Dissertations / Theses on the topic 'Luneburg Lens'

In this thesis, the design procedures, implementation methods and performance characteristics for various fan beam planar lens antennas mainly synthesized using Luneburg lens principles are developed with regard to acceptable radiation performance and ease of low cost fabrication. The lenses presented are characterised at 24 GHz for industrial, scientific, and medical (ISM) band (24 - 24.25 GHz) or for wide-band automotive short-range radar systems (21.65 - 26.65 GHz), and at 27 GHz for potential millimetre wave applications. The derivation of the original Luneburg lens equations are illustrated using ray tracing theory. Then the problems associated with conventional discrete 3D spherical LL fabrication are presented and summarised. The realization of the gradient refractive index of a cylindrical Luneburg lens achieved by three novel techniques is reported. These are: (1) use of a combination method of improved artificial refractive index grading in the lens central region together with the application of the transverse resonance method (TRM) in the lens outer region; (2) use photo lithographically etched holes of different sizes into one side of a standard low loss PCB ground plane in order to introduce a local inductive variation which partially neutralizes the intrinsic permittivity of the material in prespecified localized regions of the lens; (3) use a shape contoured fixed dielectric constant disc with no metal plates. Further the design and performance of two planar extended hemi-elliptical polystyrene lens operated at 28.5 GHz are given. This type of lens, though Supplied by The British Library - 'The world's knowledge' homogeneous, has similar characteristics to that of the planar inhomogeneous Luneburg lens. Finally the general theoretical properties of two types of reconfigurable spherically symmetrical lenses are analyzed and their potential summarized for future electronic scanning applications.

In this project, a cylindrical Luneburg lens isdesigned operating at optical frequencies. A Luneburg lens isa gradient index lens that transforms a point source into aplane wave or vice versa. The lens is rotational symmetric whichallows wide-angle beam scan. In this work, the gradient indexis discretized in layers. The refractive index of each layer isrealized with a transparent liquid. Ray tracing is used to designand evaluate the lens performance. We have simulated Luneburglenses with 4 - 10 layers. Increasing the number of layersimproves the performance. However, difficulties are present inthe manufacturing part of the lens considering that liquids withdesired refractive index cannot be mixed.
I detta projekt designas en cylindrisk Luneburg-lins som fungerar vid optiska frekvenser. En Luneburg-lins är en gradientindexlins som omvandlar en punktkälla till en plan våg eller vice versa. Linsen är rotationssymmetrisk vilket möjliggör vidvinkelstrålescanning. I detta arbete diskretiseras gradienta indexet i lager, brytningsindex för varje lager realiseras med en transparent vätska. Raytracing används för att designa och utvärdera linsprestandan. Vi har simulerat Luneburg-linser med 4 - 10 lager. Genom att öka antalet lager förbättras prestandan. Svårigheter förekommer i linsens tillverkningsprocess med tanke på att vätskor med önskat brytningsindex inte kan blandas.
Kandidatexjobb i elektroteknik 2020, KTH, Stockholm

ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, California
A broadband passive direction finding system utilizing Luneburg lens has been investigated. With the simulated power level distribution at the detectors mounted on a Luneburg lens, both Cramér-Rao bound (CRB) and the root mean square error (RMS) based on the Correlation Algorithm (CA) for the direction of arrival (DoA) estimation have been derived and calculated. Guidelines on how to design the Luneburg lens detecting system have been studied. Finally, as a proof-of-concept demonstration, the DoA performance of a Luneburg lens fabricated using the polymer jetting technology with five detectors 10° equally spaced to receive the azimuth signal from -20° to 20° is demonstrated.

