Curvilinear Fresnel-Zone Plate Lens Antenna: Vector Radiation Theory

A generalized vector diffraction theory of the half-open curvilinear Fresnel zone plate (FZP) tens antenna that is valid for any lens profile shape is presented. It is an extension to the vector Kirchhoff diffraction theory for the plane half-open FZP lens antenna and is based on the conical-segment lens profile approximation. An equation for the electric far-field vector is derived from which follow the expressions for the co- and cross-polarization radiation patterns and directive gain. The proposed theory is utilized for a numerical analysis and comparison of 140-GHz curvilinear half-open FZP lens antennas grouped in two distinct sets:

1. (a)
   Set I: antennas with different in shape FZP lenses (plane, conical, parabolic and spherical) having the same number of zones. All eurvilinear FZP antenna lenses are designed for similar gain, co- and cross-polarization performance and bandwidth, regardless of the lens-profile.
    
2. (b)
   Set II: antennas with different in shape FZP lenses and different number of zones. Since this affects gain, polarization and bandwidth performance, to make the characteristics of these FZP lens antennas practically equal to those of Set I, antenna feeds with different gain patterns have been used.
    

     

Indoor signal focusing by means of Fresnel zone plate lens attached to building wall

A simple inexpensive on-wall Fresnel zone plate (FZP) lens for indoor focusing of microwave signals is studied. It consists of concentric metal rings mounted on the outside of an exterior building wall. In our theoretical and empirical work the on-wall FZP lens is illuminated normally by a plane or spherical wave, of vertical or horizontal polarization, but other, more general incidence situations can be treated by similar means. The scalar quasi-optical focusing theory of the free-space zone plate has been modified and used for design and analysis of one-, two-, and three-ring on-wall FZP lenses. It is found that the presence of the wall does not change the FZP lens focusing efficiency significantly, but it has a strong axial defocusing effect. A 2-GHz FZP lens assembly consisting of three metal rings made out of thin antimosquito mesh has a focusing efficiency of about 15 dB (measured) and 14 dB (calculated), and axial defocusing of about 0.22 m. Some variations of on-wall/on-roof FZP lenses and their feasible applications in the microwave/millimeter-wave communication links are also discussed.     

Conical Double-Dielectric Fresnel Zone Lens and Antenna

A conical double-dielectric phase-reversal Fresnel-zone plate (FZP) lens is introduced. We present the lens design equations as functions of cone opening angle. As an example, the phase-reversal lens has been applied to four millimeter-wave antennas with different lens opening semi-angles: 45deg, 60deg, and 75deg (conical lenses) and 90deg (plane lens). The radiation characteristics of these antennas have been calculated and contrasted one-to-another, and to those with the same semi-angles and linear dimensions binary (half-open) FZP lens antennas. The double-dielectric FZP conical arrangement can serve as a conical antenna lens and a radome simultaneously     

Optimum Design of Millimeter-Wave Double-Dielectric Fresnel Zone-Plate Lens and Antenna

The microwave/millimeter-wave Fresnel-zone plate (FZP) lenses differ substantially in construction, technology and applications from their optical analogs and require specific design equations and methods of electromagnetic analysis. In this paper, optimum design equations for double-dielectric lossless FZP lens are derived. The best and worst choices of the permittivity ratio for lossless dielectrics are discussed in detail. In addition, the influence of dielectric losses on the lens thickness for given wavelength and permittivities is examined. Two versions of a 57.5-GHz double-dielectric phase-reversal zone plate are used as focusing elements of FZP lens antenna. The antenna co-polar and cross-polar radiation patterns, aperture efficiency and frequency bandwidth are analyzed numerically and contrasted with those of half-blocked FZP and horn lens antennas.     

