Nanoscale Origins of Nonlinear Behavior in Ferroic Thin Films

The nonlinear response of a ferroic to an applied field has been studied through the phenomenological Rayleigh Law for over a hundred years. Yet, despite this, the fundamental physical mechanisms at the nanoscale that lead to macroscopic Rayleigh behavior have remained largely elusive, and experimental evidence at small length scales is limited. Here, it is shown using a combination of scanning probe techniques and phase field modeling, that nanoscale piezoelectric response in prototypical Pb(Zr,Ti)O3 films appears to follow a distinctly non-Rayleigh regime. Through statistical analysis, it is found that an averaging of local responses can lead directly to Rayleigh-like behavior of the strain on a macroscale. Phase-field modeling confirms the twist of the ferroelastic interface is key in enhancing piezoelectric response. The studies shed light on the nanoscale origins of nonlinear behavior in disordered ferroics.

Nonlinear phenomena in multiferroic nanocapacitors:joule heating and electromechanical effects

We demonstrate an approach for probing nonlinear electromechanical responses in BiFeO(3) thin film nanocapacitors using half-harmonic band excitation piezoresponse force microscopy (PFM). Nonlinear PFM images of nanocapacitor arrays show clearly visible clusters of capacitors associated with variations of local leakage current through the BiFeO(3) film. Strain spectroscopy measurements and finite element modeling point to significance of the Joule heating and show that the thermal effects caused by the Joule heating can provide nontrivial contributions to the nonlinear electromechanical responses in ferroic nanostructures. This approach can be further extended to unambiguous mapping of electrostatic signal contributions to PFM and related techniques.

Nonlinear dust-acoustic solitary waves in strongly coupled dusty plasmas

Dust-acoustic waves are investigated in a three-component plasma consisting of strongly coupled dust particles and Maxwellian electrons and ions. A fluid model approach is used, with the effects of strong coupling being accounted for by an effective electrostatic "pressure" which is a function of the dust number density and the electrostatic potential. Both linear and weakly nonlinear cases are considered by derivation and analysis of the linear dispersion relation and the Korteweg-de Vries equation, respectively. In contrast to previous studies using this model, this paper presents the results arising from an expansion of the dynamical form of the electrostatic pressure, accounting for the variations in its value in the vicinity of the wave. DOI: 10.1103/PhysRevE.86.066404

Nonlinear scattering by anisotropic dielectric periodic structures

The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures. © 2012 O. V. Shramkova and A. G. Schuchinsky.

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.