Harmonic generation and wave mixing in nonlinear metamaterials and photonic crystals (Invited paper)

The basic concepts and phenomenology of wave mixing and harmonic generation are reviewed in context of the recent advances in the enhanced nonlinear activity in metamaterials and photonic crystals. The effects of dispersion, field confinement and phase synchronism are illustrated by the examples of the on-purpose designed artificial nonlinear structures. (c) 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:469482, 2012.

Gaussian pulse mixing and scattering by finite nonlinear layered structures

Multiple Gaussian pulse interactions and scattering in the nonlinear layered dielectric structures have been examined. The Gaussian pulses with different centre frequencies and lengths are incident at oblique angles on the finite stack of nonlinear dielectric layers. The properties of the reflected and refracted waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed. It is shown that the efficiency of forward emission at the combinatorial frequency can be considerably increased when the wavelengths of interacting pulses are close to the edges of electromagnetic bandgap. © 2012 IEEE.

GAUSSIAN PULSE SCATTERING BY NONLINEAR THUE-MORSE QUASIPERIODIC MULTILAYERS

The pulse mixing and scattering by finite nonlinear Thue-Morse quasi-periodic dielectric multilayered structure illuminated by two Gaussian pulses with different centre frequencies and lengths are investigated. The three-wave mixing technique is applied to study the nonlinear processes. The properties of the scattered waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed.

Three-wave Nonlinear Scattering by Quasiperiodic Dielectric Structure

The combinatorial frequency generation by a Fibonacci type quasi-periodic dielectric multilayered structure illuminated by two plane waves has been analysed. The effects of the layer parameters and Fibonacci sequence order on the properties of the combinatorial frequency waves emitted from the stacked nonlinear layers are discussed.

STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION

Stationary solutions to the equations of nonlinear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean free path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cutoff in energy space-particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for the substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven nonresonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off-a diagnostic that is in principle accessible to observation.

Gaussian pulse mixing by nonlinear photonic crystals

The properties of mixing and scattering of two non-collinear Gaussian pulses with different centre frequencies and lengths, incident on the finite nonlinear periodic layered dielectric structures, have been analysed. It is shown that at the backward emission grows with the number of layers and can reach the level of the forward emission in the direction of combinatorial frequency scattering.

Nonlinear dynamics of multidimensional electrostatic excitations in nonthermal plasmas

Electrostatic solitary waves in plasmas are the focus of many current studies of localized electrostatic disturbances in both laboratory and astrophysical plasmas. Motivated by recent experimental observations, in which electrostatic solitary structures were detected in laser-plasma experiments, we have undertaken an investigation of the nonlinear dynamics of plasma evolving in two dimensions, in the presence of excess superthermal background electrons. We investigate the effect of a magnetic field on weakly nonlinear ion-acoustic waves. Deviation from the Maxwellian distribution is effectively modelled by the kappa model. A linear dispersion relation is derived, and a decrease in frequency and phase speed in both parallel and perpendicular modes can be seen, which is due to excess superthermal electrons, and which is stronger in the upper mode, and hardly noticeable in the lower (acoustic) mode. We show that ion-acoustic solitary waves can be generated during the nonlinear evolution of a plasma fluid, and their nonlinear propagation is governed by a Zakharov-Kuznetsov (ZK) type equation. A multiple scales perturbation technique is used to derive the ZK equation. Shock excitations can be produced if we allow for dissipation in the model, resulting in a Zakharov-Kuznetsov Burgers type equation. Different types of shock solutions and solitary waves are obtained, depending on the relation between the system parameters, and the effect of these on electrostatic shock structures is investigated numerically. A parametric investigation is conducted into the role of plasma nonthermality and magnetic field strength. © 2013 IOP Publishing Ltd.

