Abstract
Two-photon excitation (TPE) in a randomly oriented liquid sample generates an anisotropic distribution of excitations that can be probed by a secondary spectroscopic transition, e.g. fluorescence or transient absorption. The orientation dependence of the secondary transition dipole (and therefore of the fluorescence or transient-absorption signal) can be exploited to generate information on molecular symmetry and orientation that is not available in two-photon absorption alone. A theoretical formalism is developed here for the orientationally averaged two-photon absorptivity taking into account the orientation of the secondary transition dipole. Spherical tensor formalism is employed to distinguish isotropic and anisotropic components of the two-photon absorptivity, and several two-photon anisotropy parameters are defined. The theory describes time-resolved detection of TPE by transient-absorption or fluorescence decay measurements. Time-resolved measurements with time-resolution that is fast relative to the rotational correlation times are shown to provide new information, including the two-photon anisotropies. Applications to TPE fluorescence anisotropy measurements and TPE induced anisotropic transient absorption are described, and illustrated by experimental measurements on bacteriorhodopsin.
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