A three-dimensional refractive index model for simulation of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed with using the so-called “split”-operator method, when the influence of the propagation medium’s refractive index inhomogeneities is accounted for only within a system of infinitely narrow layers (phase screens) where phase is distorted. Commonly, under certain assumptions, such phase screens are considered as mutually statistically uncorrelated. However, in several important applications including laser target tracking, remote sensing, and atmospheric imaging, accurate optical field propagation modeling assumes upper limitations on interscreen spacing. The latter situation can be observed, for instance, in the presence of large-scale turbulent inhomogeneities or in deep turbulence conditions, where interscreen distances become comparable with turbulence outer scale and, hence, corresponding phase screens cannot be statistically uncorrelated. In this paper, we discuss correlated phase screens. The statistical characteristics of screens are calculated based on a representation of turbulent fluctuations of three-dimensional (3D) refractive index random field as a set of sequentially correlated 3D layers displaced in the wave propagation direction. The statistical characteristics of refractive index fluctuations are described in terms of the von Karman power spectrum density. In the representation of these 3D layers by corresponding phase screens, the geometrical optics approximation is used.     

一种基于3D打印技术的结构型宽频吸波超材料

设计了一种三层宽频吸波超材料,其表层和中间层为单元尺寸不同的周期阵列结构,底层为吸波平板结构,优化后的总厚度仅为4.7 mm,并采用三维(3D)打印技术成功制备了该吸波超材料.吸波体反射率测试结果表明,在电磁波垂直入射条件下,宽频吸收峰分别出现在5.3和14.1 GHz,两峰叠加使得其在4-18 GHz频率范围内反射损耗均小于-10 dB.采用S参数反演法计算了每一层的等效电磁参数,并利用多层结构反射率公式推导得出该模型的理论反射率,理论计算结果与实测结果基本一致.通过研究能量损耗、电场分布和磁场分布揭示了吸波机理,分析表明该吸波体的宽频吸收效果源于三层结构产生的吸收带宽叠加.本文提出的吸波超材料具有良好的宽频吸收效果,尤其在低频范围吸波性能较佳,结合3D打印快速成型技术,可获得结构精细的三层吸波超材料,具有重要的实际应用价值和广阔的应用前景.     

Numerical calculation of the magnetic field and magnetic moment of ferromagnetic bodies with a complex spatial configuration

A method for numerical calculation of the magnetic field and magnetic moment of 3D ferromagnetic objects is described using the method of finite volume and absorbing boundary conditions. The magnetic moments and magnetic field of some ferromagnetic systems imitating various objects are calculated. It is shown that the configuration of ferromagnetic structures consisting of various combinations of rods determines their magnetic moments.     

Surface impedance matrices to model the propagation in multilayered media

The surface impedance matrices in stratified plates made of fluid layers and/or anisotropic absorbing solid layers link the particle velocity field to the stress field at any interface. A surface impedance matrix represents the impedance at a given interface of all the layers located between that interface and one boundary of the medium. For each interface, there are two surface impedance matrices, each one corresponding to one boundary. This notion simplifies the computations of the modal solutions. The number of elements in the matrices involved in the computations is divided by a factor of four in comparison to usual matrix methods. This paper describes the method and presents examples to illustrate its interests and its efficiency where other techniques fail, for instance in the case of modes possessing energy in layers embedded in the structure.     

Optical measurements of field-induced phenomena of the magnetic phase transition in quasi 2D MnS layers grown by MBE

We used a sensitive optical method to study the magnetic phase transition of antiferromagnetic MnS layers. The method is applicable for very small numbers of spins, e.g., thin single layers. We studied the optical and magnetic properties of MnS layers using the internal optical transition of the manganese 3d-shell. The temperature dependence of the Mn-emission exhibits a pronounced minimum revealing the para- to anti-ferromagnetic phase transition. The MnS layers were grown by molecular beam epitaxy, embedded between diamagnetic ZnSe cladding layers on a (100)-GaAs substrate. It was found that the Néel-temperature itself is influenced by the biaxial strain and can be changed in an external magnetic field in case of quasi 2D MnS-layers. The phase diagram reveals a weak Ising like anisotropic contribution in case of a 1.8 nm thin layer, whereas a 8.6 nm thick layer behaves still like an ideal isotropic Heisenberg system.     

