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The direct integral equation is formulated for describing the current on the multiple perfectly conducting strips in cylindrical geometries for an E-polarization plane wave of normal incidence. By using the Galerkin's method, the surface currents on the conducting strips are expanded in the form of a series of Chebyshev polynomials of the first kind, while the unknown expanding coefficients are solved by a set of matrix equations of finite order with a fast convergence rate and a high accuracy. Furthermore, numerical results are presented to demonstrate the variation of the penetrated near-zone field in the presence of one, two, three, four and six cylindrical apertures, and the hybrid effects of both aperture number and aperture angular widths on the penetrated fields are investigated in detail.

Propagation of electromagnetic waves along earth-space paths in forest environments is analyzed in this paper, where the transmitter is placed in the air region above the vegetation, while the receiver may be in the air region or within the vegetation. This propagation model considers the forest as a horizontally stratieed, anisotropic medium of canopy and trunk, bounded by ground below and air above. Dyadic Green’s functions in their eigenfunction expansion forms for planarly layered anisotropic media are applied to analyze this problem. The analytical close forms of these electric eelds are then obtained by using the saddle point techniques and branch cut integrations in the complex plane and, hence, expressed in terms of direct wave, multiply reeected waves, and lateral waves. Propagation mechanisms of these waves are studied and radio losses in a typical forest are calculated numerically.

In this paper, a new computer program is developed based on T-Matrix method to generate a large number of total (extinction) cross sections (TCS) values of the realistic raindrops that are deformed due to a balance of the forces that act on a drop falling under gravity, and were described in shape by Pruppacher and Pitter. These data for various dimensions of the raindrops (mean effective radius from 0 to 3.25 mm), frequencies (10 to 80 GHz), (horizontal and vertical) polarizations, and temperatures (0, 10 and 20°C) are stored to establish a data bank. Furthermore, a curve fitting technique, i.e., interpolation of order 3, is implemented for the TCS values in the data bank. Therefore, the interpolated TCS results can be obtained readily from the interpolation process with negligible or even null computational time and efforts. Error analysis is carried out to show the high accuracy of the present analysis and applicability of the interpolation. At three operating frequencies of 15, 21.225, and 38 GHz loca...

Theoretical and experimental results of a wide-band planar antenna are presented. This antenna can achieve a wide bandwidth, low cross-polarization levels, and low backward radiation levels. For wide bandwidth and easy integration with active circuits, it uses aperture-coupled stacked square patches. The coupling aperture is an H-shaped aperture. Based on the finite-difference time-domain method, a parametric study of the input impedance of the antenna is presented, and effects of each parameter on the antenna impedance are illustrated. One antenna is also designed, fabricated, and measured. The measured return loss exhibits an impedance bandwidth of 21.7%. The cross-polarization levels in both E and H planes are better than 23 dB. The front-to-back ratio of the antenna radiation pattern is better than 22 dB. Both theoretical and experimental results of S parameters and radiation patterns are presented and discussed.

In this paper, radiation patterns of a thin circular conducting loop embedded in a two-layered spherical chiral medium but illuminated by a plane wave are obtained. The method of moments is employed in this work to formulate the current distribution along the circular loop enclosed by the spherical chiral radome shell. The dyadic Green's functions defining electromagnetic fields due to sources in both the outer and inner regions are applied. In the Galerkin's procedure for the method of moments, basis functions used in the work are sine and cosine functions which form a Fourier series. The formulation itself here is quite compact, straightforward, and easy-to-use. Effects of various geometrical and dielectric parameters of the chiral radome shell are discussed. As expected, the role of the spherical chiral radome is again realized as a polarization transformer. Associated with these parameters, waves and fields in such an electromagnetic system are characterized. It should pointed that there existed some ...

In this paper, electromagnetic radiation due to a passive thin circular loop antenna when placed on the surface of a two-layered chiral sphere is analyzed and its far-zone radiation patterns are obtained. The method of moments is employed in this analysis to formulate the current distribution along the circular loop in the presence of the layered chiral sphere. The dyadic Green's functions defining electromagnetic fields due to source in the outer region are applied. In the Galerkin's procedure for the method of moments, basis functions used in the work are sine and cosine functions which form a Fourier series in the expansion. Effects of various geometrical and dielectric parameters of the chiral sphere are discussed. Associated with these parameters, waves and fields in such an electromagnetic system are characterized and discussed.

