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Based on the extended Huygens–Fresnel integral, the analytical expressions for the average intensity of a partially coherent radially polarized rotating elliptical cosine-Gaussian optical lattice (PCRPREGOL) in the anisotropic turbulence are derived. We find that the lattice intensity profile and the spatial degree of coherence will display periodicity reciprocity over a long propagation distance even though the lattices are affected by the turbulence. The periodicity reciprocity of PCRPREGOL is not only affected by the lattice parameter but also affected by the beam order factor. The intensity pattern of the PCRPREGOL in a certain distance can be modulated by the lattice lobes, and some interesting phenomena appear due to the overlap of four lattice arrays during the evolution of the PCRPREGOL. At the same time, the four periodic grid patterns and the tapered light intensity composed by four parts of the PCRPREGOL can be flexibly tuned by modulating the source correlation parameters and the lattice constant. Last but not least, we also discuss the coherent and polarized characteristics of the PCRPREGOL in the anisotropic turbulence. [ABSTRACT FROM AUTHOR]

Quantitative phase microscopy (QPM), as a label‐free and nondestructive technique, has been playing an indispensable tool in biomedical imaging and industrial inspection. Herein, we introduce a reflectional quantitative differential phase microscopy (termed RQDPM) based on polarized wavefront phase modulation and partially coherent full‐aperture illumination, which has high spatial resolution and spatio‐temporal phase sensitivity and is applicable to opaque surfaces and turbid biological specimens. RQDPM does not require additional polarized devices and can be easily switched from reflectional mode to transmission mode. In addition, RQDPM inherits the characteristic of high axial resolution of differential interference contrast microscope, thereby providing topography for opaque surfaces. We experimentally demonstrate the reflectional phase imaging ability of RQDPM with several samples: semiconductor wafer, thick biological tissues, red blood cells, and Hela cells. Furthermore, we dynamically monitor the flow state of microspheres in a self‐built microfluidic channel by using RQDPM converted into the transmission mode. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

For a partially coherent Laguerre–Gaussian (PCLG) vortex beam, information regarding the topological charge (TC) is concealed in the cross-spectral density (CSD) function phase. Herein, a flexible method for the simultaneous determination of the sign and magnitude of the TC for a PCLG vortex beam is proposed based on the measured CSD amplitude and phase after the beam propagates through a dual cylindrical lens with adjustable angles. Both the stripes in the CSD amplitude and phase exhibit quantitative relationships with the value of TC, that is, N = 2 l + 1 . Meanwhile, the angle adjustability of cylindrical lenses allows flexible measurements, thus rendering the scheme effective for both high and extreme coherences. [ABSTRACT FROM AUTHOR]

This study explored the impact of atmospheric turbulence on partially coherent light propagation. Atmospheric turbulence causes random modulation of the intensity and phase of light, resulting in a speckle pattern in the far field. This study focused on partially coherent Gaussian Schell model beams and derived an analytical expression of the cross-spectral density function for their transmission through atmospheric turbulence, based on the generalized Huygens–Fresnel principle and the Tatarski spectrum model. Numerical simulations were used to investigate the effects of the source parameters and turbulence strength on the intensity distribution, beam width, and coherence length of partially coherent light in horizontal atmospheric transmission. The results demonstrate that diffraction-induced broadening primarily affects the intensity distribution of light in free-space transmission. Short transmission distances in atmospheric turbulence have comparable characteristics to those in a vacuum; however, as the turbulence intensity and transmission distance increase, the beam broadening effect amplifies, and the coherence length is reduced. The findings are relevant to the design of acquisition, pointing, and tracking systems for wireless laser communication systems and offer insights into the optimization of optical systems for atmospheric conditions. [ABSTRACT FROM AUTHOR]

