Nonlinear photoconductivity in pump-probe spectroscopy: Method to determine the local conductivity from the optical coefficients

We analyze the optical pump-probe reflection and transmission coefficients when the photoinduced response depends nonlinearly on the incident pump intensity. Under these conditions, the photoconductivity depth profile changes shape as a function of the incident fluence, unlike when the photoinduced response is linear in the incident intensity. We consider common optical nonlinearities, including photoconductivity saturation and two-photon absorption, and we derive analytic expressions for the photoconductivity depth profile when one or more is present. By solving the wave equation for the nonlinear photoconductivity depth profile as a function of fluence, we obtain exact solutions for the optical coefficients as a function of fluence, which we can fit reliably to experimental data. Our results provide a framework for constraining the systematic uncertainty associated with nonlinear photoconductivity profile distortion. We will discuss the implications of these results for the ongoing controversy over the evidence for photoinduced superconductivity.