The characteristics of a dual-frequency compact antenna, which uses a rectangular microstrip patch with a shorting pin, are studied. Compared with the conventional rectangular patch antenna, this antenna can achieve both a significant reduction of antenna size and a dual-frequency operation with a single feed. A detailed parameter study is performed. The theoretical analysis is based on the finite-difference time-domain (FDTD) method. The FDTD codes are developed and validated by measurement results. One antenna has been designed and fabricated, and the comparisons between the measured results and the calculated results are provided. The effects of several antenna parameters on two resonant frequencies, frequency ratio, and radiation pattern characteristics of the antenna have been analyzed and compared. The results of the return loss are also presented. It is shown that various frequency ratios (2.82-4.23) can be obtained by varying the design parameters of this antenna. Several design curves are also presented.

Standard approach to calculate electrostatic force and capacitance by solving first-kind integral equation will lead to ill-conditioned linear system. The condition number of resultant discretization matrix can be improved by employing the second-kind integral equation. Adaptive integral method (AIM) is applied in this paper to solve the second-kind integral equation that can be used to calculate capacitance coefficients for three-dimensional structures. The uniformity of multipole moment approximation of the second-kind integral equation is revealed theoretically and numerically; it is realized that the present approach can guarantee the accuracy of AIM for computing capacitance of any structure. The numerical experiments demonstrate that the memory requirement and computational complexity of the present method can be reduced to O(N) and O(N log N) for three-dimensional static problems, respectively. Furthermore, the employment of the second-kind integral equation significantly improves the efficiency of...

In electromagnetic boundary value problems, the Green's dyadic has been an important kernal for electromagnetic field integral representations involving an arbitrary current distribution. An simple form of the Green's dyadic can make the problem-solving easier. In this paper, an alternative representation of magnetic dyadic Green's functions for the regions separated by a spherical radome shell is formulated by applying the principle of scattering superposition. Furthermore, their transmission and reflection coefficients of the scattering dyadic Green's functions are obtained using the boundary conditions on the interfaces. This new dyadic form provides a straightforward and convenient way for obtaining the general expression of the electromagnetic fields in the spherically layered medium (without making coordinate transformation).

The Formulation-C Green's functions for multilayered media are reformulated in this paper to extract z-dependent part when the source and observation points are in different layers. The discrete complex image method (DCIM), is applied to obtain complex images independent on z but dependent on z/spl acute/. For simulation of three-dimensional (3-D) perfectly electrical conduction (PEC) objects penetrating two or more layers, tables of complex images are built in a z/spl acute/-grid. During the matrix-filling stage of the mixed-potential integral equation, together with method of moments (MPIE-MoM), the spatial-domain Green's functions are interpolated from values in the z/spl acute/-grid, while these values are calculated from complex images in the z/spl acute/-grid. This interpolation scheme is more efficient than those directly storing the spatial-domain Green's functions. Numerical examples are given for analyzing a dipole in a two-layered media.

Numerical characterization of electromagnetic waves in cylindrically multilayered structures can be efficiently and rigorously performed by employing the method of moments (MoM) in spatial-domain. Thus the idea of obtaining spatial-domain Greens' functions in closed form or fast computational form was proposed [1] and since then many useful results were obtained for planar layered media. For cylindrically layered media, the closed form Green's functions in spatial-domain were reported in [2], where the spatial-domain Green's function components due to z- and o-oriented electrical and magnetic sources have been obtained using the generalized pencil of function (GPOF) method. This paper, as a further extension, presents spatial-domain Green's function components in fast computational form due to ρ-oriented electrical source embedded in cylindrically layered media. The Green's function components in approximate but fast computational form are compared with the exact Green's function components obtained from ...

Extensive experimental results for various square spiral inductors on GaAs substrate are presented in this paper. Through detailed studies of the inductances extracted from the de-embedded on-chip measured S-parameters, the relationships between the electrical characteristics and the geometrical parameters of the spiral inductors are revealed. Based on the curve fitting technique, a behavioral model for spiral inductors is obtained and presented. Thus, the inductances of spiral inductors with an acceptable accuracy up to their first resonance frequencies are obtained.