A Luneburg lens is a beam former that has two focal points where one isat the surface and the other lies at innity. It is a cheap passive steerableantenna at high frequencies. In this thesis, a 2D at-prole Luneburglens with all-metal structure is designed for Ka band. Commercial softwareCST Microwave Studio Suite and Ansys Electronic Desktop (HFSS)are used for simulations.The lens is composed of two glide-symmetric metasurface layers with asmall gap in between. The high order symmetry, glide symmetry, couldprovide ultra wide band property for the lens. Each layer contains manyunit cells. Dierent unit cells are tested in this thesis to nd the best solutiontaking into account both electromagnetic properties and the easinessof manufacturing. A are is designed to achieve better matching betweenthe air gap of the lens and free space. A self-designed waveguide feedingis also used, including a transition from coaxial cable to TE10 mode ofrectangular waveguide at the focus of the lens.The prototype will be built in the future and measurements will be doneto compare with simulation results in this thesis.
En Luneburg-lins ar en lobformare som har tva fokalpunkter, en vid linsensyta och en i oandligheten. Den ar en billig passiv styrbar antenn vidhoga frekvenser. I detta examensarbete konstrueras en plan Luneburg-linsi metall for Ka-bandet. De kommersiella programvarorna CST MicrowaveStudio Suite och Ansys Electronic Desktop (HFSS) anvands for elektromagnetiskasimuleringar.Linsen bestar av tva glidsymmetriska metaytor med ett litet mellanrum.En hogre ordnings symmetri, glidsymmetri, kan ge linsen ultrabred bandbredd.Metaytorna bestar av ett stort antal enhetsceller. Olika typer avenhetsceller testas for att hitta den basta losningen med hansyn till badeelektromagnetiska egenskaper och tillverkningsbarhet. En tvadimensionellhornstruktur konstrueras for att uppna god matchning mellan linsens luftgapoch frirymd. En vagledarmatning designas ocksa, inklusive overgangfran koaxialledning till TE10-moden i en rektangular vagledare, som anslutertill linsens fokalpunkt.En prototyp kommer att byggas i ett senare skede och matningar gorasfor att jamfora med simuleringsresultaten i detta examensarbete.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 55-60).
Optical beam steering has numerous applications including light detection and ranging (LIDAR) for three-dimensional (3D) sensing, free space communications, additive manufacturing, and remote sensing. In particular, there is an increasing demand for LIDAR in a variety of applications including autonomous vehicles, unammaned aerial vehicles (UAVs), robotics, and remote sensing. Ideal solutions are small in size, weight, and power consumption (SWaP) while maintaining long range, high resolution, and large field of view (FOV). Here I present a design for a planar Luneburg lens for use in a silicon photonics optical beam steering device fabricated using CMOS-compatible techniques. The gradient index of the lens is achieved using a photonic crystal consisting of amorphous silicon patterned with a triangular lattice of holes layered on top of silicon nitride. Multiple waveguides can be placed along the focal circle of the lens and the lens is designed to collimate the beam from the waveguides. Through full-wave simulations, the lens is shown to be diffraction-limited with a beamwidth of 0.55° for a lens with radius R = 100 um. The lens is also studied for robustness to fabrication variations. The lens would allow a solid-state on-chip optical beam steering device with a FOV of 1600 with no off-axis aberrations.
by Samuel Kim.
S.M.
S.M. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