In this paper, partially coherent radially polarized (RP) Laguerre-Gaussian (LG) rotationally symmetrical power-exponent phase vortex (RSPEPV) beams with the LG-correlated Schell-model (LGSM) were introduced. The statistical properties of the tightly focused beams, including intensity distribution, degrees of polarization and coherence, and Stokes vector, were studied based on vectorial Richards-Wolf diffraction integral theory. Moreover, when the distance between focal plane and the observation plane z = 0, the relationships between the tight-focusing properties of RP-LG-RSPEPV beams with LGSM and the order of LGSM p', topological charges l, power exponent n, spatial correlation δ, and radial index p were investigated. The results show that by changing the order of LGSM, topological charge, power exponent, spatial correlation length, and radial index, the focal spot distribution of various shapes can be obtained. This work provides ideas for the application of partially coherent beams in particle capture and optical tweezers. [ABSTRACT FROM AUTHOR]

The effect of anisotropic atmosphere turbulence on propagation characteristics of an electromagnetic twisted Gaussian Schell-model array (EM TGSMA) beam is investigated. An analytical expression for the cross-spectral density function of such beam propagating through anisotropic turbulent atmosphere is derived and used to explore the evolutionary behavior of the spectral intensity, degree of polarization (DOP) and degree of coherence (DOC). An example illustrates the fact that twisted strength and anisotropic turbulent factors have an important impact on the behavior of spectral density, DOC and DOP, in particular. The rotation angle of the array beams can also be controlled by adjusting twisted strength. Furthermore, strong anisotropic turbulence was also found to cause significant mergence of the array beams. Our results might be beneficial for free-space communications of the partially coherent beams endowed with twist. [ABSTRACT FROM AUTHOR]

We investigate the behavior of the orbital angular momentum (OAM) flux density of partially coherent vortex (PCV) beams in atmospheric turbulence. It is shown that for PCV beams with different spatial coherence structures, the OAM flux density distribution exhibits rich variations along the propagation path. Our findings provide insight into the use of the OAM in free-space optical communications when turbulence effects are significant.

In the ABCD optical system, the propagation properties and the radiation forces are obtained by studying the cross spectral density of partially coherent self-shifting cosine-Gaussian beams. A self-shifting phenomenon occurs when the beams propagate in the strongly nonlocal nonlinear medium. The shifting parameters could influence the bend characteristics of the propagation trajectory and the beam center, while the power ratio affects the periods of the parabolic trajectory. Furthermore, the radiation forces on a Rayleigh particle in the focusing optical system are studied, and the obtained force distributions depend on the refractive index, the shifting parameters, and the coherence widths. What we report here has potential applications in optical communication and optical tweezing.

For a partially coherent Laguerre–Gaussian (PCLG) vortex beam, information regarding the topological charge (TC) is concealed in the cross-spectral density (CSD) function phase. Herein, a flexible method for the simultaneous determination of the sign and magnitude of the TC for a PCLG vortex beam is proposed based on the measured CSD amplitude and phase after the beam propagates through a dual cylindrical lens with adjustable angles. Both the stripes in the CSD amplitude and phase exhibit quantitative relationships with the value of TC, that is, N=2l+1. Meanwhile, the angle adjustability of cylindrical lenses allows flexible measurements, thus rendering the scheme effective for both high and extreme coherences.

In this paper, partially coherent radially polarized (RP) Laguerre-Gaussian (LG) rotationally symmetrical power-exponent phase vortex (RSPEPV) beams with the LG-correlated Schell-model (LGSM) were introduced. The statistical properties of the tightly focused beams, including intensity distribution, degrees of polarization and coherence, and Stokes vector, were studied based on vectorial Richards-Wolf diffraction integral theory. Moreover, when the distance between focal plane and the observation plane z = 0, the relationships between the tight-focusing properties of RP-LG-RSPEPV beams with LGSM and the order of LGSM p’, topological charges l, power exponent n, spatial correlation δ, and radial index p were investigated. The results show that by changing the order of LGSM, topological charge, power exponent, spatial correlation length, and radial index, the focal spot distribution of various shapes can be obtained. This work provides ideas for the application of partially coherent beams in particle capture and optical tweezers.

