Search Results (35)

Extrinsic chiral metasurfaces offer a promising route for controlling chiroptical responses through incident angle variation, yet the simultaneous realization of strong circular dichroism and full-space polarization beam splitting remains challenging. In this work, we propose an all-dielectric extrinsic chiral metasurface that leverages obliquely incident terahertz waves to break in-plane symmetry, thereby activating out-of-plane multipoles and inducing strong spin-selective scattering. At an incident angle of 30°, the metasurface achieves efficient full-space separation of left- and right-handed circularly polarized waves, with a circular dichroism peak exceeding 0.7 near 0.48 THz. Moreover, by varying the incident angle or operating frequency, the polarization state of the reflected wave can be continuously tuned from linear to elliptical to nearly circular, as visualized on the Poincaré sphere. This angle-dependent, full-space polarization manipulation capability highlights the potential of the proposed metasurface for applications in advanced terahertz imaging, LiDAR, and integrated photonic systems. Full article

High-order Poincaré sphere (HOPS) beams have attracted tremendous interest due to their complex polarization and phase characteristics. However, manipulating the second harmonics generation (SHG) of HOPS beams is still challenging. Here, we developed a vector-coupled wave model to predict petal-shaped intensity patterns and reveal a linear correlation between petal number and topological order (n = 2 → 4). Moreover, we experimentally investigated the multidimensional regulation of SHG in HOPS beams through tailored phase-matching strategies. By employing three distinct configurations—(i) type-I phase matching, (ii) type-II phase matching, and (iii) orthogonally arranged BBO crystals based on Type-I phase matching—we establish a comprehensive framework for controlling the spatial and polarization properties of SHG in n = 2 HOPS beams. These results advance the manipulation of structured light in nonlinear optics, providing insights for optimizing applications in optical communication and polarization imaging. Full article

The manipulation of vector beams (VBs) with longitudinally variant polarization states is an important research topic and has potential applications in classical and quantum fields. In this study, we propose a half-wave plate dielectric metasurface composed of two interleaved sub-metasurfaces to generate longitudinally separated dual-channel vectorial structured light fields. The propagation and Pancharatnam–Berry phases are employed to construct hyperbolic, helical, and opposite gradient phases for focusing wavefronts, generating circularly polarized (CP) vortices, and deflecting CP vortices with the same chirality in opposite directions. Consequently, dual-channel higher-order or hybrid-order Poincaré (HOP or HyOP) beams are generated along the optical axis under elliptically polarized illumination, and their polarization states evolve along an arbitrary pair of antipodal meridians on the HOP or HyOP sphere by varying the ellipticity of the incident light, the propagation-phase topological charge, and the rotation order of the meta-atom. The consistency between the theoretical and simulated results demonstrates the feasibility and practicability of the proposed method. This study is significant for compact, integrated, and multifunctional optical devices, and provides an innovative strategy to extend optical field manipulation from two-dimensional to three-dimensional space. Full article

Polarimetric information is essential for scattering interpretation and target characterization in synthetic aperture radar (SAR) remote sensing, yet many resource-constrained platforms (e.g., small satellites and unmanned aerial vehicles (UAVs)) operate with limited polarization modes or even a single radio frequency (RF) chain, which limits full polarimetric scattering acquisition. To address this limitation, this paper proposes a single-channel framework for estimating the full polarization scattering matrix (PSM) enabled by time-varying polarization modulation. The transmit/receive polarization states are steered along predefined trajectories on the Poincaré sphere to generate time-varying polarization tags that are encoded into the received echoes through the target’s polarization-varying response. A compact observation model is then derived to relate the single-channel echoes, the known polarization tags, and the unknown PSM; based on this, the PSM is then estimated via a least squares formulation with a low-rank approximation. Simulation results demonstrate the robust reconstruction of the full polarimetric scattering matrix under diverse modulation trajectories. For arbitrarily chosen random point targets, when the signal-to-noise ratio (SNR) exceeds −20 dB, the polarimetric similarity coefficient approaches 1, and the estimation errors of Pauli power components converge toward zero. Furthermore, the method’s reliability is validated on distributed vegetation clutter. Quantitative metrics demonstrate near-perfect statistical consistency, with polarimetric entropy and alpha angle errors within 0.14%. Overall, the proposed approach provides a practical pathway to enhance the availability of full polarimetric scattering information under limited-observation conditions, confirming its feasibility for downstream analysis in complex natural scenes while maintaining a single radio frequency (RF) chain architecture augmented by a polarization modulator. Full article

