Higher-order Gaussian beams: new achievements

As well known, rectangular Hermite-Gaussian modes as well as cylindrical Laguerre-Gaussian modes do form an orthogonal set endowed with shape-invariance properties. So they can form an expansion basis for many propagation-invariant wave fields in the paraxial regime. Especially for those coupled from laser resonators or oscillating inside. In this contribution, the determination of the sufficient number of modes in the expansion for both sets and in different aperturing kinds: hard, soft and moderate, is addressed.