Ionization-field instability in the laser-induced breakdown of nanoporous dielectric

Abstract

The theory of ionization-field instability in a continuous homogeneous medium is generalized to the heterogeneous nanoporous one with the purpose to clear and analyze the mechanism of nanograting formation during the optical breakdown process in a transparent dielectric (fused silica) containing multiple small inclusions (nanobubbles) with a lowered ionization threshold. Based on the Maxwell Garnett approximation extended to include the size effect caused by the finite ratio of the bubble sizes to the scale of unstable perturbations, we have obtained the equation system describing the spatiotemporal evolution of the plasma density, average field, and effective dielectric permittivity and have derived the characteristic equation connecting the temporal growth rate of these perturbations with their spatial period. Analysis of the roots of this equation shows that the unstable periodic perturbation structure having the maximal growth rate is close in character to the nanogratings observed experimentally (modulation in the direction of the pump wave polarization with the period approximately equal to the half-wavelength in the host material).