Ab initio insights on the ultrafast strong-field dynamics of anatase TiO$_2$

Electron dynamics of anatase TiO$_2$ under the influence of ultrashort and intense laser field is studied using the real-time time-dependent density functional theory (TDDFT). Our findings demonstrate the effectiveness of TDDFT calculations in modeling the electron dynamics of solids during ultrashort laser excitation, providing valuable insights for designing and optimizing nonlinear photonic devices. We analyze the perturbative and non-perturbative responses of TiO$_2$ to 30 fs laser pulses at 400 and 800 nm wavelengths, elucidating the underlying mechanisms. At 400 nm, ionization via single photon absorption dominates, even at very low intensities. At 800 nm, we observe ionization through two-photon absorption within the intensity range of $1\times10^{10}$ to $9\times10^{12}$ W/cm$^2$, with a transition from multiphoton to tunneling ionization occurring at $9\times10^{12}$ W/cm$^2$. We observe a sudden increase in energy and the number of excited electrons beyond $1\times10^{13}$ W/cm$^2$, leading to their saturation and subsequent laser-induced damage. We estimate the damage threshold of TiO$_2$ for 800 nm to be 0.1 J/cm$^2$. In the perturbative regime, induced currents exhibit a phase shift proportional to the peak intensity of the laser pulse. This phase shift is attributed to the intensity-dependent changes in the number of free carriers, indicative of the optical Kerr effect. Leveraging the linear dependence of phase shift on peak intensities, we estimate the nonlinear refractive index ($n_2$) of TiO$_2$ to be $3.54\times10^{-11}$ cm$^2$/W.