Chapter 5 Optical Properties of Materials

Total Page:16

File Type:pdf, Size:1020Kb

Chapter 5 Optical Properties of Materials Chapter 5 Optical Properties of Materials Part I Introduction Classification of Optical Processes refractive index n() = c / v () Snell’s law absorption ~ resonance luminescence Optical medium ~ spontaneous emission a. Specular elastic and • Reflection b. Total internal Inelastic c. Diffused scattering • Propagation nonlinear-optics Optical medium • Transmission Propagation General Optical Process • Incident light is reflected, absorbed, scattered, and/or transmitted Absorbed: IA Reflected: IR Transmitted: IT Incident: I0 Scattered: IS I 0 IT IA IR IS Conservation of energy Optical Classification of Materials Transparent Translucent Opaque Optical Coefficients If neglecting the scattering process, one has I0 IT I A I R Coefficient of reflection (reflectivity) Coefficient of transmission (transmissivity) Coefficient of absorption (absorbance) Absorption – Beer’s Law dx I 0 I(x) Beer’s law x 0 l a is the absorption coefficient (dimensions are m-1). Types of Absorption • Atomic absorption: gas like materials The atoms can be treated as harmonic oscillators, there is a single resonance peak defined by the reduced mass and spring constant. v v0 Types of Absorption Paschen • Electronic absorption Due to excitation or relaxation of the electrons in the atoms Molecular Materials Organic (carbon containing) solids or liquids consist of molecules which are relatively weakly connected to other molecules. Hence, the absorption spectrum is dominated by absorptions due to the molecules themselves. Molecular Materials Absorption Spectrum of Water Molecular Materials • Electronic absorption – molecular orbital transition Solid State Materials Lattice vibration – phonon spectrum Solid State Materials Solid State Materials Electron transition – energy band structures Solid State Materials Electron transition – energy band structures Solid State Materials Electron transition – energy band structures Solid State Materials Conductors Almost any frequency of light can be absorbed Since there is a very high concentration of electrons, practically all the light is absorbed within about 0.1μm of the surface The metal reflects the light very well – about 95% for most metals The metal appears “silvery” since it acts as a perfect mirror Solid State Materials Conductors Flat Reflect more red Solid State Materials Semiconductor and dielectrics Dielectrics and semiconductors behave essentially the same way, the only difference being in the size of the bandgap Solid State Materials Semiconductor and dielectrics Solid State Materials Semiconductor and dielectrics Impurity levels divide up the bandgap to allow transitions with energies less than Eg Recombination can be either radiative (photon) or non-radiative (phonon) depending on the transition probabilities Practical p-n diodes usually contain a small amount of impurity to help recombination because Si has a relatively low recombination “efficiency” Part II Complex Refractive Index Wave Propagates in Absorption Medium The incident wave, The refractive wave, E E(x) k’ wavenumber in the medium. Rewrite the refractive wave in a plane wave format 0 x l The effective wavenumber is Wave Propagates in Absorption Medium The effective wave velocity, The speed of light in vacuum, The index of refraction has a complex value Let One obtain Wave Propagates in Absorption Medium According to Maxwell’s equations, n ~ 1 i 2 n~2 ~ The relative dielectric constant is also a complex 2 2 1 n , 2 2n 1 1 1 2 2 2 2 n [1 (1 2 ) ] 2 1 1 1 2 2 2 2 [1 (1 2 ) ] . 