Generalized Asymmetric Hermite–Gaussian and Laguerre–Gaussian Beams

We derive analytical formulae for the complex amplitudes of variants generalized Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams. reveal that, at particular values parameters exact solution paraxial propagation equation, these beams are converted into conventional elegant HG LG also deduce asymmetric that described by in form Hermite Laguerre polynomials whose argument is shifted plane. The are, respectively, shown to present finite superposition an explicit relationship amplitude a vortex beam, which built as with phase shifts. Newly introduced show promise study carrying orbital angular momentum through turbulent atmosphere. One may reasonably believe laser more stable against turbulence when compared radially symmetric ones.