This study explored the impact of atmospheric turbulence on partially coherent light propagation. Atmospheric turbulence causes random modulation of the intensity and phase of light, resulting in a speckle pattern in the far field. This study focused on partially coherent Gaussian Schell model beams and derived an analytical expression of the cross-spectral density function for their transmission through atmospheric turbulence, based on the generalized Huygens–Fresnel principle and the Tatarski spectrum model. Numerical simulations were used to investigate the effects of the source parameters and turbulence strength on the intensity distribution, beam width, and coherence length of partially coherent light in horizontal atmospheric transmission. The results demonstrate that diffraction-induced broadening primarily affects the intensity distribution of light in free-space transmission. Short transmission distances in atmospheric turbulence have comparable characteristics to those in a vacuum; however, as the turbulence intensity and transmission distance increase, the beam broadening effect amplifies, and the coherence length is reduced. The findings are relevant to the design of acquisition, pointing, and tracking systems for wireless laser communication systems and offer insights into the optimization of optical systems for atmospheric conditions.

We introduce a novel type of twisted partially coherent beams with a nonconventional correlation function, named the twisted Hermite-Gaussian correlated Schell-model (THGCSM) beam. The condition that a twist phase can be imposed on a partially coherent beam is addressed for Schell-model fields endowed with rectangular symmetry. Further, the analytical formula for the THGCSM beam propagating in free space has been derived with the help of the generalized Collins formula. The propagation properties, such as the spectral density and the spectral degree of coherence (SDOC) of the THGCSM beam, also have been studied in detail by some numerical examples. The numerical results show that the twist phase plays a role in resisting beam splitting, caused by the correlation structure, and induces the rotation of the distribution of the SDOC on propagation. Moreover, it is interesting to find that when the beam carries a twist phase, this will endow the beam the ability to maintain its distribution of the SDOC on propagation and enhance the self -reconstruction capability of the SDOC. Our results may provide new insights into nonconventional partially coherent beams with twisted phase and may be useful in some applications, such as optical communications and information recovery.

We report on a partially coherent power-exponent-phase vortex beam (PC-PEPV), whose spatial coherence is controllable and the initial phase exhibits a periodic power exponential change. The PC-PEPV beam was generated experimentally with various spatial coherence widths, and its propagation properties were studied both numerically and experimentally. By modulating the topological charge (TC) and power order of the PC-PEPV beam, the structure of the vortex beam can be adjusted from circular to elliptic, triangular, quadrangle, and pentagon. When the power order is odd, the PC-PEPV beam with a negative TC can be generated, and the profiles of the PC-PEPV beam can be precisely controlled via adjusting the value of the power order. For the case of high spatial coherence width, the number of the dark cores in the polygonal intensity array of the PC-PEPV beam equals the magnitude of the TC. However, when decreasing the spatial coherence width, the dark cores vanish and the intensity gradually transforms into a polygonal light spot. Fortunately, from the modulus and phase distributions of the cross-spectral density (CSD), both the magnitude and sign of the TC can be determined. In the experiment, the modulus and phase distribution of the CSD are verified by the phase perturbation method. This study has potential applications in beam shaping, micro-particle trapping, and optical tweezers.

Based on the first-order Born approximation and the Rayleigh scattering theory, the analytical expressions of the weak scattering and the radiation force of two types of partially coherent twisted beams are derived, respectively. Numerical examples show that the scattering's directionality and the radiation force's magnitude can be controlled by the twist factor and the cross-strength factor. Moreover, it can be obtained that these two beams can capture particles into the beams' center transversely and push the particles to move forward in the axial direction, which may be useful in optical micromanipulation. For example, we can use these beams to filter out high refractive index particles from clusters and separate them through axial force. This paper will be helpful to the fields of optical tweezers, optical communication, and so on. • A comparative study of two types of twisted beams is conducted. • The analytical expressions of the two types of twisted beams' weak scattering and radiation force properties are derived. • The scattering's directionality and the radiation force's magnitude can be controlled by the beam factors. • These two beams can transversely capture particles and push the particles to move forward in the axial direction. [ABSTRACT FROM AUTHOR]

