Partially coherent fractional vortex beam

Modified angular spectrum algorithm for the propagation of partially coherent beams in optical systems

A modified angular spectrum algorithm is presented for the diffraction calculation of partially coherent beams propagating in optical systems. The proposed algorithm can directly calculate the cross-spectral density of partially coherent beams at each surface of the optical system and possesses much higher computational efficiency for low coherent beams compared with that of the common modal expansion methods. Then, a Gaussian-Schell model beam propagating in a double-lens array homogenizer system is introduced to carry out a numerical simulation. Results show that the proposed algorithm can obtain an identical intensity distribution as the selected modal expansion method but with a much higher speed, thus verifying its accuracy and high efficiency. However, it's worth noting that the proposed algorithm is only suitable to the optical systems in which the partially coherent beams and optical components have no coupling effects in the x and y directions and can be dealt with individually.

Spiral fractional vortex beams

A new type of spatially structured light field carrying orbital angular momentum (OAM) mode with any non-integer topological order, referred to as the spiral fractional vortex beam, is demonstrated using the spiral transformation. Such beams have a spiral intensity distribution and a phase discontinuity in the radial direction, which is completely different from an opening ring of the intensity pattern and an azimuthal phase jump, common features that all previously reported non-integer OAM modes (referred to as the conventional fractional vortex beams) shared. The intriguing properties of a spiral fractional vortex beam are studied both in simulations and experiments in this work. The results show that the spiral intensity distribution will evolve into a focusing annular pattern during its propagation in free space. Furthermore, we propose a novel scheme by superimposing a spiral phase piecewise function on spiral transformation to convert the radial phase jump to the azimuthal phase jump, revealing the connection between the spiral fractional vortex beam and its conventional counterpart, of which OAM modes both share the same non-integer order. Thus this work is expected to inspire opening more paths for leading fractional vortex beams to potential applications in optical information processing and particle manipulation.

Radially polarized twisted partially coherent vortex beams

We introduce a new type of partially coherent vector beam, named the radially polarized twisted partially coherent vortex (RPTPCV) beam. Such a beam carries the twist phase and the vortex phase simultaneously, and the initial state of polarization (SOP) is radially polarized. On the basis of the pseudo-modal expansion and fast Fourier transform algorithm, the second-order statistics such as the spectral density, the degree of polarization (DOP) and the SOP, propagation through a paraxial ABCD optical system are investigated in detail through numerical examples. The results reveal that the propagation properties of the RPTPCV beam closely depends on the handedness of the twist phase and the vortex phase. When the handedness of the two phases is same, the beam profile is easier to remain a dark hollow shape and the beam spot rotates faster during propagation, compared to the partially coherent vortex beam or the RPTPCV beam with the opposite handedness of the two phases. In addition, the same handedness of two phases resists the coherence induced de-polarization of the beam upon propagation, and the SOP is also closely related to the handedness, topological charge of the vortex phase and the twist factor of the twist phase, providing an efficient way to modulate the beam's DOP and SOP in the output plane. Moreover, we establish an experiment setup to generate the RPTPCV beam. The average spectral density and the polarization properties are examined in the experiment. The experimental results agree reasonable well with the theoretical predictions. Our results will be useful for particle manipulating, free-space optical communications, and polarization lidar systems.

Generation of perfect helical Mathieu vortex beams

We introduced a kind of novel perfect optical vortex beam, which we termed herein as perfect helical Mathieu vortex (PHMV) beams. The theoretical mechanism regarding the construction of PHMV beams was divided into two parts: generation of helical Mathieu (HM) beams using the stationary phase method and then Fourier transform of HM beams into the PHMV beams. Accordingly, the experimental system for generating PHMV beams was built as follows. Based on the complex amplitude modulation method, HM beams of different orders and ellipticity were generated using an amplitude-type spatial light modulator (SLM) and a radial-helical phase mask. Subsequently, an achromatic Fourier transform lens was illuminated using the HM beams, and the PHMV beams were presented on the focal plane after the Fourier transform lens. The experimental results were consistent with theoretical predictions. Compared with the classical perfect optical vortex (POV) beams, the PHMV beams still retained the property of ring radius independent of topological charge values. The distribution pattern of the PHMV beams can be controlled by the topological charges and elliptical parameters. Furthermore, two important optical properties of the PHMV beams were theoretically elucidated. First, we proved that the PHMV beams carry a fractional order orbital angular momentum (OAM). Second, we found that the complex amplitudes of any two PHMV beams with the same elliptical parameter but different order numbers are orthogonal to each other.

