Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 µm

We study free-carrier nonlinearities in crystalline silicon at 1.064 microm using the Z-scan technique, with special emphasis on the dependence of their nonlinearities on the width of incident pulses. In the Z-scan experiment, the pulse duration was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in a liquid. At this excitation wavelength, linear absorption is dominant for the creation of electron-hole pairs and the photoexcited carriers can modify the refractive index and absorption coefficient just as a third-order nonlinear effect. The effective nonlinear refractive index n(2eff) and nonlinear absorption coefficient beta(eff) are proportional to the pulse duration and optical intensity, i.e. the fluence when the pulse duration is shorter than the carrier recombination lifetime. We can determine the variation of refractive index per unit of photoexcited carrier density sigma(r) and the total carrier absorption cross section sigma(ab) from the dependence of n(2eff) and beta(eff) on the pulse width, respectively. In this work we had sigma(r) =-1.0 x 10(-21) cm(3) and sigma(ab)=8.4 x 10(-18) cm(2), which agree well with previous data. We also observed the decrease in the magnitude of n(2eff) and beta(eff) at high incident fluence, which is presumably attributed to band filling. This new measurement approach has an advantage of being able to separate an ultrafast Kerr nonlinearity and a cumulative nonlinearity such as the free-carrier nonlinearity treated in this paper and can be utilized to evaluate the optical nonlinearities of other materials.