Basic Notions of Pump-Probe Spectroscopy

In the basic experiment, a first optical pulse (pump) is absorbed by the sample. A second, time-delayed pulse of weaker intensity is used to probe the change in optical response. Commonly, the test pulse probes the change in transmission, given in the small signal limit as 

In this expression K groups together a number of constant factors, ct(jj) is the cross-section of the photoinduced transition, and A(t) is the response 

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