In this work, a cost-eective at Luneburg lens antenna operating at the Ka-band is presented.The antenna is suitable for high frequency applications in future communicationnetworks such as 5G systems due to its simple feeding, high directivity, and low loss.The lens is composed of a parallel plate structure loaded with glide-symmetric holes.The holes are tailored so that the required refractive index prole of a Luneburg lensis obtained. In order to realize the highest required refractive index, a dielectric diskis placed between the upper and lower layer of the lens. Glide symmetry is employedto provide ultra-wideband properties and increase the equivalent refractive index of theholey structure. Dierent congurations of holey glide-symmetric unit cells with dierentdielectric materials have been studied to nd a simple and cost-eective solution. Thelens is fed through eleven waveguide feeds to achieve a scanning capability of 50 in theazimuth plane. The heights of the waveguide feeds are stepped in order to match theirimpedance to the parallel plate gap. The lens is ended with a are to minimize reectionsbetween the lens and free-space.The nal design is a lens with a center frequency of 28 GHz with a 20% bandwidth.The reection coecient is below -11.5 dB and the crosstalk is below -16 dB for the fullfrequency band. The lens has a realized gain of 16.7 dBi at 28 GHz. The eciency is73% at 28 GHz with a metal loss of 19% and a dielectric loss of 1.8%.
I det här arbetet presenteras en kostnadseffektiv plan Luneburg linsantenn för Ka-bandet.Antennen har tillämpningar inom högfrekventa applikationer inom framtida kommunikationsnätverk såsom 5G-nätet på grund utav sin enkla matning, höga direktivitet, och låga förluster.±Linsen består av två parallella ytor med glidsymmetriska hål. Hålen är skräddarsydda så att det nödvändiga brytningsindexet för en Luneburg lins uppnås. För att realisera det högsta nödvändiga brytningsindexet placeras en rund dielektrisk skiva mellan linsens övre och undre yta. Glidsymmetri används för att tillhandahålla ultrabredbandsegenskaper och öka det ekvivalenta brytningsindexet hos den håliga strukturen. Olika typer av konfigurationer av håliga glidsymmetriska enhetsceller med olika dielektriska material har studerats för att hitta en enkel och kostnadseffektiv lösning. Linsen matas med elva vågledare för att kunna stråla inom ett vinkelområde på 50◦ i azimutplanet. Vågledarmatningen har en sektion där höjden ändras i ett antal steg för att matcha sin impedans till impedansen från mellanrummet av de två parallella ytorna. Linsen avslutas med en endimensionell hornstruktur för att minimera reflektioner mellan linsen och fri rymd.Den slutgiltiga designen är en lins med centerfrekvensen på 28 GHz med en 20% bandbredd. Reflektionskoefficienten är lägre än -11.5 dB och överhörningen är lägre än-16 dB för hela frekvensbandet. Linsen har en antennvinst på 16.7 dB vid 28 GHz. Strålningseffektiviteten är på 73% vid 28 GHz med en förlust på 19% i metallen och 1.8%i det dielektriska materialet.

This dissertation presents the investigation of biologically inspired direction finding (DF) and localization systems, 3D printing solution for RF components and systems, and fundamental aspects of antennas regarding bandwidth and power efficiency. Biologically inspired direction finding and localization systems are explored first. Inspired by the human binaural auditory system, an improved direction of arrival (DoA) estimation technique using two antennas with a lossy scatterer in between them to achieve additional magnitude cues is proposed. By exploiting the incident-angle- dependent magnitude and phase differences between the two antennas with specially designed scatterer, the DoA of an incident signal from two-dimensional (2-D) / three- dimensional (3-D) space can be estimated. Besides, compact DF systems with enhanced directional sensitivity using a scatterer of high permittivity in between adjacent closely spaced electrically-small antennas are examined. Inspired by the human monaural auditory system, a novel single-antenna DF technique is also proposed by exploiting the incident-angle-dependent spectra for a broadband RF signal only. In addition, a wideband superior DF system utilizing Luneburg lens and uniformly placed detectors on the equator of the lens is evaluated. The DoA is estimated using the amplitude distribution of the received signals at the detectors. Moreover, A portable inventory localization system utilizing hybrid RF (for direction, using previously introduced DF techniques) and ultrasound (for distance) signals is proposed and experimentally demonstrated. Next, a multilayer phased array system is designed and individual parts are printed to demonstrate the applicability of hybrid thermal wire-mesh embedding (for conductors) and thermoplastic extrusion (for dielectrics) techniques for additively manufacturing RF17integrated systems. Finally, fundamental aspects of antennas in terms of bandwidth limit for reactive matching and power efficiency for non-Foster matching are analyzed.

