Real-time time-dependent density functional theory study of optical Kerr nonlinearities in semiconductors and metals

We employ real-time time-dependent density functional theory (rt-TDDFT) to calculate third-order nonlinear optical properties in solids, focusing on the optical Kerr effect: the Kerr coefficient n 2 , the two-photon absorption coefficient β , and the Kerr-type third-order susceptibility χ (3) (− ω ∣ ω , ω , − ω ). We consider centrosymmetric bulk materials, including semiconductors (diamond, silicon) and metals (gold, iridium), and benchmark our results against available experimental data. For semiconductors, we find good agreement with experiment and show that the nonlinear response is robust with respect to pulse duration for photon energies below the bandgap. For metals, we demonstrate that ∣ χ (3) ∣ grows monotonically with pulse duration, consistent with experimental observations, and attribute this behavior to delayed contributions from hot-electron dynamics. We further show that thermal effects in high-repetition-rate experiments can lead to significant overestimation of the measured nonlinearities. Our work establishes rt-TDDFT as a reliable first-principles framework for modeling nonlinear optical phenomena across diverse material classes, including metals, going beyond perturbative approaches by naturally capturing intraband dynamics and pulse-duration effects.