Poincare Sphere Research Articles

Cytomembrane visualization using Stokes parameter confocal microscopy.

A new, to the best of our knowledge, method for Stokes vector imaging is proposed to achieve imaging and dynamic monitoring of a non-labeled cytomembrane. In this work, a polarization state vector is described by a Stokes vector and expressed in chrominance space. A physical quantity called polarization chromaticity value (PCV) corresponding to a Stokes vector is used as the imaging parameter to perform Stokes vector imaging. By using the PCV imaging technique, the Stokes vector can be expressed in three-dimensional real space rather than in a Poincare sphere. Furthermore, a four-way Stokes parameter confocal microscopy system is designed to measure four Stokes parameters simultaneously and obtain micro-imaging. Label-free living onion cell membranes and their plasmolysis process are selected as the representative micro-anisotropy experimental analysis. It is proved that PCV imaging can perform visualization of cytomembranes, and further, microscopic orientation is demonstrated. The prospect of universal measurement of anisotropy details for analysis and diagnosis is provided.

Generalized framework of weak-value amplification in path interference of polarized light for the enhancement of all possible polarization anisotropy effects

Using the profound interferometric philosophy of weak value amplification, we propose a simple, general and a robust polarization method for the amplification and quantification of small magnitudes of all possible polarization anisotropy effects in a single experimental embodiment. The approach is experimentally realized by introducing a weak coupling between the polarization degree of freedom of light and the path degree of freedom in a Mach-Zehnder interferometer in the presence of a weak anisotropy effect. Real and imaginary weak value amplifications of different polarization anisotropy effects are manifested as characteristic changes in relevant Stokes vector elements at the exit port of the interferometer, which follow orthogonal trajectories in the Poincare sphere. The proof of concept experiment demonstrates that using this scheme, one can faithfully extract and quantify anisotropy parameter that is smaller than the typical sensitivity of measurement of a given Stokes parameter of a traditional polarimeter by a large weak value amplification factor. This opens up possibility of a sample measuring weak value polarimeter for studying rich variety of fundamental optical effects and for materials characterization and precision metrology.

Study on the Laser Beam Polarization Based on LabVIEW

With the wide application of laser technology in laser processing and photoelectric detection, the measurement and display of the laser beam polarization has become an extremely important prerequisite. In this paper, we realize the laser polarization measurement tool based on the virtual instrument LabVIEW software platform. The set-up is designated to measure the Stokes parameters for an arbitrarily polarized beam, using the rotating waveplate method provided by the stepper motor, drive circuit, photodetector, and computer processing of the digitized electrical signal in the PCI expansion card. The Poincare sphere is used for the interpretation of the state of polarization (SOP) and degree of polarization (DOP). The working wavelength range is declared to be 400 – 1100 nm, the accuracy of DOP, azimuth measurement, and ellipticity are ±2%, 0.4°, and 0.4°, respectively.

Several Classes of Plain Dynamic Systems Qualitative Investigation

Dynamic systems in applications are useful as mathematical models of those processes and phenomena, where statistical events, or fluctuations, may be disregarded. Dynamic systems may be divided into the two main categories – the systems with continuous time (the flows) and systems with discrete time (the cascades). During the investigations of flows normal autonomous systems of ordinary differential equations are used. The present work is devoted to the original rigorous research of some important family of dynamic systems having reciprocal polynomial right parts, which are the forms of theirs phase variables. The whole wide family under consideration is being split into numeric subfamilies belonging to different hierarchical levels, and is subjected to the first and second Poincare transformations, or mappings. As a result, the full qualitative pattern of trajectories is constructed – using the Poincare sphere – in the Poincare disk. A series of new special investigation methods developed, useful for further investigations of similar dynamic systems’ classes.

A Summary of the Homogeneous 5D Universe Creation Model: Expressed in the Dirac Second-Order Quantization Representation

A summary of the homogeneous 5D universe model is expressed in the Dirac second-order quantized representation for the magnetic monopoles, identified in terms of the Higgs Bosons, and through systematic ordered excitations of the Higgs vacuum obtained the non-homogeneous 4D Lorentz manifolds filled with masses, corresponding to making space dimension reduction projections, and thus realization of Newtonian gravity, followed by the 3D space symmetry breaking into 2D × 1D that produces the Perelmann-entropy and Ricci-Flow mappings, resulting in the realization of Poincare spheres, represented by nucleus such as Carbon 12, all the way to stars, and matter filled discs, such as stars in galaxies and 2D carbon-based molecular structures like nitrogenous bases. Finally, the forming of RNAs and DNAs, then life forms.

Polarization state tracing method to map local birefringent properties in samples using polarization sensitive optical coherence tomography.