The IEEE iWEM (IEEE International Workshop on Electromagnetics: Applications and Student Innovation Competition) was initiated from the AEM2C (International Conference on Applications of Electromagnetism and Student Innovation Competition Awards) by the General Co-Chairs, Prof. Dau-Chyrh Chang (Taiwan), Prof. Le-Wei Li (China), Prof. Kwai Man Luk (Hong Kong), and Prof. Hiroyuki Arai (Japan). The iWEM was approved by the IEEE Antennas and Propagation Society to receive the IEEE logo and to rename iWEM to IEEE iWEM in November, 2010. IEEE iWEM was scheduled to be held in Taiwan in 2011, and is scheduled to be held in China, Hong Kong, and Japan in 2012, 2013, and 2014, respectively. The main purpose of IEEE iWEM is to be a platform to encourage scholars and students to present innovative papers about electromagnetism. All of the papers of IEEE iWEM were submitted through the IEEE paper-submission system to guarantee the quality of the submitted format. In order to guarantee the quality of the papers, all the papers were reviewed by at least two international reviewers. All of the accepted papers will appear in IEEE Xplore as the formal record.

This Chapter review the fast Fourier transform (FFT) technique and its application to computational electromagnetics, especially to the fast solver algorithms including the Conjugate Gradient Fast Fourier Transform (CG-FFT) method, Precorrected Fast Fourier Transform (pFFT) method, Adaptive Integral Method (AIM), Greens Function Interpolation with FFT (GI-FFT) method and Integral Equations with FFT (IE-FFT) method. The basic ideas used in the FFT applications are addressed while the brief introduction to integral equation method is conducted. The general formulation and procedure in the integral equation method, surface integral equations, volume integral equations, solutions to integral equations, and their implementations of fast Fourier transform algorithm are also briefed together with fast convolution using fast Fourier transform. Fast integral equation method developed based on fast Fourier transform are reviewed where conjugate gradient fast Fourier transform method, and precorrected fast Fourier transform method (where projection operators and interpolation operators are also highlighted), adaptive integral method, Greens function interpolation with FFT approach and integral equations with FFT method are also described. While the matching schemes for gradients of Green's functions are addressed, accuracy and complexity, memory requirement and computational cost, and error controls and estimations are also discussed. Keywords: Electromagnetics; Antennas; Scattering; Fourier transform; Numerical Analysis

In this paper, an extension of the integral equation based on domain decomposition method (IE-DDM) is presented for dynamic electromagnetic scattering problems above a lossy half space. In the framework of the IE-DDM, the proposed method divides the composite object into several homogeneous sub-domains. Each sub-domain is properly described by a closed surface, and robin transmission condition is introduced to weakly enforce the continuity of tangential field across the touching-face between adjacent sub-domains. Multiple-grid precorrected fast Fourier transform (MG-pFFT) is adopted in each sub-domain independently to account for the self-interactions. Numerical experiments validate the accuracy and efficiency of this method.

In this paper, a highly efficient and robust scheme is proposed to analyzing electromagnetic (EM) scattering of arbitrary shaped perfect electrically conducting (PEC) objects in half space. The electric field integral equation (EFIE) with the half-space Green's function is chosen as the basis of this method due to its great versatility and accuracy. A perturbed dual threshold incomplete LU factorization (ILUT) preconditioner based on the near-field interactions in the improved EFIE (IEFIE) operator is proposed as an effective preconditioner. It will be further shown that such preconditioner enhances the stability of the traditional ILUT preconditioner based on EFIE, which may occasionally encounter problems of instability for real-life problems. Numerical examples are presented to demonstrate the high efficiency and robustness of this method over other existing alternative solutions.

In this paper, a multiple-grid precorrected fast Fourier transform (MG-pFFT) based on the integral equation domain decomposition method (IE-DDM) is presented for multi-scale, dynamic electromagnetic scattering problems in half space. In the framework of the IE-DDM, the proposed method employs multiple auxiliary FFT grids in each domain. Numerical experiments validate the reduced complexity and accuracy of this method. It is also shown that the proposed method is an efficient and robust preconditioner for the original IE system in half space.