Macroporous silica thin films were synthesized via the sol–gel method to elucidate the relationship between pore structure and the degree of polarization of light (DoP). The films were characterized by scanning electron microscopy (SEM) to determine their mean pore size and surface porosity, while polarization-resolved speckle imaging was employed to evaluate the degree of polarization and its distribution on the Poincaré sphere. The results show that surface porosity is a key structural parameter governing the DoP, with increasing values leading to enhanced scattering and a progressive isotropization of the polarization-state distributions. Poincaré sphere mapping further reveals distinct scattering regimes and polarization-conversion pathways, providing insights that are not accessible with conventional optical measurements. Overall, these findings show that speckle imaging is a rapid, cost-effective, and non-destructive approach to probing structural and optical anisotropies in porous materials, with direct relevance to systems where pore accessibility dictates performance, including liquid-crystal devices, photochromic coatings, and other nanostructured photonic platforms. Full article

In this paper we compare the rotation of a rigid body in the real three-dimensional Euclidean space E³ and its representation in the complex plane (Klein space), on one hand, with the transformation of polarization states of light (SOPs) by the phase-shifters figured in the complex plane and on the Poincaré sphere, on the other hand. Both the Klein space, in classical mechanics, and the Poincaré sphere, in polarization theory, are abstract spaces, whose construction is based on the classical stereographical projection between Riemann sphere and the simple complex plane C¹. They are classical abstract spaces, even if they have been largely used for representing quantum spinorial physical realities too. At the interface of classical/quantum physics persist some misaperceptions about what is intrinsically of quantum origin and nature, and what is imported from the classical domain. In this context we examine some misunderstandings that take place in the field of these spaces. I shall focus on the double angle relationship between the rotation of representative points of the SOPs on the Poincaré sphere with respect to the corresponding rotations of the azimuthal and ellipticity angles of the “form of the SOPs”, at a transformation of state given by a phase shifter. This is a classical result, that is transferred on the sphere from the complex plane, on the basis of the stereographic bijective connection between the points on the sphere and those in the complex plane. In any textbook of quantum mechanics “the double angle/half angle problem” is presented as a pure quantum spinorial one, avoiding its classical face and origin. A quantum spinorial approach, obviously, recovers the classical results, together with the specific spinorial ones, but with regards to the double angle/half angle issue it is superfluous. We shall also briefly examine the classical and quantum spinorial content of what we know today under the global name of Pauli spin matrices. Often in papers or textbooks of physics the results are presented in a mélange in which it is difficult to establish from which point on one needs to appeal to spinorial or quantum aspects. Full article

This paper starts with the transition from classical physics to quantum mechanics which was greatly aided by the concept of phase space. The role of canonical transformations in quantum mechanics is addressed. The Wigner phase-space distribution function is then defined which arises from the formulation of the density matrix, followed by the harmonic oscillator in phase space. Coherent and one- and two-mode squeezed states of light as well as the squeezed vacuum are discussed in the phase-space picture. Attention is also drawn to the fact that squeezed states naturally generate entanglement between the two-modes. Coupled harmonic oscillators are also elucidated in connection with the Wigner phase space. Note that the phase-space picture of quantum mechanics has become an important scientific language for the rapidly expanding field of quantum optics. Here, we mainly focus on the simplest form of the Wigner function, which finds application in many branches of quantum mechanics. We make use of several symmetry groups such as Lorentz groups, the symplectic group in two and four dimensions, and the Euclidean group. The decoherence problem of an optical field is examined through a reformulation of the Poincaré sphere as a further illustration of the density matrix. Full article

