Two Kinds of Square-Conservative Integrators for Nonlinear Evolution Equations

Based on the Lie-group and Gauss-Legendre methods, two kinds of square-conservative integrators for square- conservative nonlinear evolution equations are presented. Lie-group based square-conservative integrators are linearly implicit, while Gauss-Legendre based square-conservative integrators are nonlinearly implicit and iterative schemes are needed to solve the corresponding integrators. These two kinds of integrators provide natural candidates for simulating square-conservative nonlinear evolution equations in the sense that these integrators not only preserve the square-conservative properties of the continuous equations but also are nonlinearly stable. Numerical experiments are performed to test the presented integrators.     

Multisymplectic Euler Box Scheme for the KdV Equation

We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries （KdV） equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.     

Finite difference approximations for the fractional advection-diffusion equation

Fractional order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this Letter, in order to solve the two-sided fractional advection-diffusion equation, the fractional Crank-Nicholson method (FCN) is given, which is based on shifted Grünwald-Letnikov formula. It is shown that this method is unconditionally stable, consistent and convergent. The accuracy with respect to the time step is of order ²(Δt). A numerical example is presented to confirm the conclusions.     

An Explicit Scheme for the KdV Equation

A new explicit scheme for the Korteweg~：le Vries （KdV） equation is proposed. The scheme is more stable than the Zabusky Kruskal scheme and the multi-symplectic six-point scheme. When used to simulate the collisions of multi-soliton, it does not show the nonlinear instabilities and un-physical oscillations.     

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that the two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values for both the electric permittivity ? and the magnetic permeability μ in some frequency range. This follows from a recently proven general theorem. The negative values of ? and μ are found by a numerical simulation. Using values |?| and |μ| for the medium surrounding the PC slab we simulate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ? and μ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.     

Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by O ion implantation into lithium niobate

A method named intensity calculation method (ICM), which is based on beam propagation method (BPM) and image processing, was carried out to reconstruct the extraordinary refractive index profile (RIP) of single-mode planar waveguide in lithium niobate (LiNbO₃), which was fabricated by multi-energy megaelectron-volt (MeV) O²⁺ ion implantation. In addition, it has been proved reasonable that the alternation of extraordinary refractive index induced by ion implantation into LiNbO₃ is mainly due to the degradation of polarization and reduction of material physical density. As a result, the possible extraordinary RIP of the double-mode planar waveguide could be reconstructed using BPM according to such a hypothesis and the calculated guiding mode values. The end-fire coupling and m-line arrangements were carried out to obtain the near-field modal patterns and dark-mode spectra of waveguides, respectively.     

Narrow transmission bands of quasi-1D comb-like photonic waveguides containing negative index materials

Using the interface response theory, we investigate the band structure and transmission of quasi-1D comb-like photonic waveguides with side branches composed of negative index materials. Numerical results exhibit the existence of discrete modes in band structure. These discrete modes are corresponding to narrow transmission bands which separated by large forbidden band in the transmission spectrum. Meanwhile it is shown that the narrow transmission bands become narrower with the increase of the number of side branches. The above properties are still maintained when the negative index materials are dispersive and lossy.     

Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Experimental study of composite medium with simultaneously negative permeability and permittivity

Inclassicalelectrodynamics,theresponse(typicallyfrequencydependent)ofamaterialtoelectricandmagneticfieldsischaracterizedbytwofundamentalquantities,thepermittivityeandthepermeabilitym.Bothmandearepositiveinmostmaterials.In1968,Veselago[1]predictedthattheelectromagneticwavepropagationinamediumhavingsimultaneouslynegativepermittivityandpermeabilityshouldgiverisetoseveralpeculiarcharacteristics.Butnoneofhispredictionsweretestedduringthelastcentury,becausenonaturalmaterialswithsimultaneouslynegativ…     

Challenge of ultra high frequency limit of permeability for magnetic nanoparticle assembly with organic polymer—Application of superparamagnetism

