Spectral profiles of two-photon absorption: Coherent versus two-step two-photon absorption

We present a theory of two-photon absorption in solutions which addresses the formation of spectral shapes taking account of the vibrational degrees of freedom. The theory is used to rationalize observed differences between spectral shapes of one- and two-photon absorption. We elaborate on two underlying causes, one trivial and one non-trivial, behind these differences. The first refers simply to the fact that the set of excited electronic states constituting the spectra will have different relative cross sections for one-and two- photon absorption. The second reason is that the two-step and coherent two-photon absorption processes are competing, making the one-and two-photon spectral bands different even considering a single final state. The theory is applied to the N-101 molecule [di-phenyl-amino-nitro-stilbene] which was recently studied experimentally in the paper [ T.-C. Lin, G.S. He, P.N. Prasad, and L.-S. Tan, J. Mater. Chem., 14, 982, 2004.]