Transient gratings in a nonlinear medium

The excitation of a phase transient grating induced by two equal pulses from the same laser, which intersect in a nonlinear (cubic) medium, is considered theoretically. The grating parameters are calculated. The grating amplitude is shown to be spatially non-uniform and to be described by the pulse autocorrelation function, a display of the pulse coherence and of the two-pulse interference pattern. The diffraction problem of the induced grating is then solved using the electrodynamic perturbation theory. The diffraction efficiency of the grating is calculated. It is shown that the measurement of the spectral intensity of the probe light diffracted from the induced grating enables the complete computation of the grating amplitude. Such a measurement may be carried out for the whole of the time of grating decay after the excitation of the grating. Some possible applications of the induced grating are considered. The medium parameters and the autocorrelation trace of the single pulse may be determined. The shape and duration of a bandwidth-limited pulse or the spectrum of an arbitrary one are shown to be measurable.