Spectral Degree Of Polarization Research Articles

Propagation properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beams in turbulent atmosphere

In this paper, the propagation properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beams (RP-RSPEPVBs) in turbulent atmosphere were investigated. Based on the extended Huygens-Fresnel principle and unified theory of coherence and polarization, the theoretical propagation model was established. Then, the numerical simulations were carried out to reveal the evolution of intensity distribution, spectral degree of coherence (DOC) and spectral degree of polarization (DOP) in turbulent atmosphere. The results showed that although the partially coherent RP-RSPEPVBs diverged during the propagation, the spatial structure remains analogous, and the relatively larger waist widths gain smaller divergence. Moreover, the optical pattern can be evidently modulated by optical parameters, as the number of sidelobes can be changed with topological charge l, and the continuity of the light spot as well as the rotating speed around the optical axis can be influenced by power exponent n. Besides, the spectral DOC and DOP would decrease with larger propagation distance and refractive-index structure constant, but decrease less with a shorter coherence width. This work may be helpful in fields such as remote sensing and optical communication.

Coherence and polarization behaviors of partially coherent circular edge dislocation beam in biological tissue

The effects of the several factors on the changes in spectral degree of polarization P(ρ,-ρ,z) and spectral degree of coherence μ(ρ,-ρ,z), μ(ρ,0,z) for the partially coherent circular edge dislocation beam propagating in biological tissue have been studied. It is shown that both beam wavelength λ and dislocation number n have no effect on the initial values of the three, while the values of field points distance ρx and spatial self-correlation length σyy play a significant role. During the propagation, the curves of P(ρ,-ρ,z), μ(ρ,-ρ,z) and μ(ρ,0,z) with different beam parameters will undergo different fluctuation, eventually the former tends to be a certain value less than its initial one and the latter two tend to zero. The smaller ρx is, the higher the coherence of the beam is. The visible light is more suitable for biological tissue disease diagnosis compared to the far infrared and ultraviolet light. The beam with larger n will possess more richer optical distribution when propagating in biological tissues. The difference value between σyy and σxx will significantly influence the change range of P(ρ,-ρ,z), μ(ρ,-ρ,z) and μ(ρ,0,z).

Changes in the statistical properties of electromagnetic double multi-Gaussian Schell-model beams on propagation in free space.

A class of electromagnetic random sources with a multi-Gaussian functional form in the spectral density and in the correlations part of the cross-spectral density matrix is introduced based on the genuine cross-spectral density-matrix theory. The analytic propagation formulas of the cross-spectral density matrix of such beams propagating in free space are derived by use of Collins' diffraction integral. With the help of analytic formulas, the evolution of statistical characteristics, i.e.,the spectraldensity, the spectral degree of polarization, and the spectral degree of coherence for such beams in free space are analyzed numerically. Employing the multi-Gaussian functional form in the cross-spectral density matrix introduces one more freedom in the modeling of Gaussian Schell-model sources.

Propagation characteristics of radial phase-locked discrete vector beam generated from a Gaussian Schell-Model laser array in atmospheric turbulence

In this paper, combining the advantages of partial coherence, vector beam, and laser array in better resistance to atmospheric turbulence, high capacity, and high output power, we proposed a radial phase-locked discrete vector beam generated from a Gaussian Schell-Model (GSM) laser array (i.e., phase-locked GSM discrete vector beam array) and theoretically studied its propagation characteristics in atmospheric turbulence. The analytical expressions for spectral intensity, spectral degree of coherence (DOC), and spectral degree of polarization (DOP) of a phase-locked GSM discrete vector beam array were derived based on the extended Huygens-Fresnel principle. And also, based on numerical simulation, we investigated the influence of atmospheric and laser parameters on the propagation properties in detail. The results show that the beam profile will gradually evolve from hollow structure distribution, then form a flat-topped beam and finally present the Gaussian-like distribution; the spectral DOC exhibits decaying oscillation analogous to under-damping vibration; a dip appears in the distribution of the spectral DOP. The evolution rate of spectral intensity, oscillation amplitude, and period of spectral DOC and dip width of spectral DOP are determined by propagation distance, refraction structure constant, beam waist, spatial correlation length, and the number of beamlets. More importantly, by analyzing Stokes parameters, different initial polarization distributions correspond to different crosslines of S1/S0, and even with the increase of the propagation distance, the crosslines of S1/S0 still show similar performance. This work may provide novel thoughts and methods to improve propagation performance and benefit potential applications in free-space optical communication.

