Generalizing the Z-scan theory for nonlocal nonlinear media

The basic Sheik-Bahae formalism has been extended to include the possibility of nonlocal response of samples in Z-scan experiments. This is made possible by introducing a nonlocal parameter in the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample. This phase shift has been optimized to be appropriate for describing the Z-scan results of samples with thicknesses much smaller than the Rayleigh length of the Gaussian beams (thin samples). Using this kind of phase shift, the basic formulas for the on-axis Gaussian beam transmittance in the far-field and peak-to-valley separation distance and transmittance difference have been provided. A simple method has been devised for obtaining the nonlinear index of refraction as well as the nonlocal parameter from the Z-scan curves. This method can be of great assistance in determining the more precise values of the nonlinear index of refraction when the sample response is nonlocal. The main criterion for the applicability of our model has been established in terms of the measurable Z-scan data.