Fields In Anisotropic Media Research Articles

Time-reversed electromagnetic fields in anisotropic media.

Electromagnetic time reversal is commonly used for field imaging and focusing. This Letter builds upon the concept of the time-reversal cavity, which constitutes the main theoretical framework of time reversal theory. We study the behavior of the fields using modern methods of mathematical physics involving Colombeau generalized functions. This approach allows for a direct expression of time-reversed electric and magnetic fields in anisotropic time-reversal-invariant and nonreciprocal media. Moreover, the results hold for any arbitrary localized source and can readily be applied beyond the dipole approximation. Finally, a general result allows the prediction of the quality of focusing of the time-reversed fields as a function of the electrical permittivity and the magnetic permeability tensors in homogeneous anisotropic media, which contributes to the understanding of time reversal in complex media such as super-resolution enabling metamaterials.

MEMORY RESPONSE ON THERMOELASTIC BEHAVIOUR WITH TEMPERATURE DEPENDENT MATERIAL MODULI UNDER MECHANICAL STRIP LOAD

Temperature of the medium has a significant impact on the deformation and stress distribution into the medium. Material moduli is another key component that determines the deformation of the structural element. The present paper deals with the thermal memory response on stress and temperature fields in an isotropic medium. The material moduli of the medium are considered to be varying with temperature. Consequently, the classical heat conduction law is replaced by the memory dependent generalized theory of heat conduction. Analytical solutions of the field functions are obtained in the integral transform domain. The variations of the field functions in the space-time coordinate system are displayed graphically for different empirical constants and kernel functions.

Solving the eikonal equation for compressional and shear waves in anisotropic media using peridynamic differential operator

SUMMARY Traveltimes of compressional (P) and shear (S) waves have proven essential in many earthquake and exploration seismology applications. An accurate and efficient traveltime computation for P and S waves is crucial for the success of these applications. However, solving the eikonal equation with a complex phase velocity field in anisotropic media is challenging. The eikonal equation is a first-order nonlinear hyperbolic partial differential equation. It represents the high-frequency asymptotic approximation of the wave equation. The fast marching and sweeping methods are commonly used due to their efficiency in numerically solving the eikonal equation. However, these methods suffer from numerical inaccuracy in anisotropic media with sharp heterogeneity, irregular surface topography and complex phase velocity fields. This study presents a new method for the solution of the eikonal equation by employing the peridynamic differential operator (PDDO). The PDDO provides the non-local form of the eikonal equation by introducing an internal length parameter (horizon) and a weight function with directional non-locality. The operator is immune to discontinuities in the form of sharp changes in field or model variables and invokes the direction of traveltime in a consistent manner. The weight function controls the strength of association among points within the horizon. Solutions are constructed in a consistent manner without upwind assumptions through simple discretization. The robustness of this approach is established by considering different types of eikonal equations on complex velocity models in anisotropic media. The examples demonstrate its unconditional numerical stability and results compare well with the reference solutions.

Covariant formulation of electrodynamics in isotropic media

The equations of electromagnetic fields in a medium are usually written in the rest frame of the medium. We outline a method of generalizing the discussion to arbitrary inertial frames. In the discussion, we also include the possibility that the medium is optically active, a possibility that is often overlooked in discussions of electromagnetic fields in an isotropic medium.

Optimization of piezotransducer dimensions for quasicollinear paratellurite AOTF

The method of quasicollinear acousto-optic tunable filters (AOTFs) piezoelectric transducer dimensions optimization is presented. The AOTFs with large interaction length apply the bulk acoustic wave (BAW) reflection from the input optical facet. Optimization is based on spectral approach to simulation of the BAW field in anisotropic media and Raman–Nath equations numerically solved for the inhomogeneous acoustic field. It was found that variation of the transducer dimensions can minimize RF power consumption of the AOTF. Comparison of the optimized transducer dimensions with those commonly used in quasicollinear paratellurite AOTFs showed that it is possible to improve the AOTF energy efficiency in about 2 times. It was shown that acoustic field simulation results obtained for one AOTF geometry can be applied to the other geometries but for equivalent frequency providing the same ultrasound beam ray spectrum width. It was also shown that when choosing the quasicollinear AOTF with reflection geometry, one should not rely only on the AO figure of merit value, since the energy efficiency of such AOTF type will be determined by the product of the AO figure of merit and the AOTF efficiency, which takes into account the change in the acoustic beam width in the reflection process. The results aim at improving the design of AOTFs for ultrashort laser pulse shaping.