A New Principal Curve Algorithm for Nonlinear Principal Component Analysis

This paper emerged from work supported by EPSRC grant GR/S84354/01 and proposes a method of determining principal curves, using spline functions, in principal component analysis (PCA) for the representation of non-linear behaviour in process monitoring. Although principal curves are well established, they are difficult to implement in practice if a large number of variables are analysed. The significant contribution of this paper is that the proposed method has minimal complexity, assuming simple spline geometry, thus enabling efficient computation. The paper provides a foundation for further work where multiple curves may be required to represent underlying non-linear information in complex data.

A Hamiltonian approach to simulation of acoustic systems involving nonlinear interactions

Nonlinear interactions take place in most systems that arise in music acoustics, usually as a result of player-instrument coupling. Several time-stepping methods exist for the numerical simulation of such systems. These methods generally involve the discretization of the Newtonian description of the system. However, it is not always possible to prove the stability of the resulting algorithms, especially when dealing with systems where the underlying force is a non-analytic function of the phase space variables. On the other hand, if the discretization is carried out on the Hamiltonian description of the system, it is possible to prove the stability of the derived numerical schemes. This Hamiltonian approach is applied to a series of test models of single or multiple nonlinear collisions and the energetic properties of the derived schemes are discussed. After establishing that the schemes respect the principle of conservation of energy, a nonlinear single-reed model is formulated and coupled to a digital bore, in order to synthesize clarinet-like sounds.

Nonlinear optics from an ab initio approach by means of the dynamical Berry phase: Application to second- and third-harmonic generation in semiconductors

We present an ab initio real-time-based computational approach to study nonlinear optical properties in condensed matter systems that is especially suitable for crystalline solids and periodic nanostructures. The equations of motion and the coupling of the electrons with the external electric field are derived from the Berry-phase formulation of the dynamical polarization [Souza et al., Phys. Rev. B 69, 085106 (2004)]. Many-body effects are introduced by adding single-particle operators to the independent-particle Hamiltonian. We add a Hartree operator to account for crystal local effects and a scissor operator to correct the independent particle band structure for quasiparticle effects. We also discuss the possibility of accurately treating excitonic effects by adding a screened Hartree-Fock self-energy operator. The approach is validated by calculating the second-harmonic generation of SiC and AlAs bulk semiconductors: an excellent agreement is obtained with existing ab initio calculations from response theory in frequency domain [Luppi et al., Phys. Rev. B 82, 235201 (2010)]. We finally show applications to the second-harmonic generation of CdTe and the third-harmonic generation of Si. 

Nonlinear numerical modelling of lightning strike effect on composite panels with temperature dependent material properties

This paper presents a physics based modelling procedure to predict the thermal damage of composite material when struck by lightning. The procedure uses the Finite Element Method with non-linear material models to represent the extreme thermal material behaviour of the composite material (carbon/epoxy) and an embedded copper mesh protection system. Simulation predictions are compared against published experimental data, illustrating the potential accuracy and computational cost of virtual lightning strike tests and the requirement for temperature dependent material modelling. The modelling procedure is then used to examine and explain a number of practical solutions to minimize thermal material damage. © 2013 Elsevier Ltd.

NONLINEAR NUMERICAL MODELLING OF LIGHTENING STRIKE EFFECT ON COMPOSITE PANELS WITH TEMPERATURE DEPENDANT MATERIAL PROPERTIES

Lightning strike is one of the challenges that the aerospace industry is facing in an effort to increase the percentage of composite materials used in aircraft structures. Lightning strike damage is due to high orthotropic electric resistivity of the composite panels, which leads to high thermal loads that cause decomposition of the epoxy and delimitations of the laminates. Yet, experimental testing of lightning strike on aircraft panels is expensive due to the large number of design parameters that can control the inflicted damage. A coupled thermal-electrical finite element analysis is used to investigate the design variables space that can affect lightning strike damage on epoxy/graphite composite panels. The contribution of this study is modeling the composite panels’ material properties as temperature dependent, which was excluded by other researchers. A number of practical solutions to minimize the damage effect are proposed. Two set of experimental results are used to verify the numerical ones. One experimental set for plain composite panel, and second one for composite panels with joints