Mid-infrared Kerr index evaluation via cross-phase modulation with a near-infrared probe beam

We propose a simple method to measure nonlinear Kerr refractive index in mid-infrared frequency range that avoids using sophisticated infrared detectors. Our approach is based on using a near-infrared probe beam which interacts with a mid-IR beam via wavelength-non-degenerate cross-phase modulation (XPM). By carefully measuring XPM-induced spectral modifications in the probe beam and comparing the experimental data with simulation results we extract the value for the non-degenerate Kerr index. Finally, in order to obtain the value of degenerate mid-IR Kerr index we use the well-established two-band formalism of Sheik-Bahae et al., which is shown to become particularly simple in the limit of low frequencies. The proposed technique is complementary to the conventional techniques such as z-scan and has the advantage of not requiring any mid-infrared detectors.