The analytical solution of ultra-short pulsed elliptical Gaussian beams in free space is obtained based on the Fourier transform technique.The propagation properties of ultra-short pulsed elliptical Gaussian beams are investigated in detail through an example.The example shows that,in propagation,the diffraction and the spatiotemporal coupling yield some effects,such as the pulse delay at the beam periphery,the exchange between the major axis and the minor axis of the elliptical pattern,and the pattern diff...