Electromagnetic Resonances and Q-Factors of Lossy Dielectric Spheres

A theoretical and experimental study of the electromagnetic resonances of spheres is presented. In particular, the scattering characteristics of spheres inside rectangular waveguides are investigated at and around the resonant frequencies. The approach is based on the scattering theory developed by Mie in 1908. Mie's theory is valid for scattering of a plane electromagnetic wave by a homogeneous and isotropic sphere of arbitrary diameter. It encompasses both lossless and lossy spheres. Three continuous functions of frequency are presented. They contain information on the resonant frequencies, the Q-factors, and the output power losses of the sphere. The effect of losses on the resonant behavior was also studied. The theoretical results were compared to experimental data. The agreement between theory and experiment is excellent. An experimental study of the effect of inhomogenities and irregularities of the sphere's material and shape was also made.     

Probing Lossy Fields in Electromagnetic Spheres and Cylinders

Distributions of electric fields in lossy spheres and infinite lossy cylinders simulating biological objects were measured at 350, 920 and 2450 MHz. The measurements were performed in a computer-controlled scanning system using three different implantable nonperturbing probes. The results are compared with theory, and use of Iossy spheres and cylinders for calibration of implantable probes is quantitatively evaluated.     

On the Resonances of a Dielectric Resonator of Very High Permittivity

It is shown that the modes of a dielectric resonator are of two types: confined and nonconfined. Orthogonality properties and variational principles are derived for these modes, and their radiation pattern and quality factor are investigated. The material of the resonator is assumed lossless and of very high permittivity.     

Plasmon Resonances in a Graphene Ribbon on a Finite-Size Dielectric Substrate

A 2D problem of the diffraction of plane electromagnetic wave by a graphene ribbon on a finitesize dielectric substrate is considered for the TM polarization. Rigorous numerical methods are used to calculate the scattering cross sections in the terahertz frequency range. It is shown that multipole resonances vanish in the scattering spectrum in the presence of a small substrate that represents a thin dielectric film.     

MUSIC Imaging and Electromagnetic Inverse Scattering of Multiple-Scattering Small Anisotropic Spheres

The Foldy-Lax equation is used to derive a multiple scattering model for the multiple-scattering small anisotropic spheres. By this model, if the number of the non-zero singular values of the multistatic response (MSR) matrix is smaller than the number of the antennas, the range space of the MSR matrix is found to be spanned by the background Green's function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer, which indicates that the multiple signal classification (MUSIC) method could be implemented to obtain the locations of the scatterers. After estimating the positions of the scatterers, a non-iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer. Two numerical simulations show that, the MUSIC method and the non-iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple-scattering small anisotropic spheres. Such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres.     

用正交函数展开法解介质双球静电问题

本文讨论了一般介质边界条件经逆矢径变换后的表达式，证实对介质双球静电问题若采用逆矢径变换法求解，最终将得到本征展开系数的一个无穷维线性耦合方程组，实际求解困难，本文提出用正交函数展开法解介质双球静电问题，获得精确结果。数值结果进一步验证了Ｌａｐｌａｃｅ方程本征解的加法定理。     

Resonance Electromagnetic Absorption by Nonspherical Dielectric Objects

The extended boundary condition method (EBCM) is used to develop a theoretical solution for the internal fields of isotropic and homogeneous nonspherical dielectric objects. The formulation is particularly effective for resonance-sized bodies. The computational capabilities of the technique are demonstrated by presenting numerical calculations of absorption efficiency versus electrical size (ka) and internal-field distributions at resonance for a number of Iossy axisymmetric objects including spheres, spheroids, and a finite cylinder. The numerical limitations are discussed and a method is given which allows extension of the numerical technique to a larger class of problems.     

Characteristic Electromagnetic Fields in Dielectric Waveguide Array

Based on the modal solution of one dimensionally periodic structure with piecewise uniform dielectric constant distribution, characteristic solutions for two dimensionally Dielectric Waveguide Array (DWA) are rigorously formulated. By satisfying periodic boundary conditions in the interfaces inside a unit cell, semi-closed-form dispersion relation for DWA can be established. Numerical results are presented and compared with a previous method. A class of guidance and radiation problems can be solved with much more simplicity and accuracy.     