Diffraction by extremely small holes in thin absorbing and transparent screens and by disks

The generalization of Bethe-Bouwkamp diffraction theory for the case of diffraction by the hole in absorbing and transparent thin screens and by the disks is proposed. Duality transformation of Bethe-Bouwkamp solution is implemented. The approximate analytical expressions are found for the near electromagnetic diffraction field for extremely small hole or disk.     

Multilayer gyrotropic waveguide structures with azimuthal magnetization

An algorithm to obtain the dispersion equation and to determine the field configuration in the case of an arbitrary number of layers is developed by the successive joining of tangential components of the eigenwave electromagnetic field of a regular waveguide with concentric azimuthally magnetized gyrotropic layers. The electrical and magnetic field components in each layer are represented in the form of a linear combination of four particular analytic solutions of the system of generalized wave equations. By using an electronic computer the phase and dissipation characteristics of circular and coaxial waveguides with azimuthally magnetized ferrite-dielectric layers are computed for variations in their material and geometric parameters.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 24–28, April, 1981.     

Magnetization reversal process at atomic scale in systems with itinerant electrons

The magnetic response of itinerant electrons systems to an external magnetic field is investigated on the basis of a microscopic Hamiltonian from which the spin-polarized electronic structure is determined. The magnetic moment and grand thermodynamic potential of the d-electronic subsystem on a particular atomic site in the presence of the external field are calculated as a function of the moment's orientation for fixed electron configuration of its local environment. Self-consistent magnetic solutions strongly depend on the d-electron number, determined by the position of the d level relative to the Fermi energy. For parameters corresponding to α-Fe, two branches of self-consistent solutions with high and low magnetic moments are found. For parameters corresponding to bulk Cr, a Fe impurity in the Cr matrix and a Cr impurity in the Fe matrix, there are only low-spin solutions. The theory is also applied for describing magnetization reversal processes in exchange spring magnets. A slab of Fe was considered as a soft magnetic layer. The influence of the hard magnet is modeled by the inclusion of an external magnetic field applied to the interface Fe layers. The dependence of the hysteresis loop on the thickness of the Fe slab and on the value of the interface field is investigated.     

Zur Theorie der Bewegung geladener Teilchen in richtungskonstanten Magnetfeldern exponentieller Zeitabhängigkeit. I. Allgemeine Theorie und Einschaltvorgang

The general solution of the equations of motion for a charged particle in a magnetic field is given for the following case: the spatially homogeneous magnetic field having a constant direction is a superposition of a field constant in time and one decreasing exponentially in time; taken into account is the influence of the electric field induced by the time dependent magnetic field and a friction force proportional to the particle velocity. The higher transcendental functions appearing in the exact solution are approximated in various ways in dependence on the values of the argument and parameters. The important case of a switching process without a friction force is investigated in detail. The higher transcendential functions can be approximated by simplier functions in such a way, that the solutions for the switching process, valid for all times, differ from the solutions in the case of a linear increasing magnetic field only by factors consisting of elementary functions. Approximated formulae of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle. The particle orbits are classified and their dependence on the initial values and parameters of the magnetic fields is studied. A comparison between our results and a rectangular variation of the field shows that the latter is not a good approximation for a really exponential increasing field. Finally a detailed investigation shows that the electric field induced by the time dependent magnetic field has an important influence on the particle motion.     

Magnetic Branes in Brans-Dicke-Maxwell Theory

We present a new class of magnetic brane solutions in (n+1)-dimensional Brans-Dicke-Maxwell theory in the presence of a quadratic potential for the scalar field. These solutions are neither asymptotically flat nor (anti)-de Sitter. Our strategy for constructing these solutions is applying a conformal transformation to the corresponding solutions in dilaton gravity. This class of solutions represents a spacetime with a longitudinal magnetic field generated by a static brane. They have no curvature singularity and no horizons but have a conic geometry with a deficit angle δ. We generalize this class of solutions to the case of spinning magnetic brane with all rotation parameters. We also use the counterterm method and calculate the conserved quantities of the solutions.     

