  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.
