Z-scan theory based on diffraction theory with consideration of two-photon absorption

Based on Fresnel-Kirchhoff diffraction theory, a diffraction model of a nonlinear optical medium to a Gaussian beam is built. The propagation behavior of the Gaussian beam passing through the nonlinear optical medium is theoretically deduced and numerically simulated, which can explain the Z-scan phenomenon from a new approach. From this theory, a unified equation is derived, which can describe both the closed-aperture Z-scan curve and the open-aperture Z-scan curve with consideration of the two-photon absorption. It provides a new way to calculate the nonlinear refraction index and the two-photon absorption coefficients. Numeric simulation shows that for the closed-aperture Z-scan considering the two-photon absorption, the simulation results are well consistent with the conventional theory. For a given open-aperture Z-scan curve, the two-photon absorption coefficient computed by the new Z-scan theory is 1/3 of the value fitted by the conventional Z-scan theory, whereas other conclusions are identical to the conventional Z-scan theory. This theory has better accuracy than the conventional Z-scan theory because the approximate conditions are only thin sample and small nonlinear absorption.