Resonant third-harmonic generation in all-trans β-carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region

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Abstract
The dispersion of the modulus of the third-order nonlinear susceptibility, ‖χ(3)zzzz(−3ω;ω,ω,ω)‖, of an all-trans β-carotene doped polystyrene thin film has been measured by third-harmonic generation throughout the 1 1Bu absorption band of the β-carotene. The observed dispersion is interpreted in terms of a three-electronic state model including explicit regard to six Franck–Condon active normal modes in the resonant electronic state. Both the sum-over-states method and, equivalently, the time domain approach are used. A fit of the three-state model to the data shows that the large nonlinear susceptibility of β-carotene in this wavelength range can be explained by strong dipole coupling between the strong one-photon allowed 1 1Bu state and a nearby two-photon allowed n 1Ag state. The electric dipole transition moment between the 1 1Bu excited state and the n 1Ag excited state, located at 22 200 cm−1, was determined to be 31 D.