Finite Element Simulation of 3-D Marine Controlled Source Electromagnetic Fields in Anisotropic Media with Unstructured Tetrahedral Grids

Marine controlled-source electromagnetic (CSEM) method has proved to be a powerful tool and found its increasing applications for offshore resource exploration and tectonic studies. However, bathymetric variations and anisotropic structures encountered in practical measurements have posed challenges for reliable interpretation of marine CSEM data collected in increasingly complex geologic settings. In this study, we present a Finite element (FE) based forward algorithm for simulating 3-D marine CSEM responses in geologic settings characterized with rough bathymetry and electrical anisotropy. Unstructured tetrahedral meshes are employed to permit precise descriptions of arbitrary seafloor topography. After validating the accuracy of the algorithm, we investigate the effects of bathymetric variations and complicated electric anisotropy separately and jointly on marine CSEM responses. Numerical results have demonstrated that both the bathymetry and electrical anisotropy can cause significant distortions on marine CSEM responses, but to different extent. The effects of full electrical anisotropy and bathymetry have to be taken into consideration for reliable interpretations of marine CSEM data in practice.

A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

Purpose The purpose of this paper is to calculate the time-dependent electric and magnetic fields in anisotropic media with a general structure of anisotropy by symbolic computations. Design/methodology/approach An analytical approach for the computation of the time-dependent electric and magnetic fields is suggested. This approach consists of the following. Input data, electric and magnetic fields are presented in polynomial form.The exact formulae for electric and magnetic fields are computed by symbolic transformations in Maple. Findings The time-dependent second order partial differential equations for the electric and magnetic fields with polynomial data were obtained from Maxwell's equations when the current density is presented in a polynomial form with respect to space variables in a bounded region of three dimensional space. The exact solutions of obtained equations were computed symbolically using Maple. Originality/value The obtained polynomial solutions do not contain errors if data are polynomials. We have shown that these solutions are approximate solutions with good accuracy for data which are approximated by polynomials in a bounded region of 3D space.

Simultaneous computation of seismic slowness paths and the traveltime field in anisotropic media

Simultaneous computation of seismic slowness paths and the traveltime field in anisotropic media

Analytical solution of electromagnetic scattering by a general gyrotropic sphere

Electromagnetic scattering by a general gyrotropic sphere is discussed in terms of spherical vector wave functions. From the source-free Maxwell's equations and Fourier transform, the eigenvalue and eigenvectors of the electric field in a source-free gyrotropic medium can be obtained. The electromagnetic fields may then be obtained in terms of spherical vector wave functions in a source-free gyrotropic medium. Applying the continuous boundary conditions of electromagnetic fields on the surface between the free space and gyrotropic sphere, the spectral coefficients of the transmitted fields inside a gyrotropic sphere and the scattered fields in an isotropic medium (free space) can be obtained exactly by expanding spherical vector wave eigenfunctions. Numerical results are provided for some representative cases. Results from this study and those from an adaptive integral method are in agreement.

Crowdions in elasticity theory

A crowdion, which is a defect in a crystal structure, is described within the mechanics of continuous linear elastic medium. In the continual approximation, the crowdion is defined, analogously with dislocations, as a singular “carrier” of the plastic deformation of the medium and as a source of elastic deformation. The geometric and force parameters of this singularity are associated with the characteristics of the lattice crowdion. The structure of the strain and stress fields of a crowdion in an anisotropic elastic continuum is described in the general form, and explicit expressions for these fields in an isotropic medium are derived.

Integrability of anN-coupled nonlinear Schrödinger system for polarized optical waves in an isotropic medium via symbolic computation

Considering the simultaneous propagation of multicomponent fields in an isotropic medium, an N-coupled nonlinear Schrödinger system with the self-phase modulation, cross-phase modulation, and energy exchange terms is investigated in this paper. First, via symbolic computation, the Painlevé singularity structure analysis shows that such a system admits the Painlevé property. Then, with the Ablowitz-Kaup-Newell-Segur scheme, the linear eigenvalue problem (Lax pair) associated with this model is constructed in the frame of the block matrices. With the Hirota bilinear method, the bright one- and two-soliton solutions of this system are presented. In addition, the bright multisoliton solutions of the system for N=2 are straightforwardly derived by the linear superposition of soliton solutions of two independent scalar nonlinear Schrödinger equations. Furthermore, through the analysis for the soliton solutions, the corresponding propagation behavior and applications for soliton pulses in nonlinear optical fibers are considered. Finally, three significant conserved quantities, i.e., energy, momentum, and Hamiltonian, are also given.

