The Pennsylvania State University The Graduate School Department of Engineering Science and Mechanics Permittivity Measurement of Circular Shell Using a Spot-Focused Free-Space System and Reflection Analysis of Open-ended Coaxial Line Radiating into a Chiral Medium AThesisin Engineering Science and Mechanics by Kai Du Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August, 2001 We approve this thesis of Kai Du. Date of Signature Vasundara V. Varadan Distinguished Professor of Engineering Science and Mechanics Thesis Advisor Co-Chair of Committee Vijay K. Varadan Distinguished Alumni Professor of Engineering Mechanics and Electrical Engineering Co-Chair of Committee Raj Mittra Professor of Electrical Engineering Douglas H. Werner Associate Professor of Electrical Engineering Jose A. Kollakompil Senior Research Associate R. P. McNitt Professor of Engineering Science and Mechanics Head of the Department of Engineering Science and Mechanics Abstract The present thesis is concerned with electromagnetic simulations for material char- acterization. The content can be divided into two parts. The first part addresses questions related to a spot-focused free-space microwave measurement system. The goal is to establish an inversion procedure for non-planar samples. The second part is focused on the problem of an open-ended coaxial line radiating into a chiral medium. The objective is to evaluate the feasibility of using the open-ended probe method for characterization of chiral materials. The free-space system under study consists mainly of two horn-lens antennas and a vector network analyzer. Permittivity and permeability of a sample under test are determined from its reaction to beam waves generated by the antennas. The network analyzer provides measurement output in the form of S-parameters for a linear two-port network. This system has been designed and successfully tested for planar slab samples, where a uniform plane-wave model has been used in the inversion algorithm. Extension to curved objects calls for a new model in which the wave scattering needs to be numerically simulated, and the measured S-parameters have to be defined carefully so that their (mathematical) expressions conform with the physics. To simplify the problem, the incident beam is assumed to be Gaussian, and samples with the simple geometry of a circular cylindrical slab are considered. Existing theories for Gaussian beam scattering by simple shapes and antenna near- field scanning are combined together to obtain an improved model. The improvement lies in the fact that characteristics of the antenna are now manifested in formulation iii Abstract iv of the measured response. The model is first applied to simulate free-space mono-static measurement of pla- nar slab samples. Numerical results are presented to validate the plane-wave approx- imation used in the inversion. Next, a three dimensional formulation is derived for the bi-static setup. Calculation shows that, depending on the sample properties and thickness, the difference between the reflection coefficients of a Gaussian beam and a plane wave might be much smaller than the measurement error. Thus inversion of measured data using the plane wave model is appropriate even without correction for the defocusing effect. Finally, a simple technique is presented to estimate the reflec- tion of two dimensional Gaussian beam by a circular shell. The corresponding data inversion problem is studied with several approaches, including an optimization pro- cedure using only magnitude data and a curvature correction procedure. The results are carefully evaluated and possible improvements are discussed. Extensive experiments have been performed using the free-space system. The fo- cus is on the calibration method and settings of some important network analyzer parameters. For the free-space bistatic setup, it is found that an offset-short method reported previously is inappropriate. Therefore a simple two-tier calibration proce- dure is proposed. Inversion of measured data for Teflon, Plexiglas and glass slab samples shows that this procedure produces permittivity values within 10% differ- ence from published data. Curved Plexiglas samples of several radii of curvature have also been measured. The data are compared with theoretical prediction and potential causes of the deviation are identified. A practical technique is proposed for estimation of the time gating error in network analyzer measurement. This technique can be used to find out desirable minimum gate span for free space measurement. The open-ended coaxial line method has been extensively studied by other re- Abstract v searchers. However, its potential application to chiral material is an interesting prob- lem which has yet to be investigated. A spectral-domain moment method solution is presented in this thesis. The formulation obtained can also be to study the perfor- mance of aperture antennas covered with chiral medium, which has been proposed for controlling the polarization property. Contents List of Figures ix List of Tables xv Acknowledgments xvi 1 Introduction 1 1.1Motivations................................ 