Two-photon-absorption laws for coherent and incoherent radiation

The differential equation for the attenuation of a light beam transmitted through a two-photon absorber is solved for two cases: 1) nonfluctuating or 2) Gaussian-fluctuating light beams. The two cases obey entirely different absorption laws. It is further shown that the fluctuation behavior changes throughout the absorption process. The fluctuations are characterized by the intensity autocorrelation function
g^{(2)}(0)
. It is seen that with increasing absorption the fluctuations of the transmitted beam diminish and the spectrum of the light is modified. Two-photon absorption (TPA) is compared with two-step absorption. The latter type is discussed qualitatively for several combinations of parameters. It is shown that for this case the deviation from a linear absorption law is small. Only when the lifetime of the intermediate state is short compared to the duration of the intensity fuctuation, can a change of the fluctuation behavior and of the spectrum result. These changes are much smaller than in the case of direct TPA.