Helmholtz bright and boundary solitons

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently-reported Helmholtz bright solitons, for this type of polynomial non-linearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterpart

Bistable Helmholtz bright solitons in saturable materials

We present, to the best of our knowledge, the first exact analytical solitons of a nonlinear Helmholtz equation with a saturable refractive-index model. These new two-dimensional spatial solitons have a bistable characteristic in some parameter regimes, and they capture oblique (arbitrary-angle) beam propagation in both the forward and backward directions. New conservation laws are reported, and the classic paraxial solution is recovered in an appropriate multiple limit. Analysis and simulations examine the stability of both solution branches, and stationary Helmholtz solitons are found to emerge from a range of perturbed input beams

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz–Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations

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

Helmholtz solitons in optical materials with a dual power-law refractive index

A nonlinear Helmholtz equation is proposed for modelling scalar optical beams in uniform planar waveguides whose refractive index exhibits a purely-focusing dual powerlaw dependence on the electric field amplitude. Two families of exact analytical solitons, describing forward- and backward-propagating beams, are derived. These solutions are physically and mathematically distinct from those recently discovered for related nonlinearities. The geometry of the new solitons is examined, conservation laws are reported, and classic paraxial predictions are recovered in a simultaneous multiple limit. Conventional semi-analytical techniques assist in studying the stability of these nonparaxial solitons, whose propagation properties are investigated through extensive simulations

Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered as-ymptotically from the spatiotemporal formulation. Numerical simulations test new theoretical predictions for modulational instability, and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shape

Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors

Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics

A generic nonparaxial model for pulse envelopes is presented. Classic Schro¨dinger-type descriptions of wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the local time frame. By abandoning these two simplifications, a picture of pulse evolution emerges in which frame-of-reference considerations and space-time transformations take center stage. A wide range of effects, analogous to those in special relativity, then follows for both linear and nonlinear systems. Explicit demonstration is presented through exact bright and dark soliton pulse solutions

Spin Vortex Resonance in Non-planar Ferromagnetic Dots

In planar structures, the vortex resonance frequency changes little as a function of an in-plane magnetic field as long as the vortex state persists. Altering the topography of the element leads to a vastly different dynamic response that arises due to the local vortex core confinement effect. In this work, we studied the magnetic excitations in non-planar ferromagnetic dots using a broadband microwave spectroscopy technique. Two distinct resonance frequency ranges were observed depending on the position of the vortex core controllable by applying a relatively small magnetic field. The micromagnetic simulations are in qualitative agreement with the. experimental results

On the complexity of the Saccharomyces bayanus taxon: hybridization and potential hybrid speciation

Although the genus Saccharomyces has been thoroughly studied, some species in the genus has not yet been accurately resolved; an example is S. bayanus, a taxon that includes genetically diverse lineages of pure and hybrid strains. This diversity makes the assignation and classification of strains belonging to this species unclear and controversial. They have been subdivided by some authors into two varieties (bayanus and uvarum), which have been raised to the species level by others. In this work, we evaluate the complexity of 46 different strains included in the S. bayanus taxon by means of PCR-RFLP analysis and by sequencing of 34 gene regions and one mitochondrial gene. Using the sequence data, and based on the S. bayanus var. bayanus reference strain NBRC 1948, a hypothetical pure S. bayanus was reconstructed for these genes that showed alleles with similarity values lower than 97% with the S. bayanus var. uvarum strain CBS 7001, and of 99¿100% with the non S. cerevisiae portion in S. pastorianus Weihenstephan 34/70 and with the new species S. eubayanus. Among the S. bayanus strains under study, different levels of homozygosity, hybridization and introgression were found; however, no pure S. bayanus var. bayanus strain was identified. These S. bayanus hybrids can be classified into two types: homozygous (type I) and heterozygous hybrids (type II), indicating that they have been originated by different hybridization processes. Therefore, a putative evolutionary scenario involving two different hybridization events between a S. bayanus var. uvarum and unknown European S. eubayanus-like strains can be postulated to explain the genomic diversity observed in our S. bayanus var. bayanus strains