Spatiotemporal transformation of single-cycle pulses by quadratic phase media

Summary form only given. Ultrawideband single-cycle pulses of subpicosecond duration are now readily available through optical rectification or photoconductive switching techniques. At optical frequencies femtosecond pulses as short as two and one-half cycles have also been generated through passive mode locking. For these ultrashort pulses, coupling between spatial and temporal variables results in significant temporal reshaping even when these pulses propagate through lossless non-dispersive media. In this paper we show that the spatiotemporal transformation of a class of single-cycle pulses by non-dispersive quadratic phase media can be analyzed in closed form by means of the well-known ABCD matrices of Gaussian beam optics. The class of pulses discussed here are exact non-separable wavepacket solutions of the time-dependent paraxial wave equation.