This paper is devoted to the calculation of the capacitance of monolithic microwave integrated-circuit (MMIC) passive components. The method of moments (MoM) is used to solve the integral equation for the electrostatic problem with the help of the spatial-domain multilayered media Green's function that can be obtained using the discrete complex image method (DCIM). As an application, the capacitance of several MMIC passive components, including capacitors and interconnects, is calculated. The numerical experiments show the efficiency and accuracy of the present method. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 216–219, 2002.

In this paper, a new dual-frequency, compact antenna, which uses an H-shaped microstrip patch with a shorting pin, is described. Compared with the conventional rectangular patch antenna, this antenna can achieve both a significant reduction of antenna size and a dual-frequency operation with a single feed. More freedoms for tuning the resonant frequencies, the frequency ratio, and the input impedance are available because of more design parameters. A detailed parameter study is performed, and the theoretical analysis is based on the finite difference time domain (FDTD) method. The FDTD programs are developed and validated by measurement results. The effects of several antenna parameters on two resonant frequencies, frequency ratio, and radiation pattern characteristics of the antenna are analyzed and compared. It is shown that various frequency ratios (1.91–4.23) can be obtained by varying the design parameters of this antenna. Several design curves are presented.

In this paper, the eigenmodes in circular chiroferrite waveguides are studied and the dyadic Green's functions are derived for the first time. The electric and magnetic fields are expanded by cylindrical vector wave eigenfunctions. It is shown that each of the eigenmodes consists of two eigenwaves corresponding to two different polarizations. A dispersion relation is obtained by imposing boundary conditions on the eigenmodes, and the dispersion curves are depicted for various medium parameters. The effects of the uniaxial anisotropy, the gyrotropy, and the chirality are discussed individually. The mode orthogonality is built by introducing complementary testing modes. Hence, the expansion coefficients of the electric and magnetic fields are determined and the dyadic Green's functions are formulated. In order to obtain the complete expansions of the dyadic Green's functions, the singularities of chiroferrite waveguides are also discussed.

Electromagnetic fields in a circular cylindrical conducting waveguide filled with uniaxial anisotropic media are formulated in this paper by using Fourier transformations. These fields are obtained as a superposition of the TE (or ordinary) and TM (or extraordinary) modes satisfying, respectively, different characteristic equations. Lastly, the dyadic Green's function is derived using the Ohm-Rayleigh method and represented by vector wave functions expansion.

The eigenvalue problem for the determination of propagating modes in a lossless and homogeneous chirowaveguide of arbitrary cross section is again considered in this paper. A corrected analysis of the characteristic equations and the behaviors of the wave modes is made, based on the work by Eftimiu and Pearson [1989] who incorrectly formulated the problem. As an example of the application of the generalized analysis to some specific cases, a circular cylindrical chirowaveguide is then considered in the theoretical and numerical investigations. Through the solution of the characteristic equation, a dependency of cutoff wavenumbers of the various eigenmodes upon the chirality values is found.

By using the polynomial approximation and superquadric functions in the Rayleigh-Ritz procedure, a unified method has been proposed to analyze conducting hollow waveguides of a large class of cross sections in our previous paper. Some useful and complicated cross-sectional waveguides in the microwave system, namely, eccentric annular, pentagonal, L-shaped, single-ridged, and double-ridged waveguides are analyzed in this paper. Compared with other numerical methods, this method has the advantages of being straightforward, accurate, and computational effective.

Due to a TE-wave normal incidence, the penetrated and scattered fields in the presence of a nonuniform cold magnetized plasma column are investigated in this work. The mathematical treatment is based on the direct integral equation formulated for describing the currents on the surrounded multiple apertures of the plasma column. To formulate such an integral equation, two-dimensional magnetic dyadic Green's functions in multilayered cylindrical shells are derived in terms of the cylindrical vector wave functions. By using Galerkin's method, the magnetic currents on all apertures are expanded in the form of a series of Chebyshev polynomials of the first kind, and furthermore, parameter effect studies are performed to show the variation of the near- and far-zone fields with the changing of the operating frequency, angular width, and number of the surrounded apertures.

