Nonlinear surface polaritons in 2D electron system in high magnetic field

The paper deals with the theoretical investigation of nonlinear surface polaritons (NSP) in isolated two-dimensional electron system (2DES) arranged at the interface between linear and nonlinear media and placed into the external quantizing magnetic field directed perpendicularly to 2DES. We consider that nonlinear medium dielectric permeability depends upon the tangential component of electric field only. It is shown that under the integer quantum Hall effect conditions all NSP characteristics are represented by the quantized values. It is found that the NSP spectrum contains two NSP modes - high-frequency and low-frequency ones. It is shown that the NSP can exist only in the case where the value of tangential component of electric field at the interface is less than a certain critical value. It is found that the resonant interaction between the NSP high-frequency mode and surface polariton mode occurs in the vicinity of the cyclotron resonance subharmonic. Received 23 September 2001 / Received in final form 31 January 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: bludov@ire.kharkov.ua     

Enhancement of the Local Electromagnetic Field over Planar “Particles” Formed on the Surface of a Polar Crystal

Small “particles” of an open surface were formed on a SiC polar crystal with openings in the opaque metal mask covering the sample. The dimensions of the holes were about surface phonon polariton wavelength. Such a sample was irradiated with an electromagnetic wave ( λ = 10.68μm) at a frequency close to the lattice resonance of SiC. A significant enhancement in the field amplitude of surface phonon polariton waves was detected over such “particles” compared to the amplitude over an infinite open surface of SiC. Such a phenomenon, observed by us in the IR band, is similar to plasmon resonance on small metal particles in the visible band, but the lateral resolution of the ASNOM used (no worse than 30 nm at 10 μm) makes the obtained field distribution more detailed. The maps of the local field amplitude and phase obtained on SiC surface with ASNOM are in a good quantitative agreement with simulations using the Green’s function.     

三层介质超声谐振模式随材料和界面粘接性能变化的演变规律

在用超声波谐振对粘接材料的粘接强度进行无损评估时, 不同模式对粘接强度的敏感程度受到众多因素和参数的影响, 对检测结果的可靠性至关重要. 基于多层介质中声传播和界面弱粘接边界条件的理论模型, 将一个上下非对称的金属-粘接剂-金属三层结构的平面波反射系数函数中的谐振模式看作是上下铝金属层各自的Lamb波频散模式通过夹心粘接剂层相互耦合后叠加组成. 改变影响结构粘接强度的因素, 即粘接剂的性能参数(声阻抗、密度、厚度)和界面切向劲度系数k_t来分析三层结构谐振模式耦合方式的变化,得出结论: 粘接结构粘接性能的变化基本上不改变与被粘铝层相关的固有部分的Lamb波模式, 而它们的耦合模式则在谐振频率上产生平移并会与固有模式进行交换和替代; 不同参数的变化引起的模式演变有各自的规律, 大多可彼此区分.     

Analysis of surface and guided wave plasmon polariton modes in insulator–metal–insulator planar plasmonic waveguides

Theoretical and experimental study of the surface plasmon–polariton and guided wave plasmon polariton modes is presented for the Sapphire/Ag/Polycarbonate/Air structure. Theoretical results are obtained by solving complex multilayer eigenvalue equations as well as the reflectivity equation for this structure. It is proposed that the mode attenuation can be significantly reduced by inserting a low index dielectric buffer between the metal and the guiding dielectric layer. The dispersion and attenuation curves are generated. Both the surface plasmon and guided wave plasmon polariton modes are studied experimentally. The experimental values of the effective refractive indices agree well with the theoretical values. The electric field profiles are generated and used to examine the nature of modes. After optimization of various parameters the condition for low loss single mode guiding is obtained for the proposed structure. Effect of metal thickness on surface plasmon mode is also discussed. It is inferred that in a properly optimized plasmonic waveguide, the losses can be reduced by a factor of 4.     

