Bend radiation in optical fibers

A new, relatively simple way of calculating bend radiation is developed. As is often done in propagation over gently curved surfaces, the fiber curvature is accounted for by placing a straight fiber in a fictitious medium that is inhomogeneous in the plane of the bend. For a gently curved fiber, the medium is slowly varying and the WKB method is used to approximate the radial field dependence. This solution is related to the unperturbed straight fiber solution through an ansatz consistent with the WKB solution. The propagating modes in this approximation remain orthogonal, allowing an immediate generalization to the multimoded case. The radiation loss per unit length is calculated two ways and is consistent with results in the literature.     

The peculiarities of cross-correlation between two secondary precursors – Radon and magnetic field variations,induced by stress transfer changes

A model of precursor manifestation mechanisms, stimulated by tectonic activity and some peculiarities of observer strategy, whose main task is the effective measurement of precursors in the spatial area of their occurrence on the Earth's daylight, are considered. In particular, the applicability of Dobrovolsky's approximation is analyzed, when an unperturbed medium (characterized by the simple shear state) and the area of tectonic activity (local inhomogeneity caused by the change only of shear modulus) are linearly elastic, and perturbation, in particular, surface displacement is calculated as a difference of the solutions of two independent static problems of the theory of elasticity with the same boundary condition on the surface. Within the framework of this approximation a formula for the spatial distribution (of first component) of magnetic field variations caused by piezomagnetic effect in the case of perturbed regular medium, which is in simple shear state is derived. Cogent arguments in favor of linear dependence between the radon spatial distribution and conditional deformation are obtained.Changes in magnetic field strength and radon concentrations were measured along a tectonomagnetic profile of the total length of 11 km in the surroundings of the ”Academician Vernadsky” Station on the Antarctic Peninsula (W 64°16′, S 65°15′). Results showed a positive correlation between the annual surface radon concentration and annual changes of magnetic field relative to a base point, and also the good coincidence with theoretical calculation.     

Scattering from correlated systems

A difficulty usually encountered in formulating the problem of scattering of identical particles from correlated systems is that the customary choice of an unperturbed Hamiltonian as the target Hamiltonian plus the kinetic energy of the projectile is not symmetric under particle exchange. This choice of unperturbed Hamiltonian leads to wavefunctions which, if they are antisymmetrized, are not orthonormal. In this paper an orthonormal, antisymmetrized set of basis states is constructed. These states are then used to construct a symmetric unperturbed Hamiltonian, so that a formal scattering equation with appropriate boundary conditions can be written. An expression for a T matrix describing nucleon-nucleus scattering can then be obtained. The formalism leads to a two-potential form for the T matrix, the first term of which describes the effect of the orthogonality of the scattering state and the negative energy states.     

Bend radiation in optical fibers

Abstract

A new, relatively simple way of calculating bend radiation is developed. As is often done in propagation over gently curved surfaces, the fiber curvature is accounted for by placing a straight fiber in a fictitious medium that is inhomogeneous in the plane of the bend. For a gently curved fiber, the medium is slowly varying and the WKB method is used to approximate the radial field dependence. This solution is related to the unperturbed straight fiber solution through an ansatz consistent with the WKB solution. The propagating modes in this approximation remain orthogonal, allowing an immediate generalization to the multimoded case. The radiation loss per unit length is calculated two ways and is consistent with results in the literature.     

Validation of the effective-medium approximation for the dielectric permittivity of oriented nanoparticle-filled materials: effective permittivity for dielectric nanoparticles in multilayer photonic composites

A formula for the effective permittivity for two-dimensional particles embedded in a host matrix is derived and a method for its numerical evaluation is described. The method is applied to specific cases of circular, square, rectangular and triangular particles. Shapes are assumed for the inclusion particles. Data for obtaining the effective permittivity is provided for a wide range of filling fractions, geometries and dielectric contrasts between the particles and the matrix under the assumption of the quasi-static approximation, that is, the wavelength of the electric field is assumed to be much larger than the particle size. Metallic particles with complex and frequency-dependent dielectric constants are treated, as well as no-loss dielectric inclusions. Calculations are validated by comparing the results of the reflectivity obtained for a composite layer using the transfer-matrix method, assuming the layer to be an effective medium, to those using the finite-element method and accounting for the heterogeneous material. PACS 78.20.-e; 78.20.Bh; 78.20.Ci; 78.66.Sq; 78.66.Vs     

Evaluation of the dipole interaction of a pair of metal particles in the region of the plasmon resonance

We consider the electric field of an induced dipole moment of a single small particle characterized by the absence of frequency dispersion of the permittivity and the field of a metal particle, which has frequency dispersion and is described in the free electron approximation taking into account the size effects of restriction of the electron free path. The influence of the induced field on the optical properties of a system of small particles is analyzed. It is shown that, for an ensemble of particles without frequency dispersion, the effective medium theory can be used up to concentrations corresponding to filling factors ? ≤ 0.52. In the case of metal particles, with frequency dispersion of dielectric functions and, especially, for the frequency range of the plasmon resonance, this theory can be used only for concentrations not exceeding the threshold ? ≈ 0.01.     

Microwave Heating of Metal Power Clusters

The results of simulating the rapid microwave heating of spherical clusters of metal particles to the melting point are reported. In the simulation, the cluster is subjected to a plane electromagnetic wave. The cluster size is comparable to the wavelength; the perturbations of the field inside the cluster are accounted for within an effective medium approximation. It is shown that the time of heating in vacuum to the melting point does not exceed 1 s when the electric field strength in the incident wave is about 2 kV/cm at a frequency of 24 GHz or 5 kV/cm at a frequency of 2.45 GHz. The obtained results demonstrate feasibility of using rapid microwave heating for the spheroidization of metal particles with an objective to produce high-quality powders for additive manufacturing technologies.     

