Figure 1

Schematic of astigmatic transformation of LG beams and their up-conversion process. In normal incidence, an LG\(_{3,0}\) beam is focused and frequency doubled through a second order nonlinear (\(\chi ^{(2)}\)) medium into an LG\(_{6,0}\) beam with twice the amount of OAM per photon. By tilting the focusing spherical lens along \(x-\) or \(y-\)axis, different pump profiles are generated. We image the incident, the astigmatically transformed, and the converted beam profiles on several critical positions along the propagation direction. These positions are: (i) structured light generated by a spatial light modulator (SLM), (ii) fundamental beam transformed astigmatically with a tilted spherical lens, (iii) SH signal right after the \(\chi ^{(2)}\) crystal, and (iv) SH signal at the far-field.