Laser-induced collective ionization in wide band-gap crystalline dielectrics

ABSTRACT Analyzing influence of band structure of a crystalline solid on ionization rate we have discovered a new regime ofionization referred to as collective one. It cannot be discovered in the framework oftraditional approaches to analysis ofionization since they are based on specific band-structure models describing only the central part of the first Brillouinzone. 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 showoccurring of a singularity on dependence of the ionization rate on laser intensity with the ionization rate increasing up toinfinity. The singularity has a well-defined threshold that was rigorously calculated and shown to be close to 10 TW persquare centimeter for many wide band-gap dielectrics. The singularity is associated with the collective ionizationcorresponding not to individual "electron-by-electron" inter-band transitions, but to collective inter-band jumps ofelectrons. We relate its physical mechanism to Bragg-type reflections of oscillating electrons at boundaries of the firstBrillouin zone. They result in specific redistribution of pondermotive energy among the oscillating electrons in such away that the total energy of an electron does not depend on its initial quasi-momentum, i.e., it is homogeneouslydistributed over all states in the Brillouin zone. The latter effect is referred to as flattening ofthe effective band.Keywords: laser-induced ionization, laser-solid interactions, dielectric crystals, multiphoton ionization, electrons incrystals, high laser intensity