Beam diffraction by planar and parabolic reflectors

In the complex source point technique, an omnidirectional source diffraction solution becomes that for a directive beam when the coordinates of the source position are given appropriate complex values. This is applied to include feed directivity in reflector edge diffraction. Solutions and numerical examples for planar strip and parabolic cylinder reflectors are given, including an offset parabolic reflector. The main beams of parabolic reflectors are calculated by aperture integration and the edge diffracted fields by uniform diffraction theory. In both cases, a complex source point feed in the near or far field of the reflector may be used in the pattern calculation, with improvements in accuracy in the lateral and spillover pattern lobes     

Two-dimensional beam diffraction by a half-plane and wide slit

The far field of a two-dimensional beam resulting from an electric line source at a complex position is described, its half-power beamwidth determined, and its validity as an antenna beam indicated. Farfield diffraction by a half-plane is then determined from an exact uniform solution for an isotropic line source by making the source position complex. The same basic solution and technique are used for beam diffraction by a wide slit, with first-order interaction between the slit edges included. Numerical results for normal incidence illustrate the evolution of the diffraction patterns from those for an omnidirectional source to those for a highly directive beam. Results for plane wave incidence by a slit also come out of this solution. The remarkable simplicity and convenience of this method relative to alternative asymptotic procedures is discussed.     

High-frequency diffraction of a line-source field by a half-plane: Solutions by ray techniques

The diffraction of an arbitrary cylindrical wave due to a line source and incident on a half-plane is treated by the uniform asymptotic theory of edge diffraction. For large wavenumberk, an asymptotic solution for the total field up to and including terms of orderk^{-3/2}relative to the incident field is derived. This solution is uniformly valid for all observation points, including points near the edge and the shadow boundaries. In particualr, two special cases are considered: A) the line source is located on the half-plane, and radiates anE-polarized wave and B) the line source is located in the aperture complementary to the half-plane and radiates anH-polarized wave. A companion paper will show that our asymptotic solution for Case A) is in complete agreement with the asymptotic expansion of the exact solution. For the same diffraction problem, asymptotic solutions obtained by the method of slope diffraction coefficients and the method of equivalent currents are also discussed. It is found that the latter solutions agree with the exact one only when i) the observation point is away from the edge and the shadow boundaries, and/or ii) the terms of orderk^{-3/2}in the field solution are ignored.     

空心高斯光束通过光阑透镜系统的传输特性

为了研究空心光束通过硬边光阑透镜傍轴ABCD光学系统后的传输特性,利用柯林斯衍射积分公式,推导出了空心高斯光束通过受圆孔硬边光阑限制的傍轴ABCD光学系统的传输公式,所得公式可用来描述空心高斯光束通过任意傍轴ABCD光学系统的传输.研究了光阑、透镜以及光阑透镜系统对空心高斯光束传输特性的影响,并用数值例做了详细说明.结果表明,光阑和透镜均会使光束的光场分布向源平面前移,光阑会破坏空心高斯光束的空心性,而单纯的透镜只改变光场分布,不会破坏光束的空心性.这一结果对于空心光束的产生和应用有理论指导意义.     

Systematic study of fields due to extended apertures by Gaussianbeam discretization

Gaussian beams are used as basis elements in field representations. To gain insight into how the choice of beam parameters affects the final representation, a systematic study for the simple test case of a one-dimensional linearly phased cosine-aperture distribution has been undertaken. By successively adding individual displaced and/or tilted beams with large, narrow, or matched waists, one can assess how the elements in various portions of the lattice contribute to the build-up of the actual field in the aperture, near zone, and far zone. Adding enough beams always guarantees homing in on the exact solution, as is verified here by independent comparison. Different beam choices imply different modeling of the radiation process. The understanding gained thereby is helpful for selecting beam parameters in subsequent applications where it is necessary to balance requirements of good convergence, ease of computation, and ability to track the beams through perturbing environments like a radome. Indications are that the narrow beams provide the most robust and versatile formulation to deal with these generalized conditions     

