Relativistic transformations of quasi-monochromatic paraxial optical beams

A monochromatic plane wave recorded by an observer moving with respect to the source undergoes a Doppler shift and spatial aberration. We investigate here the transformation undergone by a generic, paraxial, spectrally coherent quasimonochromatic optical beam (of finite transverse width) when recorded by a moving detector. Because of the space-time coupling intrinsic to the Lorentz transformation, the monochromatic beam is converted into a propagation-invariant pulsed beam traveling at a group velocity equal to that of the relative motion and which belongs to the recently studied class of "space-time wave packets." We show that the predicted transformation from a quasimonochromatic beam to a pulsed wave packet can be observed even at terrestrial speeds.