Nonlinear surface waves in left-handed materials

We study both linear and nonlinear surface waves localized at the interface separating a left-handed medium (i.e. the medium with both negative dielectric permittivity and negative magnetic permeability) and a conventional (or right-handed) dielectric medium. We demonstrate that the interface can support both TE- and TM-polarized surface waves - surface polaritons, and we study their properties. We describe the intensity-dependent properties of nonlinear surface waves in three different cases, i.e. when both the LH and RH media are nonlinear and when either of the media is nonlinear. In the case when both media are nonlinear, we find two types of nonlinear surface waves, one with the maximum amplitude at the interface, and the other one with two humps. In the case when one medium is nonlinear, only one type of surface wave exists, which has the maximum electric field at the interface, unlike waves in right-handed materials where the surface-wave maximum is usually shifted into a self-focussing nonlinear medium. We discus the possibility of tuning the wave group velocity in both the linear and nonlinear cases, and show that group-velocity dispersion, which leads to pulse broadening, can be balanced by the nonlinearity of the media, so resulting in soliton propagation.Comment: 9 pages, 10 figure

Nonlinear interfaces: intrinsically nonparaxial regimes and effects

The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrödinger equation. For instance, large propagation angles are typically involved in external refraction at interfaces. Using a recently proposed generalized Snell's law for Helmholtz solitons, we analyse two such effects: nonlinear external refraction and total internal reflection at interfaces where internal and external refraction, respectively, would be found in the absence of nonlinearity. The solutions obtained from the full numerical integration of the nonlinear Helmholtz equation show excellent agreement with the theoretical predictions

Gyrotropic impact upon negatively refracting surfaces

Surface wave propagation at the interface between different types of gyrotropic materials and an isotropic negatively refracting medium, in which the relative permittivity and relative permeability are, simultaneously, negative is investigated. A general approach is taken that embraces both gyroelectric and gyromagnetic materials, permitting the possibility of operating in either the low GHz, THz or the optical frequency regimes. The classical transverse Voigt configuration is adopted and a complete analysis of non-reciprocal surface wave dispersion is presented. The impact of the surface polariton modes upon the reflection of both plane waves and beams is discussed in terms of resonances and an example of the influence upon the Goos–Hänchen shift is given

The potential for gamma-emitting radionuclides to contribute to an understanding of erosion processes in South Africa

Several research projects undertaken by the authors and others over the last 14 years have used fallout and geogenic radionuclides for understanding erosion processes and sediment yield dynamics in South Africa over the last 100–200 years as European settlers colonised the interior plains and plateaux of the country and imported new livestock and farming techniques to the region. These projects have used two fallout radionuclides (210Pb and 137Cs) to date sediments accumulating in reservoirs, farm dams, wetlands, alluvial fans and floodouts and have used other fallout nuclides (7Be) and long-lived geogenic radionuclides (e.g. 40K, 235U) as part of a composite fingerprint exploring contemporary sediment sources and changes to sources through time. While successful in many parts of the world, applying these techniques in Southern Africa has posed a number of challenges often not encountered elsewhere. Here we explore some of the benefits and challenges in using gamma-emitting radionuclides, especially 137Cs, in these landscapes. Benefits include the potential for discriminating gully sidewall from topsoil sources, which has helped to identify contemporary gully systems as sediment conduits, rather than sources, and for providing a time-synchronous marker horizon in a range of sedimentary environments that has helped to develop robust chronologies. Challenges include the spatial variability in soil cover on steep rocky hillslopes, which is likely to challenge assumptions about the uniformity of initial fallout nuclide distribution, the paucity of stable (non-eroding) sites in order to estimate atmospheric fallout inventories, and the limited success of 210Pb dating in some rapidly accumulating high altitude catchments where sediments often comprise significant amounts of sand and gravel. Despite these challenges we present evidence suggesting that the use of gamma-emitting radionuclides can make a significant contribution to our understanding of erosion processes and sediment yield dynamics. Future research highlighted in the conclusion will try to address current challenges and outline new projects established to address them more fully

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the amplitudes of the solitons remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula. For the interaction of two solitons with a quintic perturbation term we present more details since symmetries -- one related to the form of the perturbation and one related to the small number of particles involved -- allow the problem to be reduced to a one-dimensional one with a single parameter, an effective mass. The main results include calculations of the binding energy and oscillation frequency of nearby solitons in the stable case when the perturbation is an attractive correction to the potential and of the asymptotic "ejection" velocity in the unstable case. Numerical experiments illustrate the accuracy of the perturbative calculations and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6 figures, To appear in Phys Rev E (many displayed equations moved inline to shorten manuscript

Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of non-fundamental (multi-humped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two novel types of soliton bifurcations and other interesting findings. The later includes (i) multi-humped solitary waves without even or odd symmetry and (ii) multi-humped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.

Multi-component optical solitary waves

We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, multi-colour parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices.Comment: 12 pages, 11 figures; To be published in: Proceedings of the Dynamics Days Asia-Pacific: First International Conference on Nonlinear Science (Hong-Kong, 13-16 July, 1999), Editor: Bambi Hu (Elsevier Publishers, 2000

Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity

We investigate the effects of nonlocal response on the surface-plasmon polariton guiding properties of the metal-insulator (MI), metal-insulator-metal (MIM), and insulator-metal-insulator (IMI) waveguides. The nonlocal effects are described by a linearized hydrodynamic model, which includes the Thomas-Fermi internal kinetic energy of the free electrons in the metal. We derive the nonlocal dispersion relations of the three waveguide structures taking into account also retardation and interband effects, and examine the delicate interplay between nonlocal response and absorption losses in the metal. We also show that nonlocality breaks the complementarity of the MIM and IMI waveguides found in the non-retarded limit.Comment: 9 pages, 5 figure

Favorable outcome of early treatment of new onset child and adolescent migraine-implications for disease modification.

There is evidence that the prevalence of migraine in children and adolescents may be increasing. Current theories of migraine pathophysiology in adults suggest activation of central cortical and brainstem pathways in conjunction with the peripheral trigeminovascular system, which ultimately results in release of neuropeptides, facilitation of central pain pathways, neurogenic inflammation surrounding peripheral vessels, and vasodilatation. Although several risk factors for frequent episodic, chronic, and refractory migraine have been identified, the causes of migraine progression are not known. Migraine pathophysiology has not been fully evaluated in children. In this review, we will first discuss the evidence that early therapeutic interventions in the child or adolescent new onset migraineur, may halt or limit progression and disability. We will then review the evidence suggesting that many adults with chronic or refractory migraine developed their migraine as children or adolescents and may not have been treated adequately with migraine-specific therapy. Finally, we will show that early, appropriate and optimal treatment of migraine during childhood and adolescence may result in disease modification and prevent progression of this disease