Phase-sensitive pump-probe measurement of the complex nonlinear susceptibility of silicon across the direct band edge

The nonlinear response of materials, an increasingly important aspect of light-matter interaction, can be challenging to measure in highly absorbing materials. Here, we introduce an interferometric technique that enables a direct measurement of the nonlinear complex permittivity in a bulk medium from reflectivity alone. We demonstrate the utility of pump-probe supercontinuum (SC) spectral interferometry in reflection by measuring time-dependent variations in the complex dielectric function ($n$, $k$) over the visible wavelength range in bulk silicon. Transient phase shifts in the reflected SC due to a near infrared pump pulse allow us to track modifications to $k$; whereas changes in $n$ are derived from transient fluctuations in the reflected SC probe amplitude. The ultrafast response is attributed to effective two-photon absorption ($\beta$) and Kerr ($n_2$) coefficients. We observe the onset of strong two-photon absorption as the two-photon energy is tuned through the direct band edge of silicon ($E_1$ = 3.4 eV) for the first time to our knowledge. This technique allows straightforward spectroscopic measurements of the ${\chi }^{(3)}$ nonlinear response at the surface of absorbing materials.