3 1.2OverviewoftheIssuesStudiedinThisThesis............. 6 1.3SummaryofContributions........................ 16 1.4OrganizationoftheThesis........................ 18 2 Theoretical Model for Measuring the Dielectric Properties of Planar Slabs Using a Spot-Focused Free-Space System 20 2.1IntroductoryRemarks.......................... 21 2.2 Description of the Spot-focused Free-space Measurement System . 27 2.3ModelingAssumptions.......................... 31 2.4Meaningof“ReflectionCoefficient”forBeams............. 39 2.5 2—D Gaussian beam scattering by a dielectric slab at normal incidence 46 2.6 2—D Numerical Results and Comparison with Measurement . 48 2.7 Formulation of 3—D Gaussian Beam Obliquely Incident on a Slab . 52 2.7.1 SpecifyingtheIncidentBeam.................. 54 vi CONTENTS vii 2.7.2 SpectrumFunctionfortheReflectedField........... 58 2.7.3 “ReflectionCoefficient”for3—DGaussianBeam........ 60 2.8DirectCouplingintheBistaticSetup.................. 63 2.9 Experimental Results for Planar Slab Using Bistatic Setup . 66 2.10Conclusion................................. 79 3 Techniques for Obtaining Dielectric Properties of Curved Slab Using Only Reflection Measurement 80 3.1IntroducingtheCurvedSlabProblem.................. 80 3.2 Literature on the Scattering of Shaped Beam by Curved Objects . 82 3.3AModificationoftheFourierExpansionmethod............ 84 3.4TheReflectedFieldandReflectionCoefficient............. 87 3.5 Numerical Result for 2—D Gaussian Beam Reflection from circular shell 91 3.6ExperimentsandDataInversionforCircularShells.......... 96 3.7Conclusion................................. 104 4 Open-ended Coaxial Line Radiating into a Chiral Medium 107 4.1Introductoryremark........................... 108 4.2Basicideaforsolvingthehalfspaceproblem..............110 4.3Formulation................................ 112 4.3.1 FieldRepresentationintheChiralHalf-Space......... 112 4.3.2 Electromagnetic Fields in the Coaxial Waveguide . 114 4.3.3 SpectralDomainSurfaceAdmittance.............. 116 4.3.4 IntegralEquation......................... 118 4.3.5 Method of Moment—Derivation of Matrix Equations . 119 4.4NumericalResults............................. 122 4.5Conclusion................................. 125 5 Summary 131 Table of Contents viii Appendix A: Gaussian Beam 134 Appendix B: Near Field and Far Field 140 Appendix C: Time Gating in 8510C 143 M − M + Appendix D: Derivation of the reaction ml and ml 154 Bibliography 164 List of Figures 1.1 Magnitude plot for E-polarized uniform plane wave scattered by a per- fectlyconductingcylinder......................... 9 1.2 Phase plot for E-polarized uniform plane wave scattered by a perfectly conductingcylinder............................ 10 1.3 Result of real ray tracing for a Gaussian beam scattering by a conduct- ingcylinder................................. 11 2.1 Magnitude of plane wave reflection coefficient as a function of permit- tivity ε foradielectricslab........................ 24 2.2 Illustration of a spot-focused free-space measurement system. 28 2.3 A picture of the spot-focused free-space measurement system used in thisstudy.................................. 29 2.4Farfieldpatternofthehorn-lensantennaat11GHz........... 33 2.5 Field amplitude distribution over a 16cm × 16cm rectangular area on thefocalplane............................... 35 2.6 Phase distribution of the focal region field measured at 10.92GHz using acustom-madedipole........................... 36 2.7 The E-plane 1/e half beam width c as a function of frequency. 38 2.8 The H-plane 1/e half beam width e as a function of frequency. 39 ix LIST OF FIGURES x 2.9ThecouplingbetweentwoHermite-Gaussianbeams........... 41 2.10 Diagram for defining the coupling coefficient between two antennas. 42 2.11 Magnitude of reflection coefficient versus frequency for a 2-D E-polarized Gaussian beam reflected by a dielectric slab at normal incidence. 50 2.12 Magnitude of reflection coefficient versus frequency for a 2-D E-polarized Gaussian beam reflected by a dielectric slab at normal incidence. 51 2.13 Geometry and coordinate systems for the modeling of bistatic free spacemeasurement. ........................... 53 E˜i k , k θ k θ k ,k /k k /k 2.14 Plot of y( x 0) = ( z cos + x sin )Φ( x y) z v.s. x 0 for dif- ferent incident angle θ and beamwidth w0x. .............. 58 2.15 A schematic diagram showing the basic idea of the theoretical formu-