Statistics properties of a cylindrical vector partially coherent beam

Nonparaxial Propagation of Bessel Correlated Vortex Beams in Free Space

The nonparaxial propagation of partially coherent beams carrying vortices in free space is investigated using the method of decomposition of the incident field into coherent diffraction-free modes. Modified Bessel correlated vortex beams with the wavefront curvature are introduced. Analytical expressions are presented to describe the intensity distribution and the degree of coherence at different distances. The evolution of the intensity distribution during beam propagation for various source parameters is analyzed. The effects of nonparaxiality in the propagation of tightly focused coherent vortex beams are analyzed.

Focusing properties of a polarization mixing quadratic space-variant phase-modulated sinh-Gaussian vortex beam

This research explores the focusing characteristics of a polarization mixing quadratic space-variant phase-modulated sinh-Gaussian vortex beam. Various intriguing evolutionary trends of the focal pattern are demonstrated by the modulation of each parameter. The results show that the adjustable parameter C makes the focusing spot form an optical chain structure. The length of the structure and the number of dark optical traps in the structure can be altered by adjusting C. Simultaneously, the variation of beam order m will cause focal spot deformation. Moreover, the variation of the focal pattern indicates that polarization parameter B has the ability to adjust the position of the spot. In addition, the influence of topological charge l on the component field is also discussed. With the introduction of a polarization mixing quadratic space-variant phase, the focal pattern obtains a series of unique characteristics. These results have potential value for cutting-edge optical applications such as optical shaping, optical transmission, and multiple optical capture.

Polarization and coherence properties in self-healing propagation of a partially coherent radially polarized twisted beam

With the help of generalized Huygens-Fresnel integral, an analytical expression for the self-healing of a partially coherent radially polarized twisted (PCRPT) beam is derived. The coherence and polarization properties of the PCRPT beam in self-healing propagation are studied in detail. It shows that the existence of the twist phase is a double-edged sword for the self-healing properties of the beam. With the increase of the twist factor, the self-healing ability of beam intensity distribution decreases. However, the anti-disturbance performance of beam polarization improves at the same time. Besides, the polarization and coherence distribution of the beam are proved that own a slight self-healing ability when the obstacle is small. Our results will be helpful to the fields of optical tweezers, microscopy, optical communication, and so on.

Scattering of Partially Coherent Vector Beams by a Deterministic Medium Having Parity-Time Symmetry

We study the scattering properties of the partially coherent vector beams with the deterministic media having the classic symmetric and parity-time (PT) symmetric scattering potential functions. The closed-form expressions for the intensity and polarization matrix of the far-zone scattered field are obtained, under first-order Born approximation, when the partially coherent vector beams are taken to be radially polarized and the deterministic media are assumed as the four-point scatterers. We demonstrate both analytically and numerically that the far-zone scattered field becomes noncentrosymmetric and the directionality appears in the scattering pattern when the scattering potential function is switched from classic symmetry to PT symmetry. We show the effect of spatial coherence of the incident partially coherent vector beam on the directionality in scattering. We find that by turning the symmetry property of the spatial coherence function of the incident beam, i.e., into PT symmetry, the directionality in the far-zone scattering can be suppressed or enhanced, depending on the joint effect from the symmetry of the scattering potential and the symmetry of the spatial coherence. Our findings may be useful in the application of dynamic control of the directionality in light scattering.

Statistical properties of a partially coherent radially polarized vortex beam propagating in a uniaxial crystal

Free-space propagation and experimental generation of a partially coherent radially polarized (PCRP) vortex beam were studied recently [Opt. Express24, 13714 (2016)OPEXFF1094-408710.1364/OE.24.013714]. In this work, we explore the statistical properties of such a PCRP vortex beam propagating in a uniaxial crystal. We show that the anisotropy of the refractive index of the uniaxial crystal induces the asymmetrical distribution of the intensity, the degree and the state of polarization, as well as the degree of coherence of the beam during propagation. Further, by comparing the asymmetrical distribution of the statistical properties of the PRCP vortex beam with those of a PRCP beam without a vortex phase, we find that the asymmetrical features can be used for determining whether a PCRP beam carries the vortex phase. Further, we show that from the far-field distribution of the degree of coherence, we could quantify the topological charge and distinguish the handedness of the vortex phase. Our findings provide a novel approach for measuring the phase information of the partially coherent vortex beams.

