Electromagnetic reflection from a curved dielectric interface

The reflection of a high-frequency electromagnetic field from an arbitrarily curved dielectric interface is considered. The fields are expanded in asymptotic series ofk^{-1}, known as Luneburg-Kline expansions. Based on a ray method the zero- and first-order terms ofk^{-1}of the reflected and transmitted field are evaluated at the interface. Associated with the fields at the interface, effective surface current densities can be used to determine the reflected and transmitted field at points away from the interface, which is done analytically for the reflected far field in the case of plane wave incidence. The result consists of a frequency-independent term, which is related to geometrical optics solution, and a term ofk^{-1}, which is a useful extension of geometrical optics solution in some cases.     

A ray-tracing method for modeling indoor wave propagation andpenetration

A ray-tracing method for waves inside buildings is presented. Ray tubes are used to model the wave propagation and penetration and all the significantly reflected and transmitted ray tubes from interfaces are included. Also, the cross sections of the ray tubes at the field points are evaluated to find the spreading factors of the waves and then the geometrical optics (GO) contributions at the locations of the receiving antenna. A program has been developed according to this ray-tracing technique that can be applied to simulate waves transmitted through and reflected from electrically large complex 2D and 3D bodies. To verify this ray-tracing program, 2D moment method (MM) solutions for wave propagating in a two-room structure and also through a stair-shaped wall above a lossy ground are used to compare with those obtained from the ray tracing. Besides, comparisons of field measurements and ray-tracing simulations at 900 and 1800 MHz performed in a corridor on different floors and inside a staircase are shown. The effective complex dielectric constants of the buildings determined from a free-space method are employed in the simulations and a vector network analyzer is used for the field measurements. Good agreements are obtained. In addition, measured results for waves penetrating an exterior wall with metal-framed windows at 1290 MHz are employed to test the ray-tracing solutions, which indicate that scattering from the metal frames may be significant for field points near the windows. This ray-tracing program can be applied to evaluate the channel characteristics for the indoor wireless communications     

Refraction at a Curved Dielectric Interface: Geometrical Optics Solution

The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. We give explicit matrix formulas for calculating DF, illustrate its physical significance via examples.     

FDTD modeling of scatterers in stratified media

The FDTD technique is well suited for calculating the fields scattered by buried objects when the sources are close enough to the air/ground interface so that they can be incorporated into the solution space. Difficulties arise, however, when the sources are far from the interface since the total fields in the solution space are not all outgoing waves. Using well-known formulas for the fields transmitted and reflected by stratified media, this paper discusses a method whereby the fields scattered by a buried object can be easily calculated by the FDTD technique when the incident field is a plane wave     

Rigorous asymptotic analysis of transmission through a curved dielectric slab

A circular cylindrical dielectric layer is an idealized but rigorously analyzable model for radome covers. With a line source located on the concave side, an exact integral formulation is derived for the field transmitted to the convex side. Alternative representations are developed therefrom in terms of discrete guided modes and continuous spectra, and of ray integrals which, asymptotically at high frequencies, yield geometric optical fields that experience multiple internal reflections between the layer boundaries and also multiple reflections on the concave side. It is then shown that the higher order multiple reflected contributions can be expressed collectively as a ray field with a weighted transmission coefficient that is equivalent to the plane wave transmission coefficient for a plane parallel layer but includes a simple curvature correction. When source and observer are close to the inner and outer layer boundaries, respectively, and are also separated by a large angular interval, guided mode effects may have to be included as well. The result is a general and novel representation of the transmitted field in terms of a certain number of ordinary multiple reflected geometric optical ray fields, a single "collective" ray field, which includes in a composite manner all of the remaining internal reflections, and, possibly, the guided modes along the layer.     

Ray Optical Electromagnetic Far-Field Scattering Computations Using Planar Near-Field Scanning Techniques

For accurate scattering computations in the far-field of flat finite objects, field based ray optical methods cannot be used directly, since the finiteness of the objects is not considered in the formulations. In this paper, planar near-field scanning techniques are used to overcome this problem. In particular, scattered ray optical fields are first computed in a scanning plane in the near-field region of the involved objects and are transformed into the far-field afterwards using field expansions in terms of spectrum density functions of outgoing waves. Since evanescent waves are avoided in the scanning plane, sampling rates less than lambda₀/2 can be used for restricted angle range around the normal direction to the scanning plane. Reduced accuracy at grazing directions of observation is overcome by combining solutions provided by several scanning planes. The proposed approach is applied in the postprocessing stage of the recently developed hybrid method combining the uniform geometrical theory of diffraction with the finite element boundary integral technique and with the multilevel fast multipole method.     

