  Complete bases that are useful for beam propagation problems and that present
the distinct property of being spatially confined at the initial plane are
proposed. These bases are constructed in terms of polynomials of Gaussians, in
contrast with standard alternatives such as the Hermite-Gaussian basis that are
given by a Gaussian times a polynomial. The property of spatial confinement
implies that, for all basis elements, the spatial extent at the initial plane
is roughly the same. This property leads to an optimal scaling parameter that
is independent of truncation order for the fitting of a confined initial field.
Given their form as combinations of Gaussians, the paraxial propagation of
these basis elements can be modeled analytically.