The dyadic Green's functions for defining the electromagnetic (EM) fields for the inner and outer regions of a dielectric spheroid are formulated. The dyadic Green's function for an unbounded medium is expanded in terms of the spheroidal vector wave functions and the singularity at source points is extracted. The principle of scattering superposition is then applied into the analysis to obtain the scattering spheroidal dyadic Green's functions due to the existing interface. Coupled equation systems satisfied by scattering (i.e., reflection and transmission) coefficients of the dyadic Green's functions are obtained so that these coefficients can be uniquely solved for. The characteristics of the spheroidal dyadic Green's functions as compared with the spherical and cylindrical Green's dyadics are described and the improper developments of the spheroidal dyadic Green's function for the outer region of a conducting spheroid in the existing work are pointed out.

A generalized mathematical procedure is presented for investigating the electromagnetic response characteristics of multiple cylindrically curved thin screens excited by a line electric current source, and the mathematical treatment is based on the direct integral equation technique combined with Galerkin's procedure. Both the near- and the far-zone field solutions to such a multiple coupling system are obtained in an analytical form, and the induced electric currents on the curved thin screens are expanded in terms of a series of Chebyshev polynomials of the first kind. Furthermore, parametric studies are performed to show the variation of the penetrated near-zone and scattered far-zone fields of some typical cylindrically curved thin screens.

Dyadic Green's functions (DGFs) and their scattering coefficients are formulated in this paper for defining the electromagnetic fields in multilayered spheroidal structures. The principle of scattering superposition is applied, in a similar form of the DGF in an unbounded medium under spheroidal coordinates, the scattering DGFs due to multiple spheroidal interfaces are expanded in terms of the spheroidal vector wave functions. For the lack of general orthogonality of the spheroidal radial and angular functions, the Green's dyadics are expressed in a different way where the coordinate unit vectors are also combined in the construction, as compared with the conventional form of vector wave eigenfunction expansion. The matrix equation systems satisfied by the coupled scattering (i.e., reflection and transmission) coefficients of the DGFs are obtained so that these coefficients can be solved uniquely. The DGFs can be employed to investigate effects of spheroidal radomes used to protect the airborne or satellite antenna systems and of handy phone radiation near the spheroid-shaped human head, and so forth. Numerical calculations about the applications of the formulated multilayered DGFs are presented in part II of this paper.

This paper presents a mathematical-software functional package that is capable of performing symbolic derivation and numeric computation of dyadic Green's functions for certain multilayered structures: a planar stratified multilayered medium, a spherical multilayered medium, a cylindrical multilayered medium, and a conducting rectangular waveguide with a multilayered dielectric load. The algorithms of this software package are based on the eigenfunction-expansion method. Using Mathematica/sup TM/, two packages were written to fulfill the aforementioned objectives. Upon completion of the software development, dyadic Green's functions for three-layered media were generated. A comparison of these outputs with published results showed good agreement. This demonstrated the applicability of the symbolic package. For the numeric package, the Green's dyadics for a particular three-layered spherical isotropic multilayered medium were generated as an illustration. These packages have been successfully implemented, and future derivation of dyadic Green's functions for these media may be performed.

In this paper, the method of moments is employed to analyze finite phased arrays of radiating slots fed by rectangular waveguides. Also, the relationships among magnetic currents, reflection coefficients, and coupling coefficients are analyzed numerically using basic matrix manipulations. Active patterns of elements in phased arrays, and their relationships with reflection coefficients and magnetic currents are discussed. Numerical results of reflection coefficients compared with existing measured and theoretical results and a fairly good agreement is obtained.

We have extended the polynomial method to a unified approach to analyze hollow conducting waveguides of arbitrary cross section. It was found suitable only for lower order modes due to the singular matrix problem when the standard eigenvalue algorithm is used. In this paper, the QZ factorization for generalized eigenvalues is employed to overcome this drawback. The normalized cutoff wavelengths of the first 100 modes in the elliptic waveguides with different ellipticities are obtained using the present method and are compared with those of the analytic method. Excellent agreements are observed. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 361–364, 2001.

of ON too. The basis of the FMM is the application of the addition theorem to the free-space Green's function 1 . Coifman, Rokhlin, and Wandzura 2 , Song and Chew 3 , and Sertel and Volakis 10 have discussed how to choose the multipole expansion orders for achieving high accuracy in the FMM. The accuracy of the multipole expansion of the scalar Green's function directly affects the FMM acceleration schemes. This thus shows the motivation of this paper, that is, to address the accuracy of addition theorems for the free- space scalar Green's function and the convergence of the FMM algorithms.

