Finite Gaussian wavelet superposition and Fresnel diffraction integral for calculating the propagation of truncated, non-diffracting and accelerating beams

We demonstrate that the propagation of truncated, non-diffracting and accelerating beams can be accurately calculated by using a method that represents these beams by a finite superposition of Gaussian wavelets to be in turn propagated by means of the Fresnel diffraction integral. We support our proposal by demonstrating analytically that the Fresnel diffraction integral describes properly the non-diffracting and accelerating characteristics of non-truncated beams under propagation. We present numerical results of the propagation of this type of truncated beams and we propose analytical equations of a truncated accelerating beam with improved performance.