Three-Wave Modulational Stability and Dark Solitons in a Quadratic Nonlinear Waveguide with Grating

We consider continuous-wave (CW) states and dark solitons (DSs) in a system of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a planar waveguide with the quadratic nonlinearity, the FF components being linearly coupled by resonant reflections on the Bragg grating. We demonstrate that, in contrast with the usual situation in quadratic spatial-domain models, CW states with the phase shift between the FF and SH components are modulationally stable in a broad parameter region in this system, provided that the CW wavenumber does not belong to the system's spectral gap. Stationary fundamental DSs are found numerically, and are also constructed by means of a specially devised analytical approximation. Bound states of two and three DSs are found too. The fundamental DSs and two-solitons bound states are stable in all the cases when the CW background is stable, which is shown by dint of calculation of the corresponding eigenvalues, and verified in direct simulations. Tilted DSs are found too. They attain a maximum contrast at a finite value of the tilt, that does not depend on the phase mismatch. At a maximum value of the tilt, which grows with the mismatch, the DS merges into the CW background. Interactions between the tilted solitons are shown to be completely elastic.Comment: 10 pages, 12 figures; Journal of Optics A, in pres

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.

Tunable entangled photon states from a nonlinear directional coupler

Integrated optical platforms enable the realization of complex quantum photonic circuits for a variety of applications including quantum simulations, computations, and communications. The development of on-chip integrated photon sources, providing photon quantum states with on-demand tunability, is currently an important research area. A flexible approach for on-chip generation of entangled photons is based on spontaneous nonlinear frequency conversion, with possibilities to integrate several photon-pair sources [1] and realize subsequent post processing using thermo-optically or electro-optically controlled interference [2, 3]. However, deterministic postprocessing can only provide a limited set of output states, whereas quantum gates with probabilistic operation are needed to generate arbitrary two-photon states [4]

Semiflexible polymer conformation, distribution and migration in microcapillary flows

The flow behavior of a semiflexible polymer in microchannels is studied using Multiparticle Collision Dynamics (MPC), a particle-based hydrodynamic simulation technique. Conformations, distributions, and radial cross-streamline migration are investigated for various bending rigidities, with persistence lengths Lp in the range 0.5 < Lp/Lr < 30. The flow behavior is governed by the competition between a hydrodynamic lift force and steric wall-repulsion, which lead to migration away from the wall, and a locally varying flow-induced orientation, which drives polymer away from the channel center and towards the wall. The different dependencies of these effects on the polymer bending rigidity and the flow velocity results in a complex dynamical behavior. However, a generic effect is the appearance of a maximum in the monomer and the center-of-mass distributions, which occurs in the channel center for small flow velocities, but moves off-center at higher velocities.Comment: in press at J. Phys. Condens. Matte

Solutions to the Optical Cascading Equations

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtainedComment: 21 page

Quadratic solitons as nonlocal solitons

We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for novel analytical solutions and the prediction of novel bound states of quadratic solitons.Comment: 4 pages, 3 figure

Transport Phenomena and Structuring in Shear Flow of Suspensions near Solid Walls

In this paper we apply the lattice-Boltzmann method and an extension to particle suspensions as introduced by Ladd et al. to study transport phenomena and structuring effects of particles suspended in a fluid near sheared solid walls. We find that a particle free region arises near walls, which has a width depending on the shear rate and the particle concentration. The wall causes the formation of parallel particle layers at low concentrations, where the number of particles per layer decreases with increasing distance to the wall.Comment: 14 pages, 14 figure

Some Reflections on Age Discrimination, Referees’ Retirement Ages and European Sports (Law)

Introduction: This paper is the first in a series of reflections on the relationship between discrimination, sport and the law, a body of work that has been motivated in part by the potential impact of the 2000 Equalities Directive upon European sports law, but also by developments in human rights jurisprudence and in the domestic laws of several jurisdictions. The phenomenon of age discrimination in sport, and the social and economic impact thereof, has been far less widely considered than is the case with other forms of sports discrimination (although the literature would miraculously emerge if the subject-matter were more directly concerned with men’s professional football). In contrast, free movement and competition law have impacted significantly upon sports provisions that discriminate on the basis of nationality; it is equally evident that age discrimination in the context of sports employment has not been considered with anything approaching the degree of sophistication that pervades our understanding of discrimination in occupation or employment on the grounds of disability, sexual orientation and religion/belief (the other discriminatory forms that are covered by the 2000 Directive); and our poor understanding of age-related sports discrimination generally stands in marked contrast to our appreciation of how challenges to discrimination on the grounds of sex and race have precipitated far-reaching changes to sports practices. Throughout the EU, with the possible exception of the Irish Republic, age discrimination law is far less advanced than is the case with discrimination which takes any of those other forms, the remedies are weaker and fewer people are aware of them. However, this state of affairs will undoubtedly change under the impact of the Equalities Directive, and even though the provisions themselves (and member states’ transposing of them) attract legitimate criticism, some longstanding practices of sports bodies are now open to challenge

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency

On Dehn's algorithm

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46211/1/208_2005_Article_BF01361168.pd