We investigate the generation of an elliptical perfect optical vortex (EPOV) beam through the optical Fourier transformation of an elliptical Bessel-Gaussian beam and derive an analytical expression for its complex field amplitude. Our analysis includes the examination of the beam’s propagation in free-space and the influence of topological charge on its transmission. The EPOV beam’s propagation in free-space can be categorized into non-diffracting and diffracting stages. During the non-diffracting stage, the beam intensity and profile size are effectively preserved over a short transmission distance. Subsequently, in the diffracting stage, the beam profile initially contracts and then expands with a change in the beam intensity. Notably, the impact of topological charge on the beam intensity and profile size varies across different stages of propagation. We compare our results with those of the circular perfect optical vortex beam propagating in free-space, observing that the EPOV beam exhibits non-diffracting behavior for short propagation distances compared to its circular counterpart. The signature of the focusing behavior of the EPOV beam is observed at a relatively small propagation distance compared to the circular case.

Orbital angular momentum (OAM) light beams for high-order harmonic generation (HHG) provide an additional degree of freedom to study the light-matter interaction at ultrafast timescales. A more sophisticated configuration is a perfect optical vortex (POV) beam, a light beam with a helical wave front characterized by a phase singularity at its center and an azimuthal phase variation. POV beams are characterized by a radial profile which is independent of the OAM. Here, we study the nonperturbative process of gas-phase HHG using a linearly polarized POV beam. We observe that the harmonics are emitted with similar divergence due to the perfectness of the POV-driven harmonic generation. Furthermore, the topological charge upscaling is rigorously followed. We show that a POV beam is more advantageous than that of the Laguerre-Gaussian beam for cases where a large topological charge with a small core size is required. Our research establishes a pathway for producing bright structured extreme ultraviolet coherent radiation sources—a pivotal tool with multifaceted applications across various technological domains. Published by the American Physical Society 2024

We study correlations in the speckle patterns generated by the scattering of perfect optical vortex (POV) beams and use them to produce a new class of coherence functions, namely Bessel coherence functions. Higher (zeroth) order Bessel coherence functions have been realized in cross (auto)-correlation between the speckle patterns generated by the scattering of perfect vortex beams of different orders. We have also studied the propagation of produced Bessel coherence functions and characterized their divergence with respect to the radius of their first ring for different orders m = 0–4. We observe that the divergence varies linearly with the order of the coherence function. We provide the exact analytical expression for the auto-correlation, as well as cross-correlation functions for speckle patterns. Our experimental results are in good agreement with the analytical results.

Perfect optical vortex (POV) beams exhibit unique spatial characteristics, including a topological charge (TC)-independent ring radius and an annular intensity distribution. We investigate the propagation of POV beams in a chiral medium. Within the paraxial limit, an analytical expression for the complex amplitude of a POV beam propagating in a chiral medium is derived based on the Huygens–Fresnel integral and the ABCD matrix formalism. Our results show that the beams split into left-circularly polarized POV (LCPPOV) and right-circularly polarized POV (RCPPOV) beams, each following distinct propagation trajectories and exhibiting different longitudinal intensity distributions in the chiral medium. We numerically study the influence of various beam and medium parameters-such as the TC, the ratio of the ring radius to the half-ring width, the chiral parameter, and the refractive index-on the longitudinal intensity distributions of LCPPOV, RCPPOV, and total POV beams. We find that both non-diffracting and self-focusing effects occur at different propagation distances for LCPPOV, RCPPOV, and total POV beams. The self-focusing effect gradually diminishes as the ratio of the ring radius to the half-ring width decreases. Additionally, while the TC has no impact on intensity distributions during the non-diffracting stage, noticeable effects emerge in the self-focusing stage, including the expansion of the dark core with increasing TC and the appearance of multiple rings in the intensity distributions. Furthermore, the chiral parameter and refractive index influence the intensity distributions of LCPPOV, RCPPOV, and total POV beams in distinct ways. Our findings may be useful for applications of POV beams in optical micromanipulation.

High-order harmonic generation is a cornerstone of attosecond science, with applications spanning from spectroscopy to the creation of ultrashort light pulses with temporal duration falling in the attosecond regime. In addition, light beams carrying orbital angular momentum (OAM) allow studies of light–matter interactions mediated by OAM couplings. In this work, we present an alternative approach to generating high-order harmonic vortices using elegant Laguerre–Gaussian (eLG) beams. We examine the spatiotemporal characteristics of these harmonic vortices in the far-field regime and demonstrate how the low divergence of eLG beams makes them suitable for producing extreme ultraviolet (XUV) twisted attosecond pulses. Additionally, by solving the far-field Fraunhofer integral, we analyze the influence of azimuthal and radial indices on the spatial profile of vortex beams, thereby exploring the impact of larger topological charges. This study extends the concept of harmonic vortices generated by Laguerre–Gaussian beams to applications beyond the paraxial approximation.

Orbital angular momentum (OAM) beams have brought the nonlinear light–matter interaction to a novel, to our knowledge, regime. In this work, we investigate the generation of high-order harmonics in atomic gases when the extreme nonlinear optical process is driven by the coaxial superposition of linearly polarized Laguerre–Gaussian (LG) modes. Specifically, we discuss the cases when the waist sizes of the two superposed LG modes are different (double-ring vortex beam) or the same (optical ring lattice). Within the framework of the strong-field approximation (SFA), utilizing the thin-slab model (TSM) and the Fraunhofer diffraction integral, we compute the near- and far-field complex amplitude of the harmonic vortices. Furthermore, we demonstrate the conservation rule for the OAM by examining the far-field divergence and phase profiles. The topological richness present in the resulting superposed beams translates to a well-known OAM selection rule. Moreover, different harmonics are emitted with similar divergence. Our research provides an alternative route to customize the spatial shape of higher-order harmonics with precise control over the OAM and extend the range of application of these exotic beams down to the extreme-ultraviolet (XUV) spectral regime.