2 Part III Classical Propagation Propagation in a Dense Optical Medium Three types of oscillators: 1. Bound electron (atomic) oscillator 2. Vibrational oscillator; 3. Free electron oscillators Propagation in a Dense Optical Medium Atomic oscillator 1 1 1 , m0 mN KS 0 , p q(r r ) p(t) ex(t) Propagation in a Dense Optical Medium Atomic oscillator Propagation in a Dense Optical Medium Atomic oscillator If = 0, resonant absorption (Beer’s law) hv = E2 - E1 re-radiated photon – luminesce radiationless transition If 0, non-resonant, transparent The oscillators follow the driving wave, but with a phase lag. The phase lag accumulates through the medium and retards the propagation of the wave front, leading to smaller velocity than in free space (v =c / n). -- the origin of n Propagation in a Dense Optical Medium Vibrational oscillators K S 12 13 0 10 10 Hz Infrared spectral region In a crystalline solid form the Classical model of a polar condensation of polar molecules, molecule (an ionic optical these oscillations are associated medium) with lattice vibrations (phonons). Propagation in a Dense Optical Medium Free electron oscillators Free electrons, Ks = 0, 0 = 0 Drude-Lorentz model The Lorentz Oscillator 2 d x 2 m0 m00 x 0, mN m0 dt 2 2 d x dx 2 m0 m0 m00 x eE(t) E dt 2 dt Light wave will drive oscillations at its own Frequency: i t E (t ) E 0 e i t Assuming x (t ) X 0 e 2 it it 2 it it m 0 X 0 e im 0 X 0 e m 0 0 X 0 e eE 0 e eE0 / m0 X 0 2 2 0 i The Lorentz Oscillator The electric displacement D: D 0E P 0E 0E 0 (1 )E 0E P is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density. The Lorentz Oscillator The macroscopic polarization of medium P: Presonant Np Nexnˆ Ne2 1 2 2 E m0 (0 i) N is the number of atoms per unit volume. The electric displacement D can be expressed as D 0E P 0 E Pbackground Presonant Ne2 1 0 E 0E 2 2 E m0 (0 i) The Lorentz Oscillator The dielectric constant can be obtained Ne 2 1 ( ) 1 2 2 0 m0 ( 0 i ) 2 2 2 Ne 0 1 ( ) 1 2 2 2 2 0 m0 ( 0 ) ( ) Ne 2 2 ( ) 2 2 2 2 0 m0 ( 0 ) ( ) The Lorentz Oscillator Frequency dependence of the real and imaginary parts of the complex dielectric constant of a dipole at frequencies close to resonance. Also shown is the real and imaginary part of the refractive index calculated from the dielectric constant. The Lorentz Oscillator Low frequency limit: Ne2 (0) st 1 2 0m00 High frequency: () 1 Ne 2 Thus ( st ) 2 0 m00 2 0 Close to resonance: 1 ( ) ( st ) 4( ) 2 2 0 2 ( ) ( st ) 4( ) 2 2 Multiple Resonance Take account of all the transitions in the medium (different resonant oscillation frequency) P NPr Nexnˆ Ne2 1 2 2 E m0 j ( j i j) The dielectric constant can be expressed Ne 2 1 () 1 2 2 0m0 j ( j i j) Multiple Resonance Assign a phenomenological oscillator strength fj to each transition: 2 Ne f j () 1 2 2 0m0 j ( j i j) For each atom. where f j 1. j Schematic diagram of the frequency dependence of the refractive index and absorption of a hypothetical solid from the infrared to the x-ray spectral region. The solid is assumed to have three resonant frequencies with width of each absorption line has been set to 10% of the center frequency by appropriate choice of the j’s. Multiple Resonance 1. n >> except near the peaks of the absorption; 2. The transmission range of optical materials is determined by the electronic absorption in UV and the vibrational absorption in IR; 3. IR absorption is caused by the vibrational quanta 13 in SiO2 molecules themselves(1.4 10 Hz (21m) and 3.3 1013 Hz(9.1 m); 4. UV absorption is caused by interband electronic transition(band gap of about 10 eV), threshold at 2 1013 Hz(150 nm)(a ~ 108 m-1); 5. UV absorption departure from Lorentz model; 6. n actually increases with frequency in transparency region, the dispersion originates from wings of two absorption peaks of UV and IR; 7. The phase velocity of light is greater than c in (a) Refractive index and (b) extinction region where n falls below unity; coefficient of