Quasi-ray Gaussian beam algorithm for short-pulse two-dimensional scattering by moderately rough dielectric interfaces

We consider short-pulse (SP) time-domain (TD) two-dimensional (2-D) scattering by moderately rough interfaces, which separate free space from a slightly lossy dielectric half-space, and are excited by one-dimensional (1-D) SP-TD aperture field distributions. This study extends to the SP-TD in our previous investigation of time-harmonic high frequency 2-D scattering of Gabor-based quasi-ray Gaussian beam fields excited by 1-D aperture field distributions in the presence of moderately rough dielectric interfaces (Galdi et al.). The proposed approach is based on the Kirchhoff physical optics (PO) approximation in conjunction with the Gabor-based quasi-ray narrow-waisted Gaussian pulsed-beam (PB) discretization (Galdi et al.), which is applied to the SP-induced equivalent magnetic surface currents on the interface that establish the TD reflected/transmitted fields. We show that, for well-collimated truncated SP incident fields, the PO-PB synthesis of the reflected/transmitted fields yields an approximate explicit physically appealing, numerically efficient asymptotic algorithm, with well-defined domains of validity based on the problem parameters. An extensive series of numerical experiments verifies the accuracy of our method by comparison with a rigorously-based numerical reference solution, and assesses its computational utility. The algorithm is intended for use as a rapid forward solver in SP-TD inverse scattering and imaging scenarios in the presence of moderately rough dielectric interfaces.     

Multifrequency reconstruction of moderately rough interfaces viaquasi-ray Gaussian beams

In this paper, we present a new technique for determining the surface profile of a moderately rough interface between air and a homogeneous dielectric half-space. Based on sparsely sampled step-frequency ground penetrating radar measurements, the proposed inversion scheme uses a quasi-ray Gaussian beam fast forward model, coupled with a low-order parameterization of the surface profile in terms of B-splines. The profile estimation problem is posed as a parameter optimization problem, which is solved using a multiresolution continuation method via frequency hopping. Numerical experiments establish that the algorithm is efficient and yields accurate reconstructions throughout most of the illuminated region even in noisy environments, losing accuracy only in regions with very weak illumination     

Short-pulse three-dimensional scattering from moderately rough surfaces: a comparison between narrow-waisted Gaussian beam algorithms and FDTD

In this paper, with reference to short-pulse three-dimensional scattering from moderately rough surfaces, we present a comparison between Gabor-based narrow-waisted Gaussian beam (NW-GB) and finite-difference time-domain (FDTD) algorithms. NW-GB algorithms have recently emerged as an attractive alternative to traditional (ray-optical) high-frequency/short-pulse approximate methods, whereas FDTD algorithms are well-established full-wave tools for electromagnetic wave propagation and scattering. After presentation of relevant background material, results are presented and discussed for realistic parameter configurations, involving dispersive soils and moderately rough surface profiles, of interest in pulsed ground penetrating radar applications. Results indicate a generally satisfying agreement between the two methods, which tends to improve for slightly dispersive soils. Computational aspects are also compared.     

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.     

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.     

Excitation of layered media having rough interfaces by line sources

A method for determining the radiation characteristics of a line source embedded in a layered medium having rough interfaces is described. This technique utilizes the plane wave spectral decomposition of the relevant fields in the framework of the extended boundary condition method. It is also shown that the equations derived for the general case reduce considerably when the interfaces are periodically rough. Extensions of the problem solved here have been briefly mentioned, and some numerical examples have been provided.     

高斯光束照射下的单丝衍射

依据基尔霍夫衍射理论,利用幂级数展开的方法推导出旁轴条件下高斯光束的单丝衍射的近似计算公式,并通过计算机模拟的方法再现了单丝衍射主极大区的三分裂特性,得出一些与其他文献〔1〕及实验结果相一致的结论。     

Gaussian rough surfaces and Kirchhoff approximation

Electromagnetic scattering is often solved by applying the Kirchhoff approximation to the Stratton-Chu scattering integral. In the case of rough surfaces, it is usually assumed that this is possible if the incident electromagnetic wavelength is small compared to the mean radius of curvature of the surface. Accordingly, evaluation of the latter is an important issue. This paper generalizes the groundwork of Papa and Lemon (see ibid., vol.36, p.647-50, May 1988) by computing the mean radius of curvature for Gaussian rough surfaces with no restriction on its correlation function. This is an interesting extension relevant to a variety of natural surfaces. Relations between the surface parameters and the mean radius of curvature are determined and particular attention is paid to the relevant small slope regime     

高斯光束通过望远镜系统的变换和准直

本文利用光束变换公式分析了高斯光束通过望远镜系统的传播，讨论了最大扩束比问题。推导出了一般情况下的成象方程和物象比例公式并和其它结果作了比较。     

Excitation of self-focusing optical fibre by Gaussian beam

The launching efficiencies of the HE1m modes and the overall launching efficiency are calculated when a self-focusing optical fibre is irradiated axially by a Gaussian beam. If the spot size of a Gaussian beam is matched to the characteristic spot size of the fibre, the overall launching efficiency is nearly 100%.     