矢量衍射理论的比较研究及标量近似的有效性

光束束腰与波长相比拟时,标量近似已不再成立.以高斯光束的微小圆孔衍射为例,对矢量衍射场的级数解、非傍轴近似解以及精确解进行了详细的数值计算和比较研究.结果表明,对受硬边光阑限制的非傍轴光束,级数展开法适用于处理光束在近场区域的传播,而非傍轴近似解则适用于处理非近场区域光束的传播,具有一定的互补性.讨论了高斯光束圆孔衍射标量近似的有效性,当高斯光束的束腰半径、衍射孔孔径大于几个光波波长时,标量衍射理论是精确、有效的.     

涡旋光束经过环形孔径的衍射特性的研究

对涡旋光束经过环形孔径之后的衍射特性进行了研究。从理论和实验上研究了涡旋光束经过环形孔径的衍射情况,考虑了整数阶涡旋光束和分数阶涡旋光束的衍射光强图,并讨论了拓扑电荷数对衍射图样的影响。研究表明,拓扑电荷数与光强分布紧密相关,这一现象可以用于测定涡旋光束拓扑电荷数。     

四瓣高斯光束经过偏心圆孔限制的矢量非傍轴传输

基于矢量瑞利-索末菲衍射积分,建立了非傍轴条件下四瓣高斯光束经过偏心圆孔光阑在自由空间传输的矢量场模型。选取倾斜光轴作为参考光轴,借助于硬边圆孔的复高斯级数分解,得到了近场模型下衍射场分布的矢量解析式。通过数值计算和模拟,详细讨论了f参数、光束阶次、衍射孔位置和截断参数对像场分布的影响,包括衍射场主瓣强度的位置和光束宽度。这些结论有助于更好地理解四瓣高斯光束在离轴非对称光学系统中的传输特性。     

平顶高斯光束在失调光学系统中的传输特性

为了研究平顶高斯光束经含失调窄缝光阑的失调光学系统的传输特性,采用广义衍射积分法和用有限个复高斯函数之和来逼近窄缝光阑孔径函数的方法,得出了输出光束场分布的近似解析公式,并针对给定的光学系统和平顶高斯光束进行了分析和数值模拟。结果表明,当光阑半宽度与光束束腰半宽度之比较大时(大于1),光学系统的失调量比光阑的失调量对输出光束特性影响更显著。这一结果对分析平顶高斯光束传输特性是有帮助的。     

Two-dimensional pulsed propagation from extended planar aperture field distributions through a planar dielectric layer via quasi-ray Gaussian beams

A previously developed Gabor-based quasi-ray narrow-waisted (NW) Gaussian beam (GB) algorithm for time-harmonic propagation of aperture-excited two-dimensional (2-D) electromagnetic fields through a planar dielectric layer is extended here to the time domain (TD) to deal with short-pulse excitation. The dielectric layer is assumed to be nondispersive; however, slight Ohmic losses can be accommodated. The frequency domain (FD) algorithm is based on a self-consistent discretization of the aperture field distribution in terms of basis NW-GBs in conjunction with an efficient quasireal ray tracing scheme for tracking the individual basis beams. The TD results are obtained by analytic Fourier inversion from the FD in terms of pulsed beam wavepackets, following a procedure similar to that utilized by Galdi et al. (see IEEE Trans. Antennas Propagat., vol.49, p.1322-32, Sept. 2001) in connection with free-space aperture radiation. The proposed algorithm is validated and calibrated against a rigorous numerical reference solution via an extensive series of numerical experiments. A priori accuracy assessments in terms of critical nondimensional estimators, and computational costs, are also given attention.     