A 3-Dimensional (3D) deterministic wave propagation model is developed to study signal propagation in natural 3D terrains in the frequency range of VHF/UHF. The propagation model is based on the physical principles of Geometrical Optics (GO) and the Uniform Geometrical Theory of Diffraction (UTD). Significant ray-paths and their EM field properties at the observation point are computed efficiently from the physical theory. For the initial model, a simple 3D terrain consisting of a single mountain modelled by a dielectric circular cylinder with ground plane on both sides of the cylinder is considered. Currently, the UTD formulation for the 3D dielectric circular cylinder is not available. In this paper, the UTD formulation for the 3D dielectric circular cylinder is obtained from the direct generalisation of the UTD formulation for the 2D case.

The indirect modelling of electromagnetic scattering from two-dimensional composite uniaxial bianisotropic cylinders of arbitrary cross-section is successfully performed according to the principle of equivolumetric model. The mathematical treatment here is based on the generalized boundary-value method combined with the technique of separate variables. The solution is obtained from a system of linear equations of infinite order which is then truncated during numerical computations. Then, numerical investigation is carried out to demonstrate hybrid effects of geometrical and constitutive parameters of guest and host cylinders on the co- and cross-polarized echo widths in the far-field zone. It is shown that under certain circumstances, the indirect modelling technique is very efficient to study the scattering characteristics of many practical complex planar structures, and has some advantages over the direct numerical method. Copyright © 2001 John Wiley & Sons, Ltd.

Although numerical solutions to the electromagnetic scattering by an arbitrarily shaped object have been obtained using Waterman's (1971) T-matrix method (TMM), the general electromagnetic radiation due to an antenna of a three-dimensional (3-D) current distribution in the presence of an arbitrarily shaped object has not been well considered. In this paper, the technique of surface integral equations has been employed; and as a result, a terse and analytical representation of the dyadic Green's functions (DGFs) in the presence of an arbitrarily shaped dielectric object is obtained for the antenna radiation. In a form similar to that associated with the electromagnetic radiation in the presence of a dielectric sphere, the DGFs inside and outside of the object of arbitrary shape are expanded in terms of spherical vector wave functions. However, their coefficients are no longer decoupled due to the arbitrary surface of a 3-D object. The coupled coefficients are then determined using the surface integral equation approach, in a fashion similar to that in the T-matrix method. To confirm the applicability and correctness of the approach in this paper a dielectric sphere, as a special case, is utilized as an illustration. It is found that exactly the same expressions as in the rigorous analysis for the inner and outer spherical regions of the object are obtained using the different approaches. As applications of the approach in this paper, radiation problems of an electric dipole in the presence of superspheroids and rotational parabolic bodies are solved.

This paper deals with the electromagnetic (EM) interaction between the multilayered spheroidal head model and wire antennas. The EM fields inside and outside the dielectric spheroid are expressed by using the Green's dyadic and the superposition of EM fields in terms of vector wave functions. The distortion of the current distribution of the wire antenna is studied. Based on the multilayered spheroidal model, the Method of Moments (MoM) is applied to calculate the current distribution induced by the scattered wave due to the presence of human head. The numerical calculation is fast convergent because of the energy absorption of the dielectric spheroid. The Specific Absorption Rates (SAR) inside the spheroidal head model due to the final current distributions are presented.

This paper presents a full-wave analysis of radiation associated with an antenna located inside a conducting waveguide. The opening of such a waveguide is flush-mounted on an infinitely extended ground plane and covered by a hemi-spherical dielectric shell. The electromagnetic fields radiated by an antenna located inside the waveguide and the dyadic Green's functions in such a structure are formulated using the wave-matching technique. The scattering coefficients of the dyadic Green's functions, coupled to each other and expressed in matrix form, are derived by matching the boundary conditions on circular waveguide conducting walls and the dielectric interfaces. As an application, the radiation patterns of the open aperture excited by a dipole antenna located inside the circular waveguide are obtained for various dimensions of the radiating system.

