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Magneto-Optical Sensing Utilizing the Faraday Effect in Bulk Cd⇆‡‰Â University of Rhode Island DigitalCommons@URI Open Access Master's Theses 1988 Magneto-Optical Sensing Utilizing the Faraday Effect in Bulk Cd₁₋ₓMnₓTe Jeff C. Adams University of Rhode Island Follow this and additional works at: https://digitalcommons.uri.edu/theses Recommended Citation Adams, Jeff C., "Magneto-Optical Sensing Utilizing the Faraday Effect in Bulk Cd₁₋ₓMnₓTe" (1988). Open Access Master's Theses. Paper 838. https://digitalcommons.uri.edu/theses/838 This Thesis is brought to you for free and open access by DigitalCommons@URI. It has been accepted for inclusion in Open Access Master's Theses by an authorized administrator of DigitalCommons@URI. For more information, please contact [email protected]. MAGNETO-OPTICAL SENSING UTILIZING THE FARADAY EFFECT IN BULK Cdt-xMnxTe BY JEFF C. ADAMS A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN ELECTRICAL ENGINEERING UNIVERSITY OF RHODE ISLAND 1988 MASTER OF SCIENCE THESIS OF JEFF C. ADAMS APPROVED: Thesis Committee Major Professor Dean of the Graduate School UNIVERSITY OF RHODE ISLAND 1988 ABSTRACT A magnetic field sensor utilizing the Faraday effect in bulk Cd1-xMnx Te was investigated. The magnetic field sensitivity was found theoretically as a function of various system parameters and compared with experiment. The magneto-optical Verdet constant of Cd,5Mn5Te was measured at a wavelength of 633 nm, and found to be 0.15° cm-lGauss-1. The optical absorption was measured to be 0.9 cm-1, and the refractive index 3.1; all values agreed well with published measurements. A polarization preserving fiber was used to link the Cd,5Mn,5Te sensor in a polarization-rotated reflection scheme in order to cancel environmentally induced linear birefringence fluctuations which contribute to system noise. The linear birefringence fluctuations were modelled as a gaussian distributed random variable and included in the formulation of the sensing system's signal-to-noise ratio. Since the standard deviation of the birefringence fluctuations was not known a priori, its value was chosen to match theory with experiment, and then compared with data from recently published papers examining the statistics of linear birefringence fluctuations in polarization-preserving fibers; published values of the standard deviation of birefringence fluctuations for a given environmental perturbation compared reasonably with values inferred from our experimental data. Experimental results showed a marked improvement in the magnetic sensor's signal-to-noise ratio using this method of polarization-rotated reflection. ii ACKNOWLEDGEMENTS The author would first like to thank his major professor, Dr. Harish Sunak, whose enthusiastic support made it possible to pursue this subject. Helpful discussions also came from Dr. Lengyel, Dr. Cuomo, Dr. Letcher, Dr. Polk, Dr. Vaccaro, and Dr. Swaszek. Also, a special thanks to Joe Zieman, who made the Cd1-xMnx Te crystals at the Oregon Graduate Center with support from Dr. Russell Kremer, and Bill Dippert of Tektronix, whose recognition of the viability of optical sensors led to the support of this research. Appreciation also goes out to Andy Rosenberger of the Mechanical Engineering Department for diamond cutting new crystal samples, Ganiyu Hanidu for instruction on crystal polishing, and Jim Vincent for his assistance in acquiring needed instrumentation. Finally, I would like to thank my wife, Laurie, for enduring a long distance relationship during my stay at URI. iii CONTENTS List of Tables Vl List of Figures vu Chapter 1 Introduction 1.1 Introduction to optical sensors 1 1.2 Significance of research 2 1.3 Organization of thesis 4 Chapter 2 The Faraday Effect 2.1 Introduction 7 2.2 Faraday rotation--general theory 10 2.3 Properties of Cd1-xMnxTe 17 Chapter 3 Verdet Constant Measurement in Cd1-xMnxTe 21 Chapter 4 Determination of the Minimum Resolvable Polarization Rotation 4.1 Introduction 28 4.2 Affect of an analyzer on partially polarized light 28 4.3 Output intensity change due to a change in polarization angle 30 4.4 Signal-to-noise ratio of detected rotation t.9 31 4.5 Theory related to experiment 34 4.6 Measured degree of polarization out of crystal 35 4.7 Dynamic range of measurement 36 Chapter 5 Fiber-Linked Sensor--Theory 5.1 Introduction 39 5.2 Polarization-rotated reflection in a non-ideal sensor system 43 5.3 Total SNR in fiber-linked sensor 49 5.4 Increasing the sensitivity 51 iv Chapter 6 Fiber-Linked Sensor--Experiment 6.1 Introduction 57 6.2 Pre-exyeriment--discussion 57 6.3 Expenmental procedure 59 6.4 Procedure discussion 60 6.5 Experimental results 61 6.6 Experimental results versus theory 65 Chapter 7 Magneto-optic Sensors--Summary 7.1 Applications 71 7.2 Future