Dispersion Diagram Characteristics of Periodic Array of Dielectric and Magnetic Materials Based Spheres

In this paper, the characteristics of electromagnetic (EM) waves supported by three dimensional (3D) periodic arrays of dielectric and magneto-dielectric spheres are theoretically investigated. The sphere particles have the potential to offer electric and magnetic dipole modes, where their novel arrangements engineer desired metamaterial performance. A full wave spherical modal analysis is applied to express the electromagnetic fields in terms of the electric and magnetic dipole modes and the higher order terms. Imposing the boundary conditions, determine the required equations for obtaining $kd-beta d$ dispersion characteristics. A metamaterial constructed from unit-cells of two different spheres is created, where one set of spheres develops electric modes, and the other set establishes magnetic modes. It is demonstrated that such a composite of high dielectric spheres provides double negative (DNG) metamaterial in a narrow frequency band spectrum where $kd,beta d≪ 1$. We also investigate the dispersion diagram for a 3D array of one-set of highly coupled dielectric spheres. Here, the couplings between the electric and magnetic dipoles of the spheres generate hybrid modes, resulting in a backward wave medium for $kd> 1$. The developments of DNG and backward wave metamaterials utilizing 3D array of magneto-dielectric spheres located inside space, and dielectric spheres embedded in a negative $mu$ host, are also addressed. The use of magnetic materials allows accomplishing wider dispersion characteristic bandwidths and tunable feasibility.      

Reflection at a Curved Dielectric Lnterface--- Electromagnetic Tunneling

The reflection of a locally plane wave from a curved interface between two nonabsorbing dielectric media is investigated. Our analysis is applicable to an interface of general shape, defined at each point by the two principal radii of curvature. When the wave is incident from the denser medium at angles greater than the critical angle it is only partially reflected, due to a form of electromagnetic tunneling. Generalized Fresnel transmission coefficients and an extension of Snell's law are derived to account for this transmission into the less dense medium. Ray tracing can then be applied to determine such phenomena as the bending losses in optical slab waveguides, and the curvature loss of skew rays within straight optical waveguides of circular cross section.     

Transverse Electric Resonances in a Coaxial Line Containing Two Cylinders of Different Dielectric Constant

A coaxial line containing a medium of propagation consisting of two coaxial cylindrical cylinders of different dielectric constant is considered for the special case of TE/sub nm/ resonances, and numerical calculations are carried out for a few cases of the TE/sub 11/ type resonance. A reference paper called to the attention of the author by the reviewer treats the general condition of propagation in such a line. The numerical solutions to the cases of interest in this application were not performed, however, presumably since the interest was in propagating modes and since the general characteristic equation is quite complicated. It is shown here that consideration of transverse boundary conditions only leads to an equation which is much less complicated and which is equivalent to the reduction of the general characteristic equation (of the reference paper) when cutoff is approached.     

Hot Spots Generated in Conducting Spheres by Electromagnetic Waves and Biological Implications

The distribution of the heating potential generated by an incident electromagnetic plane wave on a conducting sphere simulating the human head was investigated. It was found that for a sphere of 10-cm radius having the same electrical characteristics as those of biological tissues, no hot spots are generated inside. While at lower frequencies the heating is relatively uniform with some polarization effects, for frequencies above 1000 MHz only skin heating takes place. For a sphere of the same size but of conductivity ?= 10 mmho/cm (which for f>1000 is lower than that of biological tissues) hot spots occur inside for f>1000 MHz. Intense hot spots also occur inside spheres of radius 5 cm having the same electrical characteristics as those of biological tissues in the frequency region of 250 MHz相似文献   

Electromagnetic Wave Propagating in Uniform Waveguides Containing Inhomogeneous Dielectric

Uniform waveguides filled with inhomogeneous dielectric whose permittivity varies along one dimension are studied. Emphasis is given to the modes of propagation and to the calculation of the propagation constants. Exact solutions are given for some special cases. In some of these only asymptotic or polynomial solutions have been available previously. No restriction is placed on the waveguide dimensions so that results developed here apply to the transmission of optical frequency waves as well as to microwaves and millimeter waves. In the waveguide problems of this paper, results obtained cannot be directly found in the existing literature and have been worked out from fundamental theory of differential equations. The theory of the confluent hypergeometric function has been of great help in our treatment of these problems.     

