Partially coherent diffraction-free vortex beams with a Bessel-mode structure

Sharp focusing of partially coherent Bessel-correlated beams by a graded-index lens

The nonparaxial focusing of partially coherent Bessel-correlated beams carrying vortices by a graded-index lens is investigated using the decomposition of the incident field into coherent modes and the quantum mechanical operator method. The influence of the coherence state and the incident beam aperture on tight focusing is analyzed. Our results show that a partially coherent Bessel-correlated beam can be focused into a spot of smaller size than coherent light.

Coherence singularity and evolution of partially coherent Bessel-Gaussian vortex beams

For a partially coherent Bessel-Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre-Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.

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.

Depolarization of Vector Light Beams on Propagation in Free Space

Nonparaxial propagation of the vector vortex light beams in free space was investigated theoretically. Propagation-induced polarization changes in vector light beams with different spatial intensity distributions were analyzed. It is shown that the hybrid vector Bessel modes with polarization-OAM (orbital angular momentum) entanglement are the exact solutions of the vector Helmholtz equation. Decomposition of arbitrary vector beams in the initial plane z = 0 into these polarization-invariant beams with phase and polarization singularities was used to analyze the evolution of the polarization of light within the framework of the 2 × 2 coherency matrix formalism. It is shown that the 2D degree of polarization decreases with distance if the incident vector beam is not the modal solution. The close relationship of the degree of polarization with the quantum-mechanical purity parameter is emphasized.

Airy beams on incoherent background

We present a class of diffraction-free partially coherent beams, each member of which comprises a finite-power, non-accelerating Airy bump residing on a statistically homogeneous, Gaussian-correlated background. We examine free-space propagation of soft apertured realizations of the proposed beams and show that their evolution is governed by two spatial scales: the coherence width of the background and the aperture size. A relative magnitude of these factors determines the practical range of propagation distances over which the novel beams can withstand diffraction. The proposed beams can find applications to imaging and optical communications through random media.

Propagation properties of partially coherent modified Bessel-Gauss beams through the gradient-index medium

Based on the ABCD matrix method and Collins diffraction integral formula, the general analytical expression for the partially coherent modified Bessel-Gauss beam propagating in a gradient-index medium is derived. The propagation trajectory, intensity, and phase distribution of such a beam are numerically investigated. The effects of the topological charge, the coherence parameter, and the coefficient of the gradient refractive index on propagation properties are considered. Results show that the propagation trajectory of such beam focuses and diverges periodically, which is different from free-space propagation. The period of intensity distribution is consistent with that of phase distribution under different cases. As propagation distance increases, the dark core always exists and the phase singularities remain stable and do not split. The dark core can be modulated by topological charge and coherence parameter, and the periodical distance can be modulated by the coefficient of the gradient refractive index. These results will help to explore such beams and find applications in optical communication and optical trapping.

Vortex preserving statistical optical beams

We establish a general form of the cross-spectral density of statistical sources that generate vortex preserving partially coherent beams on propagation through any linear ABCD optical system. We illustrate our results by introducing a class of partially coherent vortex beams with a closed form cross-spectral density at the source and demonstrating the beam vortex structure preservation on free space propagation and imaging by a thin lens. We also show the capacity of such vortex preserving beams of any state of spatial coherence to trap nanoparticles with the refractive index smaller than that of a surrounding medium.

Universal self-similar asymptotic behavior of optical bump spreading in random medium atop incoherent background

We demonstrate theoretically that the average spatial intensity profile of any partially coherent optical beam, composed of a finite-power bright intensity bump atop a fluctuating background, evolves into a universal self-similar Gaussian shape upon long-term propagation in a statistically homogeneous, isotropic linear random medium. The result depends neither on the degree of the background spatial coherence nor on the strength of the medium turbulence. To our knowledge, this is the first demonstration of universal self-similar asymptotics in linear random media.

Generation of arbitrary partially coherent Bessel beam array with a LED for confocal imaging

As the most important class of self-imaging beams, Bessel Beams (BBs) have been extensively studied, and various applications in optical trapping, communication, imaging and quantum studies have been found. In this paper, we propose a new method to generate arbitrary (quasi-) BB arrays by using a single LED light source. The method is simpler, cheaper, and more compatible than other existing methods. The key idea of the proposed method is to form spatially controllable incoherent point sources used to generate BB array imaging. Detailed theoretical deduction, analysis of properties of the generated BB array and comparison with those generated by coherent light sources are depicted. Further application to confocal imaging shows that the BB array is promising for fast, super depth-of-field imaging and multi-particle optical manipulations.

Experimental realization of dark and antidark diffraction-free beams

We report the first, to the best of our knowledge, experimental realization of high-quality dark and antidark diffraction-free beams, first theoretically proposed by Ponomarenko et al. [Opt. Lett.32, 2508 (2007)OPLEDP0146-959210.1364/OL.32.002508]. Our method employs a single spatial light modulator (SLM) and is based on superposing mutually uncorrelated but spatially coherent in the time domain Bessel modes with modal weights proportional to the SLM display times of the corresponding modes. We also experimentally verify diffraction-free properties of the generated beams upon their free space propagation.

Partially coherent fractional vortex beam

We introduce a new kind of partially coherent vortex (PCV) beam with fractional topological charge named partially coherent fractional vortex (PCFV) beam and derive the propagation formula for such beam passing through a stigmatic ABCD optical system with the help of the convolution method. We calculate numerically the propagation properties of a PCFV beam focused by a thin lens, and we find that the PCFV beam exhibits unique propagation properties. The opening gap of the intensity pattern and the rotation of the beam spot disappear gradually and the cross-spectral density (CSD) distribution becomes more symmetric and more recognizable with the decrease of the spatial coherence width, being qualitatively different from those of the PCV beam with integral topological charge. Furthermore, we carry out experimental generation of a PCFV beam with controllable spatial coherence, and measure its focusing properties. Our experimental results are consistent with the theoretical predictions.

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.

Synthesis of Im-Bessel correlated beams via coherent modes

We present the first high-quality experimental realization of a random optical beam as a linear superposition of its coherent modes. The individual modes are generated by passing a laser beam through a phase-only spatial light modulator. A random stationary beam is obtained by using a temporally randomized sequence of its coherent modes, each contributing, on average, with a weight proportional to the corresponding mode eigenvalue. As an example, the new method is applied to a I_m-Bessel correlated beam which was originally introduced in theory via the coherent mode decomposition, but could not have been experimentally generated so far by any other method.