Surface waves at the interface between tunable LC–MTMs and nonlinear media

The surface wave propagation at the interface between tunable metamaterials (MTMs) and nonlinear media is investigated. Tunable MTMs have a refractive index which can be tuned to negative?Czero?Cpositive values. The nonlinear media are assumed to have a Kerr-like refractive index. The dispersion equation is analytically derived and solved numerically. Results display the different behaviors of the propagating waves as the refractive index is tuned.     

Manipulating electromagnetic waves with metamaterials: Concept and microwave realizations

Our recent efforts in manipulating electromagnetic （EM） waves using metamaterials （MTMs） are reviewed with em- phasis on 1） manipulating wave polarization and transporting properties using homogeneous MTMs, 2） manipulating surface-wave properties using plasmonic MTMs, and 3） bridging propagating and surface waves using inhomogeneous meta-surfaces. For all these topics, we first illustrate the physical concepts and then present several typical practical real- izations and applications in the microwave regime.     

Nonlinear parameter estimation in water-saturated sandy sediment with difference frequency acoustic wave

Difference frequency acoustic wave from nonlinear interaction of two primary acoustic waves at frequencies of 76 and 114 kHz was utilized with a parametric acoustic array theory to estimate the nonlinearity parameter of water-saturated sandy sediment. Such nonlinearity parameter can be used as background information for the nonlinear acoustic investigation of bottom or sub-bottom profiling in the ocean sandy sediments. Because of its lower attenuation the difference frequency acoustic wave method can be usefully applied to estimate the nonlinearity parameter of ocean sediment in the ocean as well as under laboratory conditions. The nonlinearity parameter β for the water-saturated sandy sediment used as a reference in this study was estimated as β = 80.5 ± 5.1 at the difference frequency of 38 kHz. It was agreed very well with that estimated at the difference frequency of 67 kHz, when two primary frequencies were 137 and 204 kHz. The estimated nonlinearity parameter of water-saturated sandy sediment in this study was also compared and analyzed with those estimated in previously published literatures. It was suggested that the difference frequency wave method used to estimate the nonlinearity parameter of water-saturated sandy sediment can be employed as a good method to estimate the nonlinearity parameters of fluid-like granular media.     

Optically nonlinear phonon-polariton modes in a three-layered structure

A theory is presented for the propagation of phonon-polariton modes arising when phonons are coupled to electromagnetic waves in multilayered structures. A multi-layered structure consists of a thin film surrounded symmetrically by a bounding media. Numerical calculations are given for s-polarized phonon-polariton modes in the case where the bounding media are assumed to be semi-infinite layers with nonlinear dielectric functions of ionic crystal type supporting optical phonon modes and the thin film is characterized by a Kerr-type nonlinear dielectric function. The phonon-polaritons were found to have distinct branches characteristic of optical phonons and showing features that are different from those of plasmon-polaritons [S. Baher, M.G. Cottam, Surf. Rev. Lett. 10 (2003) 13]. The parameters that modify the modes are the in-plane wave vector, the thickness of the film, the phonon frequency and the nonlinearity of each layer. It was found that by increasing the film thickness and nonlinearity coefficient, the curves move to the left and the number of the branches increases without changing the pattern of the curves.     

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

Gap solitons in metamaterials

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity ε(?) is negative—is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.     

Second-harmonic pressure generation of a non-diffracting acoustical high-order Bessel vortex beam of fractional type α

Background and motivation

Generalized Bessel vortex beams are regaining interest from the standpoint of acoustic scattering and radiation force theories for applications in particle rotation, mixing and manipulation. Other possible applications may include medical and nondestructive imaging. To manipulate heavy particles in a host medium, a minimum threshold of the incident sound field intensity is required at relatively high wave amplitudes such that nonlinear wave propagation occurs and the generation of harmonics may be detected. Thus, predictions of the harmonics generation become crucial from the standpoint of experimental design, and the present analysis should assist in the development of more complete models related to the (nonlinear) scattering and radiation forces under such circumstances. The purpose of this research is to construct a theoretical model for the second-harmonic pressure generation associated with a category of non-diffracting Bessel vortex beams known as high-order Bessel vortex beams of fractional typeα (HOBVBs-Fα).