An improved mesh generation scheme for the wavefront construction method

Wavefront construction is an effective tool for the rapid calculation of ray fields in anisotropic media. The method explicitly tracks the propagation of a wavefront through a model, mapping it to a computational mesh that is interpolated when accuracy criteria based on paraxial ray methods are violated. Takeoff angles are used often to define the initial ray directions, but uniform sampling in the two angles leads to oversampling of the ray field in the direction of the axis. Such sampling can lead also to numerical instability associated with vanishing derivatives with respect to the azimuthal angle. We suggest a new wavefront mesh definition using the cubed-sphere mesh, which is a coordinate system used to solve partial differential equations in spherical geometries. When using this mesh, ray directions are assigned by mapping points on a regular discretization of the faces of a cube surrounding the source to corresponding rays. This scheme produces a nearly uniform distribution of rays with minimal effort and using the cubed-sphere coordinates as ray parameters to calculate partial derivatives completely eliminates the singularities that arise when takeoff angles are used as ray parameters. Numerical results for quantities related to seismic amplitudes confirm that this new mesh does provide more stable and reliable results.

A COUPLED-MODE THEORY-BASED ANALYSIS OF COUPLED MICROSTRIP LINES ON A FERRITE SUBSTRATE - ABSTRACT

Presented herein is a coupled-mode formulation for coupled microstrip lines on a magnetized ferrite substrate. The formulation discussed here is an extension of the coupled-mode theory for microstrip lines on an isotropic substrate. Since the magnetized ferrite exhibits a biaxial anisotropy in its permeability, the guided-wave fields in the magnetized ferrite are not subject to the conventional reciprocity relation for fields in an isotropic medium. Thus, a generalized reciprocity relation is first derived from two sets of guided-wave fields, which propagate in ferrite magnetized transversely along the strip surface. The reciprocity relation is then used to derive coupled-mode equations for coupled microstrip lines on a ferrite substrate. As a basic numerical example, the new formulation is applied to two coupled microstrip lines on a ferrite substrate.

Semi-analytical elastic wave-field modeling applied to arbitrarily oriented orthotropic media

Three-dimensional elastic wave-field calculation is addressed for the case of orthotropic materials with arbitrary spatial orientation. Based on a mathematical formulation involving Green’s dyadic displacement tensor function, appropriate evaluation yields a representation of the displacement vector of transducer wave fields in anisotropic media which is convenient for effective numerical computation. With respect to bulk wave propagation, the numerical evaluation of Green’s dyadic function is circumvented by applying a reciprocity-based approach, which is valid in the (point source) far field. The presented formulation involves characteristic quantities obtained from plane-wave theory and appears as a point-source superposition representation including the respective point-source directivities. Thus, it is in the same form as a corresponding formulation for scattered elastic wave fields presented previously [M. Spies, J. Acoust. Soc. Am. 107, 2755–2759 (2000)]. Focusing on orthotropic composite materials, numerical evaluation examples are presented for ultrasonic tranducer field patterns and time-dependent radio frequency (rf)-pulse propagation.

Energy considerations in vector magnetization models

Scalar magnetization model energy calculations, which are useful in calculating energy losses in open magnetization processes, are extended here to vector models. The energy loss is calculated as the difference between the energy input to the magnetic medium and the change in energy stored in the locally reversible component of the total magnetization. It is shown that under rotating magnetizing processes, the energy loss decreases as the material is saturated. For smaller rotating fields in anisotropic media, the magnetization lies between the applied field and the easy axis and the energy loss is not constant with rotation even if the magnitude of the field is constant.

Generalized Helmholtz Decomposition and Static Electromagnetics

The well-known decomposition of vector fields to solenoidal and irrotational parts, known as the Helmholtz decomposition, is generalized in terms of more general linear operators involving two arbitrary symmetric, positive-definite and complete (non-singular) dyadics. It is seen that, in terms of the generalized decomposition, potential expansions for the static electric and magnetic fields in anisotropic media can be formed in a straightforward manner. The decomposition theorem is further generalized in a form applicable to the static electromagnetic fields in the most general linear medium (bi-anisotropic medium) characterized by four medium dyadics. In this case, the decomposition theorem and potential expressions are presented in a compact form in terms of six-vectors.

