Abstract
In this paper,we discussed the nonlinear evolution of modulation instability and the steady-state process of induced modulation instability in sine-oscillatory response nonlocal nonlinear media. With plane wave plus perturbation as initial conditions, we simulated the long-term evolution of modulation instability in the nonlocal nonlinear Schrodinger equation with sine-oscillatory response numerically. For the input of modulated wave, the approximate analytical solution of the stable solution of the equation is obtained under the assumption that only the fundamental wave and the first harmonic wave are present. For the input of modulated wave with arbitrary harmonic waves, we obtained the exact numerical solution of the stable solution of the induced modulation instability.
Highlights
In this paper,we discussed the nonlinear evolution of modulation instability and the steady-state process of induced modulation instability in sine-oscillatory response nonlocal nonlinear media
It indicated that the approximate analytical solution obtained on condition of only considering plane wave and first harmonic was applicable when modulation frequency approached to the cutoff frequency, while was not suitable when modulation frequency greatly departed from the cutoff frequency
The long-term evolution of optical field under Modulation instability (MI) of nonlocal nonlinear Schrodinger equation with sine-oscillatory response was numerically simulated by taking plane wave with perturbation as initial condition
Summary
In this paper,we discussed the nonlinear evolution of modulation instability and the steady-state process of induced modulation instability in sine-oscillatory response nonlocal nonlinear media. With plane wave plus perturbation as initial conditions, we simulated the long-term evolution of modulation instability in the nonlocal nonlinear Schrodinger equation with sine-oscillatory response numerically. Beeckman first explored the nonlinear process of induced modulation instability in nonlocal nonlinear Kerr media during long-term evolution by using analytical and numerical methods[11]. We discuss the long-term (nonlinear) evolution of the optical field under MI in nonlocal nonlinear Schrodinger equation with sine-oscillatory response through numerical method, and the characteristics of the evolution was discussed. The stable solutions (approximate analytical solution and exact numerical solution) under induced modulation instability of nonlocal nonlinear Schrodinger equation with sine-oscillatory response was found and the relationship between the beamwidth in the stable solution and two degrees of freedom (DOF) in the system was surveyed
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