Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Cauchy's dispersion equation reconsidered: Dispersion in silicate glasses

We formulate a novel method of characterizing optically transparent substances using dispersion theory. The refractive index is given by a generalized Cauchy dispersion equation with coefficients that are moments of the uv and ir absorptions. Mean dispersion, Abbé number, and partial dispersion are combinations of these moments. The empirical relation between index and dispersion for families of glasses appears as a consequence of Beer's law applied to the uv spectra.     

Global Wave Solution of generalized MHD Equations in a Cylindrical Plasma

The linear eigenstate problem of generalized magnetohydrodynamics(MHD) equations in a cylindrical plasma is discussed. The effects of finite frequency and finite pressure perturbation lead to an important result: the resonant layer of the shear Alfven waves is not a singular layer. In this paper, the MHD equations are reduced to four differential equations of first order for perturbed quantities. An analytical dispersion relation for a homogeneous plasma cylinder is obtained. The K. Appert theory is a limiting case of our theory     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Kinetic theory of a nonideal plasma: Dispersion relations

The kinetic theory of plasma based on the construction of propagators for the plasma particle distribution function is generalized to the case of a nonideal plasma. This theory is used for calculating the permittivity of a homogeneous nonideal plasma consisting of one species of ions neutralized by the polarized electron background. The dispersion relations are derived for ion-acoustic and low-frequency transverse waves in the plasma.     

Flexomagnetoelectric effect in nonuniform external fields in isotropic centrosymmetric nonlinear media with spatial dispersion

The flexomagnetoelectric effects in isotropic centrosymmetric nonlinear media with spatial dispersion in nonuniform external fields are theoretically analyzed. General theoretical concepts are applied to the case of a capacitor with metallic plates in the form of two infinite cylinders with confocal elliptic generatrices that is filled with a nonlinear dielectric. The developed theory is generalized to the case of an isotropic centrosymmetric collinear antiferromagnet in a disordered phase.     

柱等离子体中广义磁流体方程组的简化形式与本征模解

本文从含有广义欧姆定律的磁流体力学方程组出发,仅作符合加热托卡马克等离子体具体实验条件的近似,把广义磁流体方程组简化成4元一阶微分方程组。对均匀密度等离子体柱情况求出解析色散关系(本征模解),并证明Appert理论是本文的极限情况。 关键词：     

Optimization of effective atom centered potentials for london dispersion forces in density functional theory

We add an effective atom-centered nonlocal term to the exchange-correlation potential in order to cure the lack of London dispersion forces in standard density functional theory. Calibration of this long-range correction is performed using density functional perturbation theory and an arbitrary reference. Without any prior assignment of types and structures of molecular fragments, our corrected generalized gradient approximation density functional theory calculations yield correct equilibrium geometries and dissociation energies of argon-argon, benzene-benzene, graphite-graphite, and argon-benzene complexes.     

Novel broadband conventional- and dual-composite right/left-handed (C/D-CRLH) metamaterials: properties,implementation and double-band coupler application

Broadband conventional- and dual-composite right/left-handed (C/D-CRLH) transmission line metamaterials are presented. The extended transmission line theory for these structures is developed and the fundamental C-CRLH and D-CRLH properties are described comparatively in terms of dispersion/attenuation diagrams and Bloch/characteristic impedances with subsequent transmission characteristics. A D-CRLHstructure, implemented in microstrip technology, is demonstrated experimentally for the first time and shown to have potential for unique applications. As an illustration of such applications, a novel double-band coupled-line coupler constituted of one C-CRLH and one D-CRLH transmission line is demonstrated and explained by generalized coupled-mode theory. PACS 81.05.Zx; 84.40.Az; 41.20.Jb; 84.30.-r     

Results of the use of generalized coupling equations in the original Fresnel theory and original theory of spatial dispersion in a gyrotropic uniaxial crystal

The generalizations of the original Fresnel theory and original theory of natural gyrotropy as manifestations of the first-order natural dispersion in uniaxial crystals are considered. The generalizations are made for magnetic crystals, taking into account the magnetic gyrotropy. The region of application of the corresponding generalized theories is found to be restricted by a particular case of the wave normal s directed parallel to the optic axis C of a uniaxial crystal.     

Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

The magnetic relaxation of a spin-1 Ising model with bilinear and biquadratic interactions is formulated within the framework of statistical equilibrium theory and the thermodynamics of irreversible processes. Using a molecular-field expression for the magnetic Gibbs energy, the magnetic Gibbs energy produced in the irreversible process is calculated and time derivatives of the dipolar and quadrupolar order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager theory. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By solving these equations an expression is derived for the dynamic or complex magnetic susceptibility. From the real and imaginary parts of this expression, magnetic dispersion and absorption factor are calculated and analyzed near the second-order phase transition.     

Dispersion and absorption of sound in nematics

The unified hydrodynamic theory for systems with a liquid crystalline phase is generalized to include a frequency dependence of the elastic and dissipative parameters of the system. Application is made to nematics for which the frequency dependent anisotropies of the velocity and absorption of sound are calculated. It is shown that the relaxation approximation for the dispersion leads to reasonable results.     

衍射光栅的第二类角色散及其特性分析

在由矢量衍射理论得到的锥面衍射情形下的广义光栅方程基础上，给出了对应于衍射极角的衍射光栅第一类角色散公式和对应于衍射方位角的衍射光栅第二类角色散公式，并通过理论和数值分析导出了第二类角色散发生突变的条件及相应的数学表达式. 关键词： 衍射光栅 锥面衍射 第一类角色散 第二类角色散     

A unified approach to the effects of symmetry and periodicity on boundary-value problems

A generalized approach to the effects of symmetry and periodicity on boundary-value problems is presented, especially as it pertains to the guiding structures encountered in electromagnetics. Several examples of structures and their dispersion behavior are given, and the theory predicts well that other authors claim.     

Analysis of inelastic x-ray scattering spectra of low-temperature water

We analyze a set of high-resolution inelastic x-ray scattering (IXS) spectra from H2O measured at T=259, 273, and 294 K using two different phenomenological models. Model I, called the "dynamic cage model," combines the short time in-cage dynamics described by a generalized Enskog kinetic theory with a long-time cage relaxation dynamics described by an alpha relaxation. This model is appropriate for supercooled water where the cage effect is dominant and the existence of an alpha relaxation is evident from molecular-dynamics (MD) simulation data of extended simple point charge (SPC/E) model water. Model II is essentially a generalized hydrodynamic theory called the "three effective eigenmode theory" by de Schepper et al. 11. This model is appropriate for normal liquid water where the cage effect is less prominent and there is no evidence of the alpha relaxation from the MD data. We use the model I to analyze IXS data at T=259 K (supercooled water). We successfully extract the Debye-Waller factor, the cage relaxation time from the long-time dynamics, and the dispersion relation of high-frequency sound from the short time dynamics. We then use the model II to analyze IXS data at all three temperatures, from which we are able to extract the relaxation rate of the central mode and the damping of the sound mode as well as the dispersion relation for the high-frequency sound. It turns out that the dispersion relations extracted from the two models at their respective temperatures agree with each other giving the high-frequency sound speed of 2900+/-300 m/s. This is to be compared with a slightly higher value reported previously, 3200+/-320 m/s, by analyzing similar IXS data with a phenomenological-damped harmonic oscillator model 22. This latter model has traditionally been used exclusively for the analysis of inelastic scattering spectra of water. The k-dependent sound damping and central mode relaxation rate extracted from our model analyses are compared with the known values in the hydrodynamic limit.     

Theory of anomalous dispersion in a-Se

A theory of multiple trapping expressed in terms of generalized first-order transport equations is used to explain the change in dispersion with temperature of the photocurrent transients in a-Se. The theory is shown to be equivalent to the continuous-time random walk (CTRW) model of Scher and Montroll, and the hopping-time distribution function is computed for the CTRW model in terms of the trap parameters.     

On the Role of the Results Obtained by the Analytical Theory of Elementary Particles

To prove that it is possible to obtain many results (such as the asymptotic relations of Pameranchuk type, Froissart inequality, Martin theorem, etc.) of the analytical theory of elementary particles in any theory where the ordinary analyticity of dispersion amplitude is replaced by a certain generalized analyticity (such as the p-analyticity of Poloji, the generalized analyticity of Vekua). Hence we cannot consider these results as criteria for the validity of the analyticity at high energies. Therefore, in order to check the analyticity we ought to establish the relations which can not be deduced from any generalized analyticity, except ordinary analyticity.