Virtual modes and the surface boundary condition in underwater acoustics

An explicit expression for the contribution of continuous normal modes to the acoustic pressure field in shallow water is derived under the assumption of constant sound speed in the bottom. An approximate evaluation of the resulting integral leads to a summation over “virtual” modes. These virtual modes are similar to the trapped modes except that their amplitudes decay with range. Their contribution is important in certain situations, for example at short ranges and where there may be few or no trapped modes. The validity of the “pressure release” boundary condition at the surface is investigated. This approximate boundary condition is justified by allowing for energy leakage into the air and examining the virtual mode contribution to the normal mode expression. These virtual modes converge identically to the usual trapped mode expression in the limit of zero air density.     

Quantum Theory of Surface Polaritons on a Rough Surface

In this paper, we present the quantum field theory of the surface phonon-polaritolis on a rough polar crystal surface. The dispersion relations of the surface phonon-polaritons and the dispersion relations of polariton leaking modes owing to the interaction between bulk TO mode with the surface effect and photons are derived. We also study the k-dependence of the electric field strength in each polariton branch. The numerical calculations for the dispersion relations and the k-dependence of the electric field strength are carried out for a stepped Gap surface. The results show that the surface roughness depressed the frequency of the surface phonon-polariton below its values in the absence of the surface roughness. For the frequencies of the polariton leaking modes, the photon-like one is enhanced by the surface roughness and the phonon-like one b depressed. Our evaluations also illustrate that the surface roughness introduces a strong dependence on the k-dependence of the electric field strength in each polariton branch.     

三元混晶四层系统的表面和界面声子极化激元

运用改进的无规元素等位移模型和玻恩-黄近似,结合电磁场的麦克斯韦方程和边界条件,研究了真空/极性二元晶体薄膜/极性三元混晶薄膜/极性二元晶体衬底四层系统的表面和界面声子极化激元.以AlxGa1-xAs/GaAs和ZnxCd1-xSe/ZnSe为例,获得了表面和界面声子极化激元模的色散关系以及表面模和界面模的频率随混晶组分和薄膜厚度的变化关系.结果表明,三元混晶四层异质结系统中存在七支表面和界面声子极化激元模,且这七支表面模和界面模的频率随混晶组分和薄膜厚度呈非线性变化,三元混晶的"单模"和"双模"性也在色散曲线中得到了很好的体现.     

Surface polariton dispersion measurement by Raman scattering excited in total reflection condition

We report the first measurement of phonon surface polariton (s.p.) dispersion by a non-forward Raman scattering geometry. The Raman scattering from surface modes was excited by the evanescent electromagnetic wave produced by total reflection at the interface between two transparent media. This Raman Scattering excited in condition of Total Reflection, RSTR, has been applied to the NaClO₃-sapphire interface for studying the surface polariton dispersion in the gap between the TO frequency at 966 cm^-1 and the LO frequency at 983 cm^-1 of sodium chlorate. Comparison is made between the experimental and theoretical dispersion curves.     

Finite-amplitude standing acoustic waves in a cubically nonlinear medium

The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted “forced” waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.     

Surface polaritons at the magnetized semiconductor-dielectric interface

Conditions for the existence of a surface polariton at the semiconductor-dielectric interface have been analyzed. With allowance for the gyrotropy and the resonance frequency dispersion of the semiconductor, which manifests itself in an external magnetic field, the dispersion relation, the characteristic frequencies determining the existence region of a surface polariton, the wave fields, and the energy flux distribution in each of the interfacing media have been obtained. A numerical analysis of the influence of the external field and absorption, which lead to the manifestation of nonreciprocal properties of the polariton and to a substantial reconstruction of the spectrum, has been performed.     