Avec la multiplication des transmissions sans fil et l'augmentation de la taille des données à transférer, il est devenu primordial d’augmenter le débit et donc de monter en fréquence. C'est pour cela que la bande des 60 GHz (57-66 GHz) a été allouée mondialement. A cause de la forte atténuation et de la coupure éventuelle du lien émission/réception du fait de la présence humaine, les antennes à 60 GHz doivent être très souvent reconfigurables. C’est dans cette optique que Canon Research Center France et l’IETR se sont associés pour mener à bien ce travail de thèse. Un nouveau procédé de fabrication de matériau à gradient d’indice a été développé. Le fait de presser un échantillon de matériau composite contenant de l’air permet d’augmenter sa masse volumique et donc sa constante diélectrique. Cette dernière est donc contrôlable par simple pression à une température optimisée. Grâce à ce procédé, divers antennes et composants à gradient d’indice ont été réalisés. L’étude s’est principalement focalisée sur la lentille de Luneburg, qui présente une loi d’indice radiale et qui possède une infinité de points focaux autour de la lentille. Cette lentille a été réalisée avec une variation d’indice progressive et est alimentée tout d’abord par un guide d’onde ouvert. L’étude s’est ensuite focalisée sur la conception de sources intégrées afin de pouvoir les positionner côte à côte et permettre d’obtenir le dépointage du faisceau. Pour ce faire, l’utilisation de guides diélectriques intégrés rayonnant (RSIW) a été étudiée. Deux sources passives sont conçues avec respectivement une transition ligne/fente/guide et une transition avec plongeur dans le guide rayonnant. Par la suite, une troisième source a été conçue utilisant un substrat unique avec une transition ligne coplanaire/plongeur/guide afin de simplifier la technologie de réalisation. Enfin, deux prototypes actifs ont été conçus afin de faire une communication complète à 60 GHz. Des puces réceptrices intégrées de chez Hittite ont été utilisées afin d’alimenter les sources rayonnantes qui illuminent la lentille de Luneburg. L’objectif in fine était d’obtenir trois faisceaux dirigés dans des directions distinctes. Enfin, une première contribution à l’étude d’antennes en bande submillimétrique est effectuée avec la réalisation d’un cornet, d’une antenne à polarisation circulaire et d’une antenne de focalisation en champ proche
With the increase of wireless communications and the required bite rate of data, it needs to increase the working frequency up to the millimeter wave range. For that purpose, the 60 GHz bandwidth (57-66GHz) has been unlicensed all over the world. Because of the loss and possible non-line-of-sight communication, the antennas should have beam scanning properties. Therefore, the Canon Research Center France and the IETR have run a study (PhD) to fulfill this project. A new technological process has been developed in order to manufacture inhomogeneous materials. By pressing a composite foam material sample, it will expel the air from the sample and so, increase its density and its relative permittivity. Using this process, several antennas and components have been manufactured. A particular focus has been done on the Luneburg lens antenna. This one has a radial index law and has infinity of focal points around the lens. This lens has been manufactured with a smooth gradient index law and first fed by an open-ended waveguide to validate the technological process. Secondly, integrated sources have been studied in order to place them side by side and to allow scanning the main beam direction. Thus, the use of Radiating Substrate Integrated Waveguide (RSIW) appears to be the solution. Two passives sources have been realized. The first one is a RSIW fed by a coupling slot from a microstrip line and the second one is a RSIW fed by a coaxial probe from a first thin SIW. A thirdly RSIW has been studied fed by a coplanar line and a coaxial probe and to simplify the manufacturing. Finally, two active antennas prototypes have been realized to perform a complete communication at 60 GHz. Complete integrated chips from the Hittite company have been used to feed the RSIW which illuminate the Luneburg lens. The objective was to implement a beam scanning antennas with three distinct beam directions. Lastly, a preliminary contribution to the sub-millimeter antennas has been performed with the manufacturing of a horn, a circular polarization antenna and a near-field focusing antenna

碩士
國立交通大學
電信工程研究所
105
This thesis, concerns the analysis and applications of periodic structure in the generalized Luneburg lens. The periodic structure in the shape of square patch we use is a kind of metasurface. The metasurface is easy to manufacture and compact that is suitable for the synthesis of Luneburg lens. Thus, it makes the SPPs propagate on the surface and has the performance we expect. We propose using the dispersion diagram of the unit cell and then retrieve the corresponding refractive index in the specific frequency. This is the key point for the synthesis of the gradient lens. Finally, we propose several methods that can improve the performance of the gradient lens including increasing the samples when we discretize the diagram of the refractive index, changing the interface of the generalized Luneburg lens that can enhance the power in the specific location and using the complete 2D dispersion diagram to analyze the variation of the refractive index when the unit cell is in the different location. Theses method construct the basement for the improving the performance and the efficiency of the lens.

