feasibility of the proposed passive dynamic polarimeter scheme, the full Stokes parameters of a quarter-wave plate are extracted and displayed on a Poincare sphere by varying the polarization state of the measured beam.

Arbitrary Polarization Syntheses Based on Spin‐Momentum Locking in Spoof Surface Plasmon Polaritons

AbstractSpin‐momentum locking is universal and an inherent property of evanescent electromagnetic (EM) waves, which transfers the spinning or handedness of electromagnetic waves onto their propagation direction. This motivates an approach to investigate the polarization‐controlled directional transmission or emission. Here, the spin‐momentum locking is demonstrated in spoof surface plasmon polariton (SSPP) waveguides, and momentum‐controlled radiation is further realized in SSPP‐patch antennas. The study shows that the circular polarization of the SSPP‐patch antennas originates from the spin‐momentum locking in the SSPP waveguides and hence is determined by the propagation direction of the SSPP modes. Two examples are presented to achieve ±45° dual‐polarizations and vertical/horizontal dual‐polarizations by combining the SSPP‐patch antenna with hybrid couplers. Finally, a straightforward method is proposed for synthesizing the polarization emitted by the SSPP‐patch antenna, allowing access to arbitrary polarization states on the Poincare sphere. The SSPP‐patch antenna is polarization responsive, shedding light on chiral sensors, Stokes polarimetry, and polarization measurement. Hence, the spin‐momentum locking and the related momentum‐controlled radiations provide additional freedom to regulate the EM waves by engineering the helicity in the SSPP waveguide.

Probing non-classicality of primordial gravitational waves and magnetic field through quantum Poincare sphere

The universe is believed to be originated from a quantum state. However, defining measurable quantities for the quantum properties in the present universe has gained interest recently. In this submission, we propose a quantum Poincare sphere as an observable quantity that can hint at the quantumness of primordial gravitational waves and large-scale magnetic fields. The Poincare sphere is defined in terms of quantum stokes operators associated with the polarization of those fields, which can be measured directly. We have further studied the effects of the initial non-BD vacuum on the power spectrum and squeezing parameter of the primordial gravitational waves and magnetic field. We have found that the initial non-BD vacuum increases the value of the squeezing parameter as expected at the end of inflation, which further enhances the possibility of measuring the quantumness of the fields under consideration. To support our results, we further explored the possible Bell violation test for a set of generalized pseudo spin operators defined in the polarization space of those fields.

Single shot polarimetric characterization of the polymer based flexible polyethylene terephthalate substrate

AbstractConducting polyethylene terephthalate (PET) substrates used for the flexible electronics and photonics are birefringent in nature. Birefringence of the PET substrate increases with the external applied stress. In this paper, we have studied the state of the polarization of the light transmitted through the flexible PET substrate. Polarimetric characterization of flexible substrate was done for red and yellow wavelengths of light. Single shot three beams interference was recorded by the polarizing Mach–Zehnder interferometer. Interferograms were recorded without bending and different external bending applied to the substrate which increases the stress. The recorded interferograms was analyzed by the Fourier transform fringe (FTF) analysis method. The single shot interferograms have the information of the amplitude and phase of orthogonally polarized field components. Stokes parameters were calculated from orthogonal polarization component extracted from the single shot interferograms analyzed by FTF. Calculated Stokes parameters were plotted on the Poincare sphere to see the change in the state of polarization (SOP) of the light transmitted through these substrates. The change in the SOP of the transmitted light was observed without and with the external stress applied to the PET substrate due to its birefringence characteristic.

Faraday Conversion in Pair-symmetric Winds of Magnetars and Fast Radio Bursts

We consider the propagation of polarization in the inner parts of pair-symmetric magnetar winds, close to the light cylinder. Pair plasmas in magnetic field is birefringent, a ∝ B 2 effect. As a result, such plasmas work as phase retarders: Stokes parameters follow a circular trajectory on the Poincare sphere. In the highly magnetized regime, ω, ω p ≪ ω B , the corresponding rotation rates are independent of the magnetic field. A plasma screen with dispersion measure DM ∼ 10−6 pc cm−3 can induce large polarization changes, including large effective rotation measures (RMs). The frequency scaling of the (generalized) RM, ∝ λ α , mimics the conventional RM with α = 2 for small phase shifts, but can be as small as α = 1. In interpreting observations, the frequency scaling of polarization parameters should be fitted independently. The model offers explanations for (i) the large circular polarization component observed in FRBs, with right–left switching; (ii) large RM, with possible sign changes (when the observation bandwidth is small); and (iii) time-dependent variable polarization. A relatively dense and slow wind is needed—the corresponding effect in regular pulsars is small.

