The performance of optical devices manufactured via laser micromachining on nonlinear transparent materials usually relies on three main factors, which are the characteristic laser parameters (i.e. the laser power, pulse duration and pulse repetition rate), the characteristic properties of host materials (e.g. their chromatic dispersions, optical nonlinearities or self-focusing features) and the relative importance of physical processes such as the avalanche impact ionization, multiphoton ionization and electron–hole radiative recombination processes. These factors act in conjunction to impose the regime of laser operation; in particular, their competition determines the appropriate laser operation regime. In this work a theoretical study is proposed to explore the effects of the competition between multiphoton absorption, plasma ionization and electron–hole radiative recombination processes on the laser dynamics in transparent materials with Kerr nonlinearity. The study rests on a model consisting of a K-order nonlinear complex Ginzburg–Landau equation, coupled to a first-order equation describing time variation of the electron plasma density. An analysis of the stability of continuous waves, following the modulational instability approach, reveals that the combination of multiphoton absorption and electron–hole radiative recombination processes can be detrimental or favorable to continuous-wave operation, depending on the group-velocity dispersion of the host medium. Numerical simulations of the model equations in the fully nonlinear regime reveal the existence of pulse trains, the amplitudes of which are enhanced by the radiative recombination processes. Numerical results for the density of the induced electron plasma feature two distinct regimes of time evolution, depending on the strength of the electron–hole radiative recombination processes.
Ultrashort laser micromachining is a versatile technology used in modern industries for manipulating transparent materials with precision. In these applications, laser systems are customized for specific power levels and wavelengths, requiring an understanding of different laser operation regimes to optimize their utilization, as well as technological advancement. This study proposes a theoretical analysis to investigate the impact of the competition between multiphoton absorption and the higher order correction term to the nonlinear refractive index on laser propagation and stability in Kerr nonlinear transparent materials. The study focuses on the mathematical model that includes a complex nonlinear K-order Ginzburg-Landau equation coupled to the Drude equation that captures the growth rate of the electron plasma density. Through global stability investigation, a diverse range of fixed points is revealed in the amplitude-frequency plane. An examination of the steady-state stability of these fixed point solutions reveals that, depending on the sign of the spatial noise, the combination of the multipho-ton absorption process with the higher-order correction term to the nonlinear refractive index can be detrimental or beneficial to the continuous-wave regime. According to numerical simulations of the mathematical model in the fully non-linear regime, we found that low values of the higher-order correction term to the nonlinear refractive index, denoted as M0 promote stable pulse trains patterns, mainly when the multiphoton absorption rate is high, whereas high values of M0 1 induced a train of anharmonic wave patterns as the multiphoton absorption rate gets stronger.
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