圆管结构中周向导波非线性效应的模式展开分析

在二阶微扰近似条件下, 采用导波模式展开分析方法研究了圆管结构中周向导波的非线性效应. 伴随基频周向导波传播所发生的二次谐波, 可视为由一系列二倍频周向导波模式叠加而成. 从动量定理出发, 结合柱坐标系下非线性应力张量及其散度的数学表达式, 针对圆管中某一基频周向导波模式, 推导出相应的二倍频应力张量及二倍频彻体驱动力的数学表达式, 建立了确定二倍频周向导波模式展开系数的控制方程, 得到了伴随基频周向导波传播所发生的二次谐波声场的形式解. 理论分析和数值计算表明, 当构成二次谐波声场的某一二倍频周向导波模式与基频周向导波的相速度匹配时, 该二倍频周向导波模式的位移振幅表现出随传播周向角积累增长的性质; 当两者的相速度失配时, 二倍频周向导波的振幅随传播周向角表现出“拍”效应.     

“Right-handed” and “left-handed” polaritons in material media

The dispersion law for polariton waves is deduced from analysis of Maxwell equations in a dielectric medium characterized by the presence of resonance in the frequency range of lattice vibrations or exciton transitions. The theory considers polariton waves with right- and left-oriented vectors $\vec E,\vec H,\vec k$ , corresponding to “right-handed” and “left-handed” polaritons. Dispersion dependences of group velocity of polariton waves and effective mass are established for “right-handed” and “left-handed” polaritons. Expressions are obtained for the effective refractive index and reflection coefficient in a wide spectral range including the resonance region. The specific features of lattice reflection spectra in alkali halide crystals are explained using the proposed theory.     

Nonlinear spoof surface plasmon polariton phenomena based on conductor metamaterials

We present nonlinear phenomena produced from spoof surface plasmon polariton (SSPP) modes. Below the THz spectrum, artificially textured conducting metastructures on a subwavelength scale generate surface-bound modes and are called SSPP modes, similar to surface plasmon polariton (SPP) modes in the visible spectrum. Even though nonlinear effects in the THz domain are negligible, subwavelength metallic gap structures are ideal candidates to realize nonlinear behavior in the THz domain because of slow light propagation, strong electromagnetic confinement, and a high quality factor Q. In particular, when SSPP structures are combined with Kerr nonlinear materials, nonlinear-bistable curves can be observed below the THz spectrum.     

Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes

The light transmission through a dispersive plasmonic circular hole is numerically investigated with an emphasis on its subwavelength guidance. For a better understanding of the effect of the hole diameter on the guided dispersion characteristics, the guided modes, including both the surface plasmon polariton mode and the circular waveguide mode, are studied for several hole diameters, especially when the metal cladding has a plasmonic frequency dependency. A brief comparison is also made with the guided dispersion characteristics of a dispersive plasmonic gap [K.Y. Kim, et al., Opt. Express 14, 320–330 (2006)], which is a planar version of the present structure, and a circular waveguide with perfect electric conductor cladding. Finally, the modal behaviour of the first three TM-like principal modes with varied hole diameters is examined for the same operating mode.     

Band structure of collective modes and effective properties of binary magnonic crystals

In this paper a theoretical study of the band structure of collective modes of binary ferromagnetic systems formed by a submicrometric periodic array of cylindrical cobalt nanodots partially or completely embedded into a permalloy ferromagnetic film is performed. The binary ferromagnetic systems studied are two-dimensional periodic, but they can be regarded as three-dimensional, since the magnetization is non uniform also along the z direction due to the contrast between the saturation magnetizations of the two ferromagnetic materials along the thickness. The dynamical matrix method, a finite-difference micromagnetic approach, formulated for studying the dynamics in one-component periodic ferromagnetic systems is generalized to ferromagnetic systems composed by F ferromagnetic materials. It is then applied to investigate the spin dynamics in four periodic binary ferromagnetic systems differing each other for the volume of cobalt dots and for the relative position of cobalt dots within the primitive cell. The dispersion curves of the most representative frequency modes are calculated for each system for an in-plane applied magnetic field perpendicular to the Bloch wave vector. The dependence of the dispersion curves on the cobalt quantity and position is discussed in terms of distribution of effective “surface magnetic charges” at the interface between the two ferromagnetic materials. The metamaterial properties in the propagative regime are also studied (1) by introducing an effective magnetization and effective “surface magnetic charges” (2) by describing the metamaterial wave dispersion of the most representative mode in each system within an effective medium approximation and in the dipole-exchange regime. It is also shown that the interchange between cobalt and permalloy does not necessarily lead to an interchange of the corresponding mode dispersion. Analogously to the case of electromagnetic waves in two-dimensional photonic crystals, the degree of localization of the localized collective modes is expressed in terms of an energy concentration factor.     

