Two-step four-photon absorption.

We report a theoretical investigation of effective four-photon absorption (4PA) process and propose a two-step 4PA model of three-photon- induced excited-state absorption (ESA). Based on three-level rate-equation theory, we find an analytical result for the effective 4PA coefficient that depends on the three-photon absorption (3PA) cross-section, excited-state photophysical properties, and laser pulse duration. We present the analytical theory of the z-dependent nonlinear transmission for straightforwardly yet unambiguously evaluating the 3PA and effective 4PA coefficients simultaneously.