DOCSLIB.ORG

Optical and Magneto-Optic Kerr Effects of Mnbi, Ni2mnga, and Gd5si2ge2 Joong-Mok Park Iowa State University

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Optical and Magneto-Optic Kerr Effects of Mnbi, Ni2mnga, and Gd5si2ge2 Joong-Mok Park Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2004 Optical and magneto-optic Kerr effects of MnBi, Ni2MnGa, and Gd5Si2Ge2 Joong-mok Park Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Condensed Matter Physics Commons, and the Optics Commons Recommended Citation Park, Joong-mok, "Optical and magneto-optic Kerr effects of MnBi, Ni2MnGa, and Gd5Si2Ge2 " (2004). Retrospective Theses and Dissertations. 1117. https://lib.dr.iastate.edu/rtd/1117 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Optical and magneto-optic Kerr effects of MnBi, NigMnGa, and Gd^SigGeg by Joong-mok Park A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Condensed Matter Physics Program of Study Committee: David W. Lynch, Co-major Professor Bruce N Harmon, Co-major Professor Paul C. Canfield John M. Hauptman R. William McCallum Iowa State University Ames, Iowa 2004 UMI Number: 3145677 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3145677 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ii Graduate College Iowa State University This is to certify that the doctoral dissertation of Joong-mok Park has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. For the Major F^ gram iii TABLE OF CONTENTS NOMENCLATURE xii ABSTRACT xiv 1. INTRODUCTION 1 2. CLASSICAL AND QUANTUM MECHANICAL THEORY 7 2.1 Electromagnetic field in a solid 7 2.2 Jones vectors and matrices to describe polarized light 10 2.3 Macroscopic explanation of magneto-optic effect 11 2.4 Classical microscopic theory 15 2.4.1 Classical Lorentz-Drude model for dielectric constants 16 2.4.2 Diagonal component of dielectric constants exx 16 2.4.3 Off-diagonal component of dielectric constants exy 20 2.4.4 Skew-scattering theory 21 2.5 Quantum-mechanical theory for MOKE 23 2.5.1 The origin of MOKE 25 2.5.2 Electron band structure and optical conductivity calculation 28 3. EXPERIMENT 32 3.1 Magneto-optic Kerr effect experiment 32 3.2 MOKE with Jones vectors and matrices 35 3.3 Calibration of Kerr signal 37 3.3.1 Kerr angle calibration 38 3.3.2 Kerr ellipticity calibration 39 iv 3.4 Reflectance difference for anisotropic materials 41 3.5 Three-phase model for a thin film on the sample 43 3.6 Ellipsometry experiment 46 3.6.1 Ellipsometry for anisotropic materials 46 4. MnBi 49 4.1 Introduction 49 4.2 Electronic structure calculation of MnBi 52 4.3 Experiment 55 4.4 Results 58 5. NigMnGa 64 5.1 Introduction 64 5.2 Experiment 67 5.3 Band structure calculation 68 5.4 Results 73 6. Gd5Si2Ge2 82 6.1 Introduction 82 6.2 Experiment 86 6.3 Results 88 7. DISCUSSION 100 8. CONCLUSION 102 APPENDIX A. JONES VECTORS AND MATRICES 104 A.l Jones vectors to describe polarized light 104 A.2 Jones matrices to describe optical components 104 APPENDIX B. USEFUL RELATIONS 106 APPENDIX C. BRILLOUIN ZONE 108 C.l Simple cubic lattice 109 C.2 Body-centered cubic lattice 110 V C.3 Face-centered cubic lattice Ill C.4 Hexagonal closed-packed lattice 112 APPENDIX D. ELECTRON-PHOTON INTERACTION ENERGY .... 113 BIBLIOGRAPHY 114 ACKNOWLEDGEMENTS 121 vi LIST OF FIGURES Figure 1.1 Two types of magneto-optic effect when linearly polarized light is inci­ dent on the sample : Faraday effect for transmission and Kerr effect for reflection in polar geometry 3 Figure 1.2 Linearly and elliptically polarized states (a) An incident linearly po­ larized wave before MOKE, (b) An elliptically polarized wave after reflection from the magnetized sample 5 Figure 2.1 (a) Linearly polarized light decomposes into RCP and LCP with the convention of exp(-iujt). (b) After reflection the phases and ampli­ tudes of the RCP and the LCP are changed and the sum of them are elliptically polarized. The definitions of RCP and LCP are changed with the convention of exp(iu)t) 12 Figure 2.2 Real (£ixx) and imaginary faxx) parts of the interband dielectric con­ stants from the Lorentz model with Hujo = 4.0 eV, TiUp = 5.0 eV, and hj = 0.5 eV 17 Figure 2.3 Real (eiXx) and imaginary {e^xx) parts of the intraband dielectric con­ stants from the Drude model