Permeability and its upper limitation frequency of superparamagnetic nanoparticle type magneto-dielectric hybrid material were theoretically and experimentally investigated. The Landau-Lifschitz-Gilbert equation without any interaction between nanoparticles revealed that the blocking resonance frequency was able to exceed the ferromagnetic resonance frequency originating from the intrinsic magnetocrystalline anisotropy field by decreasing particle size, resulting in ultra fast switching of superparamagnetic moment in GHz range. In the case of Fe nanoparticles, the blocking resonance frequency can be increased to 130 GHz by reducing particle size to 1 nm. The experiment results for Fe₃O₄ and Fe nanoparticle assemblies supported the validity of our calculation results. Thus, superparamagnetic nanoparticle assembly could be promising material for high frequency use over 10 GHz range.     

Optical delay lines using coupled slab waveguides and ring resonator with a negative refractive index core

Total delay time of a structure composed of a slab waveguide coupled with a ring resonator where negative refractive index material is replaced in the core of the structure is investigated in this work. In this paper, a two-port ring resonator (TPRR) which is made of a core with negative refractive index has been used to generate a time delay for a Gaussian-shaped pulse with 1 GHz bandwidth. It is shown that the creation of the ring how causes more n_g of a straight waveguide and results are compared with positive refractive index core TPRR. We have used metamaterial to make an n < 0 media and have used two cascaded metamaterial rings to increase the bandwidth.     

Characterization for metamaterials with a high refractive index formed by periodic stratified metallic wires array

Ultralong ZnO nanowires were successfully prepared on a large scale by a microwave-assisted aqueous route without using any surfactant or template at relatively low temperature of 120°C. The obtained nanowires were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), and energy-dispersive X-ray spectrum (EDX). The growth mechanism and photoluminescence of the one-dimensional nanostructure, and photovoltaic performances for dye-sensitized solar cell (DSSC) of the nanowires were discussed in detail.     

Band rules for the frequency spectra of three kinds of aperiodic photonic crystals with negative refractive index materials

By means of the theory of electromagnetic wave propagation and transfer matrix method, this paper investigates the band rules for the frequency spectra of three kinds of one-dimensional (1D) aperiodic photonic crystals (PCs), generalized Fibonacci GF(p,1), GF(1,2), and Thue--Morse (TM) PCs, with negative refractive index (NRI) materials. It is found that all of these PCs can open a broad zero-? gap, TM PC possesses the largest zero-? gap, and with the increase of p, the width of the zero-? gap for GF(p,1) PC becomes smaller. This characteristic is caused by the symmetry of the system and the open position of the zero-? gap. It is found that for GF(p,1) PCs, the possible limit zero-? gaps open at lower frequencies with the increase of p, but for GF(1,2) and TM PCs, their limit zero-? gaps open at the same frequency. Additionally, for the three bottom-bands, we find the interesting perfect self-similarities of the evolution structures with the increase of generation, and obtain the corresponding subband-number formulae. Based on 11 types of evolving manners Q_i(i=1,2,....,11) one can plot out the detailed evolution structures of the three kinds of aperiodic PCs for any generation.     

Omnidirectional zero-\bar {\mathsf n} gap in symmetrical Fibonacci sequences composed of positive and negative refractive index materials

The band structures of symmetrical Fibonacci sequences (SFS) composed of positive and negative refractive index materials are studied with a transfer matrix method. A new type of omnidirectional zero- gaps is found in the SFS. In contrast to the Bragg gaps, such an omnidirectional zero- gap is insensitive to the incident angles and polarization, and is invariant upon the change of the ratio of the thicknesses of two media. It is found that omnidirectional zero- gap exists in all the SFS, and it is rather stable and independence of the structure sequence.     

