DOCSLIB.ORG

Kerr Electro-Optic Theory and Measurements Of

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Kerr Electro-Optic Theory and Measurements Of IEEE Transactions on Pielectrics and Electrical Insulation Vol. 5 No. 3,June 1998 421 qerr Electro-optic Theory and Measurements ~ of Electric Fields with Magnitude and 1 Direction Varying along the Light Path A. Ustundag, T. J. Gung and M. Zahn Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science Laboratory for Electromagnetic and Electronic Systems Cambridge, MA ABSTRACT ntial equations that govern light propagation in Kerr media are derived when the ap- ectric field direction and magnitude vary along the light path. Case studies predict Kerr optic fringe patferns for the specific case of pointlplane electrodes. We apply the charac- irections theory of photoelasticity to understand these fringes. We also study birefrin- ia with small Kerr constant, in particular transformer oil. For this case we show that ions in the characteristic parameter theory is possible, resulting in simple integral re- s between the characteristic parameters and the applied electric field. We use these nships to extend the ac modulation method to measure the characteristic param- all Kerr constant media. Measurements of the characteristic parameters using the on method are presented for point/plane electrodes in transformer oil. The mea- ee reasonably well with space charge free theory for infinite extent electrodes for tical expressions are available. We finally employ the 'onion peeling' method to e axisymmetric electric field magnitude and direction from the measured charac- eters and compare the results to the analytically obtained electric field. z (propagation direction of light) E? 'Y 'Y tric liquids. The refractiv erence between optical electric field perpendicular to the applied trans- in the plane perpendicular to the di- Figure 1. The transverse component ET (in the xg plane) of the applied electric field E for light propagating in the +z direction and the angles II, and p where $ is the angle between the x-axis and the total electric field E and cp is the angle between the x-axis and the transverse component of the electric field ET. non-invasively determine the (tranverse) electric field direction p and magnitude ET. Measuring the electric field is necessary in the study and modeling of HV conduction and breakdown characteristics in insu- I 1070-9878/98/$3.00 0 1998 IEEE Authorized licensed use limited to: IEEE Xplore. Downloaded on April 1, 2009 at 13:19 from IEEE Xplore. Restrictions apply. 422 Ustiindag et al.: Kerr Electro-Optic Theory and Measurements lating liquids since the conduction laws are often unknown and the elec- 2 LIGHT PROPAGATION IN tric field cannot be found from the geometry alone by solving the Pois- ARBITRARY KERR MEDIA son equation with unknown volume and surface charge distributions. Optical measurement of high electric fields offers near-perfect electrical 2.1 GOVERNING LIGHT isolation between the measured field and the measuring instrumenta- PROPAGATION EQUATl 0N S tion, avoids interference errors and makes extensive shielding and in- When the direction of the electric field is not constant along the light sulation requirements unnecessary [2]. path, (1)indicates aninhomogeneous anisotropic medium. For Kerr me- dia An is typically very small The method is limited to transparent dielectrics. However most liq- An<1 (2) uid dielectrics, in particular the most common HV transformer oil, are in hence the anisotropy is rather weak. For this case it is possible to ob- this category, making the method very attractive. The liquid dielectrics tain a reduced set of Maxwell's equations which are simple and easy to which were investigated in past work using the Kerr electro-optic effect analyze. The derivation here is similar to that of Aben's [16]. include transformer oil [3-81, highly purified water and water/ethylene glycol mixtures [9-111 and nitrobenzene [12-141. The effect also can be We assume that light propagates in a straight line in the +z direc- used for gases (SFs) [l] and solids (polymethylmethacrylate) [15]. In tion. This assumption is not true for a general anisotropic inhomoge- this paper 'Kerr medium' refers to an electrically stressed transparent neous medium but is approximately true for Kerr media in analogy to dielectric which obeys (1). weakly inhomogeneous isotropic media. Because of (2), reflections are negligible and we also assume that the Kerr media is lossless (no ab- sorption). With no power loss or reflections in the system, the intensity Most past experimental work has been limited to cases where the of light does not change while propagating in typical Kerr media. electric field magnitude and direction have been constant along the light path such as two long concentric or parallel cylinders [I, 9,121 or parallel We begin with the