Over the past thirty years, the focus in singular optics has been on structured beams carrying orbital angular momentum (OAM) for diverse applications in science and technology. However, as practice has shown, the OAM-free structured Gaussian beams with several degrees of freedom are no worse than the OAM beams, especially when propagating through turbulent flows. In this paper, we partially fillthis gap by theoretically and experimentally mapping cyclic changes in vortex-free states (including OAM) as a phase portrait of the beam evolution in an astigmatic optical system. We show that those cyclic variations in the beam parameters are accompanied by the accumulation of the geometric Berry phase, which is an additional degree of freedom. We find also that the geometric phase of cyclic changes in the intensity ellipse shape does not depend on the radial numbers of the Laguerre–Gaussian mode with zero topological charge and is always set by changing the shape of the Gaussian beam. The Stokes parameter formalism was developed to map the beam states’ evolution onto a Poincaré sphere based on physically measurable second-order intensity moments. Theory and experiment are found to be in a good enough agreement. Full article

In this paper, the far-field topological structures (FFTSs) of the second harmonic (SH) from higher-order Poincaré sphere (HOPS) beams, including circularly polarized vortex beams (VBs), cylindrically vector beams (CVBs) and elliptically polarized CVBs (EPCVBs), were demonstrated and reported. To begin with, the hidden FFTSs of the SH after propagating the twice Rayleigh range were simulated based on the vectorial coupled wave equations and the Collins formula. Then, the experimental setup was established to achieve the SH from the HOPS by applying two orthogonal 5% MgO: PPLN crystals, the FFTSs of which were demonstrated. The theoretical and experimental results indicate that for the circularly polarized VBs, the FFTSs of the SH still exhibit the 135°-linearly polarized VBs, which is similar to that of the SH in-source plane, because the SH is the eigen-mode of free space, while for the CVBs, the FFTSs of the SH generally show the disappearance of the central dark core, replaced by the maximum light intensity at the center due to the topological phase transition during propagation. Especially of note, for the EPCVBs, the FFTSs of the SH display the maximum light intensity at the center, but the FFTSs in the horizontal and vertical directions reveal rotational symmetry related to the chirality of the EPCVBs. The results reveal the evolution mechanisms of the SH from the HOPS in the far field, which may facilitate the applications of the SH from HOPS beam. Full article

If spacetime is a physical object, it is conceivable that it loses its integrity or is destroyed in some way as a continuum in an abrupt process initiated in spacetime itself. An example is a gravitational collapse leading to a spacetime singularity, as in the interior of a black hole. We find a conservative extension of quantum mechanics by quantum set theory over the singular domain and show that it is reconcilable with the special extension of spacetime 4-diffeomorphisms by automorphisms of Boolean models of set theory. The extension of quantum mechanics supports the random sequences of the quantum mechanical outcomes that can negate Tsirelson’s conjecture, whereas the extension of 4-diffeomorphisms indicates the role of exotic smooth 4-spheres as gravitational instantons. This leads to the negation of the smooth 4-dimensional Poincaré conjecture before its final resolution by mathematicians. We also discuss the case where the Poincaré conjecture would remain true. Full article

Vector beams (VBs) with longitudinally varying polarization states provide a new dimension for light field manipulation, and promote the advancements of related areas such as optical metrology, longitudinal depth detection, and classical and quantum communications. In this study, we propose a half-wave plate dielectric metasurface based on a spatial partitioning method, realizing the longitudinal manipulation of the polarization states of higher-order Poincaré (HOP) beams by changing the elliptical polarization state of the incident light and selecting the appropriate propagation distances. The metasurface is composed of two sub-metasurfaces, and the two sets of a-Si:H meta-atoms are uniformly arranged on concentric rings of different radii with an equal interval. The propagation and Pancharatnam–Berry phases are utilized to construct the axicon and helical phase profiles. As a result, two sub-metasurfaces, respectively, generate the first- and second-order VBs with longitudinally varying polarization states. The polarization states of generated VBs correspond to points on different meridians of nth-order HOP spheres from the south pole to the north pole. The consistency between the theoretical and simulated results demonstrates the feasibility and practicability of the proposed method. This study provides an innovative strategy to extend the modulation of light fields from two-dimensional to three-dimensional space. Full article

