Z-scan theoretical analysis for three-, four- and five-photon absorption

In this work, we report a theoretical analysis of three-, four- and five-photon absorption process using the open aperture Z-scan technique. The normalized transmittance equations presented here can be used to fit the experimental data, allowing the determination of material’s multi-photon absorption cross-section. Through simulations, we observed the expected sharpening of the Z-scan curve for higher order nonlinear absorption. The normalized transmittance change as a function of the excitation irradiance displays distinct slopes for process with distinct number of photons, which can be used for determining the origin of the nonlinear processes. Optical limiting curves were also simulated for multi-photon absorption processes, demonstrating that high limiting thresholds occur for higher order processes.