<title>Laser-induced collective ionization in wide band-gap crystalline dielectrics</title>

Abstract

Analyzing influence of band structure of a crystalline solid on ionization rate we have discovered a new regime of ionization referred to as collective one. It cannot be discovered in the framework of traditional approaches to analysis of ionization since they are based on specific band-structure models describing only the central part of the first Brillouin zone. To reveal and to study the effect we reformulated the Keldysh calculation procedure for the case of cosine energy-momentum relation and derived an expression for the corresponding ionization rate. Results of the calculations show occurring of a singularity on dependence of the ionization rate on laser intensity with the ionization rate increasing up to infinity. The singularity has a well-defined threshold that was rigorously calculated and shown to be close to 10 TW per square centimeter for many wide band-gap dielectrics. The singularity is associated with the collective ionization corresponding not to individual "electron-by-electron" inter-band transitions, but to collective inter-band jumps of electrons. We relate its physical mechanism to Bragg-type reflections of oscillating electrons at boundaries of the first Brillouin zone. They result in specific redistribution of pondermotive energy among the oscillating electrons in such a way that the total energy of an electron does not depend on its initial quasi-momentum, i.e., it is homogeneously distributed over all states in the Brillouin zone. The latter effect is referred to as flattening of the effective band.