Dynamics of femtosecond lasers and induced plasma in non-Kerr nonlinear transparent materials: Competing effects of electron–hole radiative recombinations and single-electron diffusions

Modern laser micromachining utilizes ultrashort optical fields, such as femtosecond lasers, to perform high-precision processings on solid materials, including cutting, drilling, ablation, polishing, and scripturing. Femtosecond laser-based material processings can induce a plasma of free electrons whose density depends on physical phenomena such as single-electron diffusions, multiphoton ionization, and electron–hole radiative recombinations. In this work, we examine the dynamics of femtosecond lasers in transparent materials with non-Kerr nonlinearity, taking into account the generation of an electron plasma. In these specific materials, a balance between the nonlinearity and the group-velocity dispersion of the optical medium can favor the formation of optical filaments propagating with a permanent shape by virtue of their “solitonic” features. We are interested in the effects of the competition between electron–hole radiative recombination and single-electron diffusion processes on the spatiotemporal profiles of the propagating optical field and of the plasma density. The model features a complex Ginzburg–Landau equation with an optical nonlinearity of a general saturable form and a Kth-order nonlinearity term accounting for K-photon ionization processes, coupled to a rate equation for the electron plasma density where the present terms are representing avalanche ionizations, single-electron diffusion, and electron–hole radiative recombination processes. The modulational-instability analysis suggests that the continuous-wave regime will be stabilized by strong electron–hole radiative recombination processes for a fixed value of the single-electron diffusion coefficient, a stability enhanced by an increase in K. In the nonlinear regime, numerical simulations of the model equations for different combinations of the nonlinearity-saturation exponents and different values of the photon number K unveil soliton train structures forming from the laser field propagation and the time evolution of the plasma density. These structures turn out to be either dissipative soliton trains in the absence of electron–hole radiative recombinations or soliton crystals when electron–hole radiative recombination processes are taken into consideration to balance the damping effect caused by single-electron diffusions.