Picosecond Laser-Induced Transient Gratings and Anisotropic State-Filling in Germanium.

We present a comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments. Signals in both the probe and conjugate directions are discussed. The effects of recombination, non-radiative scattering and spatial and orientational diffusion are included. The analysis is applied to both a molecular and to a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. The theory is used to explain our recent observations in germanium. Included are discussions of picosecond transient grating self-diffraction measurements that can be understood in terms of an orientational grating produced by anisotropic (in k-space) state-filling. Though there have been predictions and indirect experimental evidence for isotropic state-filling in germanium, this is the first direct experimental indication of anisotropic state-filling in a semiconductor. We compare the self-diffracted signals from orientational gratings with those from band-filling induced concentration gratings and find several distinctions, all of which can be explained in terms of the theoretical model. In addition, we have performed three-pulse transient -grating lifetime measurements that indicate that the concentration grating decay is tens of picoseconds while the orientational grating decay is too rapid to resolve with our 8 psec pulses.