fused silica (SiO2) glass from the infrared to the x-ray spectral region. Free Electrons Plasma: A neutral gas of heavy ions and light electrons. Metals and doped semiconductors can be treated as plasmas because they contain equal numbers of fixed positive ions and free electrons. Free electrons in this system experience no restoring force from the medium when they interact with electromagnetic waves. driven by the electric field of a light wave. Free Electrons Drude-Lorentz model: Considering the oscillations of a free electron induced by AC electric field E(t) of a light wave with polarized along the x direction: 2 d x dx it m0 m0 eE(t) eE0e . dt 2 at it By substituting x x0e eE(t) x(t) 2 . m0 ( i) The electric displacement: D r 0 E 0 E P Ne 2 E 0 E 2 m 0 ( i ) Free Electrons Therefore, Ne 2 ( ) 1 2 0 m 0 ( i ) Or, 2 p ( ) 1 , ( 2 i ) 1 Ne 2 2 where . p p: plasma frequency 0 m 0 For a lightly damped system, = 0, so that 2 p r ( ) 1 2 n is imaginary for < p positive for > p zero for = p, Free Electrons 2 n~ 1 Later we will know that the reflectivity is R n~ 1 Reflectivity of a less damped free carrier gas as a function of frequency. Free Electrons Experimental reflectivity of Al as a function of photon energy. The experimental data is compared to predictions of the free electron model with h = 15.8 eV. The dotted line is calculated with no damping. The dashed line with = 8.010-15 s, which is the value deduced from the DC conductivity. All metals will become transmitting if > p ( UV transparency of metals) Free Electrons The Drude model: The valence electrons is free.
Recommended publications
  • Quantum Metamaterials in the Microwave and Optical Ranges Alexandre M Zagoskin1,2* , Didier Felbacq3 and Emmanuel Rousseau3
    Zagoskin et al. EPJ Quantum Technology (2016)3:2 DOI 10.1140/epjqt/s40507-016-0040-x R E V I E W Open Access Quantum metamaterials in the microwave and optical ranges Alexandre M Zagoskin1,2* , Didier Felbacq3 and Emmanuel Rousseau3 *Correspondence: [email protected] Abstract 1Department of Physics, Loughborough University, Quantum metamaterials generalize the concept of metamaterials (artificial optical Loughborough, LE11 3TU, United media) to the case when their optical properties are determined by the interplay of Kingdom quantum effects in the constituent ‘artificial atoms’ with the electromagnetic field 2Theoretical Physics and Quantum Technologies Department, Moscow modes in the system. The theoretical investigation of these structures demonstrated Institute for Steel and Alloys, that a number of new effects (such as quantum birefringence, strongly nonclassical Moscow, 119049, Russia states of light, etc.) are to be expected, prompting the efforts on their fabrication and Full list of author information is available at the end of the article experimental investigation. Here we provide a summary of the principal features of quantum metamaterials and review the current state of research in this quickly developing field, which bridges quantum optics, quantum condensed matter theory and quantum information processing. 1 Introduction The turn of the century saw two remarkable developments in physics. First, several types of scalable solid state quantum bits were developed, which demonstrated controlled quan- tum coherence in artificial mesoscopic structures [–] and eventually led to the devel- opment of structures, which contain hundreds of qubits and show signatures of global quantum coherence (see [, ] and references therein). In parallel, it was realized that the interaction of superconducting qubits with quantized electromagnetic field modes re- produces, in the microwave range, a plethora of effects known from quantum optics (in particular, cavity QED) with qubits playing the role of atoms (‘circuit QED’, [–]).