Influences of salinity and temperature on propagation of radially polarized rotationally-symmetric power-exponent-phase vortex beams in oceanic turbulence.

In this paper, the propagation properties of radially polarized rotationally-symmetric power-exponent-phase vortex beams (RP-RSPEPVBs) in oceanic turbulence were theoretically and experimentally studied. Based on the extended Huygens-Fresnel diffraction integral and vector beams theories, the theoretical propagation model of RP-RSPEPVBs in the oceanic turbulence was established. Then, the numerical simulations were carried out to study the influences of the propagation distance z, the rate of dissipation of turbulence kinetic energy per unit mass of fluid ε, the temperature-salinity contribution ratio ω, and the dissipation rate of the mean-squared temperature χT on the optical intensity, spectral degree of polarization (DOP) and spectral degree of coherence (DOC) of RP-RSPEPVBs. Further, an experiment setup was demonstrated to confirm the influences of salinity and temperature on propagation of RP-RSPEPVBs in oceanic turbulence. The results showed that increasing salinity, propagation distance, and turbulence intensity, will result in beam diffusion and intensity reduction of the RP-RSPEPVBs, as well as depolarization and decoherence. Contrarily, high temperature mitigated the intensity loss of the RP-RSPEPVBs and the spectral DOP and spectral DOC increased when the turbulence tends to be dominated by temperature. As a vector beam, the RP-RSPEPVB shows well anti-turbulence interference characteristics, which provides a new choice for optical underwater communication and imaging.

Polarization properties of random electromagnetic vortex beam propagating in gradient‐index fiber

AbstractWe built the cross‐spectral density matrix elements analytical expression of random electromagnetic Gaussian vortex (REGV) beam propagating in gradient‐index (GRIN) fiber, which is used to study the polarization properties of the beam. The distribution of spectral degree of polarization (SDOP) and state of polarization (SOP) show the same periodicity and symmetry. The distribution law of SDOP and SOP is unchanging with the topological charge m changing and is changed by adjusting the spatial self‐correlation length σxx. The research results have guiding significance for the propagation of random electromagnetic vortex beams in optical fibers, which could be considerable value in high‐speed and large‐capacity optical fiber secure communication.

Statistical properties of a spatiotemporally partially coherent vector cosine-Gaussian-correlated pulsed beam with radial polarization in atmospheric turbulence

In this study, we introduce a novel class of partially coherent vector sources, namely radially polarized spatiotemporally partially coherent cosine-Gaussian-correlated Schell-model pulsed (CGCSMP) beams, which are natural extensions of the scalar Gaussian Schell-model pulsed beams. The conditions for the physical realization of this source are established, and analytical formulae for the two-point, two-frequency cross-spectral density matrix elements of a beam propagating through turbulent atmosphere are derived within the framework of the extended Huygens–Fresnel principle and the atmospheric turbulence spectrum model. The behaviors of the spectral intensity, the spectral degree of polarization (DOP), and the spectral degree of coherence (DOC) of the beam during transmission are investigated numerically. Our work enriches the classical theory of propagating stochastic electromagnetic beams and may be useful for applications requiring a specified degree of beam coherence.

Far-zone behaviors of scattering-induced statistical properties of partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam**Project supported by the National Natural Science Foundation of China (Grant No. 11504286), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2019JM-470), the Fund from the International Technology Collaborative Center for Advanced Optical Manufacturing and Optoelectronic Measurement, and the Science

In this study, we explore the far-zero behaviors of a scattered partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam irradiating on a deterministic medium. The analytical formula for the cross-spectral density matrix elements of this beam in the spherical coordinate system is derived. Within the framework of the first-order Born approximation, the effects of the scattering angle θ, the source parameters (i.e., the pulse duration T0 and the temporal coherence length Tcxx), and the scatterer parameter (i.e., the effective width of the medium σR) on the spectral density, the spectral shift, the spectral degree of polarization, and the degree of spectral coherence of the scattered source in the far-zero field are studied numerically and comparatively. Our work improves the scattering theory of stochastic electromagnetic beams and it may be useful for the applications involving the interaction between incident light waves and scattering media.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals.

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ0, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index ne/no of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Polarization properties of stochastic electromagnetic beams modulated by a wavefront-folding interferometer.

We consider the field generated by a wavefront-folding interferometer which is illuminated by a stochastic electromagnetic beam. The specular property and anti-specular property are discussed in the vector case. Take electromagnetic Gaussian Schell-model beam as an example, we investigate the spectral density, the spectral degree of coherence, the spectral degree of polarization as well as the state of polarization of the polarized portion of the field on propagation. Results show that the polarization properties including the degree of polarization, the orientation angle and the degree of ellipse can be adjusted by the phase difference of the interferometer and the phase retardation introduced by the prism. The results may be applied in free-space optical communication.

