Generalised Hermite-Gaussian beams and mode transformations

Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function $\alpha$, which can be used to unite conventional HG modes and Laguerre-Gaussian modes (LG modes). An infinite number of normalised orthogonal modes can thus be obtained by modulation of the function $\alpha$. The gHG mode notion provides a useful tool in analysis of the deformation and transformation phenomena occurring in propagation of HG and LG modes with astigmatic perturbation.