碩士
國立交通大學
電信工程研究所
105
Nowadays, research on metasurfaces has been widespread since the potential in several areas such as optics, photonics, antennas, sensing, imaging, and spectroscopy. The metasurface lens composes of 2D periodic metallic patch possesses several advantages such as light, low-profile, compact and also cheaper than the traditional lens array which practical implementation has been proposed. However, most of them didn’t mention the flaw of the wave propagating direction of dispersion characteristic when applying on metasurface lens’ synthesis. In this thesis, a Luneburg lens applies on surface wave antenna is proposed, further, two different types of unit cell will be compared, one varies significantly with the wave propagating direction, another does not, and analyze based on the dispersion characteristic. It will be verified by the performance of surface wave antenna composed of both unit cells. Several sub efficiencies of an aperture antenna used for characterization. Also, a novel synthesis will be presented to improve the performance of the lens’ surface wave antenna application.

碩士
國立交通大學
電信工程研究所
105
In this thesis, we proposed the use of metasurfaces to design and synthesize the double-focus generalized Luneburg lens (DF-GLL) at microwave frequencies. The unit cell of the metasurface used for the synthesis of the lens is made of a square metallic patch printed on a grounded dielectric substrate. Then, we observe that the dispersion of square unit cell varies with the different incident angles, that is, this square unit cell is directionally anisotropic. However, the surface waves will bend at all locations on the lens. The use of only one surface wave propagation direction in synthesizing the refractive indices of all locations on the lens may thus be inaccurate. Thus, we propose a method to improve the synthesis of the DF-GLL. The improvement method is that tailoring the direction adapts to the orientation of the ray path direction at any position within the lens relative to square patches that represented the required refractive index at the same position. We believe the method is more accurate to synthesize the lens, and can improve the performance. Finally, with this proposed synthesis method, we have demonstrated that DF-GLL metasurfaces are able to successfully achieve two clear focal spots by simulation and experimental results.

碩士
國立交通大學
電信工程研究所
105
Research on metasurfaces has been widespread recently because they have strong potential in several fields such as optics, photonics, antennas, sensing, imaging, and spectroscopy. The metasurface is able to exude unusual properties which natural materials or ordinary structures do not possess. In this thesis, we use a periodic array of square metallic patches etched on a grounded dielectric substrate to synthesize a flat 2D Luneburg lens which is used as a surface-wave antenna. No surface wave launcher is required by this meta-lens, which would otherwise add to space and weight. We calculate the various sub-efficiencies of aperture area that collectively characterize the quality of the radiating aperture, which is bounded only by one surface but exploits the exterior free-space above the metasurface to make up the rest of the boundaries, resulting in an essentially material-less aperture that is consequently light, low-profile, compact and also cheaper to manufacture. The design is validated by simulation results.

Complex artificial materials (metamaterials) strongly interact with light and can be used to fabricate structures which mimic a material response that has no natural equivalent. Classical tools for the design of optical or radio frequency devices are often ill-suited to utilize such media or have shortcomings in their ability to capture important physics in the device behavior. Recently it has been demonstrated that the structure of Maxwell's equations can be used to exploit this newly available freedom. By leveraging the `form-invariance' of Maxwell's equations under coordinate transforms, it is possible to develop material distributions in which light will behave as though flowing through warped coordinates. This design process is termed `transformation optics' and has inspired the creation of many novel electromagnetic structures such as the invisibility cloak.

