Optical Vortices: Revolutionizing the field of linear and nonlinear optics

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.