    [Show full text]
  • Einstein and the Early Theory of Superconductivity, 1919–1922
    Einstein and the Early Theory of Superconductivity, 1919–1922 Tilman Sauer Einstein Papers Project California Institute of Technology 20-7 Pasadena, CA 91125, USA [email protected] Abstract Einstein’s early thoughts about superconductivity are discussed as a case study of how theoretical physics reacts to experimental find- ings that are incompatible with established theoretical notions. One such notion that is discussed is the model of electric conductivity implied by Drude’s electron theory of metals, and the derivation of the Wiedemann-Franz law within this framework. After summarizing the experimental knowledge on superconductivity around 1920, the topic is then discussed both on a phenomenological level in terms of implications of Maxwell’s equations for the case of infinite conduc- tivity, and on a microscopic level in terms of suggested models for superconductive charge transport. Analyzing Einstein’s manuscripts and correspondence as well as his own 1922 paper on the subject, it is shown that Einstein had a sustained interest in superconductivity and was well informed about the phenomenon. It is argued that his appointment as special professor in Leiden in 1920 was motivated to a considerable extent by his perception as a leading theoretician of quantum theory and condensed matter physics and the hope that he would contribute to the theoretical direction of the experiments done at Kamerlingh Onnes’ cryogenic laboratory. Einstein tried to live up to these expectations by proposing at least three experiments on the arXiv:physics/0612159v1 [physics.hist-ph] 15 Dec 2006 phenomenon, one of which was carried out twice in Leiden. Com- pared to other theoretical proposals at the time, the prominent role of quantum concepts was characteristic of Einstein’s understanding of the phenomenon.
    [Show full text]
  • Negative Refractive Index in Artificial Metamaterials
    1 Negative Refractive Index in Artificial Metamaterials A. N. Grigorenko Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK We discuss optical constants in artificial metamaterials showing negative magnetic permeability and electric permittivity and suggest a simple formula for the refractive index of a general optical medium. Using effective field theory, we calculate effective permeability and the refractive index of nanofabricated media composed of pairs of identical gold nano-pillars with magnetic response in the visible spectrum. PACS: 73.20.Mf, 41.20.Jb, 42.70.Qs 2 The refractive index of an optical medium, n, can be found from the relation n2 = εμ , where ε is medium’s electric permittivity and μ is magnetic permeability.1 There are two branches of the square root producing n of different signs, but only one of these branches is actually permitted by causality.2 It was conventionally assumed that this branch coincides with the principal square root n = εμ .1,3 However, in 1968 Veselago4 suggested that there are materials in which the causal refractive index may be given by another branch of the root n =− εμ . These materials, referred to as left- handed (LHM) or negative index materials, possess unique electromagnetic properties and promise novel optical devices, including a perfect lens.4-6 The interest in LHM moved from theory to practice and attracted a great deal of attention after the first experimental realization of LHM by Smith et al.7, which was based on artificial metallic structures
    [Show full text]
  • Molding of Plasmonic Resonances in Metallic Nanostructures: Dependence of the Non-Linear Electric Permittivity on System Size and Temperature
    Materials 2013, 6, 4879-4910; doi:10.3390/ma6114879 OPEN ACCESS materials ISSN 1996-1944 www.mdpi.com/journal/materials Review Molding of Plasmonic Resonances in Metallic Nanostructures: Dependence of the Non-Linear Electric Permittivity on System Size and Temperature Alessandro Alabastri 1,*, Salvatore Tuccio 1, Andrea Giugni 1, Andrea Toma 1, Carlo Liberale 1, Gobind Das 1, Francesco De Angelis 1, Enzo Di Fabrizio 2,3 and Remo Proietti Zaccaria 1,* 1 Istituto Italiano di Tecnologia, Via Morego 30, Genova 16163, Italy; E-Mails: [email protected] (S.T.); [email protected] (A.G.); [email protected] (A.T.); [email protected] (C.L.); [email protected] (G.D.); [email protected] (F.A.) 2 King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering (PSE) Division, Biological and Environmental Science and Engineering (BESE) Division, Thuwal 23955-6900, Kingdom of Saudi Arabia; E-Mail: [email protected] 3 Bio-Nanotechnology and Engineering for Medicine (BIONEM), Department of Experimental and Clinical Medicine, University of Magna Graecia Viale Europa, Germaneto, Catanzaro 88100, Italy * Authors to whom correspondence should be addressed; E-Mails: [email protected] (A.A.); [email protected] (R.P.Z.); Tel.: +39-010-7178-247; Fax: +39-010-720-321. Received: 10 July 2013; in revised form: 8 October 2013 / Accepted: 10 October 2013 / Published: 25 October 2013 Abstract: In this paper, we review the principal theoretical models through which the dielectric function of metals can be described. Starting from the Drude assumptions for intraband transitions, we show how this model can be improved by including interband absorption and temperature effect in the damping coefficients.