In this dissertation the tools used in the field of transformation optics will be explored and expanded. Several new designs are discussed, each of which expands upon the ideas that have previously been employed in the field. To begin, I show that the explicit use of a transformation which extends throughout all space may be used to reduce the overall size of an optical device without changing its optical properties. A lens is chosen as a canonical device to demonstrate this behavior. For this work I provided the original idea for a compressing transformation as well as its dielectric-only implementation. I then mentored Dan Roberts as he confirmed the device properties through simulation. I further demonstrate that currents may be succesfully employed within the framework of transformation optics-resulting in novel antenna designs. For this work I suggested handling the sheet currents as the limit of a volumetric current density. I also demonstrated how an intermediate coordinate system could be used to easily handle the types of transformatios which were being explored.

For a particular functionality the choice of transformation is, in general, not unique. It is natural, then, to seek optimized transformations which reduce the complexity of the final structure. It was recently demonstrated that for some transformations a numerical scheme could be employed to find quasi-conformal transformations for which the requisite complex material distribution could be well approximated by an isotropic, inhomogeneous media. This process was previously used to demonstrate a carpet cloak-a device which masks a bump in a mirror surface. Unlike the more common transformation optical media, which exhibit strong losses at high frequencies, isotropic designs can be readily made to function at infrared or even optical frequencies.

The prospect of leveraging transformation optics in devices which operate at high frequencies, into the infrared and visible, motivates the use of quasi-conformal transformations in lens design. I demonstrate how transformation optics can be used to take a classical lens design based on spherical symmetry, such as a Luneburg lens, and warp it to suit the requirements of a planar imaging array. I report on the experimental demonstration of this lens at microwave frequencies. In the final design a lens is demonstrated in a two-dimensional field mapping waveguide to have a field of view of ~140 degrees and a bandwidth exceeding a full decade. In this work I proposed the idea of using the inverse of the quasi-conformal transform to arrive at the lens index profile. I performed all necessary simulations and wrote ray tracing code to confirm the properties of the lens. I proposed the metamaterial realization of the lens and performed the necessary retrievals for material design. I wrote code which would create the layout for an arbitrary gradient index structure in a standard computer aided drafting format. I fabricated three lenses-two of which are described in this thesis-and took all of the data shown in the thesis.

The most well known example of a transformation optical device is the invisibility cloak. Despite the great deal of attention paid to the cloak in the literature, the most natural way in which to quantify the efficacy of the cloak-its cross-section-has never been experimentally determined. This measurement is of practical interest because the cloak provides a useful canonical example of a medium which relies on the unique properties of metamaterials-strong anisotropy, inhomogeneity and both magnetic and electric response. Thus, a cloaking cross-section measurement provides a useful way to quantify advancements in the effective medium theories which form the basis for metamaterials. I report on the first such measurements, performed on the original microwave cloaking design. The experiments were carried out in a two-dimensional TE waveguide. Explicit field maps are used to determine the Bessel decomposition of the scattered wave. It is found that the cloak indeed reduces the scattering cross-section of a concealed metal cylinder in a frequency band from 9.91 to 10.14 GHz. The maximum cross-section reduction was determined to be 24%. The total cross-section and the Bessel decomposition of the scattered wave are compared to an analytical model for the cloaking design which assumes a discrete number of loss-less, homogenized cylinders. While the qualitative features of the cloak-a reduced cross-section at the cloaking frequency-are realized, there is significant deviation from the homogenized calculation. These deviations are associated with loss and inaccuracies of the effective-medium-model for metamaterials. In this work I proposed of direct integration of the fields to perform cross-section measurements. I worked out the necessary formulas to determine the coefficients in the Bessel expansion and the resulting scattering cross-section. I mentored an undergraduate student, Dan Gaultney, who scripted the application of the cross-section analysis and took the necessary data. All of the data in this thesis, however, is based on my own implementation of the data analysis.