We develop a Q-switched degenerate laser, delivering a partially coherent light pulse of duration about 16 ns. The spatial coherence of the output laser pulse can be varied by tuning the spatial filter inside the laser resonator, and the oscillating transverse mode structure can be determined by measuring the degree of coherence of the output laser pulse. It is shown that the larger is the diameter of the spatial filter, the more are the oscillating transverse modes, and the lower is the degree of coherence. Based on coherent-mode representation for the partially coherent source, we can estimate the transverse mode contribution to the output partially coherent laser. The experimental results on suppressing speckle demonstrate that the generated partially coherent light possesses the characteristics of rapid reduction of spatial coherence, making it an ideal source for high -speed imaging and ranging applications. [ABSTRACT FROM AUTHOR]

Basic coherent diffraction imaging methods strongly rely on having a highly coherent illumination in order to reconstruct the phase accurately. However, regardless of considering the turbulent transport medium, the instability of the system or the generation mechanism of the light source, partially coherent illumination is more common in real case. In this paper, we proposed an efficient microscopic phase imaging method to study normal and abnormal cervical exfoliated cells. By applying three phase modulations in a single point of the sample's transmitted field, the phase can be retrieved with correspoding three intensities under partially coherent illumination. Compared with intensity map, we can efficiently and clearly judge the proportion of high density shrinking abnormal cells from the phase distributions, which provides a confident analysis and evaluation basis for early medical diagnosis of cervical cancer. This study also has potential applications in noninvasive optical imaging of dynamic biological tissues. [ABSTRACT FROM AUTHOR]

A partially coherent approach for computing the electromagnetic response of a layered medium having random rough interfaces and a random dielectric profile is presented as an alternative to the full-wave solution of the problem. The statistical nature of this problem, in particular, the random dielectric profile, introduces randomness in the phase of the electromagnetic field such that the field loses its phase coherency after traveling in the layered medium for a few correlation lengths of the permittivity. In this situation, there is a coherency length within which a coherent solution of Maxwell’s equation is required. For the distances beyond this coherency length, a combined coherent–incoherent cascading approach can be applied to reduce the computational complexity of the problem. The coherent response of each “block” within the medium (with a length approximately the coherency length) can be cascaded incoherently ignoring the phase response without losing accuracy. Cascading equations for block bistatic scattering are applied, and solutions of the equivalent block parameters are obtained by iteration up to the second order of multiple scattering. The proposed method is described in this article, and the numerical results are shown to compare the proposed cascading approach with the results obtained from the fully coherent solution. [ABSTRACT FROM AUTHOR]

We investigate intracavity second harmonic generation (SHG) in a degenerate laser for generating green laser with controllable degree of coherence. It is shown that spatial coherence of the SHG emission can be controlled by varying the diameter of the limiting aperture in the degenerate laser resonator. The pumping power also affects the number of the oscillating transverse modes, so that influences the spatial coherence of the output laser. The laser of low coherence for speckle reduction has been demonstrated. It is shown that the laser of low spatial coherence may find applications in imaging, and laser display etc. [ABSTRACT FROM AUTHOR]

Featured Application: The results obtained in this paper will provide a scientific reference for the applications of ultra-short pulses in laser micromachining. Partially coherent pulsed beams have many applications in pulse shaping, fiber optics, ghost imaging, etc. In this paper, a novel class of partially coherent pulsed (PCP) sources with circular spatial coherence distribution and sinc temporal coherence distribution is introduced. The analytic formula for the spatial-temporal intensity of pulsed beams generated by this kind of source in dispersive media is derived. The evolution behavior of spatial-temporal intensity of the pulsed beams in water and air is investigated, respectively. It is found that the pulsed beams exhibit spatial-temporal self-focusing behavior upon propagation. Furthermore, a physical interpretation of the spatial-temporal self-focusing phenomenon is given. This is a phenomenon of optical nonlinearity, which may have potential application in laser micromachining and laser filamentation. [ABSTRACT FROM AUTHOR]

