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

Young's double-slit experiment with a partially coherent vortex beam

We perform a Young's double-slit experiment with a partially coherent vortex beam (PCVB) and explore its cross-spectral density (CSD) at the focal plane after passing through a double-slit. Our results reveal that the phase of the CSD distribution with respect to an on-axis reference point can simultaneously quantitatively characterize the sign and magnitude of the topological charge (TC) carried by such a beam. In particular, the magnitude of the TC is half of the number of coherence singularities and the sign of the TC is determined by the phase winding of the coherence singularities (i.e., counterclockwise- and clockwise increases correspond to positive and negative, respectively). Based on this property, we present and demonstrate experimentally a simple technique to measure the sign and magnitude of the TC of a PCVB through its CSD distribution after a double-slit. Our method allows for easy measurement of the TC by being conceptually simpler than other methods.

Propagation Characteristics of a Twisted Cosine-Gaussian Correlated Radially Polarized Beam

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.

Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam

Partially coherent radially polarized (PCRP) beam was introduced and generated in recent years. In this paper, we investigate the statistical properties of a PCRP beam embedded with a vortex phase (i.e., PCRP vortex beam). We derive the analytical formula for the cross-spectral density matrix of a PCRP vortex beam propagating through a paraxial ABCD optical system and analyze the statistical properties of a PCRP vortex beam focused by a thin lens. It is found that the statistical properties of a PCRP vortex beam on propagation are much different from those of a PCRP beam. The vortex phase induces not only the rotation of the beam spot, but also the changes of the beam shape, the degree of polarization and the state of polarization. We also find that the vortex phase plays a role of resisting the coherence-induced degradation of the intensity distribution and the coherence-induced depolarization. Furthermore, we report experimental generation of a PCRP vortex beam for the first time. Our results will be useful for trapping and rotating particles, free-space optical communications and detection of phase object.

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.

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.

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.