Dissertation

碩士
國立交通大學
電信工程研究所
107
In this short paper, we study the use of metasurfaces comprising circular metallic patches printed on a grounded dielectric substrate to design and synthesize the double-focus generalized Luneburg lens (DF-GLL) at microwave frequencies. Upon illuminated by incident plane waves arriving from not just one but numerous azimuth angles, the simulated design displays two clear focal spots towards all directions, thereby exhibiting rotational symmetry which facilitates beam switching and scanning. How such circular patch elements compare with square ones is also investigated in terms of the range over which refractive indices can be synthesized as well as the bandwidths of both focal points produced by DF-GLLs composed of patches bearing those two shapes. When operated as a radiating antenna instead, for which excitation source feeds are placed at the two focal spots aligned along the azimuth angle pertaining to that intended beam direction, strong directivities towards all directions are achieved as simulated radiation patterns show. A prototype of the design was also manufactured and measurement results agree well with predictions by simulations, particularly in terms of realizing two distinct focal points towards several azimuth directions.

碩士
國立交通大學
電信工程研究所
104
The thesis presents a surface constituting arrays of periodic patches, which may serve as the metasurface to synthesize the Luneburg lens. The main purpose is by using different sizes of patches to achieve different refractive index at each stage, and get the proper function of Luneburg lens. We propose several plasmonic lens in this thesis showing their design philosophy, details, and try to refine the performance of these lens. We also put them together and make comparisons. We deliver a method to build a well-functioned Luneburg lens step by step in the context. Starting with defining surface impedance and giving formulas to turn it into a refractive index for synthesizing Luneburg lens. Most importantly, we make a linkage between periodic structures and Luneburg lens in the work.

碩士
國立臺灣大學
應用力學研究所
94
Luneberg lens is a spherical lens which its permittivity varies with normalized radial coordinates. It is fabricated by using different homogeneous dielectric centrically layered media. The lens can focus a parallel beam of rays from any direction exactly at a point on the surface. If it is made by adding a reflecting surface “metallic cap”, it is called Luneberg lens reflector. It can reflect incident wave into plane wave in incoming direction. It is usually applied in antenna, radar reflector, satellite-based, and mobile-communucation. The main points of this thesis are about wave propagation, scattering and focusing effect of Luneberg lens. First we use spherical harmonics, the Mie theory, to express the electric and magnetic field in spherical polar coordinate system. We expand a plane wave in vector spherical harmonics. This problem can not be solved by the same boundary condition, because there are two different materials, dielectric and metallic, on the surface. So we use point-matching method (PMM) to solve this mixed boundary value problem. The method consists of satisfying the boundary conditions in the contact plane only at a finite point. Then we use the boundary condition of each layer, we can find the coefficient of each layer. Finally we can find the all field of the incident wave into a Lungberg lens. In the discussion, we use different layers of lens to approach the ideal Lungberg lens. We take the balance in different layers and the focusing effect. What is the influence of the different wave length and what is the difference between Lungberg lens and Lungberg lens reflector in scattering patterns. We also provide a picture of wave propagation through Lungberg lens to see if the points are exactly on the surface, the incoming wave reflected by the metallic cap is a perfect plane wave or not. Finally, we provide the poynting vector on the special surface. The purpose is to see if the energy focuses to a point on the surface.

碩士
大葉大學
電機工程學系碩士班
91
Luneberg lens is composed from dielectric substance which has multi-layer and different permittivity. The shape of the Luneberg lens is spherical or semi-spherical. In the thesis, spherical-Luneberg lens is changed to cylindrical, in order to construct easily. The parallel metal-sheet Luneberg lens can instead of cylindrical - Luneberg lens, using different separation metal-sheet. The distance of the separate metal-sheet can be changed to substitute for multi-layer dielectric substance. Luneberg lens, one of widely use of lens antenna. It has high directivity and high antenna efficiency. Therefore, it is suitable for the application in the multiple beam antenna system. Usually, Luneberg lens operates in the linear-polarization. We can use polarizer to change linear-polarization to circular-polarization. In this thesis, a Luneberg lens and spiral-polarizer are design and implement to have five-direction antenna beam ( 、 and ). The multiple beam antenna can operates in circular-polarization when spiral-circulator is used.