ABSTRACT
The modulational instability (MI) phenomenon is theoretically investigated in birefringent optical media with pure quartic dispersion and weak Kerr nonlocal nonlinearity. We find from the MI gain that instability regions are more expanded due to nonlocality, which is confirmed via direct numerical simulations showing the emergence of Akhmediev breathers (ABs) in the total energy context. In addition, the balanced competition between nonlocality and other nonlinear and dispersive effects exclusively gives the possibility of generating long-lived structures which deepens our understanding of soliton dynamics in pure-quartic dispersive optical systems and opens new investigation routes in fields related to nonlinear optics and lasers.
ABSTRACT
We investigate the modulational instability (MI) of a continuous wave (cw) under the combined effects of higher-order dispersions, self steepening and self-frequency shift, cubic, quintic, and septic nonlinearities. Using Maxwell's theory, an extended nonlinear Schrödinger equation is derived. The linear stability analysis of the cw solution is employed to extract an expression for the MI gain, and we point out its sensitivity to both higher-order dispersions and nonlinear terms. In particular, we insist on the balance between the sixth-order dispersion and nonlinearity, septic self-steepening, and the septic self-frequency shift terms. Additionally, the linear stability analysis of cw is confronted with the stability conditions for solitons. Different combinations of the dispersion parameters are proposed that support the stability of solitons and the occurrence of MI. This is confronted with full numerical simulations where the input cw gives rise to a broad range of behaviors, mainly related to nonlinear patterns formation. Interestingly, under the activation of MI, a suitable balance between the sixth-order dispersion and the septic self-frequency shift term is found to highly influence the propagation direction of the optical wave patterns.
