Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams

We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.Comment: 6 pages, 6 figures, Lette

Effects of excitonic diffusion on stimulated emission in nanocrystalline ZnO

We present optically-pumped emission data for ZnO, showing that high excitation effects and stimulated emission / lasing are observed in nanocrystalline ZnO thin films at room temperature, although such effects are not seen in bulk material of better optical quality. A simple model of exciton density profiles is developed which explains our results and those of other authors. Inhibition of exciton diffusion in nanocrystalline samples compared to bulk significantly increases exciton densities in the former, leading, via the nonlinear dependence of emission in the exciton bands on the pump intensity, to large increases in emission and to stimulated emission

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

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

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

Towards the development of safe and commercially viable nickel–iron batteries: improvements to Coulombic efficiency at high iron sulphide electrode formulations

NiFe batteries are emerging as an important energy storage technology but suffer from a hydrogen-producing side reaction which has safety implications and reduces coulombic efficiency. This manuscript describes a systematic improvement approach for the production of Fe/FeS-based anodes at high concentrations of iron sulphide. Electrodes were made by mixing varying amounts of iron sulphide in such a way that its concentration ranges from between 50 and 100 % (compositions expressed on a PTFE-free basis). Electrode performance was evaluated by cycling our in-house-produced anodes against commercially available nickel electrodes. The results show that anodes produced with larger concentrations outperform their lower concentration counterparts in terms of coulombic efficiency although a slight decrease in the overall cell performance was found when using pure FeS anodes. At high FeS concentrations a hydrogen-producing side reaction has been virtually eliminated resulting in coulombic efficiencies of over 95 %. This has important implications for the safety and commercial development of NiFe batteries

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