source-free Maxwell equations for time harmonic plate electrodes [l,101. However, to study charge injection and break- fields in non-magnetic media which may be written in the form down phenomena, very high electric fields are necessary (=lo7 V/m) VxVxe(r')= w2pod(r') (3) and for these geometries large electric field magnitudes can be obtained V.d(F) = 0 (4) only with very HV (typically >lo0 kV). Furthermore, in these geometries Here r' is the position vector, po = 4~x10-~H/m is the magnetic the breakdown and charge injection processes occur randomly in space permeability of free space, w is the angular frequency of the light, and often due to small unavoidable imperfections on otherwise smooth elec- e(?)and d(r')are the time-harmonic complex amplitude electric field trodes. The randomness of this surface makes it impossible to localize and displacement fields respectively, related to the real time-dependent the charge injection and breakdown and the problem is complicated be- optical fields e(?, t)and d(F,t) by cause the electric field direction also changes along the light path. To cre- e(?, t)= % {e(F)eiwt} (5) ate large electric fields for charge injection at a known location and at d(F,t) = {d(F)eiwt} reasonable voltages, a point electrode is often used in HV research where 93 (6) again the electric field direction changes along the light path. Hence it where i = a, is of interest here to extend Kerr electro-optic measurements to cases For one dimensional variations with only the z coordinate we assume where the electric field direction changes along the light path, with spe- that [19,20] cific application for point/plane electrodes. aa- ax-- - ay =o (7) In this paper we present the general theory and experiments of Kerr It follows from (2), (4) and (7) that e, and d,, the z components of the electro-optic measurements of the electric field whose magnitude and electric and displacement fields are essentially zero. Thus we only have direction changes along the light path, specifically applied to point/ J: and y components of the electric and displacement fields so that (3) plane electrodes. We first derive the governing differential equations reduces to for light propagation in Kerr media and integrate them to predict bire- d2~,$z' + ,wJz[Ezz(z)ez(z) + Ezy(z)ey(z)l = o fringence patterns for a point/plane electrode geometry with specific (8) d2e,(4 parameters used for nitrobenzene, a high Kerr constant dielectric. We [q,,(z)e,(z) = dz2 + bow2 + ~~,(z)e~(z)]o introduce the characteristic parameters which have been used in pho- where we used the dielectric constitutive relation toelasticity [16]. We discuss how they can be measured and in particu- EZZ(Z) E&) lar extend the ac modulation [3,6,17] method to measure them for cases (9) when the Kerr constant is small. We present experimental values of the [w:]= [44 EdZi] Here d,(z) and dy(z)are the components of d(z),[:;::;I e,(z) and ey(z) characteristic parameters for transformer oil between point/plane elec- trodes. Utilizing the axisymmetry of the electric field distribution of the are the components of e(.) and ezj(2) are the components of the per- point/plane electrode geometry, we then use the experimental charac- mittivity tensor. For lossless Kerr media ~ij (.) are real and symmetric. teristic parameter values to recover the electric field using the 'onion Beside the fixed zyz frame it is convenient to work in the frame peeling' method [18]. Finally we compare the recovered and analytical that rotates with the applied electric field in which the Kerr effect is electric fields. expressed. This frame will be referred as the ET frame (see Figure 2) Authorized licensed use limited to: IEEE Xplore. Downloaded on April 1, 2009 at 13:19 from IEEE Xplore. Restrictions apply. IEEE Transactions 01 Xelectrics and Electrical Insulation Vol. 5 No. 3, June 1998 423 Substituting (14) in (11) yields E,,(Z) = EL(Z) + 2Eon(z)XBE&) Eyy(Z) = El(Z) + 2Eon(z)XBE,(z) (16) \ Ezy (2) = 2Eon(z)XBE,(z)E, (2) whereE,(z) = E~(z)cosp(z)andE~(z)= ET(z)sinp(z)are the respective components of the applied transverse electric field. The isotropic permittivity E of the dielectric in the absence of any ap- plied electric field is related to EL and E,, by [21] / E&) + 2E&) = 3E (17) It follows from (2) and (17) that n(z)in (14) and (16) can be replaced (0 of the page) with the isotropic refractive index n since the introduced errors to Figure 2. ET frame of I xtions parallel and perpendicular to ET in the permittivity components are on the order of ~~[An(z)]~.Conse- the xy plane. quently where the constitutive rela inship is E&) - EL(Z) k5 2EonXBE$(z) (18) and Ez,(Z) - Eyy(Z) = 2EonXB[E3z)- E341 Ezy(.) 2E0nXBEz(z)Ey(z) (19) Subscripts /I and Iare ed to indicate the respective components of the electric field, the dis %cementfield and the permittivity tensor.
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]