MICROWAVE OPTICS RESEARCH by Allen Andersen A senior thesis submitted to the faculty of Brigham Young University-Idaho In partial fulfillment of the requirements for the degree of Bachelor of Science Department of Physics Brigham Young University-Idaho April 2012 Copyright © 2012 Allen Andersen All Rights Reserved   ii BRIGHAM YOUNG UNIVERISTY-IDAHO DEPARTMENT APPROVAL of a senior thesis submitted by Allen Andersen This thesis has been reviewed by the research advisor, thesis coordinator, and department chair and has been found to be satisfactory. _____________ _____________________________________________________ Date Todd Lines, Advisor _____________ _____________________________________________________ Date David Oliphant, Thesis Coordinator _____________ _____________________________________________________ Date Stephen Turcotte, Chair   iii ABSTRACT MICROWAVE OPTICS RESEARCH Allen Andersen Department of Physics Bachelor of Science The Physics Department x-band microwave optics equipment was originally intended for use in classroom demonstrations. I evaluated this equipment for use in research, determined additional equipment needed in order to perform attenuation and other experiments, and have used it to conduct research on the transmission properties of paper and other substances. The additional equipment includes a goniometer base and Radio Frequency absorbing foam apertures. This equipment was needed in order to create a standard procedure, take reasonably accurate measurements, and reduce undesired standing wave effects. I performed mathematical and experimental analysis to determine the necessary parameters of the new equipment. The new apparatus is comparable to setups featured in published journal articles and will give research opportunities to future students.   iv With this equipment I investigated the transmission properties of paper. I showed that paper acts as linear polarizer in two independent ways. A stack of paper edge-on as the incident surface is a known linear polarizer. After researching the conductive properties of paper, I predicted then demonstrated that microwaves incident on the face of a stack of paper is also a linear polarizer. The polarizing properties of paper have educational value for demonstrating polarization and relating the macroscopic to the microscopic.   v ACKNOWLEDGMENTS I would like to thank Todd Lines, my advisor for this project. I would also like to thank David Oliphant, Charles Andersen, and Andy Johnson for their help in obtaining and creating the necessary materials for the equipment, Phil Scott for writing much of the code used to gather and analyze data, and Josh Barney for his collaboration. I appreciate the entire BYU-Idaho Physics department’s role in my education. I thank Sam Nielson and Leslie Twitchell for time they spent answering my questions about paper. I especially thank my wife for her encouragement and patience with me as I’ve worked on this project.   vi Contents Table  of  Contents                                                                                                                                                                                              vii     List  of  Figures                                                                                            ix   1  Introduction........................................................................................................................................1   1.1 Project Background................................................................................................................1   2  Design  of  the  Apparatus..................................................................................................................4   2.1 Basic Configuration...............................................................................................................4 2.2 Mathematical Models............................................................................................................8 2.3 Experimental Techniques....................................................................................................10 3  Building  and  testing  the  Apparatus.........................................................................................18   3.1 Goniometer Base..................................................................................................................18 3.2 Building the Foam Apertures...............................................................................................20 3.3 Testing the Apparatus..........................................................................................................23 4  Results................................................................................................................................................30   4.1 General Procedure for Using the Microwave Optics Apparatus.........................................30 4.2 Falsification of Paper as a Metamaterial..............................................................................31 4.3 Polarizing Properties of Paper.............................................................................................34 4.3.1 Theory...........................................................................................................................34 4.3.2 Experimental Demonstration........................................................................................38 4.3.3 Classroom Demonstration.............................................................................................45 4.4 Opportunities for Future Research.......................................................................................47 5  Conclusion........................................................................................................................................49   Bibliography........................................................................................................................................50   A  Atmospheric  Attenuation  of  Microwaves  by  Water  Vapor..............................................54               vii B  BYU-­Idaho  Physics  Department  Microwave  Optics  Equipment  Manual.....................58   B.1 Original Microwave Optics Kit...........................................................................................58 B.1.1 Microwave Transmitter................................................................................................58 B.1.2 Microwave Receiver....................................................................................................60 B.1.3 Assorted Optics and Equipment...................................................................................62 B.2 Goniometer Apparatus Instructions ...................................................................................64 B.2.1 Setup.............................................................................................................................64 B.2.2 Recording Data.............................................................................................................66 C  Thin  Film  Experiment  for  Determining  Wavelength..........................................................68   C.1 Procedure.............................................................................................................................68 C.2 Results.................................................................................................................................70   D  Microwave  