Compound Fresnel Zone Lens Conformal to Truncated Cone: Antenna Application

A millimeter wave antenna consisting of two Fresnel zone plate lenses, plane and conical, is examined numerically by use of the vector diffraction theory. The lenses are of Wood-Wiltse (double-dielectric) or Soret (half-open) type, and are designed for the frequency of 117 GHz. The lenses are made conformal to a truncated circular cone with a base diameter of 500 mm and a plateau diameter of 250 mm. Designs for two opening semi-angles, 45° and 75° each of them with a particular lens thickness are presented. For the angle of 90° the cone lens becomes a plane ring lens, which in combination with the plateau zone lens forms a plane lens of size equal to the cone base diameter. Illuminated by directive feeds set at a focal distance of 525 mm from the cone apex, the double-dielectric and half-open compound and plane lenses, form three pairs of Fresnel zone lens antennas, the co-polar and cross-polar radiation characteristics of which have been compared numerically. The double-dielectric lens antennas examined are about 5 dB superior in gain to the half-open lens antennas, which has a gain of approximately 45 dBi. Because all lenses are of equal transverse aperture, the corresponding lens antennas exhibit the same ?3 dB beamwidth of about 0.33 degrees. The plane zone lens antenna is very thin and simple. Instead, the antenna comprising a 3-D compound Fresnel zone lens is thicker but can be made conformal to a specific surface shape and possesses more levels of design and optimization freedom.     

高斯光束经过球差环形透镜的聚焦

本文讨论高斯光束经过球差环形透镜的聚焦。推导并得到了聚焦光场轴上点的光强分布的表示式。并对其进行数值计算。数值计算结果表明,对于负球差的情况下,得到的光强的最大点位置（最佳聚焦点）相对于无球差情况,往透镜方向移动,即焦移增大;并且,最佳聚焦点的光强较无球差时大,当球差环形透镜的中心拦截比ε取一定值时,得到的轴上点光强最大值远大于无球差时的光强最大值。此外,当透镜具有正球差时,聚焦光场的光强最大点（     

Multifocal three-dimensional bootlace lenses

It is well known that a two-dimensional (parallel plate configuration) bootlace lens can be designed to have more than one focal point. Wide angle scanning capabilities of these lenses in two dimensions is well established, being larger for higher number of focal points. However, no three-dimensional bootlace lens having more than one focal point has been reported. It is the purpose of this paper to report on three-dimensional bootlace lenses having two, three, and four perfect focal points. Equations for lens surfaces are obtained for all three cases. The results of the aperture phase error analysis show that a lens with a larger number of focal points can be scanned to much larger angles in one plane at the expense of the scanning capability in the orthogonal plane.     

An equal group delay waveguide lens

Analytical and experimental results are presented on a circularly polarized waveguide lens that has much greater bandwidth than conventional waveguide lenses. This is achieved by designing the lens to have equal group delay for all rays from the focal point of the lens to the aperture plane. Haft-wave-plate phase shifters in each waveguide element are then oriented to produce a planar phase front. This results in a lens whose aperture phase distribution remains essentially constant over a much wider frequency range than in conventional waveguide lenses. A comparison with a minimum thickness conventional lens and with a phase compensated (Coulbourn) lens is made. A 46-in X band lens was built and tested over a frequency range from 7-9 GHz to confirm the bandwidth performance.     

Design and analysis of a folded Fresnel Zone Plate antenna

Based on the Kirchhoff-Huygens diffraction theory, a simple analytical method of a planar folded Fresnel zone-plate (FZP), that is the case when a planar reflector is placed behind the zone plates, has been developed. According to the numerical calculation results, the design procedure of the FZP antenna has been presented, and its focusing characteristics and gain-optimized conditions have been discussed. The variations of the focal field distribution with the antenna parameters such as zone numbers, focal length and antenna diameter and the radiation power patterns of the FZP have been simulated numerically. To take a good balance of both receiving and transmitting antennas, at 60GHz operating frequency, the focal length should be designed as a half of the antenna diameter and the zone number should be from 10 to 15. The results in this work show that the folded FZP has good focal characteristics and off-axis performance, and its antenna gain can be optimized by the suitable antenna parameter design. The possibility of applying the folded FZP as a low cost and high gain antenna without strict manufacturing requirement for millimeter-wave communications has been shown.     