with fou)p = 5.0 eV, fry = 0.5 eV 19 vii Figure 2.4 (a) Spin-split states with exchange and spin-orbit interaction energy. The solid and dotted lines represent right- and left-circular polariza­ tion, respectively, (b) Optical transition matrix elements for each spin state, (c) Absorptive part of the diagonal component of the optical conductivity. The bold and narrow lines represent spin-up and -down contributions, (d) Absorptive part of the off-diagonal component of the optical conductivity 27 Figure 3.1 Experimental setup for MOKE (M: modulator, PMT: photomultiplier tube, P: polarizer, A: analyzer, DVM: digital voltmeter, PEM: piezo­ electric modulator, F: filter) 33 Figure 3.2 Energy-dependent calibration constants A and B. The lines are the fitting results after finishing the calibrations 40 Figure 3.3 3-phase model of a thin film on the sample. r\2 is the reflection coeffi­ cient at the first interface between air and the thin film and ?2z is for interface of the thin film and sample 43 Figure 4.1 MnBi (low-temperature phase) hexagonal crystal structure. The dark spheres represent Bi atoms and gray ones represent Mn atoms 50 Figure 4.2 Calculated Kerr rotations and Kerr rotation measured on single-crystal MnBi. Theoretical spectra are taken from Jaswal et al. (open squares) [60], Oppeneer et al. (dashed line) [61], Kôhler and Kiibler (thick line) [63], Ravindran et al. (asterisks) [64], Kulatov et al. (dotted line) [65], and measured Kerr spectra (closed squares) from single-crystal MnBi. 53 Figure 4.3 Spin-polarized MnBi band structure calculated with the LMTO-ASA code. The solid line represents majority spin and dashed line represents minority spin. See appendix for the symmetry lines 56 Figure 4.4 Total and partial DOS of MnBi calculated with the LMTO-ASA code. 57 viii Figure 4.5 MnBi powder X-ray diffraction pattern. The peaks indicate an MnBi phase and a minority Bi phase 59 Figure 4.6 Measured Kerr rotations of MnBi thin films and a single crystal MnBi (closed squares). Thin film data are taken from Di et al. (open squares) [55], Fumagalli et al. (open circles) [57], Huang et al. (open triangles) [56] 60 Figure 4.7 Calculated MOKE spectra with the TB-LMTO ASA method with spin- orbit interaction. Drude terms are included in the calculations 62 Figure 5.1 Fee crystal structure of the NigMnGa Heusler alloy. Ga, Ni, Mn, Ni atoms are located along the body diagonal 65 Figure 5.2 Spin-polarized band structure of the fee structured NigMnGa Heusler alloy. The spin-orbit interaction was not included. The solid and dotted lines represent majority and minority band, respectively. See appendix for the symmetry lines 70 Figure 5.3 Total and partial DOS of the fee structured NigMnGa Heusler alloy calculated with spin-polarized TB-LMTO method. The upper halves are majority spins and the lower ones are minority spins 71 Figure 5.4 Calculated Kerr effects for the fee Ni^MnGa Heusler alloy. The solid and dotted lines are Kerr spectra with and without the Drude term. 72 Figure 5.5 (a) Real part, £\, and (b) imaginary part, £2. of the diagonal component of the dielectric function of the Ni^MnGa Heusler alloy (100) and (110) surfaces measured with ellipsometry. Insert in (b) represents the optical conductivity 74 Figure 5.6 Calculated real (eixx) and imaginary (e2xx) parts of the dielectric con­ stants iTotal = £mtra çDrude including the intraband and Drude term. Measured ones (squares) with the (100) plane sample were also plotted for the comparison 75 ix Figure 5.7 Magneto-optic Kerr spectra of the Ni2MnGa Heusler alloy. The calcu­ lated Kerr rotation and ellipticity were scaled by 50 % 77 Figure 5.8 Magneto-optic Kerr spectra of the Ni (100) and (110) plane single crystals. 79 Figure 5.9 Complex off-diagonal component of the dielectric function of NigMnGa converted from the measured Kerr spectra. The solid lines are calcu­ lated with the TB-LMTO methods and scaled by 50 % 81 Figure 6.1 Interaction of polarized light with an anisotropic material at near nor­ mal incidence. Linearly polarized light is incident at angle from one of the crystal axes. 0o„t is not the same as 6a for the particular direction of an anisotropic material 83 Figure 6.2 Orthorhombic a-phase GdgSigGeg crystal structure.