We propose a method that utilizes the trajectory of output polarization states on the Poincaré sphere to derive depth-resolved birefringent information within samples using a fiber-based polarization sensitive optical coherence tomography. The apparent (or intermediate) optic axis and the local phase retardation are first obtained by fitting a plane to the adjacent output polarization states along depths in the Poincare sphere. A sequence of 3D rotation operation determined by the local birefringent property of the upper layers is then applied to the apparent axis to finally determine the local optic axis. This method requires only one input polarization state and is compatible with both free-space and fiber-based PSOCT systems, simplifying the imaging system setup. The theoretical framework is presented to derive the local phase retardation and optic axis from the output polarization states and then demonstrated by mapping local birefringent information of the mouse thigh tissue in vitro.

Nano polarimetry: enhanced AFM-NSOM triple-mode polarimeter tip

A novel application of a combined and enhanced NSOM-AFM tip-photodetector system resulted in a nanoscale Polarimeter, generated by four different holes, each sharing a different shape, and enabling that the four photonic readouts forming the tip will be the four Stokes coefficients, this in order to place the polarization state in the Poincare sphere. The new system has been built on standard Atomic Force Microscope (AFM) cantilever, in order to serve as a triple-mode scanning system, sharing complementary scanning topography, optical data analysis and polarization states. This new device, which has been designed and simulated using Comsol Multi-Physics software package, consists in a Platinum-Silicon drilled conical photodetector, sharing subwavelength apertures, and has been processed using advanced nanotechnology tools on a commercial silicon cantilever. After a comparison study of drilled versus filled tips advantages, and of several optics phenomena such as interferences, the article presents the added value of multiple-apertures scanning tip for nano-polarimetry.

Phase shift response of birefringent PANDA fiber after the end of thermal exposure during recovery to ambient temperature

The aim of this work is to point out the current possibilities of using polarized light in sensor technology. Furthermore, the aim is to demonstrate the possibility of using the fiber sensor of thermal field disturbance as a truly feasible biomedical sensor applicable in medicine and especially to analyse different ways of measuring polarization changes. This paper concludes theoretical and experimental study deal with temperature response of birefringent fiber. It is supposed to use it for design of sensor of temperature disturbance. The paper follows up on the previous works, where the response of the birefringent PANDA fiber to thermal exposure in the temperature range from 0 to 48 °C was studied. These experiments analyzed the dynamic sensitivity characteristic of birefringent fiber for the process of thermal source apposition. The present paper brings a detailed comparative analysis of fiber response to the processes of apposition and the removal of thermal source, which are evaluated from the point of view of the system’s response after the ending of the thermal exposure. For practical use in fiber recovery analyses, the phase development rotation senses are described on the observable Poincare sphere.

Poincare sphere noise filtering for singularities in dynamic speckle activity: Application to paint drying time measurement

We present an approach based on optical vortex density to characterize a dynamic process. The proposal is tested in real experiments involving the drying of paint as case study. In this case, speckle patterns are generated by coherent light scattered from the sample. The dynamic behavior of the speckle pattern during the paint drying is evaluated by using Time History of Speckle Pattern (THSP). The THSP's pseudo-phase representation is calculated via a two-dimensional Laguerre Gauss transform algorithm. The singular points in the pseudo-phase are then identified, then the number of phase singularities are evaluated over all the pseudo-phase representations of the THSP sequence.A comparison between the number of the phase singularities in THSP sequences and the gravimetric curve shows that the results are in good agreement for the active period. However, for very low activity periods noise vortices are obtained. The noise vortices are originated in the camera recoding and digitalization process. We propose the use of Stokes Parameters to configure a Vortex-Filter in order to eliminate noise vortices in each paint-drying measurement, this filter is represented using Poincare Sphere for visualization purposes. In all cases, the drying evolution curve obtained by using the optical vortex density and the Poincare Sphere filter present a good agreement with gravimetric curve, indicating that the proposed method is a valid measuring alternative.

Hysteresis in linearly polarized nonresonantly driven exciton-polariton condensates

It is shown that a condensate of microcavity exciton-polaritons exhibits bistability between its two orthogonal linearly polarized components for varying nonresonant excitation power. A non-Hermitian splitting of these components results in two parity-symmetric fixed-point solutions of opposite polarization, making up the hysteresis branches. These solutions correspond to the lowest threshold linearly polarized mode, which dominates at low pump powers, and a cross-polarized mode, which appears due to nonlinear pinning at higher excitation powers. The spin symmetry of the solutions extends the nonresonant bistable operation of polariton condensates to the entire equatorial plane of the Poincare sphere. The results pave the way towards development of tailored bistable, linearly polarized, coherent sources of light.

