Particle nature of the photonic spin Hall effect.

It is widely recognized that light exhibits a wave-particle duality. However, the explanation for the photonic spin Hall effect (PSHE) primarily relies on the wave nature of light as dictated by Maxwell's Equations. There is a lack of exploration into the particle nature of light in this regard. In this context, we offer a fresh interpretation of the PSHE from the perspective of particle nature of light. For the out-of-plane PSHE, the spin shifts result from the macroscopic manifestation of the conservation of spin-orbital angular momentum of one photon. For the in-plane PSHE, the spin shifts arise from the spread of in-plane wavevector. Based on the wave nature of light, we also obtain the same spin shifts, confirming the consistency of the wave-particle duality of light. Furthermore, we find that the spin shifts of the PSHE are not the overall displacement of photons with the same handedness, but the outcome of coherent superposition among photons of the same handedness. These discoveries further enhance our comprehension of the fundamental nature of the PSHE.

Transformation from asymmetric spin splitting to symmetric spin splitting with phase compensation in photonic spin Hall effect.

Generally, when an arbitrary polarized light beam is reflected or refracted from an isotropic interface, the spin splitting in photonic spin Hall effect (SHE) shows asymmetry properties. In this paper, we theoretically propose a phase compensation scheme to achieve the transformation from asymmetric spin splitting to symmetric spin splitting in photonic SHE. We experimentally acquire the spin splitting after phase compensation in the case of a 45 degrees linear polarized Gaussian light beam totally internally reflected from a prism-air interface. Particularly, whether or not phase compensation, the transverse shift of total barycenter of reflected field [i.e., the Imbert-Fedorov (IF) shift] does not change. These findings can solve this problem that asymmetric spin splitting cannot be observed by weak measurements.

Evolution properties of partially coherent radially polarized Laguerre-Gaussian vortex beams in an anisotropic turbulent atmosphere.

Analytical formulas for the cross-spectral density matrix of a partially coherent radially polarized Laguerre-Gaussian vortex (PCRPLGV) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens-Fresnel principle. The evolution laws of statistical properties of a PCRPLGV beam in turbulence, such as the average intensity, degree of coherence (DOC) and degree of polarization (DOP), are investigated in detail. It is found that the atmospheric turbulence induces degeneration of the intensity distribution of a PCRPLGV beam on propagation, and some new properties, such as self-shaping and self-rotating, will appear on propagation due to vortex phase. In addition, in order to verify our theoretical results, we combined the complex screen method and multi-phase screens method to simulate the propagation of PCRPLGV beam in atmospheric turbulence. And the studies indicate that the simulation results are consistent with the theoretical predictions. Our results will be useful in some potential applications, such lidar detection, remote sensing and free-space optical communications.

Propagation factor of partially coherent radially polarized vortex beams in anisotropic turbulent atmosphere.

We skillfully combined the cosine theorem with the second moment theory and the Wigner distribution function and derived the analytical expressions of the propagation factor (M2-factor) of a partially coherent radially polarized vortex beam (PCRPVB) in atmospheric turbulence. Then, we comparatively studied the propagation factors of a PCRPVB and a partially coherent electromagnetic vortex beam (PCEVB) in atmospheric turbulence. The results show that a PCRPVB has a smaller value of a relative M2-factor than a PCEVB, which means that a PCRPVB has a stronger ability to resist atmospheric turbulence than a PCEVB. To confirm our theoretical studies, the hyperbolic fitting method is combined with the random phase screen (RPS) to simulate the M2-factor of a PCRPVB and a PCEVB through atmospheric turbulence. The study results indicate that the theoretical values agree well with the simulated values. Our results may find applications in free-space optical communications and remote sensing.

Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere.

Analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M2-factor of partially coherent standard Laguerre Gaussian beams (PC-SLGBs) and partially coherent elegant Laguerre Gaussian beams (PC-ELGBs) in inhomogeneous turbulent atmosphere have been derived. The propagation properties of PC-SLGBs and PC-ELGBs in inhomogeneous atmospheric turbulence are studied numerically and comparatively. It can be found that the propagation of laser beams in inhomogeneous turbulence is different from that in homogeneous turbulence. It is also shown that relative rms spatial widths and M2-factors of PC-ELGBs are more affected by inhomogeneous turbulence than those of PC-SLGBs. Moreover, the relative rms spatial widths and M2-factors of PC-SLGBs and PC-ELGBs in inhomogeneous turbulent atmosphere are closely related with waist widths, coherence widths, zenith angles, inner scales, and beam orders. Furthermore, the saturation propagation distance of the relative M2-factor and rms angular width with zenith angles of π/6 are 20 km and 0.5 km, respectively.