Load more

Recommended publications
  • Magneto-Optical Metamaterials with Extraordinarily Strong Magneto-Optical Effect Xiaoguang Luo, Ming Zhou, Jingfeng Liu, Teng Qiu, and Zongfu Yu
    Magneto-optical metamaterials with extraordinarily strong magneto-optical effect Xiaoguang Luo, Ming Zhou, Jingfeng Liu, Teng Qiu, and Zongfu Yu Citation: Applied Physics Letters 108, 131104 (2016); doi: 10.1063/1.4945051 View online: http://dx.doi.org/10.1063/1.4945051 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/108/13?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Enhanced Faraday rotation in hybrid magneto-optical metamaterial structure of bismuth-substituted-iron-garnet with embedded-gold-wires J. Appl. Phys. 119, 103105 (2016); 10.1063/1.4943651 Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface Appl. Phys. Lett. 107, 121104 (2015); 10.1063/1.4931704 Plasmon resonance enhancement of magneto-optic effects in garnets J. Appl. Phys. 107, 09A925 (2010); 10.1063/1.3367981 The magneto-optical Barnett effect in metals (invited) J. Appl. Phys. 103, 07B118 (2008); 10.1063/1.2837667 Anisotropy of quadratic magneto-optic effects in reflection J. Appl. Phys. 91, 7293 (2002); 10.1063/1.1449436 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.104.78.155 On: Fri, 03 Jun 2016 18:26:37 APPLIED PHYSICS LETTERS 108, 131104 (2016) Magneto-optical metamaterials with extraordinarily strong magneto-optical effect Xiaoguang Luo,1,2 Ming Zhou,2 Jingfeng Liu,2,3 Teng Qiu,1 and Zongfu Yu 2,a) 1Department of Physics, Southeast University, Nanjing 211189, China 2Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Wisconsin 53706, USA 3College of Electronic Engineering, South China Agricultural University, Guangzhou 510642, China (Received 24 February 2016; accepted 15 March 2016; published online 29 March 2016) In optical frequencies, natural materials exhibit very weak magneto-optical effect.
    [Show full text]
  • Lecture 11: Introduction to Nonlinear Optics I
    Lecture 11: Introduction to nonlinear optics I. Petr Kužel Formulation of the nonlinear optics: nonlinear polarization Classification of the nonlinear phenomena • Propagation of weak optic signals in strong quasi-static fields (description using renormalized linear parameters) ! Linear electro-optic (Pockels) effect ! Quadratic electro-optic (Kerr) effect ! Linear magneto-optic (Faraday) effect ! Quadratic magneto-optic (Cotton-Mouton) effect • Propagation of strong optic signals (proper nonlinear effects) — next lecture Nonlinear optics Experimental effects like • Wavelength transformation • Induced birefringence in strong fields • Dependence of the refractive index on the field intensity etc. lead to the concept of the nonlinear optics The principle of superposition is no more valid The spectral components of the electromagnetic field interact with each other through the nonlinear interaction with the matter Nonlinear polarization Taylor expansion of the polarization in strong fields: = ε χ + χ(2) + χ(3) + Pi 0 ij E j ijk E j Ek ijkl E j Ek El ! ()= ε χ~ (− ′ ) (′ ) ′ + Pi t 0 ∫ ij t t E j t dt + χ(2) ()()()− ′ − ′′ ′ ′′ ′ ′′ + ∫∫ ijk t t ,t t E j t Ek t dt dt + χ(3) ()()()()− ′ − ′′ − ′′′ ′ ′′ ′′′ ′ ′′ + ∫∫∫ ijkl t t ,t t ,t t E j t Ek t El t dt dt + ! ()ω = ε χ ()ω ()ω + ω χ(2) (ω ω ω ) (ω ) (ω )+ Pi 0 ij E j ∫ d 1 ijk ; 1, 2 E j 1 Ek 2 %"$"""ω"=ω +"#ω """" 1 2 + ω ω χ(3) ()()()()ω ω ω ω ω ω ω + ∫∫d 1d 2 ijkl ; 1, 2 , 3 E j 1 Ek 2 El 3 ! %"$""""ω"="ω +ω"#+ω"""""" 1 2 3 Linear electro-optic effect (Pockels effect) Strong low-frequency
