The Two-Photon Polarization Ratio Explains Unusual Shape of the Two-Photon Absorption Spectra of Dyes and Detects Weak Excitonic Coupling in Fluorescent Protein Dimers

Two-photon absorption is a nonlinear optical process in which a molecule simultaneously absorbs two photons. It finds use in two-photon fluorescence microscopy, providing high spatial resolution and deep imaging of biological tissues. Understanding the physical mechanisms of two-photon absorption will help optimize excitation conditions and design brighter probes for two-photon microscopy. The two-photon polarization ratio (Ω), defined as the ratio of the two-photon absorption strength of circularly and linearly polarized light─carries indispensable information on the symmetry of electronic, vibronic, and excitonic transitions. Here, we present a physical model based on few-state approximations to derive analytical expressions for Ω as a function of molecular dipole moment matrix elements. The model accounts for an unusual, Herzberg-Teller vibronic coupling of the permanent dipole moments to the bond-length alternating vibrational coordinate(s). Using this framework, we analyze both monomeric systems (Rhodamine 6G, TM-BODIPY, and the chromophore in fluorescent protein Venus) and a dimeric Venus protein. For the monomers, Ω measurements allow us to resolve the two-photon absorption spectra into components corresponding to the Franck-Condon vibronic progressions similar to those observed in one-photon absorption, as well as new vibronic progressions built upon Herzberg-Teller replicas of the bond-length alternating vibration(s), only pertinent to two-photon absorption. Our model explains previously reported broadening and blue shift of the two-photon absorption spectra of dyes relative to their one-photon absorption counterparts. For the Venus dimer protein, spectral dependence of Ω helps to resolve strongly overlapping excitonic J- and H-transitions and specify mutual geometrical arrangement of the two chromophores.