Optimum aperture monopulse excitations

A unified formulation of the optimization of monopulse antenna performance indices for a specified sidelobe envelope function and/or specified nulls of the pattern is presented. The performance indices considered are beam efficiency, gain factor, and angular sensitivity factor of rectangular and circular apertures. The unconstrained optimization of beam efficiency result in an integral equation, the solutions of which are prolate spheroidal wave functions for rectangular aperture and hyperspheroidal wave functions for circular aperture. These functions reduce, respectively, to Legendre and Zernike polynomials in the case of gain factor and angular sensitivity factor. The double orthogonality properties of these eigenfunctions are used for constrained optimization. The results obtained by this technique for the near-in sidelobes constrained at a uniform level are shown to be in agreement with the earlier works. The method is applicable for other aperture surfaces such as elliptical, ellipsoidal, and spherical.     

Phase synthesis of antennas for a given radiation pattern in oneplane using piecewise linear aperture phase distribution

A phase-only method for the synthesis of planar aperture antennas for a given complex radiation pattern in one plane is reported. The problem is reduced to determining an appropriate aperture phase distribution in the form of a ruled function and solved for apertures with rectangular shape and an arbitrary amplitude distribution and for apertures of arbitrary shape and amplitude distribution. This method can be used for controlling the pattern of phased-array antennas. Results of computer modeling are presented     

Circular aperture pattern synthesis from collapsed equivalent line-source distributions

A novel circular aperture pattern synthesis technique is presented, which enables a linear line-source distribution to be converted to a rotationally symmetric circular aperture distribution, of which any /spl phi/-cut radiation pattern is ideally the same as the principal plane pattern of the line-source distribution. Line-source pattern synthesis techniques are numerous and versatile and the technique presented here allows these techniques to be applied to circular apertures as well. This new synthesis method is most compatible with line-source distributions which have zero edge illumination.     

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

The plane wave spectrum (PWS) method has previously been applied to analyze the near-field of planar apertures. The main goal of this paper is to present new PWS formulations for the near-fields of strip and circular apertures. Only special cases are developed in detail. For example, the uniform and parabolic aperture distributions are developed for the circular aperture. These new formulations are expressed in terms of either elementary functions or Fresnel integrals. Consequently, they permit considerably more rapid and efficient calculations than previous near-field formulations, by either the PWS or the aperture integration approach. The new formulations are especially advantageous for large circularly symmetric apertures (on the order of100lambdaand larger) in that computational efficiencies are improved by an order of magnitude or two over the original PWS formulation. The improvement over aperture integration techniques is more than a factor of 1000 for the100lambdaaperture.     

The RCS of a cylindrical array antenna coated with a dielectric layer

The scattering properties of dielectric coated waveguide aperture antennas mounted on circular cylinders are investigated. Both the single element antenna and the array case are treated. The array antenna consists of 4 /spl times/ 32 rectangular apertures placed in a rectangular grid on the surface of an infinitely long circular cylinder. The problem is formulated in terms of an integral equation for the aperture fields which is solved with the method of moments using rectangular waveguide modes as basis and test functions. An efficient uniform asymptotic technique is used to calculate the excitation vector and the backscattered far-field. The asymptotic solution is valid for large cylinders coated with thin dielectric layers away from the paraxial (i.e. near axial) region. A similar asymptotic solution is used to calculate the mutual coupling in the nonparaxial region. For the self coupling terms and for the mutual coupling in the paraxial region a planar approximation is used with a corresponding spectral domain technique. Numerical results are presented as a function of frequency, angle of incidence, cylinder radius, and electrical thickness of the coating.     

Electric and Magnetic Coupling through Small Apertures in Shield Walls of Any Thickness

A method is presented for evaluating the coupling between two identical resonant cavities coupled by a small aperture in a plane common wall of arbitrary thickness. The coupling is related to the frequencies of the symmetric and asymmetric modes of oscillation of the coupled cavity structure, and a variational technique is used to determine those frequencies. The method is applied to circular and rectangular apertures, and it is shown that the coupling is separable into electric and magnetic terms. The results enable theoretical solutions to be obtained for the electric and magnetic polarizabilities of circular and rectangular apertures in walls of zero thickness, and equivalent polarizabilities to be obtained when the wall thickness is nonzero. Curves of numerical values are given for circular and rectangular apertures. With zero wall thickness, the results obtained are the same as those of Bethe for a circular aperture and give good agreement with Cohn's experimental results for rectangular apertures.     