高斯光束通过两种球差透镜的聚焦特性比较

通过研究,比较了高斯光束通过两种不同球差透镜的聚焦特性。研究表明,高斯光束通过球差透镜的聚焦特性由球差透镜的类型、球差大小和光束的菲涅耳数共同决定。不同的球差透镜要实现无焦移聚焦和越过焦点的聚焦的条件是不同的。     

Terahertz Switching Focuser Based on Thin Film Vanadium Dioxide Zone Plate

In this paper, we propose a switchable focuser device based on a Fresnel zone plate (FZP) structure for terahertz (THz) applications. Each FZP contains seven rings, etched in thin VO₂ film with the designed focal lengths of 50 and 100 mm for 3.7-THz frequency. Temperature-induced VO₂ phase transition leads to the change in dielectric susceptibility of the material, which allows one to switch on and off the focusing properties of the device. The devices were tested with radiation of 3.1 and 3.7 THz emitted by quantum cascade lasers. Experimental results were compared with numerical simulations. In this article, we compare the FZP based on VO₂ films with different properties and show that a thicker VO₂ film reveals higher focusing efficiency, while a thinner one reveals a higher modulation ratio for the peak intensity at the focal point of FZP. We demonstrate experimentally the near-diffraction-limited size of the beam in the focal point of the device. Switching between two phase states of the VO₂ films results in up to the 38-fold change of intensity in the focal point.     

Diffraction Fields in the Focal Space of Symmetrical Hyperbolic Focusing Lens

The fields refracted by circular symmetric hyperbolic lens illuminated by a linearly polarized plane wave are calculated from the induced surface currents. It is shown that the fields in the axial region approximate to the fields in the aperture of corrugated horn under balanced hybrid condition. The image structures for different focal ratio are compared with the classical Airy pattern, deduced by scalar analysis, of optical focusing systems. The coupling between the lens and a corrugated horn at different position on focal plane are presented. The lens resolution and pix numbers are evaluated.     

用二元光学技术制作的多通道频谱分析元件

介绍了两种二元光学组合元件：一种是两个线型波带板的组合,其效果相当于两个柱面透镜的组合;另一种是一个线型波带板和一个圆型波带板的组合,效果相当于一个凸透镜和一个柱面透镜的组合。这两种元件在x方向的焦距均为y方向焦距的两倍,如果把物放在此二种元件前fx焦平面处,则在元件后fx焦平面上,x方向可以产生傅里叶频谱,y方向可以产生等大倒像,从而具有多通道频谱分析的功能。给出了制作这两种元件的原理、方法、参数和相应的实验结果。     

厄米-高斯光束通过光阑-透镜系统的聚焦特性

使用Collins公式研究了厄米高斯光束通过光阑透镜分离光学系统的聚焦特性。利用数值计算详细分析和说明了偶数模厄米高斯光束的轴上光强分布和焦移。分析得出,选择恰当的光束和光学系统参数可引起焦移相反或无焦移。特别是对于TEM22模厄米高斯光束,在几何焦面两边存在两个相等的轴上光强极大点,故存在两个符号相反的焦移。     

光子筛透镜组合的折衍混合消色差系统设计

光子筛作为一种衍射光学元件,具有较大的色散,不适用于宽光谱成像。光子筛的焦距随着入射波长的增大而减小,而正的折射透镜焦距随着入射波长的增大而增大。应用了折衍混合方法进行光子筛消色差的设计。该设计利用二者相反的色散特性,在光子筛的一侧紧密放置一平凸透镜,从而实现光子筛的消色差设计。并针对可见光光谱进行了设计,分析表明该方法能够实现消色差,且具有一定校正二级光谱的能力,消色差波长与中心波长处焦距相对误差为0.33%,成像光谱带宽为20nm。与普通单个光子筛相比,该方法有效拓宽了光子筛的成像光谱范围。与使用波带片的折衍混合系统相比,聚焦光斑更小。     

