Unified Theory Of Coherence Research Articles

Propagation properties of partially coherent vector beam with multiple off-axis vortex phases

In this paper, we investigate the propagation properties of radially polarized rectangular-symmetric cosine-Gaussian Schell-model (RCGSM) beam with multiple off-axis vortex phases by using Fourier transform and convolution method based on the unified theory of coherence and polarization. The results indicate that the radially polarized RCGSM beam has self-splitting properties and can be split into four identical lobes due to its unique spatial coherence structure. Furthermore, the modulation of multiple off-axis vortex phases can be acted on each lobe. For high coherence, the spot arrays with triangular or square hollow light intensity distribution can be generated in the focal plane by modulating the number of off-axis vortices (<i>N</i><sub>0</sub>) and the beam order, and the corresponding state of polarization on each lobe presents an inverted triangular or oblique square elliptic distribution. However, for small coherence, the modulation effect of multiple off-axis vortex phases disappears and the light intensity of each lobe degenerates into a quasi-Gaussian distribution, whereas its state of polarization keeps invariant, which is independent of the beam order and coherence length. In addition, the beam still has a certain self-healing ability for one of the off-axis vortex phases partially blocked by an obstacle, but it will be destroyed for completely blocking, resulting in a notch on each lobe.

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.

Propagation properties of partially coherent array beams with a non-uniform polarization

We study a new class of partially coherent array beams with a non-uniform polarization, named radially polarized Gaussian Schell-model array (RPGSMA) beams and analyze the reliability conditions for the array beams based on the unified theory of coherence and polarization, Moreover, the statistical properties of such beam propagating in free space are investigated in detail. It is found that, the propagation properties of the RPGSMA beams are closely related to initial beam parameters. With an appropriate choice of the beam parameters, the average intensity will evolve into optical lattice patterns, and the degree of coherence (DOC) from the lattice distribution on the original plane evolves into a Gaussian profile in the far field, and the degree of polarization (DOP) appears a periodical grid-like distribution on propagation. These results may be beneficial to particle trapping and free-space optical communications.

Average intensity and polarization evolution of aberrated partially coherent cosh-Airy beams propagating in ocean turbulence

In this paper, the cross-spectral density (CSD) of aberrated cosh-Airy beams in oceanic turbulence is first derived. And then, the corresponding CSD matrix elements can be obtained by the unified theory of coherence and polarization. Finally, the features of astigmatic cosh-Airy beams propagating in ocean turbulence, i.e. average intensity, spectral coherence and polarization properties, were investigated in detail using numerical simulation. It can be found that the astigmatism has different effects on the average intensity in x and y directions. And the distance of the polarization returning to its initial value is affected by the astigmatism coefficient, cosh modulation parameters and coherence length.

Electromagnetic Hanbury Brown and Twiss Effect in Atmospheric Turbulence

The evolution of the 4 × 4 matrix with elements being the scintillation indices of the single-point Stokes parameters of a stationary electromagnetic beam-like optical field in classic, weak atmospheric turbulence is revealed. It is shown that depending on the choice of the source parameters, the source-induced changes in the matrix elements of the propagating beam and those produced by turbulence can be either range-separated or conjoined. For theoretical analysis, the unified theory of coherence and polarization is used together with the extended Huygens-Fresnel integral approach. The results can be of interest for building robust communication and sensing systems operating in the presence of atmospheric fluctuations.

Radially polarized twisted Multi-Gaussian Schell-model beams and their statistical properties

A radially polarized twisted Multi-Gaussian Schell-model (RPT MGSM) beam based on the unified theory of coherence and polarization is introduced. The reliability conditions for the beams are also derived. We derive the analytical expressions for the elements of the cross-spectral density matrix of such beam propagating in free space and investigate the statistical properties, such as spectral density, degree of coherence, degree of polarization and state of polarization. It is found that the statistical properties of the RPT MGSM beams are closely related to the twist phase, e.g. the twist phase induces not only the rotation of the beam spot but also changes of the degree of coherence, degree of polarization and state of polarization on propagation. Specially, an interesting phenomenon is found. In the far field, when the beams without carrying twist factor, the state of polarization in the flat-top area of intensity distribution is azimuthally polarized rather than radially polarized. Our results may be useful in optical trapping and free-space optical communications.