research 74 List of References 75 Appendix 1 Hall Effect Magnetometer 79 Appendix 2 Magnetic Field Generator 83 Appendix 3 Parallelism of Crystal Sides--an Estimate 95 Appendix 4 Refractive Index Measurement 98 Appendix 5 Absorption Measurement 100 Appendix 6 Measurement of Wave-Plate Retardance 102 Appendix 7 Jones Matrix Calculations 104 Appendix 8 Evaluation of o b.fH 108 Appendix 9 Experimental data: !J.0 vs. B 110 Bibliography 115 v LIST OF TABLES 2.1 Verdet constants and temperature dependence of various materials 9 Al.l Hall output voltage vs. magnetic field 81 A2.1 Measured magnetic field above air gap vs. coil current 88 A2.2 Measured magnetic field at location above air gap where beam transversed crystal 91 A9.1 Faraday rotation ll0 vs. magnetic field 110 vi LIST OF FIGURES 2.1 Coordinate system for wave propagation in a plasma 9 2.2 Polarization rotation relative to plasma boundary 17 3.1 Set-up for determining Verdet constant 23 3.2 Polarization orientation to analyzer 23 3.3 Polarization rotation vs. B-field: 0-1000 Gauss 26 3.4 Polarization rotation vs. B-field: 0-400 Gauss 26 3.5 Polarization rotation vs. B-field: 0-100 Gauss 27 3.6 Polarization rotation vs. B-field: 0-20 Gauss 27 4.1 Elliptical polarization incident on analyzer 28 4.2 Ratiometric Faraday rotation measurement 37 5.1 Basic polarization-rotated reflection scheme 40 5.2 Polarization-rotated reflection with Faraday effect sensor 42 5.3 Jones matrices for sensor system 45 5.4 Minimum measurable B-field for ~f = 1 Khz 54 5.5 Minimum measurable B-field for ~f = 10 Mbz 55 5.6 Minimum measurable B-field for ~f = 100 Mhz 56 6.1 Fiber-linked magnetic sensor configuration 58 6.2 Signal and noise spectrum of fiber-linked magnetic sensor; environmental condition: air conditioner on. 63 6.3 Signal and noise spectrum of fiber-linked magnetic sensor; environmental conditions: air conditioner off, warm air from hair dryer. 64 vii 6.4 Theoretical Li8mi~ vs. a Li/31 for experimental conditions of Figure 6.2a (cf> = 5 ° ) 67 6.5 Theoretical Li8mifi vs. a Li/3 for experimental conditions of 0 1 Figure 6.2b (cf> = ) 68 6.6 Photograph of fiber-linked magnetic sensor experiment 70 Al.1 Functional block diagram of Hall sensor 79 Al.2 Hall sensor compensation circuit 80 Al.3 Hall output voltage vs. solenoid B-field 82 Al.4 Set-up for Hall voltage vs. B-field measurement 82 A2.1 Set-up for B-fa;ld measurement above toroid gap 86 A2.2 Plot of measured B-field in air gap vs. coil current 90 A2.3 Set-up for measuring frequency response of coil 90 A2.4 Plot of I vs. B: 0-500 Gauss 94 A2.5 Plot of I vs. B: 0-200 Gauss 94 A3.l Set-up for determining parallelism of crystal 95 A3.2 Ray analysis of light in non-parallel crystal 96 AS.l Absorption measurement set-up 100 A6.l Set-up for retardance measurement 102 viii CHAPTER 1 o INTRODUCTION 1.1 Introduction to optical sensors In its broadest definition, optical sensing is the detection and analysis of light which has been modulated or modified by some perturbation. The perturbation could be virtually anything: temperature, displacement, acceleration, acoustics, electric and magnetic fields, and so on. Characterizing the response of some light parameter to a perturbation thus enables us to measure that perturbation. Optical sensors can generally be placed into one of three catagories: (1) an optical fiber acting as the transducer, (2) an optical fiber acting simply as a link to an external transducer, and (3) the optical transducer using free space light, without an optical fiber link. Since a number of papers have been written which cover the full gamut of optical sensor technology [1]-[10], we will provide only salient features of optical sensors for the purposes of this introduction. The advantages of many optical sensors are their inherent compatability with optical fiber telemetry, immunity to electromagnetic interference and other hostile environments, and high sensitivity. Examples of sensitivities for various optically measured quantities include: (1) temperature--200° to -50° C ±0.1° C using a fiber microprobe by Luxtron Corp. [2]; (2) acceleration--6 x 10-8 g's detected at 35 Hz at Optech, Inc. [8]; (3) pH--6 - 12 ±0.02 [2]; (4) sound pressure--3 - 170 dB with reference to 1 µP [2]; (5) magnetic fields--10-9 Gauss at low frequencies [1]; (5) 1 flow--10-6 - H>5 m/s [2]. Futhermore, though many such sensors are still in the research and development stage, the market predictions are impressive. According to Kessler Marketing lntellegence, the consumption of fiber-optic sensors--not including ancillary electronics and packaging--will grow 30 percent annually, moving from about $20 million in 1983 to $278 million in 1993. From 1979 to 1981, the number of fiber-optic sensor patents increased nearly 2.5 times [11].
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