In this paper, the characteristics of a small antenna using an H-shaped microstrip patch are studied. Significant reduction of antenna size can be realized when the H-shaped patch is used instead of the conventional rectangular microstrip patch antenna. The theoretical analysis is carried out based on the finite-difference time- domain (FDTD) method. The FDTD programs are developed and validated by available measurement results. The effects of various antenna parameters on the resonant frequency and radiation patterns are shown. Several design curves are presented, which are useful for practical antenna design. The electric current distributions on the patch and those on the ground plane are described, together with the results illustrating the electric field distributions under the patch. This antenna is suitable for applications where small size and broad beamwidth are required.

The resonant scattering characteristics of a slit coupled cylindrically eccentric impedance cavity are examined using direct integration equation technique, and the incident wave is assumed to be a H-polarized plane wave. Such a slit coupled eccentric impedance cavity is assumed to be infinite in length and of infinitely thin wall surrounded by several impedance screens. By using the Galerkin's method combined with translational addition theorem for cylindrical wave functions, a system of linear equations of infinite order for determining the induced current distributions are derived in an analytical form. Therefore, numerical results are presented to show the effects of cavity geometrical and impedance parameters on the resonant scattering characteristics of some typical structures in the far zone.

This paper describes the measurement of microwave rain attenuation over a ten-year period (1988-1998) in Singapore. The rain attenuation of (vertically and horizontally polarized) microwaves at 15, 21, and 38 GHz propagating over a path length of approximately 1.1 km were recorded. A negative-exponential raindrop size distribution model is then developed by fitting of the experimental data with the total extinction cross sections of oblate spheroidal raindrops computed from the T-matrix approach. Graphs for attenuation versus rain rate (at selected frequencies) and for attenuation versus frequency (at selected rain rates) are also given.

In this paper, the method of moments is employed to analyze both planar and linear finite phased arrays of radiating slots fed by rectangular waeguides.The equi alent magnetic currents and actie patterns due to these elements of phased arrays are discussed in detail. The relationship between linear and planar arrays is analyzed, and some similar behaiors are realized. 2001 John Wiley & Sons, Inc. Mi- crowave Opt Technol Lett 30:196 199, 2001.

This paper presents an analysis of electromagnetic radiation due to thin circular loop antennas of arbitrary radii a. The electric type of dyadic Green's function expanded in terms of spherical wave functions is employed in this study. The Galerkin's method of moments is applied in the derivation of current distributions along the thin circular loop wires. With an advantage over others, the present analysis is quite general, compact and straightforward; most importantly, the current distributions are obtained analytically and expressed in a closed and simple form. Resulted from these currents, radiated fields in both near- and far-zones and both inside and outside the sphere of radius a are expressed in terms of the spherical vector wave functions. Also discussed in this paper is the validity of definitions of far-zone and electrically small size. The maximum radius of an electrically small circular loop antennas is found from a quantitative error analysis of both loop currents and the far-zone fields.

In this paper, a circular conformal radiation system is considered for the quadrant breast cancer therapy. A toroidal conformal antenna is proposed for nipple area breast cancer therapy. The specific absorption rate (SAR) values in the breast model are analyzed based on simulated results using finite element method (FEM) in HFSS software. Different sizes of toroidal antennas are assumed in simulations to find the best focusing effects in the tumor region. By comparing various simulation results, it is concluded that focusing effects in tumor region vary with sizes of antennas. At the same time, a preliminary biomedical system is proposed for adaptive therapy of breast cancer tumors with arbitrary positions. The high treatment efficiency is achieved by varying feeding signal phases on the two antenna patches for different beam scanning.

A microstrip spiral antenna with sharpening and a bi-conical over sleeve antenna have been proposed for noninvasive superficial layer breast cancer and invasive breast cancer thermotherapies of deep-located breast tumors, respectively. Some measured results are obtained by comparing results of the microwave equivalent phantom model and the swine. A process for the breast cancer treatment is also proposed and some useful results are obtained, where temperature measurement and phantom model manufacture are established.