Synthesis of ununiformly correlated radially polarized partially coherent beam

Since the unified theory of coherence and polarization for partially coherent vector beams was proposed by Gori and Wolf, the characterization, generation and propagation of partially coherent vector beams have been extensively studied. During the last decade, partially coherent vector beams with non-uniform polarization, also referred to as cylindrical vector partially coherent beams, have gained more and more attention. It was found that the intensity profile of focused azimuthally/radially polarized beam could be shaped by varying its initial spatial coherence. This characteristic may have potential applications in material thermal processing and particle trapping. Until now, there have been several reports concerning the generation of cylindrical vector partially coherent beams. However, in most of these reports a ground-glass diffuser was used, which generally restricts the generation of shell-model sources. In this paper, we theoretically and experimentally investigate the generation of radially polarized partially coherent beams with non-uniform correlation. According to the relation between phase correlation and optical coherence, we theoretically investigate the 2 × 2 cross-spectral density matrix and the coherence distribution of our generated non-uniformly correlated radially polarized partially coherent beams. In experiment, we generate dynamic random phase patterns with uniform distribution in time and inverse Gaussian distribution in space. A complete coherent radially polarized beam is divided into two parts by a polarizing beam splitter, i.e., the transmitted <i>x</i>-polarization component (HG<sub>10</sub> beam) and the reflected <i>y</i>-polarization component (HG<sub>01</sub> beam). The two orthogonally polarized components are respectively modulated with the two halves of a single phase-only liquid crystal spatial light modulator, thus generating a radially polarized partially coherent beam. We measure the correlation distribution of the generated beam in Young’s two-pinhole experiment. It is shown that the experimental observations are in agreement with our theoretical analyses. The generated partially coherent beam has an un-uniform correlation structure, and its coherence degree may be controlled by varying the Gaussian modulation half-width of the random phase. Our experimental results have also shown that the intensity profile of the radially polarized partially coherent beam can be modulated with the Gaussian modulation half-width. With the increase of Gaussian modulation half-widths and the gradual decrease of coherence degree, the intensity profile gradually transforms from a dark hollow beam profile into a flat-topped-like beam profile. The radially polarized partially coherent beams with non-uniform correlation may have some applications in optical manipulation and material thermal processing.

基于相干偏振统一理论的Schmidt棱镜衍射特性

基于相干偏振统一理论的Schmidt棱镜衍射特性

Evolution properties of a radially polarized partially coherent twisted beam propagating in a uniaxial crystal

We derived analytical formula for the cross-spectral density of a radially polarized partially coherent twist (RPPCT) beam propagating in a uniaxial crystal orthogonal to the optical axis with the help of the extended Huygens-Fresnel integral formula and unified theory of coherence and polarization. Furthermore, we explore the evolution properties of a RPPCT beam propagating in a uniaxial crystal. It is found that the RPPCT beam becomes an anisotropic RPPCT beam and the beam spot is rotating with beam propagation in uniaxial crystal. Its evolution properties change with twist factor and the ratio of extraordinary index to ordinary refractive index. The twist factor affects their rotation orientation angles, and the ratio of extraordinary index to ordinary refractive index has an effect on their twisted levels.

Twist phase-induced characteristic changes of a radially polarized partially coherent beam in a uniaxial crystal

We derived analytical formula for the cross-spectral density matrix of a radially polarized partially coherent twist (RPPCT) beam in a uniaxial crystal orthogonal to the optical axis with the help of the extended Huygens-Fresnel integral formula and unified theory of coherence and polarization. Furthermore, we explore the evolution properties of a RPPCT beam in a uniaxial crystal. It is found that the RPPCT beam becomes an anisotropic RPPCT beam and the beam is rotating with beam propagation in uniaxial crystal. Its evolution properties change with twist factor and the ratio of extraordinary index to ordinary refractive index. The twist factor affects their rotation orientation angles, and the ratio of extraordinary index to ordinary refractive index has an effect on their twisted levels.

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 properties of partially coherent high-order cylindrical vector beams through a turbulent atmosphere

On the basis of the extended Huygens–Fresnel integral formula and the unified theory of coherence and polarization of partially coherent beams, analytical formulae of the elements of the beam coherence-polarization (BCP) matrix for a partially coherent high-order cylindrical vector (HCV) beam propagating through a turbulent atmosphere are derived under a high topological charge condition. The propagation of a radially polarized partially coherent beam through a turbulent atmosphere can be treated as a special case of this general result. Numerical results indicate that the intensity distribution and the polarization evolution of the beam are dependent on the propagation distance, structure constant, transverse coherence length and topological charge. It was also found that initial intensity distribution with a hollow shape gradually changes into Gaussian distribution, and the polarization structure will be slowly degenerated during propagation through a turbulent atmosphere. Interestingly, with increase of the topological charge, a partially coherent HCV beam can effectively mitigate the turbulence effect on its scintillation. These results may find applications in connection with free-space optical communication (FSO) and remote sensing.

Propagation of specular and anti-specular Gaussian Schell-model beams in oceanic turbulence

On the basis of the extended Huygens-Fresnel principle and the unified theory of coherence and polarization of light, we investigate the propagation properties of the specular and anti-specular Gaussian Schell-model (GSM) beams through oceanic turbulence. It is shown that the specularity of specular GSM beams and the anti-specularity of anti-specular GSM beams are destroyed on propagation in oceanic turbulence. The spectral density and the spectral degree of coherence are also studied in detail. The results may be helpful for underwater communication.

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.

Propagation properties of a radially polarized partially coherent twisted beam in free space.

We introduce a radially polarized partially coherent twisted beam based on the unified theory of coherence and polarization. We also derive expressions of this beam propagating in free space and examine the influence of twist factor and coherence of the source plane on its propagation properties. It is found that both twist factor and coherence of the source plane affect its average intensity, polarization, and coherence. Those results also show that the beam is rotating with beam propagation, and the beam's rotation is independent of coherence of the source plane.

