  We present an integral of diffraction based on particular eigenfunctions of
the Laplacian in two dimensions. We show how to propagate some fields, in
particular a Bessel field, a superposition of Airy beams, both over the square
root of the radial coordinate, and show how to construct a field that
reproduces itself periodically in propagation, i.e., a field that renders the
Talbot effect. Additionally, it is shown that the superposition of Airy beams
produces self-focusing.