An efficient plane wave spectral analysis to predict the focalregion fields of parabolic reflector antennas for small and wide anglescanning

An efficient approach is described for calculating the field distribution in the focal region of an electrically large, symmetric or offset parabolic reflector antenna with an arbitrary rim contour, when the concave reflector surface is fully illuminated by an obliquely incident arbitrary electromagnetic plane wave. The dominant contribution to the focal-region fields is found by transforming the physical-optics integral over the reflector surface into a plane-wave spectral (PWS) integral. The PWS integral is evaluated rapidly via the fast Fourier transform (FET) algorithm to furnish, in only a single computation, the field for every place in the focal plane (or any plane parallel to it) within the focal region for a given direction of the incident wave. The correction to the physical-optics field is relatively small in the focal region and may therefore be neglected. Numerical results based on this PWS approach are presented, and their accuracy is established by comparison with results based on other approaches     

An FDTD/ray-tracing analysis method for wave penetration through inhomogeneous walls

A novel method of studying wave penetration through inhomogeneous walls using the hybrid technique based on combining finite-difference time-domain (FDTD) and ray tracing methods is presented . The FDTD method is used to analyze the transmission characteristics of inhomogeneous walls. Using the knowledge of the tangential electric and magnetic field distributions along the borders of the FDTD computation domain, rays are sent out to cover the rest of the environment so that prediction of signal coverage can be made more efficiently without compromising the accuracy. Numerical results of the method have been compared and shown to agree very well with those of measurement and those of full wave analysis. Examples have shown the inadequacy of the traditional ray tracing method in the presence of walls made of concrete blocks. However, the proposed method can accurately predict signal coverage by taking into account the scattered fields by the inhomogeneity inside the walls. The method does not add much to computational complexity. Reduction in computation time is even more significant when the incident waves can be approximated to be plane waves and the wall structure is periodic.     

时域近场测量采样平面选择分析

利用平面波谱展开理论和时域有限差分法对几种典型天线的远场方向图建模计算,分析和比较了不同采样平面对远场的影响,以及平面波谱理论对强、弱方向性天线的适用性,为进一步误差分析修正奠定了基础。     

On the tunneling hypothesis for ray reflection and transmission at a concave dielectric boundary

When a ray field is incident on a concave boundary confining a dielectric medium, total reflection is perturbed by leakage due to surface curvature. The resulting modification of the conventional Fresnel ray reflection coefficient, including its uniform transition through critical incidence, has previously been addressed by the so-called "tunneling hypothesis," which is based essentially on the behavior of a corresponding peripherally guided whispering gallery or leaky modal field; the former exhibits evanescent decay (tunneling) away from the boundary in the exterior region but eventually gives rise to radiation from a caustic whereon the modal phase speed equals the speed of light. It is shown here that inferring local ray field properties from global mode field properties has limited validity. The demonstration is based on a rigorous analysis of the two-dimensional Green's function for a circular boundary. Asymptotic solutions are constructed for the various ray-optical domains, and for the transition regions near caustics and especially near the critically refracted ray. Examination of the reflected and transmitted fields reveals that the tunneling hypothesis holds only near the critically refracted ray. Elsewhere, the transmitted ray field may deviate markedly from that predicted by the tunneling model. The results clarify not only the ray field behavior but also the mechanism of local energy reflection and transmission for a nonplanar interface.     

Comments on "New plane wave spectrum formulations for the near-fields of circular and strip apertures"

The above paper (see ibid., vol.24, p.438-449, July (1976)) applies a plane wave spectrum (PWS) formulation to diffraction problems involving circular and strip apertures and gives new results in terms of Fresnel integrals for the electric field near the aperture. In this note, a discussion of those new results is presented; conclusions are: As a technique for solving electromagnetic aperture diffraction problems, the particular PWS described gives inadequate results, especially for near-fields, and by using the standard Keller's formula, a geometrical theory of diffraction (GTD) solution for the diffracted field from a circular aperture is obtained, but the solution does not in general agree with the one given     

Transmission into staggered parallel-plate waveguides

The modal field transmitted into a staggered parallel-plate waveguide when illuminated by a line source is studied. To widen the limited applicability of existing ray methods, an aperture field integration (AFI) method is developed, in which the field in the waveguide aperture is first calculated by high-frequency techniques (uniform asymptotic theory (UAT) and spectral theory of diffraction (STD)) and then decomposed into modal fields via the Fourier analysis. For problems in which the exact Wiener-Hopf and/or the ray solutions are available, AFI gives excellent numerical results. New results are staggered waveguides which find application in the analysis of a waveguide lens.     