Statistical properties of a partially coherent cylindrical vector beam in oceanic turbulence.

Propagation of a partially coherent cylindrical vector Laguerre-Gaussian (PCCVLG) beam passing through oceanic turbulence is studied with the help of the extended Huygens-Fresnel integral formula and unified theory of coherence and polarization of light. Analytical formula for the cross-spectral density matrix of a PCCVLG beam propagating in oceanic turbulence is derived, and the statistical properties, such as intensity distribution and degree of polarization, of a PCCVLG beam on propagation in oceanic turbulence are illustrated in detail. It is found that the statistical properties of a PCCVLG beam in oceanic turbulence vary as the sea-related parameters, initial coherence length, and mode orders vary, and such beam is depolarized on propagation. Our results will be useful in optical underwater communications, imaging, and sensing.

Research on the coherence of partially coherent radially polarized beam during propagation

Based on the generalized Huygens theory and the unified theory of coherence and polarization, study is made on the module value of complex degree of coherence of partially coherent radially polarized beam (PCRPB) which changes with transmission distance at different reference point. Results show that the module value distribution of the complex degree changing with the transmission distance is different for different reference point while PCRPB propagates in a free space. When the reference point is at the origin, with the increase of the transmission distance, μxx and μxy hold a symmetric distribution, and the distribution range increases. When the reference point is confined on the x-axis, μxx changes from single peak to three peaks, and the two valleys lie symmetrically; and μxy changes from two peaks to four peaks, and the four valleys lie symmetrically. The transmission distance of the evolution is related to the distance between the reference point and the origin: the closer the distance between the reference point and the origin, the shorter the transmission distance is needed to achieve the evolution process. When the reference point lies on the y-axis, μxx holds a symmetric distribution, its distribution range increases, and μxy changes from two peak values to four peaks and four valleys which are in symmetric form. The transmission distance is related to the spacing between the reference point and the origin, the closer the distance between the reference point and the origin: the shorter the transmission is needed to achieve the evolution process. In addition, when the reference point lies at other positions on the observation plane, the module value distribution of μxx and μxy is obtained by combining the distribution rules of reference point at x-axis and y-axis: i.e., when the reference point lies at other positions of the observation plane, the module values μxx and μxy can be composed of three peaks and four peaks with the increase of transmission distance, respectively.

Comparison of polarization property of partially coherent beam between propagating along an uplink path and a downlink path in atmospheric turbulence

In this article, we take partially coherent electromagnetic Gaussian-Schell model (EGSM) beam as a research object. Based on the unified theory of coherence and polarization and the generalized Stokes parameters of random electromagnetic beams, the expressions of degree of polarization (DoP) and orientation angle of EGSM beam that propagates in the slant atmospheric turbulence, are derived. And the expressions are used to investigate the difference in polarization property of EGSM beam between propagating along an uplink path and a downlink path in the atmospheric turbulence. The results show that under the same conditions, the DoP distribution of EGSM beam propagating along a downlink path is more concentrated than that along an uplink path. When EGSM beam propagates along a downlink path, the maximum DoP corresponding to the propagation distance is larger than along an uplink. Therefore, when EGSM beam propagates along a downlink path, the detector can receive beam information at the longer distances.

部分相干径向偏振光束在自由空间中的传输

Based on the propagation law of the 2×2 cross-spectral density matrix and the unified theory of coherence and polarization of partially coherent beams, the transmission characteristics of partially coherent radially polarized beams (PCRPB) have been investigated in the paper. It is shown that the intensity distribution, the degree of polarization (DOP) and the Stokes parameters will change after propagation through the free space. The doughnut beam spot of the partially coherent radially polarized beam becomes a solid beam, which is related to the propagation length and the coherence length. In addition, the degree of polarization and Stokes parameters in the propagation both relate to the propagation length and coherence length. With the increase of the propagation length, the modulus values of Stokes parameters S 1 and S 2 will decrease, the rate of the distribution of the DOP with radius will decrease. In a certain propagation length, with the increase of the coherence length, the modulus values of Stokes parameters S 1 and S 2 will increase, and their distribution will close to the axis, the rate of the distribution of the DOP with radius will increase.

Analysing the behaviour of partially coherent divergent Gaussian beams propagating through oceanic turbulence

Theoretical study of propagation behaviour of partially coherent divergent Gaussian beams through oceanic turbulence has been performed. Based on the previously developed knowledge of propagation of a partially coherent beam in atmosphere, the spatial power spectrum of the refractive index of ocean water, extended Huygens–Fresnel principle and the unified theory of coherence and polarization, analytical formulas for cross-spectral density matrix elements are derived. The analytical formulas for intensity distribution, beam width and spectral degree of coherence are determined by using cross-spectral density matrix elements. Then, the effects of some source factors and turbulent ocean parameters on statistical properties of divergent Gaussian beam propagating through turbulent water are analysed. It is found that beam’s statistical propagation behaviour is affected by both environmental and source parameters variations.