Scattering and Focusing Effect of Stepped Index Luneberg Lens

Focusing effect of the Luneberg lens for wide bandwidth is studied with emphasis on experiment. A model experiment was performed using a stepped index (six-layer) spherical lens. The total electric field amplitude along the propagation axis has the maximum value (focal point) on the surface of the lens. As the size parameter ka (k: wave number, a: radius of the sphere) is larger, the electric field amplitude at the focal point becomes larger. These results correspond with the power of convergence (focusing effect) by the Luneberg lens. The experimental values are in a good agreement with theoretical ones that are calculated using homogeneous multilayered approximate method. They are also in a good agreement with the results using exact solutions for the inhomogeneous dielectric sphere (the ideal Luneberg lens). Therefore, it is found that the six-layer spherical lens has the optimum variation of dielectric constants for the Luneberg lens and maintains focusing effect for wide bandwidth.     

A Comparison of the Focusing Properties of a Fresnel Zone Plate With a Doubly-Hyperbolic Lens for Application in a Free-Space, Focused-Beam Measurement System

A Fresnel zone plate is designed to perform the function of a doubly-hyperbolic lens. The focusing characteristics of the zone plate and the lens are compared using both measured data and body-of-revolution finite-difference time-domain simulations. The results from this comparison are used to evaluate the use of zone plates as focusing elements in a free-space, focused-beam measurement system. A set of two zone plates is used to perform measurements of the material properties of a dielectric sheet, and the results are compared to the results from a standard system which uses two doubly-hyperbolic lenses.      

贝塞尔-高斯光束经球差透镜的聚焦特性

利用广义惠更斯-菲涅耳衍射积分推导了一种涡漩光束——贝塞尔-高斯光束经球差透镜聚焦后的光场表达式,并利用数值计算分析了球差系数对聚焦光束光强剖面分布的影响。研究表明,通过改变球差系数,可以改变零阶贝塞尔-高斯光束轴上光强最大值点的位置,球差的存在使轴上光强最大值减小。零阶贝塞尔-高斯光束经球差透镜聚焦后不能保持其传输不变性,在几何焦面上光强剖面类似于高斯形分布,而实际焦点所在面上的分布则仍具有零阶贝塞尔函数的特征。对于一阶贝塞尔—高斯光束,球差的存在会改变其横向光强分布。     

Fresnel zone plate antennas at millimeter wavelengths

The performance characteristics of Fresnel zone plates are described with emphasis on applications at millimeter wavelengths. Recent results are included along with a summary from numerous earlier investigations. Parameters described include design information, efficiency, bandwidth, focal characteristics, off-axis performance, axial intensity dependence, aberrations, and far-field pattern. Both transmission and reflection configurations are discussed, mostly for cases where the focal length and diameter are comparable. This type of zone plate has advantages (compared to a lens or paraboloid) of reduced loss, weight, volume, and cost, as well as simple planar construction, with similar diffraction-limited beamwidth and major sidelobe performance, but lower efficiency.     

利用球差透镜获得超衍射极限聚焦

从ＨｕｙｇｅｎｓＦｒｅｓｎｅｌ衍射积分公式出发,得到了高斯光束经过球差透镜聚焦之后聚焦光场的光强分布的表示式。数值计算结果表明,当透镜存在负球差时,可获得超衍射极限聚焦,即得到的聚焦光斑比高斯光束经过无球差透镜聚焦而得到的聚焦光斑还小。并且,透镜的负球差系数越大,得到的聚焦光斑越小。相反,当高斯光束经过正球差透镜聚焦,得到的聚焦光斑比无球差时大。透镜的球差系数愈大,得到的聚焦光斑愈大。讨论了透镜的球差对轴上光强最大点（最佳聚焦点）的影响。