Laguerre-Gaussian-to-Hermite-Gaussian mode conversion revisited

We generalize a theoretical framework for Laguerre-Gaussian-to-Hermite-Gaussian (LG-to-HG) mode conversion induced by optical astigmatism and identify threea distinct conversion scenarios depending on the astigmatism conditions. We analyze the LG beam diffraction by three types of astigmatic optical elements, cylindrical lenses, quadratic curved-line gratings, and off-axis illuminated elliptical zone plates, and show that the LG modes of different orders convert to the corresponding HG modes over different distances, if at all. We explore two families of astigmatic phase profiles that offer independent control over the stretching and orientation of the converted modes. Our theoretical predictions are in good qualitative agreement with experimental results.