Pulse and multi-pulse structures in femtosecond laser micromachining with multi-photon Scattering and plasma avalanche

Abstract

Laser inscription processes such as on-disc optical writing, metallic surface modifi- cations, and biomaterial ablations and so on, utilize laser fields of different wavelengths and powers operating in distinct dynamical regimes including continuous-wave, pulse, multi-pulse and chaotic regimes. Understanding the laser dynamics in these processes, and particularly the laser self-starting dynamics, is crucial for their efficient uses in var- ious material processing. In this work, an extensive analysis of laser dynamics in the laser inscription process is carried out, by first considering a field propagating in opti- cal media with Kerr nonlinearity on one hand, and equally examine the case when the material is of relatively stronger nonlinearity on the other. This last case is liken to that of rare-earth doped silica glass materials for example. These later materials today are highly exploited in microelectronic industry where they are used in the fabrications of optical microchips and optical storage devices. The possibility of doping enables full control of their optical properties, which can be tuned at wish, from weakly to strongly nonlinearity. Modelling that with strong nonlinearity simply requires considering a sat- urable absorber or nonlinearity instead of a quadratic (that is a Kerr) term describing a weak nonlinearity. The proposed model in compasses most of the existing ones, while providing prominent possible new passively mode-locked laser. Moreover, our study takes into account multi-photon absorption phenomena as well as a modification of material structure resulting in the generation of a plasma of nearly free electrons. The models are described by a complex Ginzburg-Landau equation gov- erning the laser dynamics in the optical medium with Kerr nonlinearity on one hand, and a saturable nonlinearity on the other as mentioned above, in which an extra Kth order nonlinear term is induced by a K -photon absorption process, and accounts also for the electron plasma generation via a linear term in the optical field. An analy- sis of singular solutions to the system dynamics reveals a rich variety of fixed points consisting of no, one or two singular points in the amplitude-frequency plane, while the modulational instability of plane waves gives rise to period-halving bifurcations in the continuous-wave amplitude growth rate reminiscent of dominant multi-pulse struc- tures in the nonlinear regime at high multi-photon absorption rate K . Pulses and multi- pulses are observed in numerical simulations of the nonlinear equations for the full sys- tem dynamics, the first structures are clearly associated with the case K = 2, whereas multipulse structures are indeed dominant at larger values of K . Furthermore, the Competing effects between Saturable Absorber, Kerr nonlinearity and multi-photon absorptions inscription processes with recombination of CWs and pulse lasers dynamics in a nonlinear optical field propagating in a transparent materials designed to operate in specific regimes characterized by their powers and wavelengths, was equally investigated, with the aim of improving and optimizing their machinery. Theirs stability analysis of the proposed model was also examined. The basic assump- tion was that the laser will operate in the mode-locked regime when the continous-wave regime become unstable. The continuous-wave stability is analyzed within the frame- work of the modulational-instability theory, and the results show a period-halving bifur- cations in the continuous-wave amplitude growth rate where, the saturable nonlinearity on modulational instability describing the absorption of losses is reduced at high opti- cal intensities as saturable absorber coefficient Γ increases. Our results are proved to be consistent with previous analyses of the dynamics of multipulse structures in several contexts of passively mode-locked lasers with a saturable absorber, as well as with predictions about the existence of multi-pulse structures and bound-state solitons in optical fibers with strong optical nonlinearity. Thus, an increase of the rate of plasma avalanche creates more and more favorable condition for cws as K is increased.