Anomalous lateral beam shift and total absorption due to excitation of surface waves in materials with negative refraction

We studied electromagnetic beam reflection from layered structures that include materials with negative refraction. Excitation of leaky surface waves leads to the formation of anomalous lateral shifts in the reflected beams with single or double peak structures. The presence of reasonable losses within material with negative refraction, besides significant influence on manifestation of the giant lateral shifts, can lead to their total suppression and anomalously high absorption of the incident radiation. If, in addition to the resonant excitation of leaky surface waves, radiation inflow exactly compensates their irreversible damping, total absorption of the incoming radiation can be achieved for moderately wide beams.     

Resonant modes and inter-well coupling in photonic quantum well with negative index materials

The transfer matrix method was used to study the resonant modes in photonic quantum well by stacking different photonic crystals consisting of positive index materials and negative index materials. The eigenfrequency equation for the resonant modes is derived. It is found that these resonant modes are omnidirectional, and the number of resonant modes is equal to the period number of photonic quantum wells. Moreover, the resonant modes become N-fold splitting in the N photonic quantum wells. The splitting intervals increase with the deceasing of photonic barrier thickness due to the coupling among the wells.     

Low-loss, compact waveguiding with TE mode in metal/dielectric waveguides for planar lightwave circuit

We propose a low-loss metal/dielectric waveguide for compact planar lightwave circuit. The basic waveguide structure is a metal-defined high-index-contrast strip waveguide based on silicon/silica. As the guide is designed for TE single mode waveguiding, extremely low propagation loss (e.g. <0.04 dB/cm), very low bend loss (e.g. 0.0043 dB/90°-turn) and small waveguide pitch of zero-crosstalk are theoretically achievable, and can be further improved by compromising with component size and density. Examples of multi-bends and device integration are demonstrated with numerical simulations. The proposal is compatible with silicon technology and appealing for development of silicon-based planar lightwave circuit.     

含负折射率介质的多层结构中倏逝波传播及隧道效应的分析

研究了倏逝波在含负折射率介质的多层平板结构中的传播特性，解析地分析了倏逝波在不同结构参数下的放大或衰减规律及其原因以及能流的分布，并着重讨论了负折射率介质的损耗对隧道效应的影响，最后通过模拟高斯光束在该结构中的传播和能量储存，形象地给出了负折射率介质的损耗对倏逝波的影响和对光子隧道效应的减弱. 关键词： 负折射率介质 倏逝波 隧道效应     

Mixed 2D molecular systems: Mechanic, thermodynamic and dielectric properties

Study of Langmuir monolayers consisting of stearic acid (SA) and dipalmitoylphosphatidylcholine (DPPC) molecules was done by surface pressure-area isotherms (π-A), the Maxwell displacement current (MDC) measurement, X-ray reflectivity (XRR) and atomic force microscopy (AFM) to investigate the selected mechanic, thermodynamic and dielectric properties based on orientational structure of monolayers. On the base of π-A isotherms analysis we explain the creation of stable structures and found optimal monolayer composition. The dielectric properties represented by MDC generated monolayers were analyzed in terms of excess dipole moment, proposing the effect of dipole-dipole interaction. XRR and AFM results illustrate deposited film structure and molecular ordering.     

Dielectric permittivity, density, viscosity and refractive index of binary mixtures of anisole with methanol and 1-propanol at different temperatures

Static dielectric permittivity, density, viscosity, and refractive index of anisole (AN), methanol (MeOH), 1-propanol (1-PrOH) and binary mixtures of AN with MeOH and 1-PrOH at nine different concentrations, were measured at 303, 313 and 323 K temperatures. Measured properties of pure AN, MeOH and 1-PrOH were compared with literature values and they were found in good agreement. The investigation of binary mixtures showed a systematic change in static dielectric permittivity, density and viscosity with change in concentration of anisole in the mixture. Measured properties of liquid samples were used to calculate Kirkwood correlation factor and excess parameters such as excess dielectric permittivity, excess molar volume and excess viscosity. Determined parameters have been interpreted in terms of molecular interaction among the molecular species of the binary mixtures.