Quartic and dipole solitons in a highly dispersive optical waveguide with self-steepening nonlinearity and varying parameters

Abstract

We show theoretically that highly dispersive optical media characterized by a Kerr nonlinear response may support the existence of quartic and dipole solitons in the presence of the self-steepening effect. The existence and stability properties of these localized pulses are examined in the presence of all the material parameters. Regimes for the modulation instability of a continuous-wave signal propagating inside the nonlinear medium are investigated and an analytic expression for the gain spectrum is obtained and shown to be dependent on the self-steepening parameter in addition to second- and fourth-order group velocity dispersion parameters. Self-similar soliton solutions are constructed for a generalized nonlinear Schr\odinger equation with distributed second-, third-, and fourth-order dispersions, self-steepening nonlinearity, and gain or loss describing ultrashort pulse propagation in the inhomogeneous nonlinear media via the similarity transformation method. The evolutional dynamics of the self-similar structures are investigated in a periodic distributed waveguide system and an exponential dispersion decreasing waveguide.