High harmonic generation with Laguerre-Gaussian beams

We summarize the development of high harmonic generation (HHG) with linearly polarized Laguerre-Gaussian (LG) beams and their superpositions to explain the non-perturbative aspects of HHG. Furthermore, we show that circularly polarized extreme ultraviolet vortices with well-defined orbital angular momentum (OAM) can be generated by HHG with bicircular LG beams. We introduce photon diagrams in order to explain how to calculate the OAM and the polarization of the generated harmonics by means of simultaneous conservation of spin angular momentum and OAM. Moreover, we show how the intensity ratio of the driving fields in HHG with bicircular LG beams further enhances the generation of circularly polarized twisted attosecond pulse trains.