Generation of soliton oscillations in nonlinear quadratic materials

Thickness-dependent slow light gap solitons in three-dimensional coupled photonic crystal waveguides

The thickness-dependent multimodal nature of three-dimensional (3D) coupled photonic crystal waveguides is investigated with the aim of realizing a medium for controlled optical gap soliton formation in the slow light regime. In the linear case, spectral properties of the modes (dispersion diagrams), location of the gap regions versus the thickness of the 3D photonic crystal, and the near-field distributions at frequencies in the slow light region are analyzed using a full-wave electromagnetic solver. In the nonlinear regime (Kerr-type nonlinearity), we infer an existence of crystal-thickness-dependent temporal solitons with stable pulse envelope and use the solitonic pulses for driving quantum transitions in localized quantum systems within the photonic crystal waveguide. The results may be useful for applications in optical communications, multiplexing systems, nonlinear physics, and ultrafast spectroscopy.

Dynamics and stability of solitary waves in optical-microwave interaction

We study the dynamics and the stability of localized bound states of optical and microwave fields, which are linked together by a quadratic nonlinearity. The system is an example of an intense interaction between low and high frequency waves, as appears in many areas of physics. Perturbed solitary waves show a number of regular but damped oscillations with strong radiation from the microwave. It is demonstrated that these oscillations are caused by the excitation of several quasibound asymmetric linear modes of the solitary wave. The associated eigenvalues are found to be complex leading to a decay of the oscillations as observed numerically. Additional quasibound linear modes with a complex eigenvalue corresponding to exponential growth also exist, but due to physical constraints cannot be excited. Therefore, in contrast to systems solely with high frequency waves, the stability of the solutions is retained.

Three-dimensional walking spatiotemporal solitons in quadratic media

Two-parameter families of chirped stationary three-dimensional spatiotemporal solitons in dispersive quadratically nonlinear optical media featuring type-I second-harmonic generation are constructed in the presence of temporal walk-off. Basic features of these walking spatiotemporal solitons, including their dynamical stability, are investigated in the general case of unequal group-velocity dispersions at the fundamental and second-harmonic frequencies. In the cases when the solitons are unstable, the growth rate of a dominant perturbation eigenmode is found as a function of the soliton wave number shift. The findings are in full agreement with the stability predictions made on the basis of a marginal linear-stability curve. It is found that the walking three-dimensional spatiotemporal solitons are dynamically stable in most cases; hence in principle they may be experimentally generated in quadratically nonlinear media.

Persistent oscillations of scalar and vector dispersion-managed solitons

We show that both orthogonal and parallel internal modes exist on the background of a dispersion-managed (DM) soliton in randomly birefringent fibers. The orthogonal modes exist for arbitrarily small values of the dispersion map strength, while the parallel modes exist only when the map strength exceeds a certain threshold value. We demonstrate that initial perturbations of a DM soliton's profile that consist of one or more internal modes, exhibit nearly stable oscillations over very long propagation distances, before decaying into radiation. (c) 2000 American Institute of Physics.

Stable solitons of quadratic ginzburg-landau equations

We present a physical model based on coupled Ginzburg-Landau equations that supports stable temporal solitary-wave pulses. The system consists of two parallel-coupled cores, one having a quadratic nonlinearity, the other one being effectively linear. The former core is active, with bandwidth-limited amplification built into it, while the latter core has only losses. Parameters of the model can be easily selected so that the zero background is stable. The model has nongeneric exact analytical solutions in the form of solitary pulses ("dissipative solitons"). Direct numerical simulations, using these exact solutions as initial configurations, show that they are unstable; however, the evolution initiated by the exact unstable solitons ends up with nontrivial stable localized pulses, which are very robust attractors. Direct simulations also demonstrate that the presence of group-velocity mismatch (walkoff) between the two harmonics in the active core makes the pulses move at a constant velocity, but does not destabilize them.

Role of internal and continuum modes in modulational instability of quadratic solitons

The role of internal and continuum modes in the modulational instability of spatial quadratic solitons is examined by asymptotic and numerical analyses. It is shown that these modes generate novel spatially symmetric and asymmetric modulation instability branches, which underline soliton dynamics throughout a wide region of the wave-vector mismatch.