Frequency-astigmatism asymmetric nonlinear conversion of structured light lasers

Nonlinear optics of structured light has recently delivered intriguing fundamental physical phenomena in light-matter interactions and advanced applications from classical imaging to quantum informatics. The mutual interaction between spin, orbital angular momentum (OAM) and wavelength is extensively studied in such cases. In this work, we go beyond only considering OAM and wavelength by taking the nonlinear frequency conversion and transverse mode astigmatism conversion as two building blocks and investigating how single modes and complicated multiplexed modes evolve after them. In particular, We found a generalized law of nonlinear conversion structured light from experiments and theories, that the converted modes are highly related to the sequence of these two blocks, obeying an inherent (non)commutative rule in which. This effect not only creates extended structured laser modes but serve as new rules in nonlinear structured light manipulation.