Propagation characteristics of partially coherent flat-topped beams propagating through inhomogeneous atmospheric turbulence.

M2-factor and root-mean-square (rms) angular width of partially coherent flat-topped (PCFT) beams propagating through inhomogeneous atmospheric turbulence are studied based on the extended Huygens-Fresnel principle and the Wigner distribution function (WDF). It is shown that the effect of turbulence on the PCFT beams can be neglected as the vertical height increases, which is different from the homogeneous turbulence. Analytical formulae of the M2-factor and rms angular width of PCFT beams have been given. The saturation propagation distances (SPDs) increase with increasing zenith angle. It can be seen that the SPDs of the M2-factor and rms angular width of PCFT beams propagating through inhomogeneous atmospheric turbulence are about 30 km and 0.5 km, respectively, when the zenith angle is π/4. It can be found that the M2-factor increases with increasing beam order and zenith angle, and with decreasing waist width, inner scale, wavelength, and transverse coherence length. The rms angular width increases with increasing beam order, wavelength, and zenith angle, and decreasing waist width, inner scale, and transverse coherence length.

Range of turbulence-independent propagation and Rayleigh range of partially coherent beams in atmospheric turbulence.

Two characteristic distances for partially coherent beams propagating in atmospheric turbulence have been proposed. The turbulent Rayleigh range is used for characterizing the range over which the beams propagate in turbulence without spreading appreciably; i.e., the concept of the well-known Rayleigh range in free space is extended to the case of turbulence. In this paper the range of turbulence-independent propagation of the beams, in contrast to similar characteristic distances in previous published works, is based on the formula of the beam propagation factor (M(2) factor) and is used for describing the range over which the spatial and angular spreading and the M(2) factor increase due to turbulence are sufficiently small and negligible. Several simple formulas used for calculating the approximate values of these distances are given, and the formulas are applied to Gaussian Schell-model (GSM) beams and illustrated by examples. Furthermore, as a typical example, the effect of the angular spread of GSM beams in turbulence on a thin-lens optical system is also discussed. We show that the turbulent Rayleigh range depends on the Rayleigh range in free space, the waist width, and the spatial power spectrum of the refractive-index fluctuations of the turbulent atmosphere, and that the range of turbulence-independent propagation depends on the waist width, the initial angular spread in the waist plane, and the spatial power spectrum.

Second moments of partially coherent beams in atmospheric turbulence.

Based on the extended Huygens-Fresnel principle, the propagation law of the beam matrix in terms of second moments of the Wigner distribution function for partially coherent beams propagating through atmospheric turbulence was obtained. The general formulas for the mean-squared spatial and angular widths, as well as the beam propagation factor (M(2) factor) of partially coherent beams in turbulence were also derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations of the turbulent atmosphere.

Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere.

The Wigner distribution function (WDF) has been used to study the beam propagation factor (M(2)-factor) for partially coherent flat-topped (PCFT) beams with circular symmetry in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle and the definition of the WDF, an expression for the WDF of PCFT beams in turbulence has been given. By use of the second-order moments of the WDF, the analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M(2)-factor of PCFT beams in turbulence have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations. The rms angular width and the M(2)-factor of PCFT beams in turbulence have been discussed with numerical examples. It can be shown that the M(2)-factor of PCFT beams in turbulence depends on the beam order, degree of global coherence of the source, waist width, wavelength, spatial power spectrum of the refractive index fluctuations, and propagation distance.

Propagation of partially coherent flat-topped beams through a turbulent atmosphere.

Based on the modified beam model for flat-topped beams and the Schell model for partially coherent light, an expression for partially coherent flat-topped (PCFT) beams has been proposed. The propagation characteristics of PCFT beams with circular symmetry through a turbulent atmosphere have been studied. By using the generalized Huygens-Fresnel integral and Fourier transform method, the expressions for the cross-spectral density function and the average intensity have been given and the analytical expression for the root-mean-square width has been derived. The effects of the beam order, the spatial coherence, and the turbulent parameter on the intensity distributions and beam spreading have been discussed in detail. Our results show that the on-axis intensity of the beams decreases with increasing turbulence and decreasing coherence of the source, whereas the on-axis intensity of the beams in the far field decreases slightly with increasing beam order. The relative spreading of PCFT beams is smaller for beams with a higher order, a lower degree of global coherence of the source, a larger inner scale, and a smaller outer scale of the turbulence.