Modulational instability of truncated Airy pulses in cubic–quintic nonlinear optical waveguides with multiphoton absorptions

Abstract

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 of chromatic dispersion. The investigation is done through a lossless and dimensionless cubic–quintic nonlinear Schrödinger equation (CQNLSE) where we launch a perturbed truncated Airy pulse. The perturbation is defined through the linear analysis of the steady-state of a continuous-wave (CW) in which we have chosen to operate with the optimal frequencies of the MI gain. The data obtained through this analysis led to generate the destabilization of the pulse through its lobes starting with the dominant peak. This MI is improved by the cooperating nonlinearities while its distance of achievement is reduced in this case growing from the main lobe to secondary sides lobes of tail. The MI is avoided in the competing case of nonlinearities for small peak power because the negative quintic Kerr nonlinearity (QKN) reduces or almost cancels the cubic Kerr nonlinearity (CKN) effect. If the peak power of the pulse increases, the deleterious effect of the competing QKN decreases while the AGVD and the CKN take over to bring the MI into existence breaking the Airy pulse into sub-pulses. This feature becomes more and more noised as the peak power increases. The TPA comes as a limiting factor of the MI for both the cases of cooperating and competing nonlinearities. The introduction of 3PA performs this TPA effect in the case of cooperating nonlinearities while in the competing case, the 3PA surprisingly cancels the TPA, increasing the AGVD effect. Since the same feature has already been observed recently in Ref. Heuteu et al, J. Opt. 23, 095503 (2021) for the supercontinuum generation (SCG) of Airy pulses, it is therefore shown that the 3PA could be used for better control the TPA effect even in the MI of this kind of pulses. Moreover, it is also shown that the increase of the Airy pulse duration drastically enhances its MI occurrence with noised outputs for large values of pulse width. However, reducing the pulse width also reduces its input energy, consequently the Airy pulse does not undergo the MI phenomenon but simply manifests the property of acceleration.