    [Show full text]
  • Course Description Learning Objectives/Outcomes Optical Theory
    11/4/2019 Optical Theory Light Invisible Light Visible Light By Diane F. Drake, LDO, ABOM, NCLEM, FNAO 1 4 Course Description Understanding Light This course will introduce the basics of light. Included Clinically in discuss will be two light theories, the principles of How we see refraction (the bending of light) and the principles of Transports visual impressions reflection. Technically Form of radiant energy Essential for life on earth 2 5 Learning objectives/outcomes Understanding Light At the completion of this course, the participant Two theories of light should be able to: Corpuscular theory Electromagnetic wave theory Discuss the differences of the Corpuscular Theory and the Electromagnetic Wave Theory The Quantum Theory of Light Have a better understanding of wavelengths Explain refraction of light Explain reflection of light 3 6 1 11/4/2019 Corpuscular Theory of Light Put forth by Pythagoras and followed by Sir Isaac Newton Light consists of tiny particles of corpuscles, which are emitted by the light source and absorbed by the eye. Time for a Question Explains how light can be used to create electrical energy This theory is used to describe reflection Can explain primary and secondary rainbows 7 10 This illustration is explained by Understanding Light Corpuscular Theory which light theory? Explains shadows Light Object Shadow Light Object Shadow a) Quantum theory b) Particle theory c) Corpuscular theory d) Electromagnetic wave theory 8 11 This illustration is explained by Indistinct Shadow If light
    [Show full text]
  • Lecture Notes in Solid State 3
    Lecture notes in Solid State 3 Eytan Grosfeld Physics Department, Ben-Gurion University of the Negev Classical free electron model for metals: The Drude model Recommended reading: • Chapter 1, Ashcroft & Mermin. The conductivity of metals is described very well by the classical Drude formula, ne2τ σ = (1.1) D m where m is the electronic mass (as decided by the band-structure) and e is the electronic charge. The conductivity is directly proportional to the electronic density n; and, to τ, the mean free time between collisions of the conducting electrons with defects that are generically present in the system: • Static defects that scatter the electron elastically, including: static impu- rities and structural defects. One can dene the elastic mean free time τe. • Dynamical defects which scatter the electron inelastically (as they can carry o energy) including: photons, other electrons, other excitations (such as plasmons). One can accordingly dene the inelastic mean free time τ'. The eciency of the latter processes depends on the temperature T : we expect it to increase as T is increased. At very low temperatures the dominant scattering is elastic, and then τ does not depend strongly on temperature but instead it depends on the amount of disorder (realized as random static impurities). We expect τ to decrease as the temperature or the amount of disorder in the system are increased. The Drude model 1897 - discovery of the electron (J. J. Thomson). 1900 - only three years later, Drude applied the kinetic theory of gases to a metal - considering it to be a gas of electrons. Assumptions: 1.
    [Show full text]
  • Chapter 5 the Drude Theory of Metals
    Chapter 5 The Drude Theory of Metals • Basic assumption of Drude model • DC electrical conductivity of a metal • Hall effect • Thermal conductivity in a metal 1 Basic assumptions of Drude model * A “ gas of conduction electrons of mass m, which move against a background of heavy immobile ions Zρ Electron density n = .0 6022 ×10 24 m A .0 6022 ×10 24 Avogadro’s number ρm Mass density in g/cm 3 A Atomic mass in g/mole Z Number of electron each atom contribute rs Radius of a sphere whose volume is equal to the volume per conduction electron V 1 4 3 3/1 = = πr 3 r = N n 3 s s 4πn r s ~ 2 − 3 in typical metal a0 Bohr radius The density is typically 10 3 times greater than those of a classical gas at normal T and P. 2 * Between collisions the interaction of a given electron, both with others and with the ions, is neglected. * Coliisons in the Drude model are instantaneous events that abruptly alter the velocity of an electron. Drude attributed them to the electrons bouncing off the impenetrable ion cores. 1 * We shall assume that an electron experiences a collision with a probability per unit time τ Probability dt during time interval dt τ τ : relaxation time * Electrons are assumed to achieve thermal equilibrium with their surroundings only through collisons 3 DC Electrical Conductivity of a Metal r n electrons per unit volume all move with velocity v . n(vdt )A electrons will cross an area A perpendicular to the direction of flow.
