Modulational instability of truncated Airy pulses in cubic-quintic nonlinearoptical waveguides with multiphoton absorptions

In this work we study the modulational instability (MI) phenomenon of truncated Airy pulses in a cubic-quintic nonlinear optical waveguide including nonlinear multiphoton absorptions as the two-photon absorption(TPA) and the three-photon absorption (3PA) in the anomalous group-velocity dispersion (AGVD) regime ofchromatic dispersion. The investigation is done through a lossless and dimensionless cubic-quintic nonlinearSchrodinger equation (CQNLSE) where we launch a perturbed truncated Airy pulse. The perturbation is definedthrough the linear analysis of the steady-state of a continuous-wave (CW) in which we have chosen to operatewith the optimal frequencies of the MI gain. The data obtained through this analysis led to generate thedestabilization of the pulse through its lobes starting with the dominant peak. This MI is improved by thecooperating nonlinearities while its distance of achievement is reduced in this case growing from the mainlobe to secondary sides lobes of tail. The MI is avoided in the competing case of nonlinearities for smallpeak power because the negative quintic Kerr nonlinearity (QKN) reduces or almost cancels the cubic Kerrnonlinearity (CKN) effect. If the peak power of the pulse increases, the deleterious effect of the competingQKN decreases while the AGVD and the CKN take over to bring the MI into existence breaking the Airy pulseinto sub-pulses. This feature becomes more and more noised as the peak power increases. The TPA comes asa limiting factor of the MI for both the cases of cooperating and competing nonlinearities. The introduction of3PA performs this TPA effect in the case of cooperating nonlinearities while in the competing case, the 3PAsurprisingly cancels the TPA, increasing the AGVD effect. Since the same feature has already been observedrecently in Ref.Heuteu et al, J. Opt. 23, 095503 (2021)for the supercontinuum generation (SCG) of Airypulses, it is therefore shown that the 3PA could be used for better control the TPA effect even in the MI ofthis kind of pulses. Moreover, it is also shown that the increase of the Airy pulse duration drastically enhancesits MI occurrence with noised outputs for large values of pulse width. However, reducing the pulse widthalso reduces its input energy, consequently the Airy pulse does not undergo the MI phenomenon but simplymanifests the property of acceleration