Coupled wave instability in pure-quartic dispersive and noninstantaneous Kerr media in presence of walk-off

The letter explores modulational instability (MI) in birefringent optical media with pure-quartic dispersion, relaxed Kerr nonlinearity, and walk-off effects. The linear stage of MI is studied using coupled biharmonic nonlinear Schrödinger equations, and the stability of their continuous wave solutions is used to calculate the growth rate of MI. The latter is then used to characterize MI under the combined effects of nonlinear responses, group-velocity mismatch, and quartic dispersion, with a focus on the pure-quartic soliton regime. The nonlinear stage of MI is also studied through direct numerical simulations, which support the analytical predictions and emphasize the impact of quartic dispersion, relaxed Kerr nonlinearity, and the walk-off effect on the emergence of various nonlinear patterns. These findings provide valuable insights into signal generation and processing in pure-quartic optical materials and have potential applications in nonlinear optics and lasers.