Spin-wave resonance spectra of films with a uniform gradient of anisotropy field

It has been shown that the number of high-intensity spin-wave modes in the spin-wave resonance spectrum of films with a uniform gradient of the effective anisotropy field depends on the thickness of the film and on the exchange stiffness. It has been established that there is a “critical” thickness of the film which depends on the exchange stiffness and the anisotropy field gradient. When the thickness of the film is less than the “critical” value, only one high-intensity mode is excited in the resonance absorption spectrum.     

Electron spin resonance and antiferromagnetic resonance of single crystals of yttrium doped with gadolinium

The nonlinear interaction of oscillation modes is investigated on the basis of Lagrangian formalism. Equations describing the changes of the bound mode amplitudes versus time, are obtained. It is shown that the energy transformation between different modes is of a periodic nature: if in the initial moment of time an appreciable part of the energy is contained, for example, in them-th mode, then after a period of timeTt (called a time of nonlinear interaction) the energy will be transformed to then-th mode. Expressions forT _t for cases with the interaction of two and three modes are obtained. As a particular case the process of nonlinear interaction of the electron “transverse” and “longitudinal” oscillations in the highfrequency hybrid resonance region of a “weakly” inhomogeneous plasma was investigated.     

Efficient second-harmonic generation in nonlinear plasmonic waveguide

We theoretically studied a nonlinear optical process in a hybrid plasmonic waveguide composed of a nonlinear dielectric waveguide and a metal film with a separation of a thin air gap. Owing to the hybridization effect of guided mode and surface plasmon polariton mode, this particular waveguide is able to confine the optical-field in a deep subwavelength scale together with low propagation loss. Based on this, efficient second-harmonic generations (SHG) were revealed at the fundamental wavelength of λ=1.55?μm with good field confinement. The SHG efficiency, as well as the coupling coefficient and mode area, were analyzed and discussed in detail with respect to the structural parameters.     

近似声斗篷的多层介质覆盖水中弹性球壳的声散射

对水中弹性球壳的低频覆盖层消声效果和消声机理进行研究。声斗篷(Acoustic cloak)是各向异性的超常材料,根据有效介质近似理论(Effective MediumApproximationTheory),采用各向同性多层介质近似各向异性材料的声斗篷,推导出覆盖多层介质水中弹性球壳散射声场的解析表达式,计算了弹性球壳覆盖多层介质前后的散射形态函数、谐振模态以及声场分布,分析了覆盖前后球壳的声散射特性和声传播机理。研究表明,覆盖层内的声波在多层介质之间的声传播方向发生改变,声场形成弯曲变形,声能流绕过目标,这不仅极大的降低了低频散射强度,而且使到达弹性体表面的声场强度非常小,散射频响中除了0阶子波产生的第一个谐振峰外,无法激发弹性球壳的其它谐振模态,有效的抑制弹性球壳的谐振散射。      

Calculations of three-dimensional magnetic excitations in permalloy nanostructures with vortex state

Dynamic susceptibility spectra of the vortex state in nanorings and nanodots are studied using three-dimensional micromagnetic simulations. Spatial maps of the susceptibility have enabled identification of various resonance modes. For an exciting field along the x axis, several resonance peaks appear for a thin dot, including a core mode, whereas only one main resonance peak is detected for a ring corresponding to a volume mode with uniform magnetization perpendicular to the exciting field (x direction). A low-frequency resonance peak related to a surface mode and a high-frequency resonance peak viewed as an edge mode are additionally observed for a thick ring. These three resonance modes (surface, volume and edge modes) which correspond to low, intermediate and high-frequency resonance peaks, respectively, are also captured for an exciting field along the y axis. In addition, a mixed edge and volume mode is revealed at a higher frequency.