Method

The weakly nonlinear wave propagation of a HOBVB-Fα is investigated based on Lighthill’s formalism. Analytical solutions up to the second-order level of approximation are derived and discussed. Closed-form solutions are obtained, which are expressed as a function of first-order quantities available from the classical linear theory. Lateral profiles of the HOBVB-Fα are computed and compared.

Results and conclusion

The results show that the beam’s width reduces and becomes narrower, the side-lobes decrease in magnitude, and the hollow region diameter (or null in magnitude) increases as the order of nonlinearity increases. Furthermore, the nonlinearity of the medium preserves the non-diffracting feature of the beam’s second-harmonic generation within the pre-shock range.     

Z-scan and optical limiting properties of Hibiscus Sabdariffa dye

The intensity-dependent refractive index n ₂ and the nonlinear susceptibility χ ⁽³⁾ of Hibiscus Sabdariffa dye solutions in the nanosecond regime at 532 nm are reported. More presicely, the variation of n ₂, β, and real and imaginary parts of χ ⁽³⁾ versus the natural dye extract concentration has been carried out by z-scan and optical limiting techniques. The third-order nonlinearity of the Hibiscus Sabdariffa dye solutions was found to be dominated by nonlinear refraction, which leads to strong optical limiting of laser.     

Band gaps and nonlinear defect modes in one-dimensional photonic crystals with anisotropic single-negative metamaterials

We propose a one-dimensional photonic crystal (1DPC) with multilayered periodic structures containing dispersive anisotropic single-negative (ASNG) (permittivity- or permeability-negative) metamaterials. The influences of the ratio of d_A/d_B and their scale on ASNG gaps are discussed. Moreover, the effect of a nonlinear defect layer introduced into the proposed structure is also analyzed, and the results show that the defect mode has two peaks of electrical fields in the defect layer and its bistability property is also different from a defect mode in PCs with isotropic SNG gaps.     

Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas

Media with a negative Kerr index (n₂) offer an intriguing possibility to self-compress ultrashort laser pulses without the risk of spatial wave collapse. However, in the relevant frequency regions, the negative nonlinearity turns out to be highly dispersive as well. Here, we study the influence of nonlinear dispersion on the pulse self-compression in a defocusing xenon gas. Purely temporal (1+1)-dimensional investigations reveal and fully spatio-temporal simulations confirm that a temporal shift of high intensity zones of the compressed pulse due to the nonlinear dispersion is the main effect on the modulational instability (MI) mediated compression mechanism. In the special case of vanishing n₂ for the center frequency, pulse compression leading to the ejection of a soliton is examined, which cannot be explained by MI.     

具有电与磁非线性效应超常介质中光束的聚焦特性

基于Drude模型,采用解析法与数值模拟法研究了具有电与磁非线性效应超常介质中光束的聚焦特性。结果表明超常材料中光束聚焦现象不但可以发生在自聚焦非线性介质中(正折射区)而且可以发生在自散焦非线性介质中(负折射区),且光束中心频率离介质的等离子频率越近,其聚焦效应越明显。特别是当电与磁非线性极化率为异号时,超常介质的非线性符号可以通过调控电与磁等离子频率的相对大小控制,这为主动操控光束的传输提供一种新的自由度。     

