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How the laser-induced ionization of transparent solids can be suppressed

A capability to suppress laser-induced ionization of dielectric crystals in controlled and predictable way can potentially result in substantial improvement of laser damage threshold of optical materials. The traditional models that employ the Keldysh formula do not predict any suppression of the ionization because of the oversimplified description of electronic energy bands underlying the Keldysh formula. To fix this gap, we performed numerical simulations of time evolution of conduction-band electron density for a realistic cosine model of electronic bands characteristic of wide-band-gap cubic crystals. The simulations include contributions from the photo-ionization (evaluated by the Keldysh formula and by the formula for the cosine band of volume-centered cubic crystals) and from the avalanche ionization (evaluated by the Drude model). Maximum conduction-band electron density is evaluated from a single rate equation as a function of peak intensity of femtosecond laser pulses for alkali halide crystals. Results obtained for high-intensity femtosecond laser pulses demonstrate that the ionization can be suppressed by proper choice of laser parameters. In case of the Keldysh formula, the peak electron density exhibits saturation followed by gradual increase. For the cosine band, the electron density increases with irradiance within the low-intensity multiphoton regime and switches to decrease with intensity approaching threshold of the strong singularity of the ionization rate characteristic of the cosine band. Those trends are explained with specific modifications of band structure by electric field of laser pulses.