Modulation instability asymmetry in optical fibers beyond Kerr nonlinearity: The role of Raman scattering

This study presents a rigorous theoretical framework that extends conventional nonlinear fiber optics through a controlled first-order generalization based on a modified Lagrangian formulation. By introducing a weak power-law deformation of the action density, , the model preserves variational consistency, dimensional correctness, and the correct recovery of standard nonlinear optical theory in the limit . Under a systematic first-order asymptotic expansion within the slowly varying envelope approximation, the proposed deformation gives rise to an effective intensity-dependent correction to the conventional cubic Kerr nonlinearity, resulting in a generalized nonlinear Schrödinger equation characterized by a logarithmic intensity dependence in the nonlinear phase. This formulation naturally introduces a reference intensity scale through the logarithmic structure, thereby providing a physically consistent description of weak departures from the standard Kerr response. A variational reduction, complemented by Raman-response modeling, demonstrates that even small perturbations of the nonlinear exponent can substantially modify modulation instability (MI) and soliton dynamics. In particular, the sign of the deformation parameter determines whether the effective nonlinear response is super-cubic or sub-cubic, leading to distinct changes in nonlinear phase accumulation, propagation constants, and stability characteristics. The inclusion of the Raman contribution further breaks the spectral symmetry of the MI gain spectrum, giving rise to asymmetric Stokes and anti-Stokes sidebands. Numerical simulations corroborate the analytical predictions, revealing either enhancement or suppression of the MI gain depending on the sign of the deformation parameter, together with logarithmic corrections to the soliton propagation constant relative to the classical cubic nonlinear Schrödinger equation.