Gaussian beam techniques for illuminating reflector antennas

Simple design procedures are presented for use when a Gaussian beam is used to illuminate a classical reflector antenna. Displacement of the location of the beamwaist toward the focusing element in the case of electrically small antennas where the aperture is in the near field of the feed was calculated together with modification of the required beamwaist radius. Dual reflector antennas were discussed and design procedures appropriate for systems with large and small focal length to diameter ratio developed. Cases where a reflector or subreflector is electrically small, or in the near field of a feed, are readily treated. For elliptical beam antennas, a simple illumination system using only a scalar horn and a single cylindrical lens can generally be found; this has no ray optics analogue. A configuration of this type is discussed, with a practical case study of a 28-by-80-λ elliptical Cassegrain antenna operating at a wavelength of 3 mm. The design process for designing the feed system is discussed in detail. Despite the small size and relatively large aperture blockage, an aperture efficiency of 0.48 was measured, which compared quite well with the expected efficiency of 0.53, thus verifying the validity of the Gaussian beam design approach     

刀口法测量高斯光束光斑半径研究

根据高斯光束光强分布公式,讨论了P（x）%/（1-P（x)%)为任意值时,高斯光束光斑半径与刀口-光斑中心距比值及相应的光斑半径的测量误差;根据理论分析结果,在P(x)%为不同值条件下,对基模高斯光束光斑半径进行了实验测量,实验结果与理论分析符合较好。     

基于高斯光束与射线追踪的短波波场计算算法

短波通信中几何光学理论难以计算焦散波场的传播问题,提出一种基于高斯光束的短波传播计算算法.首先,采用高斯光束法将产生高频波场的波源分解为若干个高斯光束;然后,通过射线追踪法与拉格朗日公式计算每个高斯光束,通过沿光束中心射线的ODE(常微分方程)计算曲率与光束宽度等定量;最终,采用泰勒展开式决定中心射线附近光束的贡献度,将接收点附近的高斯光束进行加权求和,获得接收端的波场.实验结果表明,本算法可有效地计算焦散的短波传播,并且与几何光学法的误差极为接近.     

Gaussian beam distortion caused by saturable gain or loss

Results are given for the beam distortion suffered by low order Gaussian-Laguerre modes propagating through a saturable laser amplifier. Both uniform and Bessel small-signal gain distributions are considered. Beam narrowing caused by saturable loss is also treated.     

Accuracy of a Gaussian beam

The accuracy of a multimode Gaussian beam is discussed. Novel modifications are given to the conventional Gaussian beam formulation derived using the paraxial approximation. With the modifications, the field can be calculated accurately with the Gaussian beam. Modified multimode Gaussian beam techniques are used for calculation of the beam of a corrugated horn antenna. Phase and amplitude patterns given by this method are compared with measurements and other theoretical methods, namely Huygen's principle and the modal matching technique. The meaning of the phase and phase center is also discussed     

衍射高斯波束分析方法

毫米波与亚毫米波在军事、民用方面都有广泛的用途.反射面分析通常采用几何光学法和物理光学法.本文首先对这2种方法进行了简单的比较分析,然后特别介绍了基于几何光学的衍射高斯波束分析方法,并在此基础上将其改进为可以分析三维系统的分析方法.并将其高效性、精确性与基于物理光学的商用软件进行对比验证.可以看出,三维衍射高斯波束分析方法是一种高效准确的分析设计三维准光网络的方法.     

High-order exponential approximations for the Gaussian Q-function obtained by genetic algorithm

This article presents new and accurate approximations for the Gaussian Q-function, which is an important tool in the field of communication theory. A genetic algorithm was employed to find the optimum coefficients of the proposed approximations. The accuracy of the new approximations was examined and compared with those of previous works in the literature. It was shown that the presented high-order exponential approximations provide better accuracy compared to the previously introduced approximations, in general, at the cost of slightly increased mathematical complexity.     

Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves

This paper is dedicated to the theoretical approach to the problem of modelling quasi-optical launchers of plasma waves in the lower-hybrid range of frequencies, when a gaussian beam is the incident field. Numerical results are presented and discussed comparing the cases of a gaussian beam and a plane wave as an incident field [1].     

手征涂覆球对高斯波束的散射

在广义米理论的基础上,通过把入射高斯波束、散射场和内部场用适当的球矢量波函数展开,给出了一种求解手征涂覆球对高斯波束散射的解析方法。待定的展开系数可由从边界条件得到的线性方程组求出。对于波束的区域近似模型,给出了微分散射截面的数值结果。结果表明：与介质涂覆的情况相比,手征涂覆对微分散射截面和散色场的极化特性都产生了较大的影响。     

A hybrid (parabolic equation)-(Gaussian beam) algorithm for wavepropagation through large inhomogeneous regions

The wide-angle split-step parabolic equation (PE) algorithm is used to model electromagnetic wave propagation over general inhomogeneous terrain up to a height h. The PE-computed fields at h are then projected onto a complete Gabor basis from which we effect Gaussian beam propagation at altitudes greater than h. The Gaussian beams can be propagated through general inhomogeneous media, devoid of failures at caustics and shadow boundaries (as befalls ray tracing). The accuracy of the Gaussian beam algorithm is demonstrated via two realistic examples: (1) low-frequency (HF) ionospheric propagation with application to over-the-horizon radar and (2) near-grazing high-frequency propagation for communication or surveillance applications. In the context of these examples, we discuss relevant numerical issues associated with the hybrid algorithm from which general advantages and disadvantages are addressed