Beam  Shape...............................................................................................................71   D.1 Purpose................................................................................................................................71 D.2 Procedure............................................................................................................................72 D.3 Results.................................................................................................................................74 E  Computer  Code................................................................................................................................78   E.1 Matlab Code to Plot Beam Shape........................................................................................78 E.2 Maple GUI for Diffraction through Square, Round and Slit Apertures..............................79 E.3 LabView Program for Collecting Microwave Intensity Data.............................................79 E.4 IntensityAvgNorm.m...........................................................................................................82 E.5 SimpsonsForAvg.m.............................................................................................................83 E.6 NormalizeColumn.m...........................................................................................................84 E.7 SimpsonsNormalization.m..................................................................................................85 F  Accessing  Data.................................................................................................................................88                                           viii List of Figures Figure 2.1 Experimental setup used by Velazquez-Ahumada et al. ...........................................5 Figure 2.2 Apparatus design........................................................................................................6 Figure 2.3 Graph of reflectivity versus frequency for absorbing foam.......................................7 Figure 2.4 Plot of diffraction pattern through a circular aperture..............................................10 Figure 2.5 Photograph of first experiment to determine aperture size......................................12 Figure 2.6 Photographs of second experiment to determine aperture size................................12 Figure 2.7 Plot of the data from the second aperture size experiment.......................................13 Figure 2.8 Photograph of third experiment to determine aperture size.....................................14 Figure 2.9 Plot of the improved data from the third aperture size experiment..........................14 Figure 2.10 Plot of the first attenuation experiment..................................................................16 Figure 2.11 Plot of the second attenuation experiment.............................................................16 Figure 2.12 Plot of predicted diffraction pattern for 5cm circular aperture ..............................17 Figure 3.1 Photograph of goniometer base................................................................................18 Figure 3.2 Photograph of transmitter stand...............................................................................20 Figure 3.3 Photograph of aperture frames.................................................................................21 Figure 3.4 Photograph of apertures with foil backing...............................................................21 Figure 3.5 Photographs of aperture assembly............................................................................22 Figure 3.6 Photograph of finished RF aperture.........................................................................22 Figure 3.7 Photograph of RF aperture test.................................................................................24 Figure 3.8 Plot of RF aperture test results for standing waves..................................................25 Figure 3.9 Plot of RF aperture angular diffraction test..............................................................27 Figure 3.10 Plot of RF aperture parallel diffraction test............................................................28 Figure 3.11 Plot of waveguide test data.....................................................................................29   Figure 4.1 Photograph of complete microwave optics apparatus..............................................31 Figure 4.2 Prism diagram...........................................................................................................32 Figure 4.3 Plot of intensity versus angle for a paper prism.......................................................33 Figure 4.4 Images of wood fibers..............................................................................................35 Figure 4.5 Photograph of paper sample with highlighted fibers................................................36 Figure 4.6 Photograph of destructive grain direction test..........................................................38 Figure 4.7 Photograph of edge-on polarization test...................................................................39   ix Figure 4.8 Plot of intensity patter for edge-on polarization test................................................40 Figure 4.9 Photograph of broad side polarization test...............................................................41 Figure 4.10 Plot of intensity patter for broad side polarization test..........................................41 Figure 4.11 Photograph of known linear polarizer....................................................................42 Figure 4.12 Photograph of known polarizer test........................................................................42 Figure 4.13 Plot of intensity patter for known polarizer test.....................................................43 Figure 4.13 Plot comparing the polarization test results...........................................................44 Figure 4.14 Photograph of classroom demonstration setup.......................................................47   Figure B.1 Photograph of microwave transmitter and power supply........................................59 Figure B.2 Photograph of microwave receiver..........................................................................61 Figure B.3 Photographs of additional microwave optics and equipment .................................63 Figure B.4 Photographs of how to orient goniometer base ......................................................64 Figure B.5 Photograph of complete microwave optics apparatus ............................................66   Figure C.1 Photograph of ‘thin film’ experiment......................................................................70   Figure D.1 Beam shape diagram................................................................................................71 Figure D.2 Experiment diagram................................................................................................72 Figure D.3 Photograph of beam shape experiment....................................................................73 Figure D.4 Beam shape plots.....................................................................................................75 Figure D.5 Plots of data matrix..................................................................................................76         x