Javid Atai

Absorption and amplification of dark solitons

Propagation of dark solitons in nonlinear media that include gain and loss is investigated. Two-photon absorption is shown to lead to dark-soliton broadening and attenuation, whereas gain (such as that arising from stimulated Raman scattering) is shown to lead to their narrowing and amplification. The relations describing the adiabatic evolution of dark solitons in the weakly perturbed media are presented. In comparison with fundamental bright solitons, dark solitons are shown to be less sensitive to the perturbations. Stationary propagation of dark solitons is also found to be possible in the presence of both absorption and amplification, but it differs from that in the passive lossless nonlinear media.

Nonlinear mismatches between two cores of saturable nonlinear couplers

The effect of the mismatch in nonlinearities between two cores of a saturable nonlinear coupler is explored. For a passive saturable nonlinear coupler, the impact of a mismatch in the nonlinearities on the operation of the coupler is shown to be interchangeable with that of a linear mismatch (resulting from a difference between the two individual cores in the absence of nonlinearity) except at low power limit. However, when both nonlinear mismatch and linear mismatch are present, new features appear, depending on the mismatches. This is reflected in the emergence of the novel bifurcation (or mode) diagrams which are shown to lead to new devices. Nonlinear couplers that include gain are also examined. It is found that a nonlinear mismatch can lead to the improvement of the switching using nonlinear couplers. >

Nonlinear couplers composed of different nonlinear cores

Nonlinear couplers composed of two different saturable nonlinear cores are examined. By combining one self‐focusing core appositely with another core of different nonlinearity, which can be self‐focusing, linear, or self‐defocusing, the detrimental effect of nonlinear saturation on the coupler formed is greatly reduced compared with that on the conventional coupler composed of two identical self‐focusing cores. This finding provides a way of relaxing the practical limitation to operational power of a saturable nonlinear coupler especially when high nonlinearity is involved for low‐power operation.

PARAMETRIC SPATIAL SOLITARY WAVES

We consider the copropagation of three (pump, Stokes, and anti-Stokes) self-trapped beams that interact through the parametric four-photon-mixing process in a (1 + 1 dimension) uniform self-focusing nonlinear medium. The stationary propagation involving three trapped beams is shown to be possible below a critical frequency shift when the phase difference between the three waves is either matched or highly mismatched. Most importantly, the steady-state solutions are found to be stable, as in the case of presence of only one soliton beam, except that the two (in-phase) fundamental stationary states launched in parallel will not return to their original states periodically after collision; rather, they may repel each other on collision and propagate in summetrically tilted directions thereafter with increasing separation.

Gray and dark modes in nonlinear waveguides

Propagation of light waves in a thin, self-defocusing, nonlinear film bounded by an infinite self-defocusing medium of a different nonlinearity is investigated. It is shown that both gray and dark solitary waves can be trapped in the film when the linear refractive index of the film, nf, is smaller than that of the cladding, no, and the wave’s effective index, ne, is nf < ne < no. On the other hand, a series of trapped dark oscillatory solitary waves results when ne < min{nf, no}.

Dark optical bullets in light self-trapping

Dark optical bullets-the stationary states of pulsed (3 + 1)-dimensional dark self-trapped beams propagating in uniform self-defocusing Kerr-law media without change in space and time-are found possible in the anomalous dispersion region, and the states are shown to be stable. This contrasts with the corresponding light bullets in self-focusing media that collapse in Kerr-law nonlinearity. On the other hand, in the normal dispersion region the pulsed dark self-trapped beams break as a result of the combined effects of diffraction, dispersion, and nonlinearity.

Dynamics of optical-vortex solitons in perturbed nonlinear media: errata

We examine the perturbation effect of loss (or gain) and two-photon absorption on the evolution of optical-vortex solitons. For a small perturbation the vortex soliton is shown to follow an adiabatic evolution. The analytical expression for describing the evolution is presented. We also find that the intensity-dependent loss resulting from the two-photon absorption can be counterbalanced by the constant gain (resulting from Raman effect), to lead to stable stationary propagation of the optical-vortex solitons in the perturbed media.

Stability of black, gray, and bright nonlinear guided waves in a thin film bounded by a self-defocusing medium

Stability of nonlinear guided waves trapped in a thin linear film bounded by an infinite self-defocusing nonlinear medium is investigated. In addition to the trapped black and gray nonlinear guided waves, the existence of a novel class of bright nonlinear guided waves (with nonzero intensity background) is demonstrated. The gray and fundamental bright nonlinear guided waves are found stable whereas the black nonlinear guided waves are unstable to an asymmetric perturbation (but stable to a symmetric perturbation). The instability of the black nonlinear guided waves is shown to develop into various states, including stable gray and bright nonlinear guided waves, depending on initial excitations.

Stability of the asymmetric nonlinear mode trapped in symmetric planar waveguides

The authors examine the reliability of the numerical approach for studying the asymmetric nonlinear mode trapped in a thin linear film sandwiched in an infinite self-focusing medium, and thus resolve a controversy in the literature on the stability of the mode trapped between the bifurcation point and the transition point on the dispersion curve reported. They demonstrate that as a result of the instability there exists a class of quasi-periodic solutions arising from the instability in the asymmetric mode on the unstable branch and weakly stable branch. In addition, the effect of loss on the propagation characteristics of the nonlinear mode is investigated. The evolution is shown to follow the dispersion curve adiabatically in the stable region provided the loss is small, whereas the initial excitation on the unstable branch leads to evolution away from oscillation around the dispersion curve. >

Asymmetric dark modes in symmetric nonlinear waveguides

We show that symmetric nonlinear waveguides can support the asymmetric dark modes. The existence of a novel class of bright nonlinear guided wave with nonzero-intensity background is also demonstrated. >