Transformation of Hermite-Gaussian beams into complex Hermite-Gaussian and Laguerre-Gaussian beams

Hermite-Gaussian, Laguerre-Gaussian and complex Hermite- Gaussian modes are solutions of the paraxial wave equation. Using an astigmatic optical system each type of beams can be transformed into the others. This allows a generation of complex Hermite-Gaussian modes with twist whose propagation behavior is investigated in detail.