We present a framework to optimize the voltage range of electro-optic polarization controllers (EPC) in polarization-based quantum key distribution (QKD) subsystems. In this study, we consider an EPC capable of modifying both the phase difference between its fast and slow axes and the orientation of the fast axis. This capability allows it to transform any input state of polarization (SOP) into any desired output SOP on the Poincaré sphere using a single wave-plate. When multiple wave-plates are available, properly distributing the required polarization modulation across them effectively reduces the electronic demands, lowers the implementation costs, and enhances the polarization modulation speeds. This optimization is achieved through the application of multi-objective optimization (MOO) and wave-plate splitting techniques. Within a simulation model, using the calibration parameters from a commercially available six-wave-plate EPC, we determined the optimized voltage ranges required to achieve the six, four, and three SOPs typically used in polarization-based QKD protocols. Two voltage reference points are considered in our study: bias voltage points, which result in zero birefringence, and zero voltage points. For optimization procedures centered around the bias voltage points, we observe a significant reduction in the voltage range, from $\pm 37$ V, for a single wave-plate, to approximately $\pm 6$ V, for six wave-plates. Furthermore, using wave-plate splitting techniques, we conclude that only two independent wave-plates (four variables) need to be considered in our model to achieve optimized results, which contributes to the efficient design of polarization-based QKD subsystems by minimizing voltage transitions while ensuring precise SOP control, ultimately enabling cost-effective and high-speed polarization modulation. Full article

Quarter-wave plate (QWP) metasurfaces provide a novel approach for generating three-dimensional (3D) hybrid-order Poincaré sphere (HyOPS) beams and enabling longitudinal polarization modulation, owing to their unique spin-decoupling properties. In this work, we designed a set of QWP meta-atom metasurfaces that generate 3D HyOPS beams with continuously varying polarization states along the propagation direction. The third-, fourth- and fifth-order HyOPS beams are generated by three metasurface devices, respectively. The HyOPS beams exhibit a focal depth of 30 μm, a stable longitudinal propagation, and a continuously evolving polarization state. Notably, complete polarization evolution along the equator of the HyOPS occurs within a depth of 20 μm. Numerical calculations in MATLAB R2022b validated the feasibility of the designed QWP metasurfaces. The finite-difference time-domain (FDTD) simulations further confirmed the stable propagation and continuous polarization evolution of the longitudinal light field. Additionally, the concentric arrangement of the QWP meta-atoms on the metasurface effectively mitigates scattering crosstalk caused by abrupt edge phase variations. This work offers new insights into the generation and control of HyOPS light fields and contributes significantly to the development of miniaturized, functionally integrated high-performance nanophotonics. Full article

An analogy with the polarization Stokes parameters and symplectic methods of the second-order intensity moment matrix allowed us to develop a simple technique for measuring the orbital Stokes parameters followed by mapping the structured beam states onto the orbital Poincaré sphere. The measurement process involves only two shots of the beam intensity patterns in front of a cylindrical lens and in its double focus. Such a simple measurement approach is based on the reciprocity effect between the experimentally measured cross-intensity element $W_{xy}$ and the orbital angular momentum of the intensity moment matrix. For experiments, we chose two types of two-parameter structured beams, namely, structured Laguerre–Gaussian beams and binomial beams. We obtained a good agreement between our theoretical background and the experiments, as well as the results of other authors. Full article

We present one of the main lines of development of Poincaré sphere representation in polarization optics, by using largely some of our contributions in the field. We refer to the action of deterministic devices, specifically the diattenuators, on the partial polarized light. On one hand, we emphasize the intimate connection between the Pauli algebraic analysis and the Poincaré ball representation of this interaction. On the other hand, we bring to the foreground the close similarity between the law of composition of the Poincaré vectors of the diattenuator and of polarized light and the law of composition of relativistic admissible velocities. These two kinds of vectors are isomorphic, and they are “imprisoned” in a sphere of finite radius, standardizable at a radius of one, i.e., Poincaré sphere. Full article