    [Show full text]
  • Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser
    applied sciences Review Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser Shingo Yamamoto and Iwao Matsuda * Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-(0)4-7136-3402 Academic Editor: Kiyoshi Ueda Received: 1 June 2017; Accepted: 21 June 2017; Published: 27 June 2017 Abstract: We present a new experimental magneto-optical system that uses soft X-rays and describe its extension to time-resolved measurements using a free electron laser (FEL). In measurements of the magneto-optical Kerr effect (MOKE), we tune the photon energy to the material absorption edge and thus induce the resonance effect required for the resonant MOKE (RMOKE). The method has the characteristics of element specificity, large Kerr rotation angle values when compared with the conventional MOKE using visible light, feasibility for M-edge, as well as L-edge measurements for 3d transition metals, the use of the linearly-polarized light and the capability for tracing magnetization dynamics in the subpicosecond timescale by the use of the FEL. The time-resolved (TR)-RMOKE with polarization analysis using FEL is compared with various experimental techniques for tracing magnetization dynamics. The method described here is promising for use in femtomagnetism research and for the development of ultrafast spintronics. Keywords: magneto-optical Kerr effect (MOKE); free electron laser; ultrafast spin dynamics 1. Introduction Femtomagnetism, which refers to magnetization dynamics on a femtosecond timescale, has been attracting research attention for more than two decades because of its fundamental physics and its potential for use in the development of novel spintronic devices [1].
    [Show full text]
  • Chapter 7 Kerr-Lens and Additive Pulse Mode Locking
    Chapter 7 Kerr-Lens and Additive Pulse Mode Locking There are many ways to generate saturable absorber action. One can use real saturable absorbers, such as semiconductors or dyes and solid-state laser media. One can also exploit artificial saturable absorbers. The two most prominent artificial saturable absorber modelocking techniques are called Kerr-LensModeLocking(KLM)andAdditivePulseModeLocking(APM). APM is sometimes also called Coupled-Cavity Mode Locking (CCM). KLM was invented in the early 90’s [1][2][3][4][5][6][7], but was already predicted to occur much earlier [8][9][10] · 7.1 Kerr-Lens Mode Locking (KLM) The general principle behind Kerr-Lens Mode Locking is sketched in Fig. 7.1. A pulse that builds up in a laser cavity containing a gain medium and a Kerr medium experiences not only self-phase modulation but also self focussing, that is nonlinear lensing of the laser beam, due to the nonlinear refractive in- dex of the Kerr medium. A spatio-temporal laser pulse propagating through the Kerr medium has a time dependent mode size as higher intensities ac- quire stronger focussing. If a hard aperture is placed at the right position in the cavity, it strips of the wings of the pulse, leading to a shortening of the pulse. Such combined mechanism has the same effect as a saturable ab- sorber. If the electronic Kerr effect with response time of a few femtoseconds or less is used, a fast saturable absorber has been created. Instead of a sep- 257 258CHAPTER 7. KERR-LENS AND ADDITIVE PULSE MODE LOCKING soft aperture hard aperture Kerr gain Medium self - focusing beam waist intensity artifical fast saturable absorber Figure 7.1: Principle mechanism of KLM.