Abstract With the increasing demands for detection range and accuracy in heterodyne lidars, precise analyses of system efficiency are of growing importance. An extended system efficiency model is established for the detection of heterodyne lidar returns backscattered by aerosols in turbulent atmosphere; the extended Huygens–Fresnel integral and the Tatarskii spectrum are used in the derivations of system efficiency and effective coherent solid angle(ECSA). The impacts of beam truncation, optical aperture, atmospheric turbulence and laser source coherence on the performance of a monostatic heterodyne lidar are analyzed in detail. Numerical results suggest that the optimal system efficiency and beam truncation change with laser coherence, turbulence and distance for a collimated system. Lidars with larger optical apertures may have worse system efficiencies which can be below 5.5% with the aperture of 160 mm when C n 2 is 1 0 − 14 m − 2 ∕ 3. Moreover, similar ECSAs can be obtained with both small and large optical apertures. When C n 2 is 1 0 − 18 m − 2 ∕ 3 and 1 0 − 14 m − 2 ∕ 3 , the ECSAs with the laser source coherence factor of 101 have extra attenuations of 16.52dB and 4.83dB within 30 km, which indicates that the partial coherence of laser source should be considered in the performance analyses. [ABSTRACT FROM AUTHOR]

A new family of partially coherent pulsed beams with spatial cosine-Gaussian and temporal Laguerre–Gaussian correlations, named spatial cosine-Gaussian and temporal Laguerre–Gaussian correlated Schell-model (SCTLGSM) pulsed beams, is introduced. An analytic propagation formula is derived for the SCTLGSM pulsed beam through the spatiotemporal ABCD optical system characterizing a continuous dispersive medium. As an example, the evolution of spatiotemporal intensity of the SCTLGSM pulsed beam in a still, pure water column is then investigated. It is found that the SCTLGSM pulsed beams simultaneously exhibit spatiotemporal self-splitting and self-focusing phenomena, which can be attributed to the special spatial/temporal coherence structures and the presence of pulse chirper in the source plane. The physical interpretation of the obtained phenomena is given. The results obtained in this paper will be of interest in underwater optical technologies, e.g., directed energy and communications.

In this paper, we study the second-order statistics of a modified complex Lorentz–Gaussian-correlated (MCLGC) beam, which is a new type of partially coherent beam capable of producing an Airy-like intensity pattern in the far field, propagation through marine atmospheric turbulence. The propagation formula of spectral density is derived by the extended Huygens–Fresnel integral, which could explicitly indicate the interaction of turbulence on the beams’ spectral density under propagation. The influences of the structure constant of the turbulence, initial coherence width and wavelength on the spectral density are investigated in detail through numerical examples. In addition, analytical expressions for the r.m.s beam width, divergence angle and M2 factor of the MCLGC beam in the marine turbulence are also derived with the help of the Wigner distribution function. The results reveal that the beam spreads much faster, and the M2 factor deteriorates severely with the increase of the structure constant and the decrease of the inner scale size, whereas the outer scale size has little effect on these two quantities.

Vortex beams with helical phase, carrying phase singularity and orbital angular momentum, have attract great attention in the past decades due to their wide applications in optical communications, optical manipulation, super-resolution imaging and so on. Vortex beams with low spatial coherence, i.e. partially coherent vortex beams, carrying correlation singularity, display some unique properties during propagation, e.g. self-shaping, self-splitting and self-reconstruction. Partially coherent vortex beams exhibit some advantages over coherent vortex beams in some applications, such as remote sensing, laser radar and free-space optical communications. This review summarizes research progress on partially coherent vortex beams, including theoretical models, propagation properties, generation and topological charge determination.

We derived analytical expressions for the correlation of intensity fluctuations of a partially coherent Gaussian Schell-model plane-wave pulse scattered by deterministic and random media. Our results extend the study of correlation of intensity fluctuations at two space points for scattered stationary fields to that at two time points for scattered non-stationary fields. [ABSTRACT FROM AUTHOR]

This work presents the exact symbol error rate (SER) analysis of semi-coherent demodulated systems in the presence of imperfect knowledge of the channel estimates. The SER is derived in the context of orthogonal frequency division multiplexing (OFDM) systems where a modulation-hybrid frame structure is considered to enable blind channel estimation using a decision-directed approach. The exact SER is derived and presented in a closed-form analytical expression, which is then used to compute an accurate formula for the mean squared error (MSE) of the channel estimates. The obtained analytical and simulation results show that the SER and MSE are highly dependent on the channel correlation factor. However, reliable SER can still be obtained for most practical channel models, particularly when receiver diversity is incorporated. [ABSTRACT FROM AUTHOR]