Use of q-plate as a coupler.

A coupler is a device that allows interconversion of angular momentum of the optical beam among spin and orbital parts, without absorbing any angular momentum. In this paper, we demonstrate that a q-plate with q=1 can act as a coupler for any of the polarization distribution that can be represented by a point on a Poincare sphere (PS), or on a higher-order PS, or on a hybrid-order PS. A q-plate with any q-value can act as a coupler for polarization distribution that can be represented by an equatorial point on any of these spheres. It is also possible to find a q-plate with an appropriate q-value that can act as a creation or annihilation operator that raises or lowers the polarization singularity index. The q-plate being a coupler and made of half-wave plate segments, the singularity index change is concomitant with the helicity inversion of C-points. Interconversion of bright and dark C-points is possible by using a q-plate.

Nonlinear geometric phase shifting in optically generated gigahertz radio frequency signals for microwave photonics

We present a method for predicting the geometric phase introduced by wave plates and a polarizer, wherein mathematical formulas to calculate the phase using the Mueller formalism are visualized as a triangle on the surface of the Poincare sphere. These constructions are used to describe a simple experiment with a birefringent medium in a Mach–Zehnder interferometer and polariscopic setup. A geometric radio frequency (RF) phase shifter for controlling the geometric phase introduced by the birefringent medium is also presented. The RF phase generated from orthogonally polarized light signals was shifted from 0 deg to 360 deg; this phase shift exhibited nonlinear characteristics. Thus, the proposed phase-shifter device improves phase control sensitivity in the partial region.

Mapping of retardance, diattenuation and polarizance vector on Poincare sphere for diagnosis and classification of cervical precancer.

The mapping of diattenuation, polarizance and retardance vector (normalized Stokes vector) on Poincare sphere, evaluated from Mueller matrix of optically anisotropic stromal region of cervical tissues, is presented for cervical precancer detection and its staging. This reveals that the changes in the polarization states shown by these normalized Stokes vectors corresponds to the degradation of linearly arranged collagen fibers, breakage of the collagen cross links in the stromal region and change in the density of scattering sites when cervical cancer evolves. The distinct nature of real and imaginary parts of the refractive index for linear, linear-45 and circular polarization from the optically anisotropic stromal region underscore the various polarization structures of the connective tissue region which get modified during the pathological changes. It has been found that versatility of these vectors for normal and precancerous cervical tissue of various grades may be utilized as a key distinction for qualitative staging of cervical precancer tissue. Quantitative classification of precancerous stages of cervical precancer has been determined with 95%-100% sensitivity and 93%-100% specificity through the evaluation of linear and circular diattenuation, linear polarizance and linear birefringence from the components of the respective vectors.

Evolution properties of vector vortex beams passing through a paraxial optical system

The arbitrary vector vortex beams on a higher-order Poincare sphere (HOPS) are generated and manipulated using the combination of a Mach–Zehnder interferometer and a spatial light modulator. In terms of the transfer matrix method, the analytical expressions of the arbitrary vector vortex beams on the HOPS through a paraxial optical system are derived. The characteristics of the transformation of vector vortex beams by three typical optical systems, such as free space, Fourier transform, and fractional Fourier transform system, are investigated theoretically and verified experimentally. The intensity distribution of the vector vortex beams is found to be form-invariant under paraxial transformations. In addition, the intensity and polarization properties of the vector vortex beams are closely related to the several independent complex parameters of the beams and the optical systems. This research provides a reliable and flexible approach to manipulating the vector vortex beams in practical optical systems.

Experimental study on dissipative soliton fiber laser with dynamically tunable polarization trajectory

In this paper, a dissipative soliton mode-locked fiber laser is established based on carbon nanotube in order to study the polarization dynamics of dissipative soliton by using a commercial polarimeter. Under the pump power of 160 mW, stable dissipatives soliton are observed to have a limited cycle polarization trajectory shown on Poincare sphere, indicating the periodic modulation of anisotropy in cavity. The stable dissipative soliton possesses a high signal noise ratio of 57.7 dB at fundamental frequency. Moreover, the fast oscillation of state of polarization leads to a lower degree of polarization (DOP). In addition, the polarization controllers are employed to compensate for the birefringence in the cavity to adjust the ratio between cavity length and birefringence length. As a result, we can observe the polarization evolving from the polarization locked attractor to the limited cycle attractor by adjusting polarization controllers. It is noted that this dynamic polarization trajectory can be manually controlled. By comparing polarization attractor with DOP, it is clear that the size of trajectory shown on Poincare sphere is inversely proportional to DOP. We expect our work to be conducible to studying the physics in lasers and creating a new type of polarization tunable laser.