Magnetic error suppression in Polarization-Maintaining fiber optic gyro system with orthogonal polarization states

In this paper, a polarization-maintaining fiber optical gyro (PMFOG) based on orthogonal polarization states is constructed. The clockwise light and counterclockwise light in the PMFOG pass through the same fiber coil with X/Y polarization and Y/X polarization respectively. Theory and experiments have shown that this system not only doubles the sensitivity of the PMFOG at the same length, but also suppresses the magnetic error obviously compared with the single-polarization PMFOG. The Poincare sphere model is established in the PMFOG with orthogonal polarization states under the radial magnetic field, which intuitively shows that magnetic error is opposite in the orthogonal polarization state, and can offset through each other. The radial magnetic error is suppressed from 0.112°/h/Gs to 0.011°/h/Gs, and the suppression reaches 10.07 dB. Meanwhile, the axial magnetic error is suppressed from 0.183°/h/Gs to 0.092°/h/Gs, achieving a suppression effect of 2.9 dB. The results of this research are of great significance to the miniaturization, the improvement of signal-to-noise ratio, and the optimization of environmental adaptability in fiber optic gyroscope.

Dual-Mode Index Modulation Aided 3D-OFDM

In this letter, a novel modulation scheme named orthogonal frequency division multiplexing (OFDM) using dual-mode three-dimensional (3D) constellation is proposed, which is capable of enhancing spectral efficiency (SE) and energy efficiency (EE) compared with the conventional 3D-OFDM. In the proposed scheme, the subcarriers are divided into two groups and modulated by dual-mode 3D constellations. Extra information bits are conveyed by the index pattern without energy consumption. Dual-mode 4- and 8-ary 3D constellations are designed and the signal points are distributed on the surface of Poincare sphere. Two detectors based on the maximum likelihood (ML) and log-likelihood ratio (LLR) are employed at the receiver. The simulation results demonstrate that error performance of the proposed scheme is significantly better than the conventional 3D-OFDM in high signal-to-noise ratio (SNR) region under the Rayleigh and Rician fading channels.

Spatial dynamics of light quasispin vector in an anisotropic medium with twisting

On the Poincar's sphere the spatial evolution of the light's polarization state has been studied quantitatively in the smoothly inhomogeneous anisotropic media with gyrotropy. The main features of the dependence on the sample?s thickness, the gyration vector and the azimuth of the polarization of the incident linearly polarized wave were revealed. An analytical solution of the system of coupled equations relative to Cartesian components of light's wave electric component obtained by transition to rotating coordinate system has been used for analysis. Keywords: Poincar' sphere, polarization evolution, medium with gyrotropy, rotating coordinate system.

Characterization of Biological Tissue Structures Using Poincare Sphere

Characterization of Biological Tissue Structures Using Poincare Sphere

Polarization-Aware Prediction of Mobile Radio Wave Propagation Based on Complex-Valued and Quaternion Neural Networks

It is important to predict the characteristics of radio waves propagating in wireless environment for compensating information loss caused by fading effects. Though fading is often analyzed as the changes of intrinsic electric-field phasor describing a communication channel, it is also attributed greatly to its polarization state (PS). In this paper, we propose PS and phasor prediction methods based on quaternion neural networks (QNNs) and complex-valued neural networks (CVNNs). Quaternion is a hypercomplex number system for representing three dimensional (3-D) spatial rotation and orientation. It realizes adaptive prediction more stably and effectively than a real-valued rotation matrix. The time trajectories of PS are expressed as 3-D rotational motions on the Poincare sphere. We show that QNNs learn the spatiotemporal movements of the PS with high generalization ability and thus provide a superior prediction performance. In addition, CVNNs are efficient predictors for processing complex-valued signals such as the phasor of an incident wave. We evaluate the precision of the proposed QNN-CVNN prediction scheme in channel equalization in a time-division-duplex (TDD) orthogonal-frequency-division-multiplexing (OFDM) communication system. In physical wireless-environment experiments, we find that the proposed scheme provides 3.0 dB and 6.0 dB improvements of bit error rate (BER) at 10^-4, showing almost the same BER performance as a system perfectly knowing the actual radio-wave characteristics in future TDD frames. Accordingly, this work also reveals that PS needs to be considered as one of the significant characteristics in various radio-wave systems in the near-future technology.

Polarization sensitive optical coherence tomography with single input for imaging depth-resolved collagen organizations

Collagen organization plays an important role in maintaining structural integrity and determining tissue function. Polarization-sensitive optical coherence tomography (PSOCT) is a promising noninvasive three-dimensional imaging tool for mapping collagen organization in vivo. While PSOCT systems with multiple polarization inputs have demonstrated the ability to visualize depth-resolved collagen organization, systems, which use a single input polarization state have not yet demonstrated sufficient reconstruction quality. Herein we describe a PSOCT based polarization state transmission model that reveals the depth-dependent polarization state evolution of light backscattered within a birefringent sample. Based on this model, we propose a polarization state tracing method that relies on a discrete differential geometric analysis of the evolution of the polarization state in depth along the Poincare sphere for depth-resolved birefringent imaging using only one single input polarization state. We demonstrate the ability of this method to visualize depth-resolved myocardial architecture in both healthy and infarcted rodent hearts (ex vivo) and collagen structures responsible for skin tension lines at various anatomical locations on the face of a healthy human volunteer (in vivo).