A basis set of non-sinusoidal spatio-temporal pulsed beams

With interest in increasingly compressed intense laser pulses for laser-plasma electron and ion acceleration techniques, a description of pulsed beams in the few- and single-cycle regime is sought. In this regime, optical pulses exhibit an intrinsic spatial chirp which presents differently depending on the details of pulse transport, and to capture these polychromatic effects in simulations requires many terms. The form of these polychromatic pulses, however, can be calculated directly and can be chosen to form a generating set. Since relativistic laser-plasma interactions generally depend on spatial and temporal pulse structure, this set is extended to the spatio-temporal case. A complete orthogonal set of functions based on derivatives of the Faddeeva function is presented which intrinsically captures their broadband behavior.