Sum-frequency generation with modified anomalous vortex beams

Abstract

Light beams carrying orbital angular momentum (OAM) provide an additional degree of freedom to control and manipulate light-matter interactions across different energy regimes. Precise control over the beam and dark-core sizes, while maintaining a high value of the topological charge (TC) is crucial for their applications in optical tweezing, optical communication, and microscopy. While perfect optical vortices were engineered to feature TC-independent intensity distribution, their generation method typically involves bulky experimental setup. Furthermore, their detection is non-trivial, as they are not propagation eigenmodes and thus do not maintain their perfect vortex structure during propagation. A more sophisticated beam configuration is the modified anomalous vortex (MAV) beam — a novel class of anomalous vortex beam engineered with controlled self-focusing characteristics. MAV beams are typically characterized by their TC, beam order, and a so-called modification parameter. For extremely high beam order and a unity modification parameter, the beam and dark-core sizes of MAV beams remain nearly independent of the TC. Despite such novel beam properties, their role in driving nonlinear optical phenomena remains largely untested. In this work, we investigate the sum-frequency generation driven by MAV beams. For this nonlinear process, we derive an analytical expression for the complex field amplitude of the sum-frequency beam at the waist plane. Furthermore, we study the evolution of the generated sum-frequency beam in free-space. We thoroughly discuss the underlying OAM selection rule, and analyze how different parameters of the input MAV beams, such as their TC, beam order, modification parameter, and wavelength affect the sum-frequency beam. Moreover, we compare both the power of the sum-frequency beam generated by fundamental MAV, traditional AV, and Laguerre–Gaussian vortex beams, as well as the corresponding conversion efficiency of the process.