Optical vortices: revolutionizing the field of linear and nonlinear optics

Light is fundamental to human perception and understanding of the world. Modern technology now harnesses it as a versatile tool for controlling a wide range of natural processes. Generally, light fields carry both energy and momentum: their linear momentum creates radiation pressure, while their intrinsic spin angular momentum is linked to polarization. Light fields embedded with orbital angular momentum (OAM)- also known as optical vortices (OVs)- have truly revolutionized optics and deepened our understanding of light-matter interaction across scales. OVs—characterized by twisted phase fronts and a central intensity null—have found applications in microparticle manipulation, microscopy, optical communication, and quantum information science, among others. In this review, we revisit some of the fundamental concepts on OVs and discuss extensively on how this new dimension of light has been exploited in both linear and nonlinear optical regimes. We briefly discuss the different types of vortex beams, the techniques used to generate them and detect their OAM, and their propagation in various media. Particularly, we put a special emphasis on the utilization of vortex beams in nonlinear perturbative and non-perturbative regimes to explain different optical phenomena such as the second harmonic generation, sum frequency generation, parametric down-conversion, and high-order harmonic generation.