Nondestructive Measurement of a Dielectric Layer Using Surface Electromagnetic Waves

In this investigation, the possibility of nondestructively measuring the thickness and dielectric constant of a layer of dielectric material on a conducting substrate by surface electromagnetic waves (SEW) has been demonstrated. The theoretical approximate dispersion relations near cutoff were derived for both the TE and TM modes and found to be linear functions of frequency, the thickness and dielectric constant were then calculated as simple algebraic functions of the slope and intercept of the dispersion curve. An experimental apparatus utilizing a prism-coupler was constructed to excite surface electromagnetic waves in a dielectric layer whose characteristics were known. By suitable measurements of the frequency and the coupling angle of the source, the dispersion curve was determined experimentally and the resulting dielectric constant and thickness of the layer calculated.     

The Diffraction of Electromagnetic Waves by Dielectric Steps in Waveguides

The problem of determining the scattered electromagnetic fields when a dielectric step discontinuity is placed in a waveguide is considered. Although an exact method of solution is not presently known, the recently introduced modified residue-calculus technique (MRCT) can be successfully extended to obtain a very accurate and numerically efficient approximate solution of the semi-infinite dielectric step. A still further extension of the modified residue-calculus method yields the approximate solution for the case of a finite dielectric step. A unique advantage of the present methods is that the degree of accuracy obtained is independent of the relative permittivity of the dielectric material and of the frequency. Thus very high permittivities or frequencies can be considered without an attendant increase in computational complexity. Numerical data are presented which confirm the accuracy of the method.     

用单光束扫描法测量球状电介质悬浮液的非线性折射率

利用单光束扫描法研究了球状电介质悬浮液的非线性光学性质，对直径为０．０５９μｍ，浓度为２．５％的聚苯乙烯悬浮液的非线性光学系数。。进行了测量，给出ｎ２值为４．３×１０－９ｃｍ２／Ｗ．从实验中得出这种悬浮液中。。引起的折射率变化远大于热效应弓；起的折射率变化．     

Broadband Müller-MLFMA for Electromagnetic Scattering by Dielectric Objects

The multilevel fast multipole algorithm (MLFMA) is very efficient for solving large-scale electromagnetic scattering problems. However, at low frequencies, or when the discretization is small compared with the wavelength, both the MLFMA and the underlying integral equation formulation typically suffer from a subwavelength breakdown. For the electromagnetic scattering from a homogeneous dielectric object, we obtain a stable and well-conditioned surface integral formulation using a variant of the classical Muumlller formulation and linear basis functions. To overcome the subwavelength breakdown of the MLFMA, we use both propagating and evanescent plane waves to represent the fields. The implementation is based on a combination of the spectral representation of the Green's function and Rokhlin's translation formula. We also present a new interpolation scheme for the evanescent part, which significantly improves the error-controllability of the MLFMA-implementation. Several numerical results verify both the error-controllability and scalability of the proposed algorithm     

基于谐振腔体法的材料电磁参数测试

本文介绍了一种全新的分裂圆柱体谐振腔体,并且以聚四氟乙烯的测量为例,详细介绍了采用这种腔体完成介质材料测试的具体过程.此项方法具有精度高、操作简单的特点,最适合于衬底,薄膜,PCB等材料的测量,并且遵循IPC测试规范TM-650 2.5.5.13.     

The Electromagnetic Fields and the Phase Constants of Dielectric Image Lines

A method is described for the exact calculation of the field distributions and the phase constants of single and coupled dielectric image lines of rectangular cross section. Field distributions and phase constants calculated by this method are presented as well as experimental results from lines fabricated of paraffin wax. The physical properties of the electromagnetic fields and the mode designation are discussed. The theory is compared to approximate calculation methods known from the literature.     

Rigorous Analysis of Electromagnetic Wave Propagation in Cylindrical Dielectric Waveguide Array

Cylindrical Dielectric Waveguide Array(CDWA) should be considered as a kind of two-dimensionally periodic(2DP) medium. Based on the established rigorous theory for 2DP medium, a great amount of numerical results for CDWA were presented. Wave propagation in CDWA was analyzed in detail in this paper. Firstly, given the longitudinal wave vector (k _z=0), Brillouin dispersion relations between transverse wave vectors were analyzed when modulation coefficients or the rate of different dielectric areas in a unit cell varied. Interactions between space harmonics were also studied. Secondly, when the area of dielectric cylinder in the unit cell varied within a given range, CDWA dispersion relations were compared with Rectangle Dielectric Waveguide Array's, some interesting conclusions were obtained.