Simulation of Electromagnetic Wave Logging Response in Deviated Wells Based on Vector Finite Element Method

The vector finite element method of tetrahedral elements is used to model 3D electromagnetic wave logging response. The tangential component of the vector field at the mesh edges is used as a degree of freedom to overcome the shortcomings of node-based finite element methods. The algorithm can simulate inhomogeneous media with arbitrary distribution of conductivity and magnetic permeability. The electromagnetic response of well logging tools are studied in dipping bed layers with the borehole and invasion included. In order to simulate realistic logging tools, we take the transmitter antennas consisting of circular wire loops instead of magnetic dipoles. We also investigate the apparent resistivity of inhomogeneous formation for different dip angles.     

On uniqueness of solution of a reverse problem of magnetic location

An analysis of solution uniqueness for a problem of magnetic dipole localization based on known values of magnetic field strength vectors at two points is presented. It is shown that a usage of two triples (pairs) of sensors is sufficient to solve a 3D (2D) problem of arbitrary magnetic dipole localization with a satisfactory number of crude errors.     

Effective dielectric constant of two-dimensional photonic crystals in optical bands

By using the Fourier expansion method, we have developed an approach to calculate the effective dielectric index of a two-dimensional photonic crystal. The approach is very general: it can take into account various Bravais lattice structure as well as arbitrary spatial variation of the dielectric index. It has been found that near a nondegenerate frequency ω_n(Γ) at Γ point, the transverse magnetic (TM) mode is ordinary, as it is independent of the propagation direction, whereas in general the transverse electric (TE) mode depends on the propagation direction, it is extraordinary. Therefore, a two-dimensional photonic crystal can always be described by an effective dielectric index for TM mode near the nondegenerate frequency ω_n(Γ). However, the TE mode is much more complicated unless the lattice structure is highly symmetric. Moreover, a two-dimensional square photonic crystal has been identified as an effective birefringent crystal having two negative refractive indexes from the perspective of Snell's law.     

General magnetostatic shape-shape interaction forces and torques

Expressions for the magnetostatic interaction force and torque between two magnetic objects of arbitrary shape are derived within the shape amplitude formalism. A generalized force is derived as the gradient of the magnetometric tensor field, which is the convolution of the cross-correlation of the object shapes with the dipolar tensor field. Expressions for the mechanical and magnetic torques are also derived in terms of the magnetometric tensor field. Expressions suitable for numerical evaluation are given as finite Fourier summations. Example computations are given for the interactions between pairs of uniformly magnetized spheres (for which analytical results are compared to numerical results), cubes, octahedra, tetrahedra, and cuboctahedra. The accuracy of the derived numerical relations for energy, force, and torques is of the order of 0.1% for object spacings smaller than the object dimensions.     

Non-perturbative approach to high-index-contrast variations in electromagnetic systems

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.     

Investigation of one-dimensional photonic crystals composed of dispersive materials

One-dimensional photonic crystals (1DPCs) composed of dispersive materials (including negative refractive index materials, negative μ materials, and negative ? materials) are proposed. The dependence of the band gaps on the angle of incidence and thickness scale are investigated by using the transfer matrix method. Simulation results show that the band gaps of these dispersive material 1DPC are insensitive to the thickness scale. The defect modes of these doped 1DPCs behave specially when the thickness of the defect layer, the angle of incidence and the thickness scale of PC change.     

Copropagation of two pulses of different frequencies and modulation instabilities induced by cross-phase modulation in metamaterials

Nonlinear coupled equations describing the copropagation of two light pulses of different central frequencies in metamaterials (MMs) are derived. Based on the derived equations and the Drude model for dispersive MMs, the modulation instabilities (MIs) induced by cross-phase modulation (XPM) for different combination of the signs of refractive index experienced by the two optical pulses, respectively, are analyzed. It is shown that, in the absence of group-velocity mismatch, the property of MI only depends on the sign of group-velocity dispersion the two pulses experience, irrespective of the sign of refractive index. The group-velocity mismatch plays an important role in the occurrence of MI, especially when the central frequencies of the two pulses near the electric or magnetic plasma frequency of the MM. The theoretical results are confirmed by numerical simulations.     

Improved amplitude–frequency characteristics for T-splitter photonic crystal waveguides in terahertz regime

Based on the plane-wave expansion method, we calculate TE/TM gaps of 2-D photonic crystals (PCs) with typical square lattices composed of the silicon rods in air. Using the finite-difference time-domain method, we simulate the electromagnetic field distribution of THz waves in photonic crystals T-splitters. By the improved T-splitter with a rod in the junction, we achieved the amplitude–frequency characteristics of a pass band of 84% from 1.12 to 1.22 THz and surpassed by 76% the amplitude consistency of common T-splitters. And using the finite-difference time-domain method, we demonstrated that the improved T-splitter excels a common T-splitter in the degree of separation between the two output ports. These results provide a useful guide and a theoretical basis for the developments of THz functional components.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Effective chiral magnetic currents, topological magnetic charges, and microwave vortices in a cavity with an enclosed ferrite disk

In microwaves, a TE-polarized rectangular-waveguide resonator with an inserted thin ferrite disk gives an example of a nonintegrable system. The interplay of reflection and transmission at the disk interfaces together with the material gyrotropy effect gives rise to whirlpool-like electromagnetic vortices in the proximity of the ferromagnetic resonance. Based on numerical simulation, we show that a character of microwave vortices in a cavity can be analyzed by means of consideration of equivalent magnetic currents. Maxwell equations allows introduction of a magnetic current as a source of the electromagnetic field. Specifically, we found that in such nonintegrable structures, magnetic gyrotropy and geometrical factors leads to the effect of symmetry breaking resulting in effective chiral magnetic currents and topological magnetic charges. As an intriguing fact, one can observe precessing behavior of the electric-dipole polarization inside a ferrite disk.     