光阑约束超几何激光束的传输特性

基于广义惠更斯-菲涅耳衍射积分和圆孔光阑函数展开为有限复高斯函数之和的方法,导出了超几何激光束通过有圆孔光阑约束的近轴ABCD光学系统传输的近似解析表达式,并对其传输特征进行了数值计算和分析。研究结果表明,超几何激光束光强的分布及其衍射效应与光阑的孔径大小、传输的距离以及光束参数等因素密切相关。此外,文中采用的近似解析方法与直接利用衍射积分计算相比,具有更高的计算效率,可以大大节省计算机时。     

Pattern analysis of corrugated horn antennas

The corrugated horn has been established as an antenna with low sidelobes and backlobes, rotationally symmetric patterns (for square pyramidal and conical horn shapes), and broad-band performance [1]-[9]. These properties make this horn useful for many applications. Previous studies have used conventional aperture integration techniques to evaluate the patterns of the corrugated horn. In general, the near axisE-plane radiation pattern of a pyramidal corrugated horn may be adequately predicted from standard analysis established for theH-plane patterns of conventional horn geometries [3]. This method, however, fails to predict the far-out sidelobe and backlobe radiation levels. The work presented here uses a knowledge of the aperture fields to predict the pattern using aperture integration and diffraction theory. The assumptions made concerning the aperture fields were verified by probing the internal fields and aperture fields of anXband corrugated horn. The results of this field probing are contained in the Appendix. The method of solution used in this paper parallels that used in previous publications [10]-[12]. Specifically, the pattern in the main beam region is computed using conventional aperture integration procedures, the contribution of theH-plane edges is found using a slope diffraction analysis, and the contribution of theE-plane edges is found by use of duality.     

Diffraction of an electromagnetic beam by infinite planar periodicmetal-strip grating

An hybrid angular spectrum method-Galerkin moment procedure has been developed to analyze the diffraction of an electromagnetic beam incident obliquely on an infinite planar periodic metal-strip grating. The integral expression obtained for the scattered field is expanded by means of an asymptotic method for determining the diffracted far-field. Some numerical examples show the decomposition of the incident beam in several beams corresponding to the propagating Floquet harmonics excited in the grating. The propagation directions of these beams show deviations with respect to the directions predicted by the Floquet theorem. The profile of the scattered far-field is analyzed as a function of the geometrical and electrical parameters     

A comparison among 1-, 3-, and 7-horn feeds for a 37-beam MBA

A very common multiple beam antenna (MBA) configuration consists of a collimating device illuminated by an array of feeds. The collimating device is usually a reflector or a lens. The feeds are usually horn antennas with a circular aperture. The reflector is usually offset-fed to eliminate aperture blockage; the lens is center fed. The antenna's feeds are excited to produce a finite number of beams, so as to provide contiguous coverage of the field of view. The designer is forced to minimize the angular spacing between adjacent beams in order to maximize the minimum gain over the antenna's field of view. On the other hand, the feed horn's aperture gain is maximized when the feed horn spacing and its aperture diameter are equal. This results in antenna efficiency of the order of 30% when a single feed horn is excited to produce a beam. When a cluster of 3 or 7 adjacent feed horns are excited to produce a single beam, antenna efficiency can be increased to 50%. When it is tolerable, several identical antenna apertures can be used to replace a single aperture configuration. In this case, each of M apertures produces approximately N/M beams of an MBA that produces N beams. Horns producing adjacent beams do not illuminate the same aperture. This permits the use of a much larger horn aperture for a given beam spacing. This results in reduced spillover, higher gain of each beam, and increased antenna efficiency of each aperture. This paper investigates the maximization of gain for several lens antennas. It shows that antenna gain is increased as its focal length is decreased. That is, a focal length-to-diameter ratio (F/D) less than 1 is preferred     

轨道角动量叠加态的产生及其检验

带有螺旋相位分布的波束都具有轨道角动量（Orbital Angular Momentum,OAM）,其螺旋相位取决于OAM态拓扑荷数。理论分析了叠加涡旋光束的相位及光场分布,然后将叠加态涡旋光束的相位分布图加载到空间光调制器上产生了多态涡旋光束,讨论了不同拓扑荷数叠加时光场衍射图的分布情况。实验结果表明,叠加态的涡旋光束光场衍射图随着叠加光束拓扑荷数的正负以及数值而呈一定规律性变化,即当叠加的两束光拓扑荷数为异号时,衍射产生的光斑数为两束光拓扑荷数绝对值之和;当叠加的两束光拓扑荷数为同号时,衍射产生的光斑数为两束光拓扑荷数之差的绝对值。通过此性质可以检验涡旋光束的拓扑荷数,为叠加涡旋光束在自由空间光复用通信系统的拓扑荷数检测提供了新的方法。     

