An alternative analytical description of truncated Gaussian beams

The paper presents a simple analytical method for the diffraction and propagation of truncated or apertured Gaussian beams. The Bessel function, which appears in the Fresnel and Fraunhofer field integrals, is expanded into an approximate sum of a set of Gaussian functions. The field integrals for a truncated Gaussian beam are then analytically performed in terms of the elementary exponential or Gaussian functions only. Analytical results show that there is a good agreement between the present method and direct numerical integration. Some possible extensions of this method to other apertured beams are also suggested.