Analytical model of time-dependent photoionization and nonlinear absorption of few-cycle laser pulses in dielectrics

Rate of the photoionization is the key quantity employed in all simulations of nonlinear absorption and generation of free carrier associated with high-intensity interactions of ultrashort laser pulses with transparent solids. The rate is evaluated by either numerical methods or by analytical models. However, they meet significant challenges when applied to the pulses carrying from 3 to 20 cycles because of the single-frequency approximation underlying the analytical models and the difficulties met by the numerical methods in modeling of parametric scaling of the rate. Here, we report an analytical time-domain model of the photoionization that fits that range of the pulse width. Analytical relations for the photoionization rate are derived in the form of asymptotic series. The zero-order term of the series is the Keldysh-type rate evaluated at central frequency of pulse spectrum. Higher-order terms describe departures from the single-frequency approximation of the Keldysh-type models and accurately evaluate the photoionization rate by the pulses carrying 3 or more cycles. Significant influence of carrier-envelope phase in magnitude of the photoionization rate is reported. Substantial departure from the Keldysh-type monochromatic models of the photoionization is demonstrated and discussed. The reported model may serve as a highly effective simulation tool for modeling of nonlinear interactions of high-intensity few-cycle laser pulses with transparent solids.