Analytic description of nonideal Bessel beam propagation

Since the experimental demonstration in 1987, Bessel Beams have attracted much attention because of their main features to resist diffractive effects over distances exceeding the usual diffraction length of gaussian beams. Despite that fact, to the best of our knowledge, the study of Bessel Beam's propagation has no closed analytic form and it often leads to the numerical evaluation of diffraction integrals, which can be very awkward. Based on Schrödinger equation of quantum mechanics and adequate choice of basis function in a Hilbert space, we introduce a new technique able to expand the optical wave field in a series, allowing to obtain analytic expressions for the propagation of any given initial field distribution. To demonstrate the robustness of the method two cases were taken into account: gaussian and zeroth-order Bessel beam propagation.