    [Show full text]
  • Theoretical and Experimental Investigations of the Kerr Effect and Cotton-Mouton Effect
    Theoretical and Experimental Investigations of the Kerr Effect and Cotton-Mouton Effect BY ANGELA LOUISE JANSE VAN RENSBURG B Sc Hons (UKZN) Submitted in partial fulfilment of the requirements for the degree of Master of Science in the School of Physics University of KwaZulu-Natal PIETERMARITZBURG AUGUST 2008 I Acknowledgements I wish to express my sincere gratitude and appreciation to all those people who have assisted and supported me throughout this work. I would like to make special mention of the following people: My supervisor, Dr V. W. Couling, for his constant assistance and encourage­ ment. For all the extra time and effort he took in helping and guiding me during this work. The staff of the Electronics Centre, in particular Mr G. Dewar, Mr A. Cullis and Mr J. Woodley for their endless assistance in maintaining, repairing and building the electronic apparatus used in this work. The staff of the Mechanical Instrument Workshop for repairing and con­ structing components used in the experimental part of this work. Mr K. Penzhorn and Mr R. Sivraman of the Physics Technical Staff for their help in accessing tools from the Physics Workshop. Also from the Physics Technical Staff, Mr A. Zulu for helping me move dewars of liquid nitrogen from the School of Chemistry to the School of Physics. The National Laser Centre for providing a new laser for the experimental aspect of this work and for their interest in my work. Mr N. Chetty, a fellow postgraduate student, for assisting in my learning of HP-Basic and Latex. Finally, my family, my parents for financing all of my studies and for their constant support and encouragement.
    [Show full text]
  • Casimir Force Control with Optical Kerr Effect (Kawalan Daya Casimir Dengan Kesan Optik Kerr)
    Sains Malaysiana 42(12)(2013): 1799–1803 Casimir Force Control with Optical Kerr Effect (Kawalan Daya Casimir dengan Kesan Optik Kerr) Y.Y. KHOO & C.H. RAYMOND OOI* ABSTRACT The control of the Casimir force between two parallel plates can be achieved through inducing the optical Kerr effect of a nonlinear material. By considering a two-plate system which consists of a dispersive metamaterial and a nonlinear material, we show that the Casimir force between the plates can be switched between attractive and repulsive Casimir force by varying the intensity of a laser pulse. The switching sensitivity increases as the separation between plate decreases, thus providing new possibilities of controlling Casimir force for nanoelectromechanical systems. Keywords: Casimir effect; optical kerr effect (OKE) ABSTRAK Kawalan daya Casimir antara dua plat selari boleh dicapai dengan mencetuskan kesan optik Kerr dalam suatu bahan tak linear. Dengan mempertimbangkan suatu sistem dua-plat yang terdiri daripada satu plat metamaterial dengan satu bahan tak linear, kami menunjukkan bahawa daya Casimir antara plat-plat tersebut boleh ditukar antara daya tarikan Casimir serta daya tolakan Casimir dengan mengubah keamatan laser. Tahap kesensitifan pertukaran tersebut meningkat apabila jarak pemisah antara plat-plat tersebut dikurangkan, justeru mencetus idea baru untuk mengawal kesan Casimir bagi sistem mekanikal nanoelektrik. Kata kunci: Kesan Casimir; kesan optik Kerr INTRODUCTION ε or permeability μ (single-negative materials, SNG) (Pendry As boundary conditions are being introduced in a et al. 1996, 1999) or simultaneously negative permittivity ε quantized electromagnetic field, the vacuum energy level and permeability μ over a band of frequency (left-handed changes. This change is then observed as a vacuum force materials, LHM) (Lezec et al.
    [Show full text]
  • Multi-Wavelength Optical Kerr Effects in High Nonlinearity Single
    Multi-wavelength Optical Kerr Effects in High Nonlinearity Single Mode Fibers and Their Applications in Nonlinear Signal Processing KWOK Chi Hang A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Philosophy in Electronic Engineering © The Chinese University of Hong Kong September 2006 The Chinese University of Hong Kong holds the copyright of this thesis. Any person(s) intending to use a part or whole of the materials in the thesis in a proposed publication must seek copyright release from the Dean of the Graduate School. M统系储書Ej |(j 1 OCT 1/ )l) ~university-遞 X^Xlibrary system Xn^ Abstract of dissertation entitled: Multi-wavelength Optical Kerr Effects in High Nonlinearity Single Mode Fibers and Their Applications in Nonlinear Signal Processing Submitted by Chi Hang KWOK for the degree of Master of Philosophy in Electronic Engineering at The Chinese University of Hong Kong in June 2006 Abstract Optical Kerr nonlinear effects originating from the intensity-induced refractive index change in a nonlinear medium are of much interest for high-speed optical signal processing owing to its ultra-fast response. The change of refractive index in a medium leads to a phase modulation to the light propagating in it. There are two types of intensity-induced nonlinear phase modulation known as self-phase modulation and cross-phase modulation (XPM) respectively for the phase modulation by an intense signal itself or by a separate intense signal co-propagating in the same medium. These two types of nonlinear phase modulation have a tremendous impact for nonlinear signal processing in optical communication networks.