An asymptotic closed-form microstrip surface Green's function forthe efficient moment method analysis of mutual coupling in microstripantennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Green's function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Green's function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Green's function     

A hybrid technique for combining the moment method treatment of wire antennas with the GTD for curved surfaces

This hybrid technique is a method for solving electromagnetic problems in which an antenna is located near a conducting body. The technique accomplishes this by casting the antenna structure in a moment method (MM) format, then modifying that format to account for the effects of the conducting body via the geometrical theory of diffraction (GTD). The technique extends the moment method to handle problems that cannot be solved by GTD or the moment method alone. Wire antennas are analyzed to find their input impedance when they are located near perfectly conducting circular cylinders, although the methods used are not restricted to circular cylinders. Three orthogonal orientations are identified, and antennas to match them are analyzed. For each case, the hybrid solution is checked with one of three independent solutions: an MM-eigenfunction solution, image theory, or experimental measurement. In almost all cases, excellent agreement is obtained due in large part to the fact that the moment method near fields are, for the first time, cast into a ray optical form.     

Compact range reflector analysis using the plane wave spectrumapproach with an adjustable sampling rate

An improved method for determining the test zone field of compact range reflectors is presented. The plane wave spectrum (PWS) approach is used to obtain the test zone field from knowledge of the reflector aperture field distribution. The method is particularly well suited to the analysis of reflectors with a linearly serrated rim for reduced edge diffraction. Computation of the PWS of the reflector aperture field is facilitated by a closed-form expression for the Fourier transform of a polygonal window function. Inverse transformation in the test zone region is accomplished using a fast Fourier transform (FFT) algorithm with a properly adjusted sampling rate (which is a function of both the reflector size and the distance from the reflector). The method is validated by comparison with results obtained using surface current and aperture field integration techniques. The performance of several serrated reflectors is evaluated in order to observe the effects of edge diffraction on the test zone fields     

High frequency fields in the presence of a curved dielectric interface

A high-frequency line source in a dielectric medium that is separated by a concave cylindrical boundary from an exterior medium with lower dielectric constant generates a variety of wave phenomena which have been explored extensively. This problem is reexamined here with a view toward clarifying relevant reflection and transmission characteristics within the framework of ray optics, with emphasis on the more complicated transmitted field. The exterior domain is divided into illuminated and shadow regions separated by the transmitted tangent ray launched by a ray incident at the critical angle. Conventional ray optics is valid far from the tangent ray shadow boundary on the illuminated side. The shadow boundary is surrounded by transition regions wherein Fock type integrals and Weber functions yielding local lateral waves provide alternative representations. On the shadow side, not too far from the shadow boundary, the field can be interpreted via "tunneling" and subsequent radiation along a ray from a virtual caustic to the observer. The tunneling is associated with the initial evanescent decay of the transmitted field excited by a totally reflected incident ray. However, deeper inside the shadow, this mechanism is inapplicable, and the field is expressed either in terms of the Fock integrals or a creeping wave-type residue series. The results are presented in a format that permits insertion into a geometrical theory of diffraction (GTD) user's manual.     

Thermomechanical analyses of laser precision joining for optoelectronic components

Thermomechanical analyses in laser-spot-welding (LSW) technique for a dual-in-line (DIP) type package has been studied experimentally and numerically to predict post-weld-shift (PWS). Experimental results show that the PWS of optoelectronic component changes sensitively depending on process parameters such as laser energy, beam delivery position, weld joint design and so on. This indicates that the PWS in laser packaging can be minimized by properly controlling the process parameters. A finite element method (FEM) has been carried out on the analysis of the effect of laser parameters and geometry of joint variation on PWS in laser packaging. And experimental studies of laser spot welding and electronic speckle pattern interferometry (ESPI) have also been conducted to validate the numerical model. A satisfactory agreement between the experimental results and FEM calculations suggests that the FEM provides one of the effective methods for predicting the PWS and optimizing package design in LSW technique for optoelectronic packaging. By using the numerical method above this work has led to an understanding of the effect of laser energy variation and joint design on thermal distortion. Hence the PWS can be controlled to produce a reliable laser module with high yield and high performance.     

口径/谱域积分-表面积分法的研究

 通过分析口径积分、平面波谱理论关于天线近场计算的特点,获得一种混合的天线近场计算方法.结合表面积分技术,提出了口径/谱域积分-表面积分法,用于三维天线-罩系统电性能数值仿真.该方法吸取了口径积分和平面波谱理论的优点,对于天线近场的分析更为精确、实用.以弹载天线罩为仿真实例,结果表明,与口径积分-表面积分法和平面波谱-表面积分法相比,口径/谱域积分-表面积分法的计算结果与实验结果更为吻合,证明了该算法具有更高的精确度.     

Plane wave spectrum-surface integration technique for radome analysis

The purpose of this paper is to report an accurate boresight analysis for practical three-dimensional antenna-radome systems. The analysis of practical three-dimensional antenna-radome combinations has been impractical for antenna aperture areas greater than about75lambda^{2}. The principal difficulty encountered is the excessive computation time required for the large number of antenna near field calculations. The key feature of the approach taken by the authors is the use of the plane wave spectrum (PWS) formulation for calculation of the antenna near fields. The PWS formulation provides much improved efficiency over other nearfield analyses and makes this analysis possible. The method can also be applied to analyze other antenna distortion.