    [Show full text]
  • Drude-Lorentz Analysis of the Optical Properties of The
    DRUDE-LORENTZ ANALYSIS OF THE OPTICAL PROPERTIES OF THE QUASI-TWO-DIMENSIONAL DICHALCOGENIDES 2H-NbSe2 AND 2H-TaSe2 A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Dinesh Marasinghe August, 2018 DRUDE-LORENTZ ANALYSIS OF THE OPTICAL PROPERTIES OF THE QUASI-TWO-DIMENSIONAL DICHALCOGENIDES 2H-NbSe2 AND 2H-TaSe2 Dinesh Marasinghe Thesis Approved: Accepted: Advisor Dean of the College Dr. Sasa V. Dordevic Dr. Linda Subich Faculty Reader Dean of the Graduate School Dr. Ben Yu-Kuang Hu Dr. Chand Midha Faculty Reader Date Dr. Sergei F. Lyuksyutov Department Chair Dr. Chris Ziegler ii ABSTRACT The reflectivity of a material basically depends on the collisions of free electrons. Existing spectroscopic reflectance data of two dichalcogenide materials, 2H-NbSe2 and 2H-TaSe2, is studied in this work. We analyzed this information with the Drude- Lorentz model for 2D electron gases. Using the program RefFIT, we explored the materials' reflectance and the conductivity and their dependance on temperature across frequencies ranging from infrared to ultraviolet. We examined both the in- plane (ab-plane) and out-of-plane (c-axis) components. In both materials, the ab- plane had greater reflectance and conductivity, with 2H-NbSe2 having the largest of both quantities. The anisotropy-direction dependence-effects are most pronounced in 2H-TaSe2. When frequency increased, collisions of free elections increased, decreasing the reflectance and conductivity. We also determined that the reflectance and the conductivity of the materials decreased with increased temperature for the same reason. Once the plasma edge was reached, interband transition occurred, causing an increase in conduction electrons and a decrease in both reflectance and conductivity.
    [Show full text]
  • Drude Model 1 in 1897, J. J. Thomson Discovered Electrons. in 1905
    Drude Model In 1897, J. J. Thomson discovered electrons. In 1905, Einstein interpreted the photoelectric effect In 1911 - Rutherford proved that atoms are composed of a point-like positively charged, massive nucleus surrounded by a sea of electrons. - Drude constructed his theory of electrical and thermal conduction in metals by (1) considering the electrons to be a gas of negatively charged particles traversing in a medium of uniformly distributed positive ions, and (2) applying the kinetic theory of gas to the electron sea. Below is a schematic diagram of Drude’s model of metals: (In 1922, Bohr was awarded the Nobel Prize for his contribution to the understanding of the structure of atoms. In late 1925, the Schrödinger equation was formulated.) Core electrons Zc e +Ze Zc e +Ze Zc e +Ze Zc e +Ze Positively charged ions Electron sea due to the delocalized valence electrons, (Z – Zc) from each atom. There is one important parameter of the model: (1) Electron number density, n 23 n = N/V = 6.02 x 10 x (Z Zc)m/A, (1.1) Avogadro’s number where N is the total number of electrons in the metal, V is the volume, m is the mass density, and A is the mass number. Note that only the valence electrons ((Z Zc) per atom) contribute to n. (2) Average electron separation, rs. 3 V/N = 1/n = (4/3) rs 1/3 rs = [3/(4n)] (1.2) 1 Drude Model The value of n varies from 0.911022/cm3 for Cs to 24.71022/cm3 for Be among different metals.
