Analytical Z-scan model for multiphoton absorption in inhomogeneous media

This work presents an analytical model for multiphoton absorption in inhomogeneous materials, developed within the framework of the Z-scan technique using the weak nonlinearity approximation. The model addresses arbitrary order n of multiphoton absorption processes and considers linear variations in material properties. Three cases are investigated: purely axial, purely radial, and combined axial and radial inhomogeneities in the absorption coefficient. Simulations reveal distinct normalized transmittance profiles for each case, demonstrating the significant impact of linearly varying inhomogeneities on multiphoton absorption. The purely axial case shows symmetric, broad dips in transmittance centered at the focal point, while the purely radial case exhibits narrower, more localized absorption profiles. The combined case demonstrates a synergistic effect, resulting in enhanced absorption.