Efficient Analysis of Millimeter Wave Circuit Using Numerical Calibration Technique

In this paper, A numerical technique, called short-open calibration (SOC), in conjunction with edge-based finite element method (FEM) is employed to analyze millimeter wave circuit that can be segmented into two distinct section: static model of feedlines and dynamic model of circuit discontinuity. The derivation of reflection coefficient of 3D discontinuities is arranged in two steps. In the first step, this SOC technique is incorporated into the FEM for mesh truncation of computaional domain. In this way, much faster convergence is achieved for large-sparse linear matrix equations from FEM by this termination than by perfectly matching layers (PML). The field distribution of the dominated mode in uniform feedlines and entire circuit is obtained individually by exciting a pair of even and odd impressed voltages along the struture. In step two, Scattering parameters based on the voltages and current defintion is calculated by integral of electric and magnetic fields. Numerical solutions for a class of planar circuit discontuities are very well compared with those published in the available literatures.     

An FDTD absorbing boundary condition for anisotropic media based on NPML

Based on the nearly perfectly matched layer (NPML) theory, a finite-difference time-domain (FDTD) absorbing boundary condition (ABC) is presented for truncating three-dimensional (3-D) anisotropic medium. In the proposed technique, the complex coordinate stretching in the NPML scheme and the spatial interpolation method are employed. The associated ABC formulations have the advantage of simplicity in the FDTD implementations. The radiation fields of an electric dipole in anisotropic media are calculated using the presented ABC. The results are numerically verified by the comparison with the reference solutions. Furthermore, in order to clearly show the effective absorbing performance of the proposed method, the reflection coefficient and time-dependent relative error for different layers NPML absorbing boundary are also simulated.     

Waveguide modes of 1D photonic crystals in a transverse magnetic field

We analyze waveguide modes in 1D photonic crystals containing layers magnetized in the plane. It is shown that the magnetooptical nonreciprocity effect emerges in such structures during the propagation of waveguide modes along the layers and perpendicularly to the magnetization. This effect involves a change in the phase velocity of the mode upon reversal of the direction of magnetization. Comparison of the effects in a nonmagnetic photonic crystal with an additional magnetic layer and in a photonic crystal with magnetic layers shows that the magnitude of this effect is several times larger in the former case in spite of the fact that the electromagnetic field of the modes in the latter case is localized in magnetic regions more strongly. This is associated with asymmetry of the dielectric layers contacting with the magnetic layer in the former case. This effect is important for controlling waveguide structure modes with the help of an external magnetic field.     

A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields

Using the Nikiforov–Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field inside dot and Aharonov–Bohm (AB) field inside a pseudodot. The exact solutions for energy eigenvalues and wave functions are computed as functions of the chemical potential parameters, applied magnetic field strength, AB flux field, magnetic quantum number and temperature. Analytical expression for the light interband absorption coefficient and absorption threshold frequency are found as functions of applied magnetic field and geometrical size of quantum pseudodot. The temperature dependence energy levels for GaAs semiconductor are also calculated.     

Two-dimensional transport behavior in PbTeBi superlattices

We report on the 2D charge transport behavior observed in PbTeBi superlattice films. The logarithmic behavior with temperature and magnetic field was observed for the samples having the thickness of the PbTe layers larger than 45 A. This 2D behavior disappeared with annealing and, eventually, the sample showed a 3D nature for the fully annealed case.     

Prediction of radiative heat transfer in 3D complex geometries using the unstructured control volume finite element method

In this paper, a 3D algorithm for the treatment of radiative heat transfer in emitting, absorbing, and scattering media is developed. The numerical approach is based on the utilization of the unstructured control volume finite element method (CVFEM) which, to the knowledge of the authors, is applied for the first time to simulate radiative heat transfer in participated media confined in 3D complex geometries. This simulation makes simultaneously the use of the merits of both the finite element method and the control volume method. Unstructured 3D triangular element grids are employed in the spatial discretization and azimuthal discretization strategy is employed in the angular discretization. The general discretization equation is presented and solved by the conditioned conjugate gradient squared method (CCGS). In order to test the efficiency of the developed method, several 3D complex geometries including a hexahedral enclosure, a 3D equilateral triangular enclosure, a 3D L-shaped enclosure and 3D elliptical enclosure are examined. The results are compared with the exact solutions or published references and the accuracy obtained in each case is shown to be highly satisfactory. Moreover, this approach required a less CPU time and iterations compared with those of even parity formulation of the discrete ordinates method.     