Self-modulation of acoustic waves in resonant bars

Observations of the induced transparency in the oscillations of a glass bar containing an “artificial crack” in the form of a saw-cut with a tightly inserted small metal plate are reported. In such a configuration, the increase of the resonator quality factor with increasing wave amplitude (denoting a decrease of dissipation which will be referred to as self-induced transparency) has been observed indicating an important role of the amplitude-dependent losses introduced by the inter-surface contacts. The self-induced transparency manifests itself also by the discontinuities (jumps) in the acoustic wave amplitude measured as a function of sweeping excitation frequency around the sample eigenfrequencies and by a self-modulation instability of the primary acoustic wave. This instability leads to the generation of side-lobes in the wave spectrum near the fundamental excitation frequency. The developed theoretical model confirms that all these observations can be self-consistently attributed to nonlinearity of the sound dissipation process. Possible physical mechanisms of the nonlinear dissipation are discussed. Although self-modulation has already been observed in nonlinear acoustical systems, to the knowledge of the authors, the reported data constitute the first observation of the instabilities due to essentially dissipative system behaviour that requires neither nonlinear elasticity nor multimode interaction.     

饱和非线性正折射异向介质中的调制不稳定性

直接从异向介质中包含饱和非线性、自陡峭和二阶非线性色散效应的非线性扩展传输方程出发,采用线性稳定性分析法,导出了调制不稳定性的色散关系、不稳定条件、无量纲的临界扰动频率和增益谱。计算和讨论了异向介质正折射区无量纲的增益谱随归一化角频率和入射功率密度的变化关系。结果表明,在异向介质正折射区,随归一化角频率和入射功率密度的不同,增益谱将会出现扰动频率大于零、扰动频率大于某个非零临界值、扰动频率大于零而小于某个非零临界值3种形式。在归一化角频率较小时,调制不稳定性可能出现阈值入射功率密度;且在较小的入射功率密度时,调制不稳定性只能出现在大于某个临界频率时。     

Solitons and cnoidal waves of the Klein–Gordon–Zakharov equation in plasmas

This paper studies the Klein?CGordon?CZakharov equation with power-law nonlinearity. This is a coupled nonlinear evolution equation. The solutions for this equation are obtained by the travelling wave hypothesis method, (G??/G) method and the mapping method.     

Wave turbulent statistics in non-weak wave turbulence

In wave turbulence, which is made by nonlinear interactions among waves, it has been believed that statistical properties are well described by the weak turbulence theory, where separation of linear and nonlinear time scales derived from weak nonlinearity is assumed. However, the separation of the time scales is often violated. To get rid of this inconsistency, closed equations are derived in wave turbulence without assuming the weak nonlinearity according to Direct-Interaction Approximation (DIA), which has been successful in Navier-Stokes turbulence. The DIA equations is a natural extension of the conventional kinetic equation to not-necessarily-weak wave turbulence.     

Damping of internal soliton modes in media with quadratic nonlinearity

Optical solitons in media with quadratic nonlinearity and frequency dispersion are theoretically analyzed. Internal soliton modes and the rate of their radiative damping as a function of detuning from the phase-matching condition and the nonlinear shift of phase velocity for different soliton dimensions (d=1, 2, 3) are found. The length of a nonlinear medium required to form a stationary soliton is determined.     

Temperature and magnetic field tunability of composite metamaterials containing spherical semiconductor particles in far-infrared and terahertz regimes

The effect of temperature and dc magnetic field variations on effective electromagnetic parameters of metamaterials (MTMs) containing spherical semiconductor particles is studied theoretically. The effect of temperature is taken into account through its influence on semiconductor carrier density and mobility. The effect of dc magnetic field is included using an extension of the Mie theory, describing the interaction of a plane wave with a gyrotropic sphere. The effective parameters such as relative permittivity and permeability are calculated by proper application of the Maxwell Garnett (MG) theory and its extensions to quasi-static condition and multi-phase structures. Based on these theories, the temperature and dc magnetic field tunability of three different MTM structures is investigated. First a single phase medium is considered which contains spherical semiconductor particles of one kind, randomly dispersed in a dielectric host. Then two multi-phase structures containing (a) two kinds of spherical semiconductor particles or (b) spherical particles with core-shell topology are investigated. The two multi-phase MTM structures can exhibit negative index of refraction in far-infrared spectral region. The measure of the temperature and dc magnetic field tunability of effective parameters such as relative permittivity and refractive index of the structures is evaluated and it is shown specifically that the real part of refractive index can be tuned to get negative, zero or positive values in far-IR or THz regimes, but the imaginary part of the index and the Figure of Merit (FOM) are also quite sensitive to the temperature and magnetic field variations. The tunable MTMs can find new applications in THz devices such as switches, tunable mirrors, isolators, converters, polarizers, filters and phase shifters.     