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 Ince-Gaussian beams

We report on the study and generation of Ince-Gaussian beams in the spatially partially coherent regime. The inherent random fluctuations both in time and space of these partially coherent fields make their characterization difficult. Our results show that the cross-correlation function (CCF) provides insight into the composition of the Ince-Gaussian beam, as well as into its spatial coherence structure and singularities. Our experimental findings are in very good agreement with the numerical simulations, particularly revealing a rich structure of nodal lines in the CCF.

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.

Propagation properties of partially coherent crescent-like beams under maritime environment

Based on the extended Huygens-Fresnel principle, the analytical expressions for the intensity distribution, effective radius of curvature, beam wander, Strehl ratio, and the power in the bucket of a partially coherent crescent-like (PCCL) beam under the maritime environment are derived. The propagation properties of the PCCL beams through the maritime environment are investigated in detail. Numerical results indicate that, for the maritime environment, the propagation properties and beam quality of a PCCL beam are closely related to its initial beam parameters and the turbulence parameters. Comparative analyses are performed for the new models under the marine turbulence and the terrestrial turbulence. It turns out that the marine turbulence influences the beam width and the beam wander more than the terrestrial turbulence does. Also, the beam quality of the PCCL beams in marine turbulence can be improved by choosing a large beam width, high coherence length, or short wavelength. The PCCL beams have a range-dependent tilt, which can be useful for some practical applications, such as traveling around an obstacle. The results are of significance for over-the-sea communication systems.

Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge

In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

Hyperbolic sine-correlated beams

An explicit expression is given for the cross-spectral density that characterizes a new family of partially coherence sources with hyperbolic sine correlated function. Beam conditions for such sources are established. The propagation properties of such partially coherent beams are studied by numerical simulations. It is demonstrated that, unlike the reciprocity theorems relating to radiation from classical Schell-model sources, such beams possess both the invariance of coherent distribution and of hollow intensity shape.

Vortex strength and beam propagation factor of fractional vortex beams

Fractional vortex beams (FVBs) with non-integer topological charges attract much attention due to unique features of propagations, but different viewpoints still exist on the change of their total vortex strength. Here we have experimentally demonstrated the distribution and number of vortices contained in FVBs at the Fraunhofer diffraction region. We have verified that the jumps of total vortex strength for FVBs happen only when non-integer topological charge is before and after (but very close to) any even integer number that originates from two different mechanisms for generation and movement of vortices on focal plane. Meanwhile, we have also measured the beam propagation factor (BPF) of such FVBs and have found that their BPF values almost increase linearly in the x component (along the initial edge dislocation) and oscillate increasingly in the y component (vertical to the initial edge dislocation). Our experimental results are in good agreement with numerical results.

Propagation of Optical Coherence Vortex Lattices in Turbulent Atmosphere

Propagation properties in the turbulence atmosphere of the optical coherence vortex lattices (OCVLs) are explored by the recently developed convolution approach. The evolution of spectral density distribution, the normalized M 2 -factor, and the beam wander of the OCVLs propagating through the atmospheric turbulence with Tatarskii spectrum are illustrated numerically. Our results show that the OCVLs display interesting propagation properties, e.g., the initial Gaussian beam distribution will evolve into hollow array distribution on propagation and finally becomes a Gaussian beam spot again in the far field in turbulent atmosphere. Furthermore, the OCVLs with large topological charge, large beam array order, large relative distance, and small coherence length are less affected by the negative effects of turbulence. Our results are expected to be used in the complex system optical communications.