透镜球差对拉盖尔-高斯涡旋光束聚焦特性的影响及改善方法

涡旋光场调控对涡旋光在激光通信、生物操控等领域的应用研究具有重要意义。为了揭示透镜球差对拉盖尔-高斯(Laguerre-Gaussian,LG)涡旋光束传输特性的影响,本文基于菲涅尔衍射理论,模拟研究了不同透镜球差系数下的LG光束聚焦场的强度、相位以及螺旋谱分布。结果表明:光学系统初级球差系数的增大恶化了LG光束聚焦场的强度分布和螺旋相位,弥散了轨道角动量(orbital angular momentum,OAM) 。由此,本文提出了一种光阑补偿方案,通过在透镜前添加大小合适的圆孔光阑,以消除透镜像差。光阑补偿后的LG光束聚焦场由星芒状空心分布恢复为空心圆环分布,OAM态保持单一稳定。本研究工作为改善透镜像差对涡旋光的传输影响提供了解决方案。     

A note on the coupling efficiency between an antenna and a Gaussian beam

In this communication a note on the coupling efficiency between an antenna and a Gaussian beam is presented. The calculations of the coupling efficiency from both methods, a nomorlized inner product between the antenna radiation pattern and the Gaussian-beam pattern or alternatively, between the electric field at the antenna aperture and a two-dimensional field representation of a Gaussian beam, are compared for different aperture size in wavelength. How a correct solution can be gotten is stated.     

Anomalous diffraction of light in liquid upon the ultrasonic coagulation of suspended microparticles

Anomalous diffraction by the periodic filamentary structure that consists of coagulated heavy particles in water is experimentally studied under the conditions for the standing acoustic wave in cavity. The diffraction is sensitive to both the conventional photoelastic effect and the filamentary structure. The width of the narrow beams that are formed in the near-field diffraction zone is several times less than the aperture of the incident beam, and the narrow beams propagate in space with the same angular divergence as the incident broad beam does.     

A phase-space beam summation formulation for ultrawide-band radiation

A new discrete phase space Gaussian beam (GB) summation representation for ultrawide-band (UWB) radiation from an aperture source distribution is presented. The formulation is based on the theory of the windowed Fourier transform (WFT) frames, wherein we introduce a novel relation between the frequency and the frame overcompleteness. With this procedure, the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent, so that only a single set of beams needs to be traced through the medium for all the frequencies in the band. It is also shown that a properly tuned class of iso-diffracting (ID) Gaussian-windows provides the "snuggest" frame representation for all frequencies, thus generating stable and localized expansion coefficients. Furthermore, due to the ID property, the resulting GBs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies. Consequently, the theory may also be expressed directly in the time-domain as will be presented elsewhere. The localization implied by the new formulation is demonstrated numerically for an UWB focused aperture. It is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties, i.e., those residing near the phase space Lagrange manifold. Further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point. It is thus shown that the total number of beams is much smaller than the Landau Pollak bound on the aperture's degrees of freedom.     

Analysis of EM penetration into and scattering by electricallylarge open waveguide cavities using Gaussian beam shooting

Gaussian beam (GB) representation methods are used to analyze the electromagnetic coupling into and the scattering by a large nonuniform cavity. The aperture field in the cavity is decomposed into beams using the Gabor expansion, and shooting techniques are then employed. The method is illustrated only for the two-dimensional (2-D) case. The GBs are tracked axially using the rules of beam optics which ignore any beam distortion upon reflection at the walls. The effects of beam distortion are not significant for relatively slowly varying waveguide cavities. The field scattered into the exterior by the termination within the cavity is found using a reciprocity integral formulation which requires a knowledge of the beam fields near the termination. Numerical results based on this GB approach are presented and compared with results based on an independent reference solution