    [Show full text]
  • Third Order Optical Nonlinearities
    Preprint of OSA Handbook of Optics, Vol. IV, Chapter. 17, (2000) THIRD ORDER OPTICAL NONLINEARITIES Mansoor Sheik-Bahae Michael P. Hasselbeck Department of Physics and Astronomy Department of Physics and Astronomy University of New Mexico, University of New Mexico, Albuquerque, NM 87131 Albuquerque, NM 87131 I. INTRODUCTION................................................................................................................................................. 2 II. QUANTUM MECHANICAL PICTURE........................................................................................................ 4 III. NONLINEAR ABSORPTION (NLA) AND NONLINEAR REFRACTION (NLR) .................................. 6 IV. KRAMERS-KRONIG DISPERSION RELATIONS.................................................................................... 8 V. OPTICAL KERR EFFECT ........................................................................................................................... 11 • BOUND ELECTRONIC OPTICAL KERR EFFECT IN SOLIDS.................................................................................... 11 • RE-ORIENTATIONAL KERR EFFECT IN LIQUIDS ................................................................................................. 12 VI. THIRD-HARMONIC GENERATION......................................................................................................... 13 VII. STIMULATED SCATTERING .................................................................................................................... 13 • STIMULATED
    [Show full text]
  • Silicon Kerr Effect Electro-Optic Switch
    Silicon Kerr Effect Electro-optic Switch Deepak V. Simili and Michael Cada Department of Electrical and Computer Engineering, Dalhousie University, 1459 Oxford Street, Halifax, Canada 1 RESEARCH PROBLEM range of 10 or lower. • Average switching energy lower than 10 pJ/bit The research problem that we are investigating deals with a target of 10 fJ/bit. with designing and testing an ultrafast silicon • Overcome coupling losses due to polarization electro-optic switch for integrated-optic applications dependence. that employs the Kerr effect. Silicon photonics for The above mentioned objectives are based on a optical interconnects offers a possibility to provide a review of silicon-based electro-optic modulators low cost, mass manufacturable solution for data present in the literature, which are discussed in the communication applications such as data centers, next section. high performance computing, mobile devices (cell phones or tablets) to server interconnects, and desktop computers (Reed G.T et. al., 2010). A 3 STATE OF THE ART switch or a modulator is one of the building blocks in an integrated-optic data transmitter connected to a The most commonly used electro-optic effect to fiber-optic channel. In order to better utilize the THz achieve modulation in silicon devices has been the bandwidth capabilities of fiber optic channels and to plasma dispersion effect. This is because electric meet increasing bandwidth demands of future field effects based on electro-refraction such as the communication networks, it is highly desired to Pockels effect do not exist in silicon while the Kerr develop optical switches with modulation effect induces a small refractive index change bandwidths in the range of 100 GHz and higher.
    [Show full text]
  • Nonlinear Birefringence Due to Non-Resonant, Higher-Order Kerr Effect in Isotropic Media
    Nonlinear birefringence due to non-resonant, higher-order Kerr effect in isotropic media George Stegeman,1,2,3,* Dimitris G. Papazoglou,1,4 Robert Boyd,5,6 and Stelios Tzortzakis1 1Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas, 71110, Heraklion, Greece 2Department of Physics, King Fahd University of Petroleum and Minerals, P.O. Box 5005, Dhahran 31261, Saudi Arabia 3College of Optics and Photonics and CREOL, University of Central Florida, 4000 Central Florida Boulevard, Florida 32751, USA 4Materials Science and Technology Department, University of Crete, 71003, Heraklion, Greece 5Institute of Optics, University of Rochester, Wilmot Building, 275 Hutchison Road, Rochester, New York 14627- 0186, USA 6University of Ottawa, Ottawa, Ontario K1N 6N5, Canada *[email protected] Abstract: The recent interpretation of experiments on the nonlinear non- resonant birefringence induced in a weak probe beam by a high intensity pump beam in air and its constituents has stimulated interest in the non- resonant birefringence due to higher-order Kerr nonlinearities. Here a simple formalism is invoked to determine the non-resonant birefringence for higher-order Kerr coefficients. Some general relations between nonlinear coefficients with arbitrary frequency inputs are also derived for isotropic media. It is shown that the previous linear extrapolations for higher-order birefringence (based on literature values of n2 and n4) are not strictly valid, although the errors introduced in the values of the reported higher- order Kerr coefficients are a few percent. ©2011 Optical Society of America OCIS codes: (190.0190) Nonlinear optics; (190.3270) Kerr effect; (190.5940) Self-action effects. References and links 1.
