Transformation of pulsed nonideal beams in a four-dimension domain

A tensor method is presented to treat the transformation of pulsed nonideal beams in a four-dimension spatiotemporal domain. The equivalent beamwidth, mean pulse duration, divergence, spectrum width, radius of curvature, and pulsed beam quality factor for arbitrary-amplitude profile pulsed beams are introduced. The transformation rules of these parameters are derived by means of the four-dimension Huygens integral.