Featured Application: The results provide a useful guideline for manipulation of novel vector structure beams by using twist phases and customized correlation functions, and promote important potential applications, ranging from beam shaping, optical tweezers, optical imaging, and free space optical communications. Recently, partially coherent beams with twist phases have attracted growing interest due to their nontrivial dynamic characteristics. In this work, the propagation characteristics of a twisted cosine-Gaussian correlated radially polarized beam such as the spectral intensity, the spectral degree of coherence, the degree of polarization, the state of polarization, and the spectral change are investigated in detail. Due to the presence of the twisted phase, the beam spot, the degree of coherence, and the state of polarization experience rotation during transmission, but the degree of polarization is not twisted. Meanwhile, although their rotation speeds closely depend on the value of the twist factor, they all undergo a rotation of π / 2 when they reach the focal plane. Furthermore, the effect of the twist phase on the spectral change is similar to the coherence, which is achieved by modulating the spectral density distribution during transmission. The twist phase opens up a useful guideline for manipulation of novel vector structure beams and enriches potential applications in the field of beam shaping, optical tweezers, optical imaging, and free space optical communications. [ABSTRACT FROM AUTHOR]

We study the problem of coupling partially coherent radially polarized (PCRP) vortex beams into a single-mode optical fiber. Using the well-known concept of the cross-spectral density (CSD) matrix, we derive a general expression for the coupling efficiency of the partially coherent beam into a single-mode fiber. We adopt PCRP vortex beams for incident beams and use our general results to discuss the effects of the coherence, topological charge, and wavelength on the coupling efficiency of an optical beam focused onto a single-mode fiber with a lens. Our results should be useful for any application that requires coupling of partially coherent beams into optical fibers. [ABSTRACT FROM AUTHOR]

The beam wander properties of coherent and partially coherent Airy beam arrays in a turbulent atmosphere are investigated. Based on the analytical results, we find that the beam wander of partially coherent Airy beam arrays is significantly reduced compared with the wander of a partially coherent Airy beam by numerical simulation. Moreover, the beam wander of a 2 × 2 partially coherent Airy beam arrays is significantly reduced compared with the wander of a 2 × 2 partially coherent Gaussian beam arrays. By using the definition of beam wander arrays factor which is used to characterize the capability of beam arrays for reducing the beam wander effect compared with a single beam, we find that the arrays factor of partially coherent Airy beam arrays is significantly less than that of partially coherent Gaussian beam arrays with the same arrays order. We also find that an artificial reduction of the initial coherence of laser arrays can be used to decrease the beam wander effect. These results indicate that the partially coherent Airy beam arrays have potential applications in long-distance free-space optical communications. [ABSTRACT FROM AUTHOR]

Partially coherent pulsed beams have many applications in pulse shaping, fiber optics, ghost imaging, etc. In this paper, a novel class of partially coherent pulsed (PCP) sources with circular spatial coherence distribution and sinc temporal coherence distribution is introduced. The analytic formula for the spatial-temporal intensity of pulsed beams generated by this kind of source in dispersive media is derived. The evolution behavior of spatial-temporal intensity of the pulsed beams in water and air is investigated, respectively. It is found that the pulsed beams exhibit spatial-temporal self-focusing behavior upon propagation. Furthermore, a physical interpretation of the spatial-temporal self-focusing phenomenon is given. This is a phenomenon of optical nonlinearity, which may have potential application in laser micromachining and laser filamentation.

We derived analytical expressions for the correlation of intensity fluctuations of a partially coherent Gaussian Schell-model plane-wave pulse scattered by deterministic and random media. Our results extend the study of correlation of intensity fluctuations at two space points for scattered stationary fields to that at two time points for scattered non-stationary fields.

We study the problem of coupling partially coherent radially polarized (PCRP) vortex beams into a single-mode optical fiber. Using the well-known concept of the cross-spectral density (CSD) matrix, we derive a general expression for the coupling efficiency of the partially coherent beam into a single-mode fiber. We adopt PCRP vortex beams for incident beams and use our general results to discuss the effects of the coherence, topological charge, and wavelength on the coupling efficiency of an optical beam focused onto a single-mode fiber with a lens. Our results should be useful for any application that requires coupling of partially coherent beams into optical fibers.

