Gaussian pulsed beams with arbitrary speed

It is shown that the homogeneous scalar wave equation under a generalized paraxial approximation admits of Gaussian beam solutions that can propagate with an arbitrary speed, either subluminal or superluminal, in free-space. In suitable moving inertial reference frames, such solutions correspond either to standard stationary Gaussian beams or to temporal diffracting Gaussian fields. (C) 2004 Optical Society of America.