Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules

We provide a nonperturbative theory for photoionization of transparent solids, which consistently accounts for the selection rules related to the parity of the number of absorbed photons (odd or even). We derive closed-form analytical expressions for the photoionization rate within the two-band structure model. Our model exhibits excellent agreement with measurements for the frequency dependence of the two-photon absorption and nonlinear refractive index coefficients in sapphire and silica, two highly relevant materials for industrial applications. We demonstrate the crucial role of the interference of the transition amplitudes, which in the semiclassical limit can be interpreted in terms of interfering quantum trajectories that were disregarded in Keldysh's foundational work of laser physics [Keldysh, Sov. Phys. JETP 20, 1307 (1965)], resulting in the violation of selection rules.