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 the 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 are exact non-separable wavepacket solutions of the time-dependent paraxial wave equation. These wavepackets are isodiffracting in the sense that their Fourier spectrum is composed of a distribution of Gaussian beams all of which have the same Rayleigh range z/sub R/. Such an isodiffracting pulse can be produced, for example in a confocal resonator that forces all the modes to have the same frequency-independent confocal parameter 2z/sub R/. The spatiotemporal behavior of such a pulse can then be characterized in the time domain by a single q-parameter which contains the radius of curvature R, the radius a, and the pulse width /spl tau//sub 0/ of the pulsed beam.