Controlling the Gouy phase of coherent beams by necklace-like structures of optical vortices

Beyond its importance in physical optics, the Gouy phase also plays a crucial role in highly nonlinear processes such as above-threshold ionization and high-harmonic generation, owing to its scaling with the order of the nonlinear interaction. In this work, first, we show that the Gouy phase of coaxial superpositions of Laguerre–Gaussian vortex beams and Gaussian beams is always equal to the Gouy phase of an unperturbed Gaussian beam. Next, we numerically and experimentally demonstrate that the Gouy phase of a nearly Gaussian beam can be controlled when it carries a necklace-like structure of single-charge optical vortices in its wings. For this approach to work, it is essential for the vortices to be generated by pure phase modulation, which subsequently leads to their expected amplitude/intensity modulation. The presented numerical and experimental results indicate that the control of the Gouy phase is most effective when the number of vortices in the necklace-like structure is constant and its radius changes.