Stability of Spatial Optical Solitons

We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations. In particular, we demonstrate that the soliton internal modes are responsible for the appearance of the soliton instability, and outline an analytical approach based on a multi-scale asymptotic technique that allows to analyze the soliton dynamics near the marginal stability point. We also discuss some results of the rigorous linear stability analysis of fundamental solitary waves and nonlinear impurity modes. Finally, we demonstrate that multi-hump vector solitary waves may become stable in some nonlinear models, and discuss the examples of stable (1+1)-dimensional composite solitons and (2+1)-dimensional dipole-mode solitons in a model of two incoherently interacting optical beams.Comment: 34 pages, 9 figures; to be published in: "Spatial Optical Solitons", Eds. W. Torruellas and S. Trillo (Springer, New York

Nonlocal homogenization for nonlinear metamaterials

©2016 American Physical Society. We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analyzing resonant nonlinear metamaterials

Self-oscillations in nonlinear torsional metamaterials

We study the nonlinear dynamics of torsional meta-molecules - sub-wavelength resonators with strong coupling between electromagnetic excitation and rotational deformation - and show that such structures may undergo self-oscillations. We develop a semi-analytical model to evaluate the electromagnetic-elastic coupling in such structures. By analysing the local stability of the system, we reveal two different mechanisms leading to self-oscillations. Contrary to many previously studied optomechanical systems, self-oscillations of torsional meta-molecules can be extremely robust against mechanical damping. Due to the chiral nature of the structure, a consequence of self-oscillations in this system is dynamic nonlinear optical activity, which can be actively controlled by a range of parameters such as the field strength and polarization of the incident wave. © IOP Publishing and Deutsche Physikalische Gesellschaft

Broadband diamagnetism in anisotropic metamaterials

We discuss the strategy for achieving the values of the effective magnetic permeability much smaller than unity by employing an appropriate arrangement of metamaterial elements ("meta-atoms"). We demonstrate that strong diamagnetism over a very wide frequency range can be realized in metamaterials by employing nonresonant elements with deeply subwavelength dimensions. We analyze the effect of the lattice parameters on the diamagnetic response and find that selecting an appropriate lattice type is crucial for optimal performance. Finally, we discuss the optimal characteristics required to obtain the lowest possible values of magnetic permeability and point out an efficient tuning possibility. © 2013 American Physical Society

Nonlinear response via intrinsic rotation in metamaterials

We propose and experimentally verify a way to achieve strong nonlinear coupling between the electromagnetic and elastic properties in metamaterials. This coupling is provided through a novel degree of freedom in metamaterial design: the internal rotation within structural elements. Our meta-atoms have high sensitivity to electromagnetic wave power, and the elastic and electromagnetic properties can be independently designed to optimize the response. We demonstrate a rich range of nonlinear phenomena including self-tuning and bistability, and provide a comprehensive experimental demonstration of the predicted effects. © 2013 American Physical Society

Suppression of Anderson localization in disordered metamaterials

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced. © 2007 The American Physical Society

Broadband isotropic μ-near-zero metamaterials

Natural diamagnetism, while being a common phenomenon, is limited to permeability values close to unity. Artificial diamagnetics, to the contrary, can be engineered to provide much lower values and may even possess an effective permeability close to zero. In this letter, we provide an experimental confirmation of the possibility to obtain extremely low permeability values by manufacturing an isotropic metamaterial composed of conducting cubes. We show that the practical assembly is quite sensitive to fabrication tolerances and demonstrate that permeability of about μ = 0.15 is realisable. © 2013 AIP Publishing LLC

An instability criterion for nonlinear standing waves on nonzero backgrounds

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a finite interval. Localized standing wave solutions on a non-zero background, e.g., dark solitons trapped by the inhomogeneity, are identified and studied. A novel instability criterion for such states is established through a topological argument. This allows instability to be determined quickly in many cases by considering simple geometric properties of the standing waves as viewed in the composite phase plane. Numerical calculations accompany the analytical results.Comment: 20 pages, 11 figure