Picosecond multiple-pulse experiments involving spatial and frequency gratings: a unifying nonperturbational approach

The concept of a grating in real and frequency space is examined in the context of a three-pulse optical excitation cycle applied to a pseudo two-level model system. The calculations are done analytically using the Liouville-operator formalism in matrix form. It is shown that a continuous transition occurs from a grating in real space to a grating in frequency space when the first two excitation pulses separate in time. During this transition, the role of the population-relaxation time constant (T1) is taken over by the dephasing time constant (T2) bringing out the irreversible nature of the loss of coherence in an excited state. The underlying space-time transformation when moving from a grating in real space to a grating in frequency space further clarifies the loss in symmetry of the scattering pattern induced by a probe pulse by attributing it to the law of causality. It is finally concluded that the generalized grating concept is a powerful means of analyzing or predicting the effects of multiple-pulse multicolor optical-coherence experiments.