Electronic states of the icosahedral quasiperiodic systems in magnetic fields

The electronic properties of the icosahedral quasiperiodic system in a tile-dependent or uniform magnetic field is studied by quasi-Bloch scheme and the general solutions are obtained for the electronic states. The behavior of the three-dimensional (3D) non-interacting electrons in an icosahedral quasiperiodic system may be treated as the projection of that of the non-interacting pseudo-electrons in 6D. In the presence of the tile-dependent magnetic field, the non-interacting electrons are quasi-Bloch electrons, while they are partial quasi-Bloch electrons when the magnetic field is uniform.     

Zur Theorie der Bewegung geladener Teilchen in richtungskonstanten Magnetfeldern exponentieller Zeitabhängigkeit. III. Allgemeine Schaltprozesse

The motion of a charged particle in a magnetic field is calculated for the following case: the spatially homogeneous magnetic field having a constant direction is a superposition of a field constant in time and one decreasing exponentially in time; taken into account is the influence of the electric field induced by the time dependent magnetic field and a friction force proportional to the particle velocity. The higher transcendental functions appearing in the exact solutions are approximated in various ways in dependence on the values of argument and parameters. In this manner approximated formulae of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle, and the domain of validity of these formulae is determined. The particle orbits are classified, and their dependence on the initial values, parameters of the magnetic field and on the magnitude of the friction force is studied. A comparison between our results and a rectangular variation of the field is given. It is shown that the electric field induced by the time dependent magnetic field has an important influence on the particle motion.     

High-frequency absorption properties of gallium weakly doped barium hexaferrites

The BaFe_12-xGa_xO₁₉ (x?2O₃ additive in the amount of 3?wt% was applied. The features of crystal structure and unit cell parameters were refined using powder X-ray diffraction at 300?K. It is shown that with the substitution level increase the parameters of unit cell monotonically decrease. The magnetisation and susceptibility versus temperature and field for these solid solutions were investigated by the vibration magnetometry method. The concentration dependence of the main magnetic parameters is constructed. It is shown that with the substitution level increase the magnetic parameters monotonically decrease. The microwave properties of the samples including the external magnetic bias field are also investigated at 300?K. It is shown that with the increase of Ga³⁺ concentration from x?=?0.1 to x?=?0.6 the frequency value of natural ferromagnetic resonance (NFR) decreases in the beginning, and at further increase in concentration up to x?=?1.2 it increases again. With the increase in Ga³⁺ concentration, the line width of the NFR increases that indicates the increase of frequency range where there is an intensive absorption of electromagnetic radiation (EMR). At the same time, the peak amplitude of the resonant curve changes slightly. The frequency shift of NFR in the external magnetic bias field takes place more intensively for the samples with small Ga³⁺ concentration. It is shown the prospects of use of the Ga-substituted barium hexagonal ferrite as the material effectively absorbing the high-frequency EMR.     

Modeling of magnetic field perturbations in electrophysical devices due to the steel reinforcement of buildings

We have proposed an effective method for modeling the steel reinforcement in the buildings for electrophysical devices to take into account the magnetic field perturbation caused by the magnetization of bars. The reinforcement lattice has been represented by one or several layers of a homogeneous isotropic material with preliminarily calculated equivalent (averaged) magnetic properties. Examples of calculating these magnetic properties have been considered using a simplified analytic approach, as well as by the numerical simulation of the magnetic field in a 3D cell of a periodic reinforcement lattice. The efficiency of the method has been demonstrated based on an important practical example of simulating the perturbation of a uniform magnetic field caused by the reinforced slab. The results have been compared with the simulation data based on different approaches.