Partially coherent radially polarized circular Airy beam

We propose and demonstrate a new, to the best of our knowledge, kind of partially coherent vector beam called the partially coherent radially polarized circular Airy beam (PCRPCAB). The PCRPCAB inherits the autofocusing ability of the radially polarized circular Airy beam (RPCAB) and can create an optical potential well at the center of the beam, whose depth can be adjusted by changing the coherent width. We find that, as coherent width decreases, the intensity becomes higher in the dark notch caused by the polarization singularity, and the singularity of the degree of polarization (DOP) remains along propagation, with its waist controllable by the coherent width. Our results make the PCRPCAB a good candidate for optical micromanipulation, disordered optical lattices, etc.

Partially coherent radially polarized fractional vortex beam

A new kind of partially coherent vector beam, named a partially coherent radially polarized fractional vortex (PCRPFV) beam, is introduced as a natural extension of the recently introduced scalar partially coherent fractional vortex beams [Zeng et al., Opt. Express26, 26830 (2018)10.1364/OE.26.026830]. Realizability conditions and propagation formulas for a PCRPFV beam are derived. Statistical properties of a focused PCRPFV beam, such as average intensity, degree of polarization, state of polarization and cross-spectral density matrix, are illustrated in detail and compared with that of a partially coherent radially polarized integer vortex beam and a scalar partially coherent fractional vortex beam. It is found that the statistical properties of a PCRPFV beam are qualitatively different from these simpler beam classes and are strongly determined by the vortex phase (i.e., fractional topological charge) and initial coherence width. We demonstrate experimental generation of PCRPFV beams and confirm their behavior. Our results will be useful for the rotating and trapping of particles, the detection of phase objects, and polarization lidar systems.

Statistical properties of partially coherent radially and azimuthally polarized rotating elliptical Gaussian beams in oceanic turbulence with anisotropy

A new class of partially coherent radially and azimuthally polarized rotating elliptical Gaussian (PCRPREG and PCAPREG) beams is introduced. The analytical expressions of the PCRPREG and PCAPREG beams propagating through anisotropy oceanic turbulence are derived based on the extended Huygens-Fresnel principle and the spatial power spectrum of oceanic turbulence. The effects of beam waist size w₀, coherence width σ₀, propagation distance z and oceanic turbulence parameters on the evolution statistics properties of PCRPREG and PCAPREG beams are studied in detail by numerical simulation. Our results indicate that with the increase of the propagation distance in the far field region, the normalized initial profile with a doughnut-like distribution of PCRPREG and PCAPREG beams gradually converts into a flat-topped one, and finally evolves into a Gaussian-like beam profile. We also find that the salinity-induced turbulence fluctuation makes a greater contribution to the decrease of beam quality compared with the temperature-induced turbulence fluctuation. Furthermore, the full width at half maximum becomes wider for the larger propagation distance z and wavelength λ or the smaller dissipation rate ε. Our work will pave the way for the development of underwater optical communication and underwater laser radar in oceanic environment.

Propagation characteristics of partially coherent circular Airy beams

The abruptly autofocusing properties of partially coherent circular Airy beam (CAB) with different spatial coherent length are theoretically investigated in this paper. It is found that, as spatial coherent length decreases, the size of the focal spot would increase and the focal intensity would decrease. But the abruptly autofocusing property for partially coherent CAB is still quite obvious, when comparing with the common partially coherent Gaussian beam under the same conditions; and its autofocusing position is less easily influenced by coherence. The influences of initial radius r₀ and decaying parameter a on the autofocusing property have also been investigated in the end.