Since Nikola Tesla proposed the Wardenclyfee Tower in 1889 for the wireless power transmission to date, it has been over a century. The idea was later picked up and implemented continuously in the last half a century. Recently in 2007, MIT research group picked up the old concept and implemented for potential applications into telecommunications. This talk will address briefly the state of-the-art research and development progresses in the wireless power transmission technology and also potential applications. The talk is categorized into two aspects, that is, (a) the long-distance and high-power wireless energy transmission and (b) the short-range and low-power wireless energy transmission. For the long-distance high-power transmission, the talk will cover atmospheric effects, high-power microwave generation, transmitting antennas, EMC/EMI effects on radio frequency wireless system, rectennas, and biological effects on human being and animals. For the short-range wireless power transmission, the review will touch inductive couple effects and their applications onto power-grid systems, wireless power charging systems, mine-tunnel power charge system, and medical applications. The talk will, of course, discuss on advantages and short-comings of these proposals.

The use of asymmetric coupled lines realizing the method to miniaturize a bandpass filter with equal capacitive, which has the advantages of low cost and simplicity. Furthermore, by adding the split ring resonator (SRR) what obtain magnetic coupling with transmission line that can mitigate frequency parasitic parameters and the parasitic inductance. These two applied methods overcome the limitation of previous research methods to achieve the improved performances and a higher operating frequency. As a result, the Miniature Bandpass filter achieves the maximum insertion loss is -1.66 dB in the frequency band of proposed filter between 5.16 GHz and 5.4 GHz. And return loss is more than 10 dB. Stop band rejection is more than 25 dB until 7.4 GHz.

Figure 4 Optical power at the two lasing wavelengths, as measured by photodiodes 1 and 2 in the experimental setup. The changing between the two states every 10 ms can be seen clearly The optical powers at wavelengths l and l were observed 12 . on an oscilloscope via photodiodes PD 1 and PD 2 . The oscilloscope traces are shown in Figure 4. The switching between states every 10 ms can be seen clearly. Furthermore, the flip-flop state is stable in the time between the state changes. 4. CONCLUSION An optical flip-flop was presented based on two simple lasers diodes which act as a master]slave pair. The two lasers are coupled so that only light at the lasing wavelength of one laser is injected into the other laser. The flip-flop state at any given time is determined by which laser is the master and which is the slave. A rate equation model was used to model the flip-flop. Steady-state characteristics of the flip-flop were obtained from the rate equation model. Flip-flop operation is not dependent on second-order laser effects such as resonant frequency shifts or gain saturation. Hence, the flip-flop should be able to be implemented in a wide variety of technologies, particularly integrated optics using semiconductor gain regions and gratings for wavelength-dependent mirrors. The flip-flop was experimentally demonstrated using laser diodes with antireflection coatings. ACKNOWLEDGMENT

Waveguides of various geometries have found many applications. The analysis of the wave modes inside these waveguides are usually subject to cross sections of the waveguides and specific, but convenient, coordinate systems have to be chosen in the analysis. In this paper, the boundary geometries of waveguides (which include rectangular, circular, elliptical, triangular, coaxial, etc.) are represented in a unified manner by a superquadric function. In this paper, with the Rayleigh-Ritz method, the wave propagation characteristics in a hollow conducting waveguide of the superquadric cross section are analyzed in a unified manner. From the analysis, it is realized that the superquadric function can be utilized to accurately model the boundary of various waveguide structures through variation of the shape parameters. The comparisons between the analytical and computational results show this method is accurate and efficient.

In this paper, both gyrotropy and chirality are introduced in some composite fin-line structures. The propagation characteristics are inestigated using the generalized exponential technique in the spectral domain combined with Galerkin's method. These fin lines include symet- rical unilateral and bilateral fin lines. Numerical calculations are per- formed so as to examine the combined effects of changing different ¤ariables associated with the operating frequency, slot width, gyrotropy, and chirality parameters on the dominant mode propagation constant or effectie dielectric constant. It is shown that the influences of chirality are just dierse. Q 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 40)44, 2000.