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 waves in hyperbolic metamaterials: focus on solitons and rogues

The investigation of hyperbolic metamaterials, shows that metal layers that are part of graphene structures, and also types I and II layered systems, are readily controlled. Since graphene is a nicely conducting sheet it can be easily managed. The literature only eveals a, limited, systematic, approach to the onset of nonlinearity, especially for the methodology based around the famous nonlinear Schrödinger equation [NLSE]. This presentation reveals nonlinear outcomes involving solitons sustained by the popular, and more straightforward to fabricate, type II hyperbolic metamaterials. The NLSE for type II metatamaterials is developed and nonlinear, non-stationary diffraction and dispersion in such important, and active, planar hyperbolic metamaterials is developed. For rogue waves in metamaterials only a few recent numerical studies exist. The basic model assumes a uniform background to which is added a time-evolving perturbation in order to witness the growth of nonlinear waves out of nowhere. This is discussed here using a new NLSE appropriate to hyperbolic metamaterials that would normally produce temporal solitons. The main conclusion is that new pathways for rogue waves can emerge in the form of Peregrine solitons (and near-Peregrines) within a nonlinear hyperbolic metamaterial, based upon double negative guidelines, and where, potentially, magnetooptic control could be practically exerted

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give suficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.Comment: 16 page

Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses

To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1–11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely

Physics programs

x, 485 p.; 23 cm

Physics program : optics

vii, 123 p.; 23 cm

NONLINEAR SURFACE AND GUIDED POLARITONS OF A GENERAL LAYERED DIELECTRIC STRUCTURE

Les modes de surface et les modes guidés, à la fois TE et TM, sont étudiés pour une structure générale où un film non linéaire est pris en sandwich entre deux milieux différents non linéaires. Qu'elles admettent des modes du type TE ou TM, on montre que pour toutes ces structures l'équation de dispersion a la même forme, à la fois générale et compacte. Ceci vient du fait que le paramètre physique entrant dans les équations de dispersion est l'amplitude du champ électrique à l'une des limites du film. A titre de comparaison, nous présentons aussi l'autre approche du problème qui est celle développée habituellement dans la littérature. Des cas particuliers sont ensuite étudiés numériquement à partir d'une équation pour le flux de puissance. Cette équation montre aussi, en termes physiques, les trois types de solution susceptibles d'exister dans les structures lamellaires.The surface and guided modes of a general structure, consisting of a nonlinear plane slab bounded by dissimilar nonlinear media, are analysed for both TE and TM modes. It is shown that all structures, independently of whether if they are supporting TE or TM waves, are governed by a compact generic dispersion equation with the same appearance. This is proved by emphasising that the physical entry parameter to the dispersion equations is the electric field amplitude at one slab boundary. The alternative approach that corresponds to the current literature is also developed for comparison. Specialisations are then made to generate some numerical examples through a power flow equation. This equation also shows, in physical terms, the three classes of solution that are possible for layered systems

THE INFLUENCE OF COLLISIONAL DAMPING ON SURFACE PLASMON-POLARITON DISPERSION

Nous présentons une analyse détaillée, analytique et numérique, de l'influence conjointe de l'amortissement dû aux collisions et de la dispersion spatiale sur les plasmons-polaritons de surface. On trouve que les courbes de dispersion présentent plusieurs branches, dont l'une est le mode couramment admis comme étant à inversion de courbure et qui correspond à une fréquence réelle et un nombre d'onde complexe. On montre qu'une interaction importante entre l'amortissement dû aux collisions et la dispersion spatiale peut supprimer cette inversion de courbure.A detailed analytical and numerical analysis is given of the joint influence of collisional damping and spatial dispersion on surface plasmon-polaritons. It is shown that the dispersion has several branches, one of which is the currently accepted bend-back mode that arises under real frequency and complex wave number assumptions. It is proved that an important interaction between collisional damping and spatial dispersion occurs that can cause this bend-back to be suppressed