Virtual source for a Hermite-Gauss beam

A virtual source that generates a Hermite-Gauss wave of mode numbers m and n is introduced. An expression is obtained for this Hermite-Gauss wave. From this expression, the paraxial approximation and the first 3 orders of nonparaxial corrections for the corresponding paraxial Hermite-Gauss beam are determined. When both m and n are even, leading to maximum amplitude along the axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to (m + n)/2.