Yuanjie Yang

Generation and propagation of an anomalous vortex beam

A theoretical model is proposed to describe a novel vortex beam named anomalous vortex (AV) beam. Analytical propagation formula for the proposed beam passing through a paraxial ABCD optical system is derived, and the propagation properties of such beam in free space are studied numerically. It is interesting to find that an AV beam will eventually become an elegant Laguerre-Gaussian beam in the far field (or in the focal plane) in free space. Furthermore, we report experimental generation of an AV beam and measure its propagation properties. Our experimental results are consistent with the theoretical predictions.

Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions.

By analysis of the far-field cross-correlation function (CCF) of partially coherent optical beams, we demonstrate an implicit rule that the number of ring dislocations (dark zones) of the far-field CCF is equal to the original topological charge of an optical vortex rendered partially coherent. This novel link between an optical vortex and its correlation singularity may offer an efficient method for measuring the orbital angular momentum of partially coherent optical vortices in fields such as astrophysics and astronomy, as well as atmospheric laser communication.

Research on near-field distributions of axisymmetric folded-combined CO2 laser

The near-field-intensity distributions of diffusion-cooled axisymmetric folded-combined CO 2 lasers are investigated. Formulas representing the near-field distributions for some typical kinds of folded-combined CO 2 lasers are suggested, and the near-field-intensity profiles are calculated numerically and simulated. For several centimeters from the output mirror along the direction of the symmetric axis, the intensity in the output beam is very high and its radius (or width) is very small (approximately double waist radius). The frequency differences between different cavities would induce fluctuations of the intensity distribution, but the fluctuations are not distinctive. The near-field beam can be used directly in some industrial material processing.

Autocorrelation properties of fully coherent beam with and without orbital angular momentum.

The spatial correlation singularity of a partially coherent vortex beam was demonstrated recently [Phys. Rev. Lett. 92, 143905 (2004)], and it was shown that the cross-correlation singularity disappears when the spatial coherence is high. In this paper, we demonstrate that the spatial autocorrelation function of a fully coherent beam in the far-field is equivalent to the Fourier transform of its intensity in the source plane. Our theoretical and experimental results show that, depending on both the radial and azimuthal mode indices (p, λ) of the incident light beam, the distribution of the far-field autocorrelation function displays a series of concentric, alternate bright and dark rings. This phenomenon may be used to determine the topological charge (the azimuthal index) of light beam with a nonzero radial index.

Spectral shifts and spectral switches of a pulsed Gaussian beam from a rectangular aperture in the far field

The far-field anomalous spectral behaviours of a space–time-dependent Gaussian pulsed beam passing through a rectangular aperture are studied. By expanding a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral intensity of a space–time-dependent Gaussian pulsed beam passing through a rectangular aperture is derived. Meanwhile, the corresponding closed-forms for the slit and the unapertured cases are also given as special cases of the general results. The red and blue shifts and the spectral intensity distribution are studied and illustrated with numerical calculations. Specifically, it is shown that the spectral switch takes place when the truncation parameter is equal to particular values or the observation position is at the critical diffraction angle. The possibility of tunable spectral switching in the far field with an apertured pulsed beam by varying the size of the rectangular aperture is highlighted.

Study of performance of a He-Ne laser having an annular gain zone

A He-Ne laser with an annular gain zone is studied theoretically. It is demonstrated that the He-Ne medium in the annular discharge zone possesses enough gain to maintain laser oscillation. A multipass ring resonator, which is composed of two annular spherical mirrors, is described, and it is shown that the resonator is suitable for extracting optical energy from the He-Ne medium in the annular gain zone. Considering the availability of population inversion in the traveling-wave cavity and the influence of the crossover of the folded light beam in the resonator on the output power, a calculation formula for the output power of the laser with the multipass ring resonator is given. Calculating results prove that a 1 W output of the He-Ne laser can be obtained by a 1 m length annular discharge zone.

Far-field spectral characteristics of a space-time-dependent Gaussian pulsed beam from an annular aperture

The far-field spectral characteristics of a space-time-dependent Gaussian pulsed beam passing through an annular aperture are studied. Based on the expansion of a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, some analytical expressions for the spectral distribution of the diffraction field are derived. The expressions for a circular black screen and a circular aperture are given as special cases of the general results. The red and blue shifts of the spectral intensity maximum and the spectral intensity shape distortion and distribution are studied and illustrated with numerical calculations.

Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation

Abstract Zero-order and higher-order Bessel beams are well-known nondiffracting beams. Namely, they propagate with invariant profile (intensity) and carry a fixed orbital angular momentum. Here, we propose and experimentally study an anomalous Bessel vortex beam. Unlike the traditional Bessel beams, the anomalous Bessel vortex beam carries decreasing orbital angular momentum along the propagation axis in free space. In other words, the local topological charge is inversely proportional to the propagation distance. Both the intensity and phase patterns of the generated beams are measured experimentally, and the experimental results agree well with the simulations. We demonstrate an easy way to modulate the beam’s topological charge to be an arbitrary value, both integer and fractional, within a continuous range. The simplicity of this geometry encourages its applications in optical trapping and quantum information, and the like.

Self-recovery effect of orbital angular momentum mode of circular beam in weak non-Kolmogorov turbulence

It is generally true that the orbital angular momentum (OAM) mode persistently degenerate when a vortex beam propagates in the atmospheric turbulence. Here, however, we unveil an interesting self-recovery effect of OAM mode of the circular beam (CiB) in weak non-Kolmogorov turbulence. We show that the CiB displays the self-focusing effect and has clear focus in the weak non-Kolmogorov turbulence if we choose proper complex parameters, and the detection probability of the original OAM mode reaches the maximum at the focus. Our study proposes a method to alleviate the turbulent effects on OAM-based communication.

Nonparaxial propagation of vectorial hollow Gaussian beams diffracted at an annular aperture

Based on the vectorial Raleigh-Sommerfeld diffraction integral, an analytical propagation equation of vectorial nonparaxial hollow Gaussian beams (HGBs) through an annular aperture is derived. The corresponding closed-forms for a circular aperture, a circular black screen, and unapertured case are given as special cases of the general results. The typical numerical examples are given to illustrate our analytical results. It is shown that the f parameter plays an important role in determining the nonparaxiality of vectorial apertured HGBs