Photonic band gap of one-dimensional periodic structure containing dispersive left-handed metamaterials

Band structures of one-dimensional(1D)photonic crystals(PCs)containing dispersive left-handed metamaterials are studied theoretically.The results show that the structure possesses a type of photonic band gap originating from total internal reflection(TIR).In contrast to photonic band gaps corresponding to zero average refractive index and zero phase.the TIR gap exhibits sharp angular effect and has no polarization effect.It should also be noted that band structures of transverse electric(TE) and transverse magnetic(TM) mode waves are exactly the same in the PCs we studied.     

Dispersive medium’s normal coupled modes and low threshold optical bistability in a symmetric one-dimensional photonic crystal

We present a detailed study of the dispersive medium’s normal coupled modes in a symmetric one-dimensional photonic crystals (1D PCs). The splitting, homogeneous broadening effect, and the detuning effect of the normal coupled modes can be well controlled by adjusting the parameters of the dispersive medium. The bistable behavior of the PCs with Kerr medium is also investigated and it is found that the threshold intensity of nonlinear optical bistability (OB) of 1D PCs with dispersive medium is much lower than that of structure without dispersive medium. The threshold intensity is strikingly sensitive to the coupling strength of the dispersive medium.     

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.     

Power frequency magnetic properties and aging of 4130 steel

Cr–Mo steels are utilized in large, high-speed rotating machines where the mechanical stress requirements limit available soft magnetic laminate choices. Because this is currently a niche application, the magnetic properties of these steels are relatively undocumented. This paper presents the magnetic hysteresis behavior of a quenched and tempered 4130 steel at alternating frequencies up to 1200 Hz and temperatures up to 100 °C. The high coercivities and core losses are contrasted with a 3.2%Si–Fe alloy. “Aging” of this behavior over time of cyclic field application was not observed in 300 h. However, surface embrittlement was observed. Designers should be aware that cyclic magnetic fields, even in the absence of temperature excursions and mechanical stress, can lead to a relaxation of the 4130 microstructure and possible deterioration of yield strength.     

Linewidth Narrowing in Microstrip Resonator Using Medium

An effective highly dispersive medium is proposed by utilizing strong dispersion of localized defect mode in a microstrip photonic crystal. Linewidth narrowing in a composite microstrip resonator using this photonic- crystal-based effective medium is investigated and its dependence on the structure parameters is presented. Both numerical simulations and experimental results demonstrate that compared to the traditional resonator, the Qfactor increases much more quickly and the peak transmission decreases more slowly at the same time for the composite resonator.     

Effects of metal and “magnetic wall” on the dispersion characteristic of magnetostatic waves

The dispersion relation of magnetostatic waves tangentially magnetized to saturation ferrite film, with a “magnetic wall” condition (tangential component of microwave magnetic field is equal to zero) on one of the film surface and with a metal condition on the opposite surface is analyzed. The dispersion characteristics show that unidirectional magnetostatic waves appear in this structure: they can transfer energy in one direction only and fundamentally cannot transfer energy in the opposite direction. The dispersion-free propagation of magnetostatic waves also is possible in the structure in a wide frequency interval.     

Electromagnetic cavity to explore disordered systems

In the course of characterizing an electromagnetic cavity we have come to understand details of transmission and reflection traces, some of which may be useful as tools to investigate local modes in random media. We have demonstrated quantitative agreement of frequency shift observations with theory, have demonstrated that the spatial distribution of electric and magnetic fields can be measured using insulating and conducting spheres, and have used perturbation due to wires and disks to demonstrate the local direction of electric and magnetic fields. We have observed that not only frequency shifts but also spatial shifts of modes can be used to observe the intensity of interaction of modes with extended objects in the cavity.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

A generalized 2D FDTD model for photonic crystal fibers with frequency dependent media

A generalized model based on the two-dimensional finite-difference time-domain (2D FDTD) method for photonic crystal fibers (PCF) with frequency dependent media is presented. The Maxwell’s curl equations are formulated using flux density and the magnetic field. Auxiliary differential equations are used with complex-conjugate pole-residue pairs which incorporate the material dispersion of the dispersive media. The model is demonstrated to be a unified approach for arbitrary dispersive materials; therefore, it definitely reduces implementation cost when dealing with different frequency-dependent materials.     

Static observables of relativistic three-fermion systems with instantaneous interactions

We show that static properties like the charge radius and the magnetic moment of relativistic three-fermion bound states with instantaneous interactions can be formulated as expectation values with respect to intrinsically defined wave functions. The resulting operators can be given a natural physical interpretation in accordance with relativistic covariance. We also indicate how the formalism may be generalized to arbitrary moments. The method is applied to the computation of static baryon properties with numerical results for the nucleon charge radii and the baryon octet magnetic moments. In addition, we make predictions for the magnetic moments of some selected nucleon resonances and discuss the decomposition of the nucleon magnetic moments in contributions of spin and angular momentum, as well as the evolution of these contributions with decreasing quark mass.