Laser dynamics and stability of continuous-waves in nonlinear optical transparent medium with saturable absorber: competing effects between Kerr nonlinearity, saturable absorber, and electron–hole radiative recombination processes

Femtosecond laser micromachining of transparent material is a powerful and versatile technology, which can be applied to several materials. These materials ranged from one-disc inscriptions to cell ablations, through DNA combing and imprinting, for the manufacturing of micro and nanofluidic devices. In these applications, lasers are developed to function in specific pattern characterized by their powers and wavelengths. Thus, understanding the characteristic properties of the well-defined possible laser operation regimes turns out to be a pertinent and important step toward the optimization of their uses, as well as the enhancement of technology. In this work, we established the exact structures of the laser field in the mode-locked regime, where the model equations were solved. For it achievement, numerical simulations enables us explore all the possible operation regimes inherent to the dynamics of our proposed model. Moreover, it outlines the competing effect between Kerr effect and saturable absorber, taking into consideration multi-photon absorption inscription processes and the pulse lasers dynamics in a nonlinear optical field, propagating in transparent materials with strong nonlinearity is carried out. The model is characterized by a complex Ginzburg–Landau equation describing the dynamics of the laser, where an extra nonlinear K-order term is induced by K-photon absorption processes and plasma generation associated to a Drude’s equation for time evolution of the electron plasma density with electron–hole recombination effects. This help us to evaluate the transient states of our system model, characterized by period-doubling cascades and chaotic phases.