Polarization scrambling characteristic analysis based on density of polarization states statistics

We report a new method to deeply analyze the scrambling characteristic of polarization scramblers based on density of polarization states (DPS) statistics that makes it possible to describe the DPS distribution in detail on the whole Poincare sphere, thus easy to locate accurately the nonuniform areas of defective polarization scramblers, which cannot be realized by existing methods. We have built a polarization scrambling system to demonstrate the advantages of our method compared with others by experiments and suggested effective evaluation indexes whose validity is well confirmed by applying to a commercial scrambler. Our conclusions are valuable for accurately analyzing and diagnosing the performance of any polarization scrambler, and quality evaluation of polarization controllers or other polarization devices.

Geometrical Optics of an Anisotropic Media with Space Modulated Gyrotropy

The problem of the polarized light propagation in an optically homogeneous anisotropic medium with spatially modulated gyrotropy is considered. The analysis was carried out using a numerical solution of a system of coupled equations obtained in the approximation of geometric optics. For illustrative purposes, the results of numerical analysis are also presented on the Poincare sphere. The resonance character of the dependence of the amplitude of polarization beats as a function of the spatial frequency of gyrotropy modulation is shown.

COVID-19: A Physical Model

The coronavirus structure is explained as a fractal representation of the Poincare sphere of proteins, dotted with t-spikes having the geometric realization of the SU(3) Lie group for the protein spike, and encompasses an RNA of SU(2) topologies representations, while within the core contains a virus DNA. Through this suggested model, the virus must possess a critical temperature Tc, induced by the EEM mechanism for the completion of the Poincare sphere surface. Thus above Tc it will disintegrate. We then discuss how the virus transmission progresses within the patient’s body, and explain a very fast recent detection method currently used consistent with this model, as well as a corresponding possible cure based on this same principle of the body’s immune system. Hopefully the model can be also used as a guide to finding possible medications, so far is lacking.

Spatial-Dependent Hamiltonian Formulation of Cross-Mode Modulation

In the absence of random mode mixing (RMM), linearization of the cross-mode modulation (XMM) under pump-probe configuration is in general complicated because the evolution of the pump light depends on the local mode decomposition of itself. In this work, general derivation of the Hamiltonian of the XMM system without RMM is carried out and discussed under two interesting scenarios where the pump evolution can be effectively linearized, leading to spatial dependent Hamiltonian of the probe light. Representative evolutions of pump and probe light over transmission are investigated with the assistance of Poincare sphere based on the Hamiltonian approach. Our results are benchmarked against the results given by precession equations examined by Lin and Agrawal and numerical simulations using nonlinear coupled mode equations (CMEs). By highlighting the eigenstates as well as eigenvalues of the system, our approach provides an intuitive yet powerful approach to understand the XMM nonlinear problems and to dynamically manipulate the spatial profiles of the probe light.

Polarization evolution dynamics of dissipative soliton fiber lasers

Dissipative solitons emerge as stable pulse solutions of nonintegrable and nonconservative nonlinear physical systems, owing to a balance of nonlinearity, dispersion, and loss/gain. A considerable research effort has been dedicated to characterizing amplitude and phase evolutions in the spatiotemporal dynamics of dissipative solitons emerging from fiber lasers. Yet, the picture of the buildup process of dissipative solitons in fiber lasers is incomplete in the absence of corresponding information about the polarization evolution. Here, we characterize probabilistic polarization distributions in the buildup of dissipative solitons in a net-normal dispersion fiber laser system, mode-locked by single-wall carbon nanotubes. The output optical spectra under different pump powers are filtered by a tunable filter, and are detected by a polarization state analyzer. The laser system operates from random amplified spontaneous emission into a stable dissipative soliton state as the cavity gain is progressively increased. Correspondingly, the state of polarization of each spectral wavelength converges towards a fixed point. To reveal the invariant polarization relationship among the various wavelength components of the laser output field, the phase diagram of the ellipticity angle and the spherical orientation angle is introduced. We find that, within the central spectral region of the dissipative soliton, the state of polarization evolves with frequency by tracing a uniform arc on the Poincare sphere, whereas in the edges of the dissipative soliton spectrum, the state of polarization abruptly changes its path. Increasing cavity gain leads to spectral broadening, accompanied by a random scattering of the state of polarization of newly generated frequencies. Further increases of pump power result in dissipative soliton explosions, accompanied by the emergence of a new type of optical polarization rogue waves. These experimental results provide a deeper insight into the transient dynamics of dissipative soliton fiber lasers.