Complexificated generalized gaussian beams

This work continues the authors' research about mutual transformations of Hermite-Gaussian and Laguerre-Gaussian beams by astigmatic optics. Recently, a parametrical beam family, which contains HG and LG beams as particular cases, has been found. The beams, called Hermite-Laguerre-Gaussian beams, keep some important properties of HG and LG beams, such as completeness, orthogonality and structural stability under propagation. In this work, an additional generalization of HLG beams through a complexification of an introduced parameter is proposed. The generalized beams are investigated theoretically. Results of numerical simulation and experiments are presented.