Transformation of few-cycle ultrashort pulsed Gaussian beams by an angular disperser

A theoretical analysis of the transformation of pulsed Gaussian beams through a grating is presented under paraxial scalar approximation. By introducing the concepts of local carrier frequency and stationary phase frequency, the angular dispersive process is effectively modelled by two formulas for pulses with only single- or few-cycle duration. The expressions predict some spatiotemporal coupling phenomena, which are found to be associated with high-order angular dispersion, which distorts the electric field with varied pulse width, chirp, pulse front and energy distribution. Related results are confirmed by a rigorous numerical simulation at last. The method proposed here can be generalized to other dispersive systems with the aid of the theory of paraxial optics.