Nonlinear shoaling of shallow water waves: perspective in terms of the inverse scattering transform

Summary We study nonlinear interactions in measured surface wave trains obtained in the Northern Adriatic Sea about 16 kilometres from Venice, Italy.Nonlinear Fourier analysis is discussed in terms of the exact spectral solution to the Korteweg-deVries (KdV) equation as given by theinverse scattering transform (IST). For the periodic and/or quasi-periodic boundary conditions assumed herein, the approach may be viewed as a nonlinear, broad-banded generalization of the ordinary, linear Fourier transform. In particular, we study solition interactions, their properties and the nonlinear dynamics of the radiation (or oscillation) modes as found from the inverse scattering transform analysis. We also conduct a number of computer experiments in which measured wave trains are numerically propagated forward in time toward shallow water and backward in time into deep water in order to assess how the nonlinear wave dynamics are influenced by propagation over variable bathymetry. On this basis we develop a scenario for the evolution of nonlinear wave trains, initially far offshore in deep water, as they propagate into shallow water regions. The deep-water waves have a small Ursell number and are hence not very nonlinear; as they propagate toward shallow water, the Ursell number gradually increases in the numerical experiments by about an order of magnitude. A useful parameterization of nonlinearity in these studies is the ?spectral modulus,? a number between 0 and 1, which is associated with each IST spectral frequency. Small values of the modulus mean that a particular spectral component is linear (a sine wave); large values of the modulus (≈1) indicate that the component is nonlinear (a soliton). There is a systematic increase of the modulus as the waves propagate into shallow water where nonlinear effects predominate; we describe how the modulus varies as a function of spectral frequency during this shoaling process. The results suggest that the effect of increasing nonlinearity ?saturates? the IST spectrum (i.e. the modulus ≈1 for all frequencies) to that virtually all spectral components become solitons in sufficiently shallow water.     

Nonlinear focusing of picosecond baseband pulses in paraelectric crystals

The nonlinear baseband electromagnetic pulses of a wide spectrum that lies in terahertz (THz) range are investigated theoretically in the paraelectric crystals like SrTiO₃ at the temperatures ~ 77 K. The frequency dispersion is important in THz range there. The dominating nonlinearity of the crystal is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability of long input envelope pulses, whereas in the transverse direction the modulation instability is absent. When the nonlinear wave is uniform in the transverse direction, the existence of soliton-like baseband pulses without a carrier frequency has been demonstrated. There exists a possibility to generate the regular sequences of short baseband pulses due to the nonlinearity in the paraelectric crystals. The nonlinear focusing of input long baseband pulses by the exciting antenna results in the formation of extremely short baseband pulses localized both in the longitudinal and transverse directions.     

非线性左手材料中的二次谐波

基于电磁场理论，推导了无耗非线性左手材料中二次谐波的曼利－诺关系，及相位匹配条件下正向基波与逆向二次谐波的能量转换过程及其空间分布.验证了可将无耗非线性左手材料的入射面作为反射镜，把能量以二次谐波的形式反射.同时分别给出有限厚度介质板中基波和二次谐波的场强分布数值结果，验证了结论的正确性.最后从相位失配角度说明了相位匹配是分析非线性左手材料二次谐波的重要条件.这为研究左手材料的非线性理论奠定了基础.