Dynamics and stability of cw and pulse lasers in Kerr optical media with K-photon absorption

Abstract

The laser dynamics in inscription processes involving transparent media is carried out, by considering an optical field propagating in a transparent medium with Kerr nonlinearity. The study takes into account multi-photon absorption phenomena, as well as a possible modification of the material structure resulting in the generation of a plasma of nearly free electrons. The model is described by a complex Ginzburg–Landau equation governing the laser dynamics, in which an extra Kth-order nonlinear term is induced by K-photon absorption processes. The model also takes into consideration the electron plasma generation via a linear term in the optical field. A global stability analysis of the system dynamics reveals a rich variety of fixed points consisting of no, one or two singular points in the amplitude-frequency plane. The modulational instability of plane waves gives rise to period-halving bifurcations in the continuous-wave amplitude growth rate, reminiscent of dominant multi-pulse structures in the nonlinear regime at large multi-photon absorption rate K. Pulses and multi-pulses are observed in numerical simulations of the nonlinear equations for the full system dynamics, the first structures are clearly associated with the case K = 2 whereas multi-pulse structures of increasing amplitudes and shorter perioids are dominant at larger values of K.

Laser dynamics in nonlinear transparent media with electron plasma generation: effects of electron–hole radiative recombinations

“…Values of model parameters are given in the captions, and different curves in each graph correspond to different values of the radiative recombination coefficient a. Recall that the sign of δ determines the dispersion regime [24,25,34]. Indeed a positive δ corresponds to a normal group-velocity dispersion, whereas a negative δ will correspond to an anomalous group-velocity dispersion well known [24,25,34] to favor the generation of pulse structures, of course provided the intrinsic refractive index of the host medium is of a self-focusing Kerr nonlinearity.…”

“…In the fully nonlinear regime, solutions to the laser equation ( 1) are high-intensity fields which can be represented as realamplitude pulses, undergoing spatio-temporal modulations i.e. [33,34]…”

“…with y = g ′ , M = ϕ ′ and the prime symbol refers to the derivative with respect to τ . Let us focus on the system dynamics in the particular case v = 0 [26,33,34]. For this value of v the set of coupled first-order nonlinear ordinary differential equations ( 20)-( 22) reduces to…”

“…According to figure 3, for K = 2 the laser dynamics is dominated by weakly nonlinear pulse trains with maximum amplitudes for ω = 0. An increase of K (see graphs for K = 3, 4 and 5) favors strongly nonlinear pulse trains of larger amplitudes [33,34]. We have also plotted the instantaneous frequency M as a function of the amplitude g of laser (figure 4), and the laser amplitude g as a function of the electron plasma density ρ (figure 5), for four different values of K. Note that the expression of M given in formula (28) does not contain the radiative recombination coefficient a but is controlled mainly by the laser propagation constant ω, whereas g as a function of ρ extracted from equation (28) depends on a but not on ω.…”

Self-starting dynamics of continuous-waves stability in a generalized complex nonlinear transparent media for passively mode-locked lasers with fast saturable absorbers

“…Other characteristic parameters are labeled in the captions. For δ negative, we have an anomalous group-velocity dispersion [42][43][44], which is much more advantageous and preferred for the propagation of pulse and multi-pulse structures, with δ positive, analogous to a normal group-velocity dispersion [42][43][44]. It is important for us to note that, for ( ( ))…”