Numerical simulations of negative-index refraction in a lamellar composite with alternating single negative layers

Negative-index refraction is demonstrated in a lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials stacked alternatively. Based on the effective medium approximation, simultaneously negative effective permittivity and permeability of such a lamellar composite are obtained theoretically and further proven by full-wave simulations. Consequently, the renowned left-handed metamaterial comprising split ring resonators and wires is interpreted as an analogy of such ENG--MNG layers. In addition, beyond the effective medium approximation, the propagating field squeezed near the ENG/MNG interface is demonstrated to be left-handed surface waves with backward phase velocity.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonic model of a two-dimensional oscillator having Kratzer potential energy functionis used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interactionbetween the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a real polyatomic molecular species.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Light scattering by homogeneous and multilayer ellipsoids in the quasi-static approximation

The quasi-static approximation for homogeneous and multilayer ellipsoidal particles is considered in detail. Expressions for the elements of the amplitude scattering matrix, as well as for the absorption and scattering cross sections, are presented for an arbitrary orientation of the particles relative to the incident radiation. The accuracy and the domain of applicability of the approximation are investigated for the elements of the scattering matrix of absorbing particles. Comparison of some approximate and exact methods showed that the quasi-static approximation gives good results (it is substantially more preferable than the Rayleigh and Rayleigh-Gans approximations), if the ratio of the largest size of a particle (or the boundaries of the main layer) to the smallest one does not exceed ～3. A new rule of the effective medium theory for multilayer ellipsoidal particles is proposed, which adequately takes into account their structure.     

Effective potential method for active particles

ABSTRACT

We investigate the steady-state properties of an active fluid modelled as an assembly of soft repulsive spheres subjected to Gaussian coloured noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified coloured noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of coloured noise and interactions enhances the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.     

Effective scatterer approximation for mean field modeling with application to vegetation

A new electromagnetic method is developed for the mean field analysis of discrete random media in which particles are distributed in disjoint regions in space. This type of distribution can be observed in organized vegetation canopies, photonic band gap materials and disordered crystals. The method is based on an ‘effective scatterer’ concept. As far as the mean field is concerned, the random problem is approximated by a deterministic one composed of effective scatterers. Application of the effective scatterer approach to two-dimensional mean field propagation through a cylinder distribution that is periodic on average is verified by Monte Carlo simulations. Comparisons with other known methods such as the Foldy approximation are also presented.     

Effective medium approximation for optical bistability in nonlinear metal-dielectric composites

A general theory based on the spectral representation method and effective medium approximation is adopted to investigate the optical bistable behavior in a nonlinear two-phase composite with symmetrical microstructure, in which the metal particles of the volume fraction p and the dielectric particles of the volume fraction 1−p are randomly dispersed but oriented with respect to one another. The relation between the spatial average of local field squared and the external applied field is established through the spectral density function m(x), obtained from the modified Bruggeman effective medium approximation. We find that the optical bistability (OB) is dependent on the depolarization factor L of the components and the volume fraction p. For a given p, we predict that OB can be observed only when L is larger than the critical value L_c, and bistable behavior is more pronounced at large L. Moreover, numerical results show that both the upper threshold field and the width of OB region increase monotonically as L increases. The field-dependent reflectance at normal incidence R in random composites is also investigated.     

Statistical description of an ensemble of ultrarelativistic particles in a spatially flat universe

The kinetic equation for massless particles in an unperturbed Friedman universe with gravitational interactions taken into account is obtained by averaging the collisionless kinetic equations over local background gravitational field fluctuations. Uniformly distributed spherically symmetric fluctuations of an ultrarelativistic fluid serve as local inhomogeneities in a spatially flat universe. It is shown that the collision integral of our kinetic equation does not vanish when the distribution function is homogeneous and isotropic.     

The effective interaction in a nuclear model

The effective interactionU belonging to a given subspace ofn unperturbed model functions can be related to the free nucleon-nucleon interaction by means of an exact integral equation. The conditions for a Born-v. Neumann expansion ofU and for an approximation by a slowly energy dependent interaction with adjustable parameters are investigated. It appears that effective interactions which have been used successfully in shell model calculations of bound state properties do not necessarily describe the actual dynamics of a nucleus.     

Post-Newtonian equations for the metric perturbation generated by a rotating elastic earth

By using Synge's approximation method to describe the unperturbed problem, we obtain the equations for the gravitational field perturbation and the Lagrangian displacement that occur when an isolated and initially self-gravitating spherical and static elastic earth gets into steady rotation. These equations are explicitly derived in an order of approximation for the initial problem where both rotation and elastic structure manifest themselves in the perturbed state.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

Effective scatterer approximation for mean field modeling with application to vegetation

A new electromagnetic method is developed for the mean field analysis of discrete random media in which particles are distributed in disjoint regions in space. This type of distribution can be observed in organized vegetation canopies, photonic band gap materials and disordered crystals. The method is based on an 'effective scatterer' concept. As far as the mean field is concerned, the random problem is approximated by a deterministic one composed of effective scatterers. Application of the effective scatterer approach to two-dimensional mean field propagation through a cylinder distribution that is periodic on average is verified by Monte Carlo simulations. Comparisons with other known methods such as the Foldy approximation are also presented.