Evolution properties of polarization states of far-zone electromagnetic field scattered from an anisotropic medium.

Within the accuracy of the first-order Born approximation, expressions are derived for the cross-spectral density matrix of the electromagnetic field scattered from a three-dimensional (3D), spatially anisotropic medium. By using the analytical forms of the spectral degree of polarization (SDOP), semi-major axis, semi-minor axis, and orientation angle of the polarization ellipse, we illustrate the evolution properties of the polarization states of the far-zone scattered field. Dependences of the polarization ellipses on different combinations of correlation lengths of the medium and polarization of incident plane wave are also revealed through numerical simulations. It is shown that the polarization ellipse of the scattered field can be either stretched or squeezed along certain scattering angles, strongly depending on the anisotropic statistics of medium and polarization of incident plane wave. Our results substantially enrich the study on the reciprocal relations between the far-zone scattered properties and correlation statistics of a spatially anisotropic medium.

Coherence and polarization properties of laser propagating through biological tissues

Based on the extended Huygens-Fresnel principle, the analytical expressions of the cross-spectral density matrix elements for random electromagnetic Gaussian Schell-model (GSM) beam propagating in biological tissues are derived, and used to study the changes in spectral degree of coherence μ and spectral degree of polarization P of random electromagnetic GSM beams with the propagation distance z propagating through the different biological tissues. It is shown that the changes closely depend on the species of the biological tissues, beam wave length, the interval between two field points and propagation distance. The spectral degree of coherence μ and the spectral degree of polarization P of the ultraviolet ray (λ=0.325μm) will quickly decrease during the propagation process, which implies that the damage of the ultraviolet ray to biological tissues is strong. The bigger structure constant of the refractive-index Cn2 corresponds to the smaller change of μ and P. There exists the obvious effect of the interval between two field points on the spectral degree of coherence and the spectral degree of polarization of random electromagnetic GSM beams passing biological tissues. The obtained results can provide the theoretical and experimental basis for the analysis to the coherence and polarization properties of random electromagnetic beams propagating through the complex biological tissues.

Scrutinizing the effects of turbulence on partially coherent Gaussian beam propagating through Caspian Sea

In this paper, the total attenuation due to scattering, absorption and turbulence is considered in investigation of link parameters of the underwater horizontal optical communication system in the Caspian sea. In the present paper, based on extended Huygens-Fresnel principle and the unified theory of coherence and polarization, analytical formulas for Cross-Spectral Density (CSD) matrix elements and the Spectral Degree of Polarization (SDP) are derived. By using the matrix elements of cross-spectral density, some valuable analytical expression for defining Power In Bucket (PIB), Signal to Noise Ratio (SNR) and Bit Error Rate (BER) are presented. Then, the effects of some source and turbulent ocean factors on link parameters of partially coherent Gaussian beam propagating through turbulent water are scrutinized. It is deduced that underwater communication link parameters are affected by environment’s factors (e.g. Chlorophyll concentration (CC), turbulence parameters) and source parameters (e.g. laser wavelength). Investigating spectral degree of polarization shows that by increasing the strength of oceanic turbulence, the fluctuation of spectral degree of polarization becomes smaller. The obtained results are displayed with graphs.

Propagation of stochastic electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence

Recently, the laser beam propagation in the oceanic turbulence has become a hot research topic. In addition to the characteristics of free diffraction and self-reconstruction, the high-order Bessel-Gaussian beam is a kind of typical vortex beam because of the existence of a spiral phase factor with orbital angular momentum. Researchers have investigated the self-reconstruction property of the high-order Bessel-Gaussian beams in the free space, also carried out intensive researches on the transmission characteristics of high-order Bessel-Gaussian beam in the ABCD optical system and in the atmospheric turbulence. However, to the best of our knowledge, to date there has been no investigation on the propagation of this laser beam in the oceanic turbulence. In this paper, we will study the propagation characteristics of the random electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence, and discuss the variation of the normalized spectrum intensity, the spectral degree of polarization, and the spectral degree of coherence. By using the extended Huygens-Fresnel diffraction integral formula, the general expression for the cross spectral density matrix of the stochastic electromagnetic high-order Bessel-Gaussian beams propagating in the oceanic turbulence is obtained, and the statistical properties of the random electromagnetic high-order Bessel-Gaussian beams propagating in the seawater are investigated by numerical calculation. The numerical results show that the oceanic turbulence can affect the normalized spectral intensity distribution of the random electromagnetic beam. With the increase of the transmission distance, the center of the zero-order Bessel-Gaussian beam becomes depressed, and the center of the higher-order Bessel-Gaussian beam will become flat and then depressed. As the transmission distance increases far enough, regardless of the zero-order or higher-order, the intensity distribution will eventually evolve into the quasi Gaussian shaped distribution. The variation of the degree of polarization of each point on the x axis is related to the coherence length (xx，yy) and the oceanic turbulence parameters. The spectral coherence of the origin and any point on the x axis also changes with the increase of x, and the rate of dissipation of mean-square temperature T has influence on the spectral coherence. This research is of great value for applying the high-order Bessel-Gaussian beam to the optical communication, optical imaging and underwater exploration in the ocean.

