Investigation of high-order optical nonlinearities by the Z-scan technique

Abstract

We demonstrate theoretically and numerically how to identify and separate the high-order absorptive and refractive nonlinearities. We give, for multiphoton absorption, the formulas of the nonlinear imaginary phase shift, and thus the normalized transmittance of open aperture <i>Z</i>-scan. In order to determine the two-photon and three-photon absorptions immediately, we also give two empirical formulas with considerable accuracy, which require only the nonlinear normalized transmittance at the focus. Moreover, we show the Gaussian decomposition method and zeroth-order Hankel transform to obtain the complex optical field at the far-field aperture. We find that the former frequently used fails to describe the propagation process for the large nonlinear imaginary phase shift. The influence of linear transmittance of aperture and the multiphoton absorption on the measurement of nonlinear refractive index are also analyzed in detail. In addition, we show the competition relationship between low-order and high-order optical nonlinearities, depending on the intensities at different z positions.