Numerical analysis of multi-photon parameters from ultrafast laser measurements

We describe a unique mathematical/numerical model to analyze ultrafast laser experimental data and obtain two-photon (TPA) and multi-photon (MPA) absorption parameter(s). The material used to demonstrate the numerical method is a hybrid organic-inorganic nano-structured semiconductor quantum dot-polymer composite. Chemical, biological and engineering studies require advancements in TPA/MPA absorbers for microscopy, fluorescence, imaging, and microprocessing of materials. We illustrate the numerical method by fitting data from the well-known z-scan experimental method. Often an analytical model is used to analyze data from such experiments, which is limited in scope with certain restrictions on laser intensity and material thickness. A more general mathematical/numerical method that includes TPA/MPA and can be extended to free carrier absorption and stimulated emission is described. Under certain circumstances, we can also calculate the electron population density on every electronic level to demonstrate physical effects such as saturation. Additionally, we include diffraction in our numerical calculation so that the TPA/MPA can be obtained even for thick optical samples. We use the numerical method to calculate published z-scan measurements on quantum-dot CdS-polymer composites, and show excellent agreement with published analytical results.

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