Dark-Soliton Timing Jitter Caused By Fluctuations In Initial Pulse-Shape

The dark-soliton timing jitters caused by fluctuations in either the soliton initial phase angle or the background amplitude when such a soliton propagates in a monomode optical fiber under the influence of the stimulated Raman scattering are investigated and compared with those that exist when the stimulated Raman scattering is not present. In addition, it is demonstrated that in the presence of the stimulated Raman scattering, there exists a distance at which, for the negative soliton initial phase angle, the dark-soliton timing jitter caused by fluctuations in the background amplitude becomes zero

Polychromatic solitons in a quadratic medium

We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed (WDM) models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate.Comment: 9 pages, 8 figures, accepted to Phys. Rev.

Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.Comment: 4 pages with figure

Vessel bifurcation detection in scale space

Several methods have been proposed for segmentation of vessels, many based on scale-space. However, none of the existing methods for blood vessel segmentation is appropriate for extension to bifurcation detection. Existing bifurcation detection algorithms use an inherently serial “track and detect” approach, requiring a seed point. We present a comprehensive scale space analysis of vascular bifurcations, resulting in a simple, novel algorithm for direct detection of blood vessel bifurcation points based not only on spatial variation across scales, but also on the variation at a single spatial point across scales, without training data or seed points. We present an analytical model for the bifurcation evolution with scale, combined with eigenvalue analysis to create a "bifurcationness" filter. We reveal, for the first time, a hybrid structure of bifurcations in scale-space. The algorithm was tested for validation in both 2D and 3D, with synthetic data and medical images

Solitary-wave interactions in quadratic media near type I phase-matching conditions

The interaction between two optical soliton beams during type I second-harmonic generation in quadratically nonlinear materials has been investigated numerically. The product of the interaction is found to be highly sensitive to the relative phase between the launched beams. Threshold phenomena were found that persisted even when the input beams were only approximately solitary waves. Cases of both small and large collision angles were investigated, and the effect of walk-off was also taken into account. © 1997 Optical Society of America

Modulational instability of a strip beam in a bulk type I quadratic medium

The evolution of a strip (one-dimensional) fundamental beam with propagation distance owing to spatial modulational instabilities was analyzed in a quadratic medium near type I phase matching. We obtained the gain coefficient for the modulational instability and showed that the wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam. © 1998 Optical Society of America

Interaction of soliton-like light beams in second-order non-linear materials

We investigate numerically the interaction between two light beams, initially monochromatic, during the excitation of solitary waves in quadratically non-linear media. We show that the result of the interaction is strongly dependent on soliton oscillations occurring during excitation, generating a new class of threshold phenomena