  Optical orbital angular momentum (OAM), as an important degree of freedom of
light, has been attracted extensive attention, due to its intrinsic feature of
natural discrete infinite dimension. Manipulation of OAM spectra is crucial for
many impressive applications from classical to quantum realms, in particular,
nonlinear manipulation of OAM spectra. Here we realized the nonlinear
manipulation of OAM spectra by using the simultaneous second- and
third-harmonic generation in a single nonlinear crystal of quasi-periodically
poled potassium titanyl phosphate, for fundamental waves with a variety of OAM
spectra, especially for customized OAM spectra of the second and third
harmonics. The experimental results confirmed the theoretical predictions. Our
approach not only provides a novel way to manipulate OAM spectra at new shorter
wavelengths that are hard to be directly generated, but also may find new
applications towards multiplexing in classical optics and high-dimensional
information processing in quantum optics.
