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.
© 1986 Optical Society of America
Original Manuscript: September 23, 1985
Manuscript Accepted: November 19, 1985
Published: April 1, 1986
Koos Duppen and Douwe A. Wiersma, "Picosecond multiple-pulse experiments involving spatial and frequency gratings: a unifying nonperturbational approach," J. Opt. Soc. Am. B 3, 614-621 (1986)