Vector optical coherence lattices generating controllable far-field beam profiles

We introduce partially coherent vector sources with periodic spatial coherence properties, which we term vector optical coherence lattices (VOCLs), as an extension of recently introduced scalar OCLs. We derive the realizability conditions and propagation formulae for radially polarized VOCLs (i.e., a typical kind of VOCLs). We show that radially polarized VOCLs display nontrivial propagation properties and generate controllable intensity lattices in the far zone of the source (or in the focal plane of a lens). By adjusting source coherence, one can obtain intensity lattices with bright or dark nodes. The latter can be employed to simultaneously trap multiple particles or atoms as well as in free-space optical communications. We also report the experimental generation of radially polarized VOCLs and we characterize VOCLs propagation properties.

Random sources for cusped beams

We introduce two novel classes of partially coherent sources whose degrees of coherence are described by the rectangular Lorentz-correlated Schell-model (LSM) and rectangular fractional multi-Gaussian-correlated Schell-model (FMGSM) functions. Based on the generalized Collins formula, analytical expressions are derived for the spectral density distributions of these beams propagating through a stigmatic ABCD optical system. It is shown that beams belonging to both classes form the spectral density apex that is much higher and sharper than that generated by the Gaussian Schell-model (GSM) beam with a comparable coherence state. We experimentally generate these beams by using a nematic, transmissive spatial light modulator (SLM) that serves as a random phase screen controlled by a computer. The experimental data is consistent with theoretical predictions. Moreover, it is illustrated that the FMGSM beam generated in our experiments has a better focusing capacity than the GSM beam with the same coherence state. The applications that can potentially benefit from the use of novel beams range from material surface processing, to communications and sensing through random media.

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.

Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization

Scalar cosine-Gaussian-correlated Schell-model (CGCSM) beams of circular or rectangular symmetry were introduced just recently. In this paper, a new kind of partially coherent vector beam named vector CGCSM beam with radial polarization (i.e., radially polarized CGCSM beam) is introduced. The realizability conditions for a radially polarized CGCSM source and the beam condition for radiation generated by such source are derived. The statistical properties, such as the average intensity, the degree of coherence, the degree of polarization and the state of polarization, of a radially polarized CGCSM beam focused by a thin lens are analyzed in detail. It is found that the statistical properties of a radially polarized CGCSM beam are quite different from those of a conventional radial polarized partially coherent beam with Gaussian correlated Schell-model function. Furthermore, we first report experimental generation of a radially polarized CGCSM beam and measure its focusing properties. Our experimental results are consistent with the theoretical predictions.

Correlation singularities in a partially coherent electromagnetic beam with initially radial polarization

We have investigated the correlation singularities, coherence vortices of two-point correlation function in a partially coherent vector beam with initially radial polarization, i.e., partially coherent radially polarized (PCRP) beam. It is found that these singularities generally occur during free space propagation. Analytical formulae for characterizing the dynamics of the correlation singularities on propagation are derived. The influence of the spatial coherence length of the beam on the evolution properties of the correlation singularities and the conditions for creation and annihilation of the correlation singularities during propagation have been studied in detail based on the derived formulae. Some interesting results are illustrated. These correlation singularities have implication for interference experiments with a PCRP beam.

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.

Statistical properties in Young's interference pattern formed with a radially polarized beam with controllable spatial coherence

Experimental generation of a radially polarized (RP) beam with controllable spatial coherence (i.e., partially coherent RP beam) was reported recently [Appl. Phys. Lett. 100, 051108 (2012)]. In this paper, we carry out theoretical and experimental studies of the statistical properties in Young's two-slit interference pattern formed with a partially coherent RP beam. An approximate analytical expression for the cross-spectral density matrix of a partially coherent RP beam in the observation plane is obtained, and it is found that the statistical properties, such as the intensity, the degree of coherence and the degree of polarization, are strongly affected by the spatial coherence of the incident beam. Our experimental results are consistent with the theoretical predictions, and may be useful in some applications, where light field with special statistical properties are required.

Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov's power spectrum on the propagation factor are also analyzed in detailed.

Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited]

Partially coherent beams with nonconventional correlation functions have displayed many extraordinary properties, such as self-focusing and self-splitting, which are totally different from those of partially coherent beams with conventional Gaussian correlated Schell-model functions and are useful in many applications, such as optical trapping, free-space optical communications, and material thermal processing. In this paper, we present a review of recent developments on generation and propagation of partially coherent beams with nonconventional correlation functions.

Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam

In a recent publication (Appl. Phys. Lett. 100 (2012) 051108), a monochromatic partially coherent radially polarized (RP) beam was generated experimentally. In this paper, we analyze the spectral changes of a polychromatic partially coherent RP beam focused by a thin lens for the first time, and compare with that of a focused scalar polychromatic GSM beam. Furthermore, we report experimental generation of a polychromatic partially coherent RP beam and carry out experimental measurement of the spectral changes of such beam focused by a thin lens. Our results show that the behavior of the spectral changes of a focused polychromatic partially coherent RP beam is different from that of a focused scalar polychromatic GSM beam. Our experimental results are consistent with the theoretical predictions.

Nonparaxial propagation properties of a vector partially coherent dark hollow beam

Based on the generalized Raleigh-Sommerfeld diffraction integrals, analytical nonparaxial propagation formulas for the elements of the cross-spectral density matrix of a vector partially coherent dark hollow beam (DHB) in free space are derived. The effect of spatial coherence and beam waist sizes on the statistical properties of a nonparaxial vector DHB is studied numerically. It is found that one can modulate the statistical properties of a nonparaxial vector DHB by varying its initial spatial coherence, which will be useful in some applications where nonparaxial beams are commonly encountered.

Coherence and polarization properties of a radially polarized beam with variable spatial coherence

In a recent publication [Appl. Phys. Lett, 100, 051108 (2012)], a radially polarized (RP) beam with variable spatial coherence (i.e., partially coherent RP beam) was generated experimentally. In this paper, we derive the realizability conditions for a partially coherent RP beam, and we carry out theoretical and experimental study of the coherence and polarization properties of a partially coherent RP beam. It is found that after passing through a thin lens, both the degree of coherence and the degree of polarization of a partially coherent RP beam varies on propagation, while the state of polarization of the completely polarized part of such beam remains invariant. The variations of the degree of coherence and the degree of polarization depend closely on the initial spatial coherence. Our experimental results agree well with the theoretical predictions.

Statistical properties of a nonparaxial cylindrical vector partially coherent field in free space

Analytical nonparaxial propagation formula for the cross-spectral density matrix of a cylindrical vector partially coherent beam in free space is derived based on the generalized Raleigh-Sommerfeld diffraction integrals. Statistical properties, such as average intensity, degree of polarization and degree of coherence, of a nonparaxial cylindrical vector partially coherent field are illustrated numerically, and compared with that of a paraxial cylindrical vector partially coherent beam. It is found that the statistical properties of a nonparaxial cylindrical vector partially coherent field are much different from that of a paraxial cylindrical vector partially coherent beam, and are closely determined by the initial beam width and correlation coefficients. Our results will be useful for modulating the properties of a nonparaxial cylindrical vector partially coherent field.

Degree of coherence in curvilinear coordinates and its application to scattering

In the traditional treatment of the spectral degree of coherence, the Cartesian coordinate system is deployed to describe the electromagnetic field. In the description of the far field scattered from random media, however, the spherical polar coordinates system is more suitably used due to the field's outgoing spherical form. We hence derive the expression for the spectral degree of coherence in the spherical polar coordinates system. An example of one polychromatic plane wave scattered by a collection of identical particles is given.

Modulation of spectral intensity, polarization and coherence of a stochastic electromagnetic beam

Analytical formula for the cross-spectral density matrix of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam truncated by a circular phase aperture propagating in free space is derived with the help of a tensor method, which provides a reliable and fast way for studying the propagation and transformation of a truncated EGSM beam. Statistics properties, such as the spectral intensity, the degree of coherence, the degree of polarization and the polarization ellipse of a truncated EGSM beam in free space are studied numerically. The propagation factor of a truncated EGSM beam is also analyzed. Our numerical results show that we can modulate the spectral intensity, the polarization, the coherence and the propagation factor of an EGSM beam by a circular phase aperture. It is found that the phase aperture can be used to shape the beam profile of an EGSM beam and generate electromagnetic partially coherent dark hollow or flat-topped beam, which is useful in some applications, such as optical trapping, material processing, free-space optical communications.