    [Show full text]
  • Magneto-Optic Kerr Effect
    MAGNETO-OPTIC KERR EFFECT PHOTOELASTIC MODULATORS APPLICATION NOTE MAGNETO-OPTIC KERR EFFECT BY DR. THEODORE C. OAKBERG The Magneto-Optic Kerr Effect (MOKE) is the study of the refl ection of polarized light by a material sample subjected to a magnetic fi eld. This refl ection can produce several effects, including 1) rotation of the direction of polarization of the light, 2) introduction of ellipticity in the refl ected beam and 3) a change in the intensity of the refl ected beam. MOKE is particularly important in the study of ferromagnetic and ferrimagnetic fi lms and materials. GEOMETRY OF MOKE EXPERIMENTS There are three “geometries” for MOKE experiments, the POLAR, LONGITUDINAL and TRANSVERSE geometries. These arise from the direction of the magnetic fi eld with respect to the plane of incidence and the sample surface. These relationships are summarized in Table I. TABLE I: DEFINITION OF MOKE GEOMETRIES GEOMETRY MAGNETIC FIELD ORIENTATION OBSERVABLE AT DIAGRAM NORMAL INCIDENCE? POLAR Parallel to the plane of incidence, Yes Figure 1 normal to the sample surface LONGITUDINAL Parallel to the plane of incidence No Figure 4 and the sample surface TRANSVERSE Normal to the plane of incidence, No Figure 5 parallel to the sample surface 1 In the polar and longitudinal cases, MOKE induces a Kerr rotation θk and an ellipticity εk. POLAR MOKE For polar MOKE, the magnetic vector is Plane of incidence parallel to the plane of incidence and normal to the refl ecting surface. (Figure 1.) Polar MOKE is most frequently studied at near-normal angles of incidence and refl ection to the refl ecting surface.
    [Show full text]
  • Terahertz Kerr Effect
    Terahertz Kerr effect The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Hoffmann, Matthias C., Nathaniel C. Brandt, Harold Y. Hwang, Ka- Lo Yeh, and Keith A. Nelson. “Terahertz Kerr effect.” Applied Physics Letters 95, no. 23 (2009): 231105. As Published http://dx.doi.org/10.1063/1.3271520 Publisher American Institute of Physics Version Original manuscript Citable link http://hdl.handle.net/1721.1/82604 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike 3.0 Detailed Terms http://creativecommons.org/licenses/by-nc-sa/3.0/ Terahertz Kerr effect Matthias C. Hoffmann, Nathaniel C. Brandt, Harold Y. Hwang , Ka-Lo Yeh, and Keith A. Nelson Massachusetts Institute of Technology, Cambridge, MA 02139 We have observed optical birefringence in liquids induced by single-cycle THz pulses with field strengths exceeding 100 kV/cm. The induced change in polarization is proportional to the square of the THz electric field. The time-dependent THz Kerr signal is composed of a fast electronic response that follows the individual cycles of the electric field and a slow exponential response associated with molecular orientation. The Kerr effect is a change Δn in the optical refractive index which is quadratic in the externally applied electric field. In the DC limit, this is usually expressed as Δn=KλE2 with the Kerr constant K and the vacuum wavelength λ. At optical frequencies an intensity-dependent modulation of the I refractive index Δn=n2 I(t) is observed, resulting in well-known nonlinear optical effects like self-focusing (Kerr-lensing), self-phase modulation, and birefringence that is usually measured through the depolarization of a separate, weak optical beam in what is conventionally designated the optical Kerr effect (OKE) measurement.
    [Show full text]