The doughnut mode is of great importance in optical tweezers and spanners. Such mode is generated by transforming the Hermite-Gaussian mode of a laser-diode end-pumped Nd:YAG laser through a rotated cylindrical lens system. The field distribution and the intensity profile of the doughnut mode were calculated theoretically from the field of the input Hermite-Gaussian mode. The beam transformation was confirmed in the experiments.
"New doughnut mode for optical tweezers and spanners", Proc. SPIE 4224, Biomedical Photonics and Optoelectronic Imaging, (11 October 2000); doi: 10.1117/12.403920; https://doi.org/10.1117/12.403920