Theory of two-photon photothermal deflection spectroscopy in stationary and flowing media for arbitrary optical pulse length

A general theory of pulsed two-photon photothermal deflection spectroscopy (PTDS) is presented. We find that there are significant enough differences in the amplitude and temporal evolution of PTDS signals between the results of the single- and two-photon theories that if one tries to interpret two-photon data with single-photon theory, the extracted values may be considerably in error. Our theory is sufficiently general that it incorporates both stationary and flowing media and considers optical pulses of arbitrary length. Moreover, the temporal profile of the optical pulse is explicitly taken into account. The two-photon absorption coefficient is explicitly expressed in terms of oscillator strengths and Clebsch-Gordan coefficients, and the Doppler width for both co-propagating and counter-propagating beams is taken into account. Although the theory is primarily developed for atomic and molecular vapors, it can easily be adapted for condensed matter by expressing the absorption coefficient in terms of the properties of the liquid or solid under investigation.