Recently, partially coherent beams with twist phases have attracted growing interest due to their nontrivial dynamic characteristics. In this work, the propagation characteristics of a twisted cosine-Gaussian correlated radially polarized beam such as the spectral intensity, the spectral degree of coherence, the degree of polarization, the state of polarization, and the spectral change are investigated in detail. Due to the presence of the twisted phase, the beam spot, the degree of coherence, and the state of polarization experience rotation during transmission, but the degree of polarization is not twisted. Meanwhile, although their rotation speeds closely depend on the value of the twist factor, they all undergo a rotation of π / 2 when they reach the focal plane. Furthermore, the effect of the twist phase on the spectral change is similar to the coherence, which is achieved by modulating the spectral density distribution during transmission. The twist phase opens up a useful guideline for manipulation of novel vector structure beams and enriches potential applications in the field of beam shaping, optical tweezers, optical imaging, and free space optical communications.

Propagation properties of a partially coherent anomalous vortex beam (PCAVB) through the anisotropic turbulent atmosphere are studied. Based on the generalized anisotropic von-Karman spectrum and Rytov approximation, the mathematical expressions of mode probability, energy content, and spiral spectrum of the PCAVB are obtained. The effects of anisotropic turbulence and source parameters on the PCAVB's signal orbital angular momentum (OAM) modal crosstalk are investigated. According to numerical findings, the transmission performance of the PCAVB can be improved by increasing the anisotropy coefficient, the beam order, the partial coherence length of the beam source, or reducing the OAM mode. In some instances, the PCAVB also shows stronger resistance to turbulence than the partially coherent Laguerre-Gaussian beam (PCLGB). This research may be helpful for constructing optical vortex communication systems as well as for comprehending the optical transmission mechanism in turbulent fluids. • Propagation properties of partially coherent anomalous vortex beam through the anisotropic turbulence are studied. • The formulas of mode probability and spiral spectrum of the partially coherent anomalous vortex beam are obtained. • The effects of atmospheric conditions and beam parameters on the OAM modal crosstalk are numerically analyzed. • Some strategies to reduce modal crosstalk in the anisotropic turbulence are discussed. [ABSTRACT FROM AUTHOR]

An analytical formula for the multi-Gaussian Schell model is derived for the beam propagating in a uniaxial crystal orthogonal to the optical axis. The propagation properties of multi-Gaussian Schell model beams in a uniaxial crystal orthogonal to the optical axis is investigated by using the analytical formula. Some results are illustrated by numerical examples related to the propagation properties of multi-Gaussian Schell model beams. It is found that the propagation properties of the multi-Gaussian Schell model beams are very different from the propagation properties in the free space. They are closely related to the initial coherence and the ratio of the extraordinary and ordinary refractive indices. The results provide a way for studying the propagation properties of the multi-Gaussian Schell model beams in the uniaxial crystal orthogonal to the optical axis. [ABSTRACT FROM AUTHOR]

This paper investigated the focal shift of partially coherent dark hollow Gaussian beams through a thin lens system. An analytic expression of the irradiance distribution of the focusing partially coherent dark hollow Gaussian beams in the back focal plane has been given by using the Collins formula. The focus shift of focused partially coherent dark hollow Gaussian beams in different parameters is studied in detail by numerical calculations. It is found that the absolute value of the focal shift of partially coherent dark hollow Gaussian beams decreases as the transverse coherence width or the order of the dark hollow Gaussian beams or a parameter of the dark hollow Gaussian beams increases. [ABSTRACT FROM AUTHOR]

Multidimensional synthetic aperture radar (SAR) imaging is a technique based on coherent SAR data combination for space (full 3-D) and space/deformation-velocity (4-D) analysis. It extends SAR interferometry and differential interferometry concepts, offering new options for the analysis and monitoring of ground scenes. In this paper, we consider the problem of detecting scatterers showing partial correlation properties induced by simultaneous acquisitions from satellite formations or an uneven temporal distribution of satellite constellations. To this end, we first provide a general model for the pixel imaged by a multidimensional SAR system. Then, we design a constant false alarm rate (CFAR) decision rule accounting for the presence of partially coherent scatterers. At the analysis stage, we assess the performance of the new detector also in comparison with a previously proposed CFAR scheme, developed in the context of SAR tomography for fully coherent scatterers. [ABSTRACT FROM PUBLISHER]

