Modulational instability with higher-order dispersion and walk-off in Kerr media with cross-phase modulation

摘要

We investigate the cross-phase-modulation-induced modulational instability (MI) of two co-propagating opticalnbeams in the system of relaxing Kerr nonlinearity with the effect of higher-order dispersion (HOD) and walk-offneffect. We identify and discuss the salient features of relaxation of nonlinear responses and HOD using suitablentheoretical model. First, we analyzed the impact of HOD and walk-off on the MI spectrum and found bothnanalytically and numerically that the MI exhibits alternate characteristics like the evolution of different spectralnbands in addition to the conventional MI bands. The walk-off effects in the virtue of HOD not only consist ofnthe conventional group velocity mismatch (GVM) but also the difference in third-order dispersion (TOD) of thentwo beams, and thereby significantly modify the dynamical behavior of the MI. We also consider the combinedneffect of relaxation of nonlinear response and the HOD effects, and we observe that any finite value of delaynleads to the evolution of two unstable modes and thereby extends the range of unstable frequency; HOD on thenother hand along with the walk-off effect brings other characteristic spectral bands. A detailed discussion aboutnthe various combinations of parameters and the relative competence of one over the other on the MI spectrum isnpresented. Thus the evolution of MI from cross-phase modulation in the system of relaxing Kerr nonlinearity isnemphasized in detail and the influence of HOD and the walk-off effect are highlighted.