Nonlinear refractive index of solids at THz frequency

We report on the nonlinear spectroscopy of crystalline quartz in the terahertz (THz) region. We observe that with increasing of the THz peak amplitude, the pulse experiences a larger delay in travelling through the sample. We estimate a nonlinear refractive index of the order of 10(-13) m(2)/W, which is several orders of magnitude larger than the typical values for nonlinear refractive indices of solids in the visible region. Furthermore, a negative fifth-order susceptibility of the order of 10(-30) m(4)/V-4 is measured. In the second part, we present a simple method to model the propagation of a broadband THz pulse in a nonlinear medium with nonlinear refractive index dispersion using a spectral solution to the wave equation based on Fourier analysis. This method is a useful tool to investigate the effects of the nonlinear dispersion on the propagation of ultrashort THz pulses in a straightforward fashion. Furthermore, based on the same model, we derive an expression to extract the nonlinear refractive index dispersion for broadband sources and compare it with the approximate methods previously proposed: monochromatic approximation and sharp-resonance approximation. We perform a simulation on a sample with an arbitrary dispersion for nonlinear refractive index, and successfully extract the dispersion from the simulated propagation output.