    [Show full text]
  • Engineering Nonlinearities in Nanoscale Optical Systems: Physics and Applications in Dispersion-Engineered Silicon Nanophotonic Wires
    Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires R. M. Osgood, Jr.,1 N. C. Panoiu,2 J. I. Dadap,1 Xiaoping Liu,1 Xiaogang Chen,1 I-Wei Hsieh,1 E. Dulkeith,3,4 W. M. J. Green,3 and Y. A. Vlasov3 1Microelectronics Sciences Laboratories, Columbia University, New York, New York 10027, USA 2Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, UK 3IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA 4Present address, Detecon, Inc., Strategy and Innovation Engineering Group, San Mateo, California 94402, USA Received October 7, 2008; revised November 24, 2008; accepted November 25, 2008; posted November 25, 2008 (Doc. ID 102501); published January 30, 2009 The nonlinear optics of Si photonic wires is discussed. The distinctive features of these waveguides are that they have extremely large third-order susceptibility ␹͑3͒ and dispersive properties. The strong dispersion and large third-order nonlinearity in Si photonic wires cause the linear and nonlinear optical physics in these guides to be intimately linked. By carefully choosing the waveguide dimensions, both linear and nonlinear optical properties of Si wires can be engineered. We review the fundamental optical physics and emerging applications for these Si wires. In many cases, the relatively low threshold powers for nonlinear optical effects in these wires make them potential candidates for functional on-chip nonlinear optical devices of just a few millimeters in length; conversely, the absence of nonlinear optical impairment is important for the use of Si wires in on-chip interconnects.
    [Show full text]
  • Fundamentals of Modern Optics", FSU Jena, Prof
    Script "Fundamentals of Modern Optics", FSU Jena, Prof. T. Pertsch, FoMO_Script_2017-10-10s.docx 1 Fundamentals of Modern Optics Winter Term 2017/2018 Prof. Thomas Pertsch Abbe School of Photonics, Friedrich-Schiller-Universität Jena Table of content 0. Introduction ............................................................................................... 4 1. Ray optics - geometrical optics (covered by lecture Introduction to Optical Modeling) .............................................................................................. 15 1.1 Introduction ......................................................................................................... 15 1.2 Postulates ........................................................................................................... 15 1.3 Simple rules for propagation of light ................................................................... 16 1.4 Simple optical components ................................................................................. 16 1.5 Ray tracing in inhomogeneous media (graded-index - GRIN optics) .................. 20 1.5.1 Ray equation ............................................................................................ 20 1.5.2 The eikonal equation ................................................................................ 22 1.6 Matrix optics ........................................................................................................ 23 1.6.1 The ray-transfer-matrix ............................................................................
    [Show full text]
  • Random Polarization Dynamics in a Resonant Optical Medium
    Random Polarization Dynamics in a Resonant Optical Medium Katherine A. Newhall,1 Ethan P. Atkins,2 Peter R. Kramer,3 Gregor Kovaˇciˇc,3,∗ and Ildar R. Gabitov4 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 2 Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, CA 94720-3840 3Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180 4Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, AZ 85721 ∗Corresponding author: [email protected] Compiled January 8, 2013 Random optical-pulse polarization switching along an active optical medium in the Λ-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte-Carlo numerical simulations. c 2013 Optical Society of America OCIS codes: 190.5530, 190.7110, 250.6715 ∗ ∗ The model of light interacting with a material sample ∂tµ = [E+ ρ− + E−ρ+ ] /2, (1d) composed of three-level active atoms has made possi- ∗ ∗ ∂t = [E+ρ+ + E+ ρ+ ble the descriptions of several nontrivial optical phenom- N − ∗ ∗ +E−ρ− + E− ρ−] /2, (1e) ena, including lasing without inversion [1], slow light [2], ∗ ∗ and electric-field polarization of solitons in self-induced ∂tn± = [E±ρ± + E± ρ±] /2. (1f) transparency [3]. Its simplest version including a non- Here, E±(x, t) are the envelopes of the electric field degenerate upper and two degenerate lower working and ρ±(x, t, λ) and µ(x, t, λ) of the medium-polarization, atomic levels — the Λ configuration — is completely in- n±(x, t, λ) and (x, t, λ) the population densities of the tegrable when the pulse width is much shorter than the ground and excitedN levels, respectively, λ the frequency ∞ medium relaxation times [4].
    [Show full text]