Analytical modeling of nonlinear absorption in Z-scan measurements using super-Gaussian beams

This study presents a comprehensive theoretical and numerical investigation of multiphoton absorption (MPA) in Z-scan experiments using super-Gaussian laser beams. We developed an analytical model for normalized optical transmittance under weak nonlinearity approximation and performed extensive simulations examining the effects of varying MPA absorption order and super-Gaussian beam parameter. Our results reveal that flatter beam profiles consistently produce stronger nonlinear absorption effects across all multiphoton orders due to extended high-intensity regions that enhance interaction volumes. Lower-order MPA processes demonstrate greater overall absorption efficiency, with two-photon absorption showing the most dramatic transmittance reductions, while higher-order processes exhibit progressively weaker absorption despite their enhanced intensity sensitivity. Remarkably, while minimum transmittance varies significantly with beam profile, the Full Width at Half Maximum increases linearly with super-Gaussian parameters, revealing fundamental scaling relationships governing nonlinear interaction spatial extent. These findings establish important design principles for optical limiting systems, precision laser manufacturing, medical applications, and material characterization techniques, providing a comprehensive framework for optimizing nonlinear optical interactions through strategic beam profile selection and offering valuable insights for both fundamental research and practical applications in modern photonics.