Seismic radiation from explosively loaded cavities in isotropic and transversely isotropic media

Abstract We analyze the influence of cavity shape on far-field seismic-wave radiation from small explosion sources in isotropic and transversely isotropic media using the indirect boundary-element method (BEM). The analysis utilizes two possible mathematical models for the pressure fields generated by the explosion in the acoustic medium inside the cavity. One simple model for the source is a volume injection (explosion) point source inside the cavity, which generates a pressure field that arrives approximately instantaneously at each point on the cavity wall. The amplitude of the field decays at a rate inversely proportional to propagation distance. We use this model to compare results with finite-difference solutions, and the test confirms the accuracy of the BEM implementation. Strong compressional and shear signals propagate into the far-field from the source cavity, and the compressional-wave amplitude depends strongly on direction of propagation. The behavior is similar at frequencies up to 200 Hz, including those typical of regional seismic-wave propagation (1 to 10 Hz). A second model of the source, one that has been applied in previous analytical and numerical work, is to assume that the explosion will instantaneously and uniformly pressurize the source cavity. This approach yields a radiation pattern that is very different from the point source model. The compressional-wave radiation patterns have a large variation in signal strength and very strong shear waves when frequencies up to 200 Hz are included, but seismograms computed for frequency ranges of interest in regional wave propagation (around 1 Hz) have a nearly isotropic compressional-wave radiation pattern and a much smaller shear wave. This shear wave is largest for long, tunnel-like cavities or short, disklike cavities. When the cavity is located in a transversely isotropic medium, quasi-shear waves are generated, but, for the media we consider, their magnitude decreases for long, tunnel-like cavities and is larger for more equidimensional cavities. These somewhat counterintuitive results show that anisotropy can actually cause a radiation pattern to appear more isotropic than the corresponding wave fields in an isotropic medium.

(3+1)-dimensional optical soliton dragging logic.

A review of the varieties of optical solitons and their possible interactions, combined with the requirements for a robust digital logic gate motivate the use of (3+1)-dimensional optical solitons (light bullets) as information carriers and soliton dragging gates as switches. Soliton dragging is the asymmetric interaction between two initially overlapping, orthogonally polarized solitons propagating at different angles so that a weak signal soliton can drag a strong pump out of a spatial aperture, thereby implementing a phase-insensitive, high-contrast, logical switch with gain. Light bullets may be an ideal choice for use in these soliton dragging gates but are unstable in Kerr media, but stable (for sufficient pulse energy) in materials with physically reasonable saturating or negative ${\mathit{n}}_{4}$${\mathit{I}}^{2}$ nonlinearities. An efficient technique for the propagation of spherically symmetric (3+1)-dimensional field envelopes is developed and used to verify the theoretical stability predictions. A split-step numerical algorithm that models the propagation and phase-independent interaction of arbitrary (3+1)-dimensional, vector e.m. fields in anisotropic media with up to sixth-order tensor nonlinearities is developed and used to demonstrate the features of the gates. NOT and single-stage, two- and four-input NOR light-bullet dragging logic gates are simulated and their performance over a range of operating parameters is presented. It is shown that, with material parameters in the range of those currently available from highly nonlinear organic crystals, high-contrast, all-optical, soliton logic gates with a clock rate greater than 1 THz, latency of a few picoseconds, and switching energy of 25 pJ may be possible.

Anisotropic FDFD computed on conformal meshes

An algorithm is presented to compute the scattered field in anisotropic media, using finite differences (FD) applied to grid points on a cylindrical unconstrained triangular mesh, illuminated by obliquely incident plane waves. The material boundaries and electromagnetic characteristics are prescribed in x-y coordinates only, independent of z. The permittivity and permeability are tensors, with non-zero xy and yx elements, and with each element also independent of z. The ability to analyze arbitrarily polarized waves incident from any direction in space gives the proposed method an advantage over previously reported techniques of computing the fields in the presence of anisotropy.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

WKBJ seismogram theory in anisotropic media

The Wentzel, Kramers, Brillouin, and Jeffreys (WKBJ) seismogram theory has proved useful for computing impulsive waveforms in vertically inhomogeneous media. In this article, the WKBJ seismogram theory is applied to compute the displacement fields in anisotropic media. Several numerical examples of transversely isotropic media are presented with a particular emphasis on the waveforms at and near cusps. Synthetic seismograms are computed for a line as well as for a point source including those regions of space where shear wave triplication occurs. The waveform of the reverse branch is the Hilbert transform of the forward branches. For a line source, the region between the forward branches and the reverse branch carries no energy, and is the region of complete silence known as a lacuna. Diffracted signals due to cusps on the shear wave surface are also observed. The waveform of the diffracted signal depends upon the waveform of the branch with dominant energy at the cusp.