Discretized Gabor-based beam algorithm for time-harmonic radiation from two-dimensional truncated planar aperture distributions .I. Formulation and solution

In this first part of a two-paper sequence, we develop a Gabor-based Gaussian beam (GB) method for the representation of three-dimensional (3-D) time-harmonic vector electromagnetic fields excited by two-dimensional (2-D) truncated arbitrarily polarized planar aperture field distributions. The biorthogonal Gabor basis is tied to a lattice in the discretized four-dimensional (4-D) [configuration (space)]-[spectrum (wavenumber)] phase space which spans the 2-D aperture plane. This study generalizes previous investigations of the simpler corresponding procedure for 2-D fields excited by one-dimensional (1-D) apertures. By subsequent specialization, in the 1-D aperture case, to narrow-waisted 2-D ray-like GBs, we have shown that tracking such beams through interactions with complex environments and recombining them to synthesize the total 2-D field produces robust, efficient and accurate algorithms that are useful for a variety of forward and inverse scattering scenarios. Extension to the time domain via narrow-waisted pulsed GBs has likewise been considered. These potential applications have motivated the extension here to general 3-D EM fields excited by time-harmonic 2-D truncated apertures. The presentation relates each step in the analytic development to a corresponding step in the 1-D aperture case, thereby highlighting the complications (in the parameterizing phase space) associated with the 2-D aperture problem. The outcome is the formal exact solution of the problem under consideration.     

Electromagnetic coupling through small apertures in a conducting screen

The electromagnetic field coupling through small apertures illuminated by an arbitrary incident plane wave is discussed for general aperture shapes. A set of new integral equations in a form highly amenable to numerical solution techniques is derived. Based on the application of the Rayleigh series method, an analytical solution is obtained for the first few terms of the expansion of the apertureE- field of a circular aperture. Numerical results are also constructed for the aperture field and the diffracted field of small rectangular apertures and compared with those of the circular apertures.     

The transmission coefficient of elliptical and rectangular apertures for electromagnetic waves

A simple scalar method using Kirchhoff's boundary values is applied to the diffraction problems of circular, elliptical, and rectangular apertures for normally incident electromagnetic waves. As far as circular apertures are concerned, a simple formula can be derived not only for the diffraction pattern but also for the transmission coefficient. This formula yields good results for apertures greater than0.8lambda. Even in the ease of elliptical apertures a simple formula can he derived for the diffraction pattern. For the elliptical aperture, as well as the rectangular one, the transmission coefficient was found in the form of an integral. Relief models and diagrams are given for the transmission coefficients of the elliptical and the rectangular apertures as a function of the two aperture parameters. Diagrams are given which explain the dependence of the transmission coefficient on the aperture parameters. A comparison with other more complicated methods of approximation and with measurements shows both good agreement and the great practical value of the simple method of approximation used.     

高斯光束圆环衍射与光学系统质量评价

根据任意波型的光波的小孔衍射公式计算了高斯光束圆环衍射的光强分布与环围功率分布;分析了以平面波的圆孔衍射分析激光发射光学系统的光学质量所造成的误差。指出:正确地评价光学系统的质量,必须考虑入射波型和光学系统的具体结构。     

Radiation pattern synthesis of planar antennas using the iterative sampling method

A synthesis method is presented for determining an excitation of an arbitrary (but fixed) planar source configuration. The desired radiation pattern is specified over all or part of the visible region. It may have multiple and/or shaped main beams with low sidelobes. The iterative sampling method is used to find an excitation of the source which yields a radiation pattern that approximates the desired pattern to within a specified tolerance. In this paper the method is used to calculate excitations for line sources, linear arrays (equally and unequally spaced), rectangular apertures, rectangular arrays (arbitrary spacing grid), and circular apertures. Examples using these sources to form patterns with shaped main beams, multiple main beams, shaped sidelobe levels, and combinations thereof are given.     

Impulse responses of aperture antennas with arbitrary aperture distributions

On the basis of the equation of the Fresnel-Kirchhoff scalar diffraction field, it is shown that the impulse responses of parallel-fed aperture antennas of arbitrary configuration with arbitrary aperture amplitude distributions and those of end-fed rectangular aperture antennas with arbitrary aperture amplitude distributions can all be expressed by the aperture amplitude distributions, and that the impulse responses of rectangular aperture antennas with separable aperture distributions and those of circular aperture antennas with circularly symmetric distributions are special cases of the above general ones.     

口径天线在任意口径分布时的冲激响应

本文从夫累涅尔-基尔霍夫标量衍射场方程出发,证明了任意形状的并馈口径天线在任意口径幅度分布时的冲激响应和端馈矩形口径天线在任意口径幅度分布时的冲激响应都可以用口径幅度分布表达出来;而矩形口径天线在口径分布可分离时的冲激响应和圆形口径天线在口径分布圆对称时的冲激响应则为上述一般情况的特例。     

Phase-only control of antenna sum and shaped patterns through nullperturbation

Satisfactory sum or shaped antenna radiation patterns can often be synthesized by modifying just the phase distribution of an initial excitation by an arbitrary amplitude distribution. As examples, we calculate linear and circular apertures with uniform, Taylor, or cosine-section amplitude distributions, affording symmetric sum patterns with low sidelobe levels or symmetric shaped patterns with low ripple and sidelobe levels; linear aperture distributions, affording patterns with low sidelobe levels on one side of the beam; and planar arrays, with uniform or cosine-section amplitude distributions affording φ-symmetric or elongated-oval footprints     

