Optical Vortices: Revolutionizing the field of linear and nonlinear optics

TL;DR

The review surveys optical vortices and orbital angular momentum (OAM) as a controllable light degree of freedom, detailing how LV beams, BG, POV, and related families are generated, detected, and propagated in diverse media. It emphasizes both linear and nonlinear regimes, including perturbative processes (SHG, SFG, PDC) and non-perturbative high-harmonic generation in gases and solids, with a focus on OAM conservation, mode coupling, and phase-matching. The work highlights key developments such as POV beams to stabilize beam size across TC, spatiotemporal vortices, and the burgeoning field of vortex-driven HHG, underscoring implications for high-capacity communications, super-resolution microscopy, and attosecond science. Collectively, the paper demonstrates how structured light with OAM expands the functional envelope of modern optics and opens routes for compact, high-performance photonic devices and light–matter explorations in extreme regimes.

Abstract

Light is the fundamental medium through which we perceive the world around us. In the modern era, light can not only be used in its raw form but can also be used as a versatile tool. Generally, light fields carry energy and momentum (both linear and angular). Due to the transfer of linear momentum from light to matter, the radiation pressure is exerted, whereas, the intrinsic spin angular momentum (SAM) is associated with the polarization states of light. Light fields embedded with optical orbital angular momentum (OAM) -- also known as optical vortices or phase singular beams -- have truly revolutionized the field of optics and extended our basic understanding of the light-matter interaction process across various scales. Optical vortices -- spatially characterized by the presence of twisted phase fronts and a central intensity null -- have found a myriad of applications starting from microparticle trapping and manipulation to microscopy, optical communication, and quantum information science, among others. Here, we revisit some of the fundamental concepts on optical vortices and discuss extensively on how this new dimension of light i.e., the OAM, has been exploited in both linear and nonlinear optical regimes. We discuss the different types of vortex beams, the techniques used to generate and detect their OAM, and their propagation. Particularly, we put a special emphasis on the utilization of vortex beams in nonlinear regimes to explain different optical phenomena such as the second harmonic generation, parametric down-conversion, and high-order harmonic generation. The generation of vortex beams in the UV to XUV regimes, encoded with higher OAM values, could potentially extend their application range to areas such as high-capacity data transmission, stimulated emission depletion microscopy, phase-contrast imaging, and particle trapping in optical tweezers, among others.

Figures (38)

• Figure 1: Timeline of research developments on vortices (from 1989 to 2019). Reprinted with permission from Ref. ShenYijie
• Figure 2: Timeline of research developments on vortices (from 2016 to 2025). Reprinted with permission from Refs. JhajjGSpektorGaoHuiRegoselfHuang:18AlonWanChenhaodelasHerasVVBYavorskyBoChenAhmedHDorrah
• Figure 3: Transverse (top) and line intensity (bottom) profiles of the fundamental Gaussian beam in (a), free-space propagation of the fundamental Gaussian beam in (b). In the line plot, we define $w$ as the beam width or beam radius i.e., the radial distance at which the intensity of the beam becomes $\frac{1}{e^2}$ of the peak intensity. In (b), the horizontal axis denotes the propagation distance and the vertical axis denotes one of the transverse coordinates (either $x$ or $y$).
• Figure 4: Transverse intensity distributions of different HG modes at the source plane.
• Figure 5: Transverse intensity distributions of different HG modes propagating in free space.