With the help of the Rayleigh-Sommerfeld diffraction integral, an analytical formula for the spectral density of a nonparaxial polychromatic partially coherent (NPPC) standard or elegant Laguerre-Gaussian (LG) beam propagating through free space is derived. The evolution properties of the intensity distribution of a NPPC standard or elegant LG beam are studied numerically. It is found that the behavior of the intensity distribution of the NPPC standard or elegant LG beam is determined by the initial beam parameters (i.e., beam waist size, spatial coherence width and beam orders). Furthermore, we also study the influence of the initial beam parameters on the spectral change of a NPPC standard or elegant LG beam upon propagation in free space. It is shown that the on-axis spectral shift of a NPPC standard LG beam is almost the same with that of a NPPC elegant LG beam when the initial beam parameters of two type beams are identical. However, the difference between the off-axis spectral shift between a NPPC standard LG beam and a NPPC elegant LG beam is enhanced with the decrease of beam waist size or with the increase of spatial coherence width and beam mode orders. [ABSTRACT FROM AUTHOR]

Abstract: Based on the extended Huygens-Fresnel integral principle and unified theory of coherence and polarization of light, the change in various propagation properties of partially coherent radially polarized doughnut (PCRPD) beam through the turbulent ocean is studied. The ocean-induced fluctuations in the refractive index are assumed to be driven by temperature and salinity fluctuations. Numerical examples of change in the optical intensity, degree of polarization, degree of coherence are presented for the PCRPD beam. The results show that the oceanic turbulence parameters and the initial parameters of light source have significant influence on the intensity, degree of polarization, and degree of coherence for the PCRPD beam. [Copyright &y& Elsevier]

Abstract: According to the definition of the degree of paraxiality for a monochromatic light beam, analytical expressions for the degree of paraxiality of coherent and partially coherent Airy beams are derived. Numerical results show that the degree of paraxiality of coherent and partially coherent Airy beams is determined not only by the characteristic length of the incident beam, but also by the exponentially truncation factor of the beam. The degree of paraxiality is also dependent on the initial coherence length of Airy beam. Our results are helpful to determine an Airy beam be paraxial or nonparaxial. [Copyright &y& Elsevier]

Abstract: Based on the extended Huygens–Fresnel principle, we study the propagation properties of partially coherent double-vortex beams in turbulent atmosphere. The intensity distribution of the beams on propagation and the influence of the characteristic parameters are investigated in great detail. It is shown that when the beams propagate in turbulent atmosphere, the intensity distributions are of double-ring structure near the source plane, but they will experience change, which are determined by the topological charges, the spatial coherence, source beam width and atmospheric turbulence. These results may have applications in space optical communication. [Copyright &y& Elsevier]

Abstract: The scattering of a partially coherent plane-wave pulse on a deterministic sphere is investigated. Analytical expression for the mutual coherence function of the scattered field is derived. It is shown that we can obtain the information of the sphereʼs position and its effective radius by measuring the time delay and pulse duration of the scattered field. The dependence of the pulse duration and temporal coherence length of the scattered field on the scattering angle and the parameters of the incident pulse is also illustrated numerically. [Copyright &y& Elsevier]

Abstract: In view of second-order coherence theory, the generalized diffractive axicon illuminated by partially coherent Gaussian Schell-model (GSM) beams is analyzed. An analytical equation for focal depth of axicon without aperture illuminated by spatial partially coherent GSM beam is derived. We showed that the off-axis images can be evaluated by using the method of stationary phase at any correlation state, hence we demonstrated that the intensity distribution of diffracted beam is a superposition of Bessel Beams of various orders. We also showed that the diffracted beam is nondiffractive only on the boundaries of the focal depth. [Copyright &y& Elsevier]

Abstract: By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities. [ABSTRACT FROM AUTHOR]