Discretized Gabor-based beam algorithm for time-harmonic radiation from two-dimensional truncated planar aperture distributions .II. Asymptotics and numerical tests

For pt.I see ibid., vol.50, no.12, p.1751-59 (2002). In this second part of the two-part sequence dealing with Gabor-based Gaussian beam (GB) representations for the excitation of time-harmonic three-dimensional (3-D) vector electromagnetic fields excited by two-dimensional (2-D) arbitrarily polarized truncated planar aperture distributions (set in a discretized [configuration (space)]-[spectrum (wavenumber)] phase space), we employ high-frequency asymptotic approximations to reduce the formal solutions developed in part I to efficient algorithms for implementation. The resulting explicit expressions for the 3-D GB propagators are applied to the species of narrow-waisted GBs, which possess ray-like features without the failures of ray fields in ray-optical transition regions. The potential utility of such GBs in the synthesis of wave interactions with complex environments has been discussed previously. The narrow-waisted GB algorithms for the aperture and radiated near-to-far zone fields are calibrated for robustness, accuracy and efficiency by comparison with numerically generated reference solutions in a series of tests involving coordinate-separable rectangular aperture distributions with cosine amplitude tapers.     

On an algorithm for analysis of the radiation patterns of dual reflector and segmented reflector antennas

Large reflector antennas, from cost and weight considerations, appear to be the best configurations for achieving the very large apertures needed for antennas mounted on orbiting spacecraft. Radiation pattern calculations for such antennas are, in general, quite costly both in terms of computer time and the considerable memory required to perform the large surface integrations. The method presented here treats the large aperture as a set of small subapertures for which the radiation fields are computed separately, stored and then added with due regard to phase to yield the radiation pattern of the large reflector. Numerical methods developed to provide the illumination of each subaperture to avoid overlap of the aperture fields of adjacent subapertures and to simplify the surface integrations are discussed. The algorithm is straightforward and has considerable intuitive appeal. The methods of geometrical optics (GO) are used to calculate the aperture plane tangential field components; and electric vector potential is then used to compute the antenna radiation fields. The algorithm includes a set of options for different reflector surfaces. If high accuracy of the far sidelobe levels is required, a subroutine accounting for edge diffraction should be added to the algorithm given here. Calculations made with this algorithm are compared with calculations made by other methods and with measured patterns.     

Diffraction loss of stable optical resonators with internal limiting apertures

In many stable laser resonators, the diffraction loss is principally or entirely due to internal occluding elements with two or more limiting apertures, rather than to any mirror size limitations. Such resonators, with any number of arbitrarily located circular or rectangular limiting apertures, can be decomposed into a set of equivalent empty symmetric cavities with finite size mirrors. When the end mirrors are convex, with radii of curvature greater than the distance to the nearest aperture, the equivalent symmetric cavities are stable, and their diffraction losses are given by graphs published by Fox and Li [6]-[8] and reproduced here for the reader's convenience. The method is illustrated by examples with circular and rectangular limiting apertures.     

Gaussian field expansions for large aperture antennas

An approximate theory of large aperture antennas is developed where aperture, Fresnel, and far fields are expressed in the form of Ganssian field expansions. First, aperture fields, i.e., aperture distributions, are expanded in orthogonal Hermite-Ganssian and Laguerre-Gaussian functions for antennas with rectangular and circular geometries, respectively. Then solution of the Fresnel-Kirchoff diffraction integrals yields the Fresnel and far field expansions. Care is taken to assure the direct transformability of the aperture fields. Optimal scale factors contained in the aperture field expansions are derived and lead to structured field distributions where sidelobes are added sequentially as more terms in the expansions are used in the computations. Tables of optimal scale factors and series coefficients are provided for cosine, truncated Ganssian and Taylor aperture distributions. Several examples are provided that demonstrate the usefulness of the formulas.     

Electromagnetic plane wave scattering by a system of two uniformlylossy dielectric prolate spheroids in arbitrary orientation

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric prolate spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric prolate spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation     

Coupling phenomena in concentric multi-applicator phased arrayhyperthermia systems

The coupling between the waveguide applicators of a four-element phased array hyperthermia system irradiating a three-layered cylindrical tissue model of circular cross section is analyzed theoretically. The fields inside the tissue layers are expressed in terms of cylindrical vector wave functions satisfying the corresponding wave equations, while the fields inside each waveguide are expanded in terms of guided and evanescent normal modes. Then, by implementing the appropriate boundary conditions, a system of four coupled integral equations is derived in terms of the unknown electric field distributions on the open waveguide apertures. This system is solved by expanding the unknown electric field on each aperture into waveguide normal modes and by applying a Galerkin's procedure. The self reflection coefficient and the mutual coupling coefficients are then determined and numerical results for a four-element phased array hyperthermia system are computed and presented for different waveguide applicator sizes and settings