Two-photon-induced excited-state nonlinearities

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We report a theoretical investigation of laser-pulse-duration dependence of excited-state nonlinearities induced by two-photon absorption (2PA). We investigate the spatiotemporal characteristics of the transmitted pulses caused by 2PA-induced excited-state absorption, which strongly depends on laser pulse duration. By taking into account 2PA cross-section, excited-state photophysical properties, as well as laser pulse duration, we quantitatively determine the effective fifth-order nonlinearities caused by excited-state absorption and refraction. The results are capable of predicting the magnitude of 2PA-induced excited-state nonlinearities on the time scales where laser pulse duration is less than or comparable to the lifetime of 2PA-induced excited states. We also develop Z-scan theories for quickly yet unambiguously estimation of 2PA coefficient, third-order nonlinear refraction index, and excited-state absorption and refraction cross-sections.