Soliton trains induced by femtosecond laser filamentations in transparent materials with saturable nonlinearity

Abstract

Femtosecond laser inscriptions in optical media current offer the most reliable optical technology for processing of transparent materials, among which is the laser micromachining technology. In this process, the nonlinearity of the transparent medium can be either intrinsic or induced by multiphoton ionization processes. In this work, a generic model is proposed to describe the dynamics of femtosecond laser inscription in transparent materials characterized by a saturable nonlinearity. The model takes into account multiphoton ionization processes that can induce an electron plasma of inhomogeneous density and electron diffusions. The mathematical model is represented by a one-dimensional complex Ginzburg–Landau equation with a generalized saturable nonlinearity term in addition to the residual nonlinearity related to multiphoton ionization processes, coupled to a rate equation for time evolution of the electron plasma density. Dynamical properties of the model are investigated focusing on the nonlinear regime, where the model equations are transformed into a set of coupled first-order nonlinear ordinary differential equations, which are solved numerically with the help of a sixth-order Runge–Kutta algorithm with a fixed time step. Simulations reveal that upon propagation, spatiotemporal profiles of the optical field and of the plasma density are periodic pulse trains, the repetition rates and amplitudes of which are increased with an increase of both the multiphoton ionization order and the saturable nonlinearity. When electron diffusions are taken into account, the system dynamics remains qualitatively unchanged; however, the electron plasma density gets strongly depleted, leaving almost unchanged the amplitude of pulses composing the femtosecond laser soliton crystals.