Propagation of laser beams beyond the paraxial region

Making use of the angular-spectrum representation of a radiation field a formula for the second moments [x(2)(z)] is given, which applies to the propagation of non paraxial beams. The formula was originally derived by Belanger et al. [Bel94] for coherent fields and here it is extended to partially coherent fields. Formally a quadratic propagation law for the second moments [x(2)(z)] is obtained. With the help of an equation of motion for the Wigner distribution function that accounts for non paraxial fields, an analogous propagation equation for the second moments [x(2)(z)] is derived, which yields a quadratic z-dependence of the moments as well. The coefficients, which in the paraxial approximation are identified as measures of the beam parameters, suffer in the general case from convergency problems. Therefore the field descriptions are modified in such a way that finite beam parameters exist. The effects of extending the beam propagation formalism from the paraxial approximation to the non paraxial region are studied with sample fields.