Generalized Stokes parameters and polarization behavior of flat-topped array laser beam propagating through oceanic turbulence

In present paper, the analytical expression for the cross-spectral density of the phase-locked Partially Coherent Flat-Topped (PCFT) array beams propagating through oceanic turbulence based on the extended Huygens–Fresnel integral is derived. Then, the polarization behavior and generalized Stokes parameters of the phase-locked PCFT array beam propagating through oceanic turbulence using the cross-spectral density matrix elements have been achieved. In this paper, the case of the clearwater oceanic turbulence has been considered, i.e. it has been assumed that the light wave is not affected by suspended organic and inorganic impurities. Due to the above-mentioned reason and the turbulence importance, the impacts of oceanic turbulence have been scrutinized, while the effects of absorption and scattering have been ignored. The changes in the Stokes parameters, the fluctuation of Stokes parameters, and consequently the state of polarization (including the spectral degree of polarization, the orientation angle and the degree of ellipticity) of the phase-locked PCFT array beams for different turbulence conditions upon propagation have been investigated. The results may find possible applications in underwater communication.

Propagation of electromagnetic multi-Gaussian Schell-model beams with astigmatic aberration in turbulent ocean.

An analytical expression for the elements of the cross-spectral density matrix of electromagnetic multi-Gaussian Schell-model beams with astigmatic aberration propagating through the turbulent ocean is derived. We investigate the statistical characteristics of the beams on propagation in great detail. It is found that, due to astigmatism, the circular symmetry of such beams suffers a certain degree of damage in the near field. In addition, astigmatism also destroys the attractive far-field flat profiles in free space. Meanwhile, we also show that astigmatism and oceanic turbulence both have certain effects on the spectral degree of polarization.

Scattering of an electromagnetic light wave from a quasi-homogeneous medium with semisoft boundary

Based on the first-order Born approximation, the scattering of an electromagnetic plane wave from a relatively more realistic random medium, a quasi-homogeneous medium with semisoft boundary, has been investigated. The analytic expressions for the spectral density, the spectral degree of coherence and the spectral degree of polarization have been derived, and the effects of the characteristics of the medium and the polarization of the incident light wave on the far-zone scattered field are determined. The numerical simulations indicate that, with the increasing of the edge softness M of the medium, the spectral density presents a pattern with interference fringes, and the number, position and width of interference fringes can be modified by the parameter. It is also found that there is an obvious value saltation in the coherence profile. Besides, unlike the intensity and the coherence are significantly affected by the properties of the medium, the polarization of the scattered field is irrelevant to them due to the quasi-homogeneity and isotropy of the medium, and it is only connected with the polarization of the incident light.

Second-order statistics of a radially polarized cosine-Gaussian correlated Schell-model beam in anisotropic turbulence.

Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications.

Stokes parameters of phase-locked partially coherent flat-topped array laser beams propagating through turbulent atmosphere

In this study, generalized Stokes parameters of a phase-locked partially coherent flat-topped array beam based on the extended Huygens–Fresnel principle and the unified theory of coherence and polarization have been reported. Analytical formulas for 2 × 2 cross-spectral density matrix elements, and consequently Stokes parameters of a phase-locked partially coherent flat-topped array beam propagating through the turbulent atmosphere have been formulated. Effects of many physical attributes such as wavelength, turbulence strength, flatness order and other source parameters on the Stokes parameters, and therefore spectral degree of polarization upon propagation have been studied thoroughly. The behaviour of the spectral degree of coherence of a delineated beam for different source conditions has been investigated. It can be shown that four generalized Stokes parameters increase by raising the flatness order at the same propagation distance. Increasing the number of beams leads to a decrease in the Stokes parameters to zero slowly. The results are of utmost importance for optical communications.