Optics and Optical Design. Chapter 5: Electromagnetic Optics. Lectures 9 & 10
|
|
- Mervin Dawson
- 5 years ago
- Views:
Transcription
1 Optics and Optical Design Chapter 5: Electromagnetic Optics Lectures 9 & 1 Cord Arnold / Anne L Huillier
2 Electromagnetic waves in dielectric media
3 EM optics compared to simpler theories
4 Electromagnetic spectrum Electromagnetic optics describes all kinds of EM waves in all possible spectral ranges in possible kinds of media (vacuum, dielectric, conductive, etc.).
5 Example: THz imaging The THz Network,
6 Particle wave X-ray imaging (shadow-graphy) X-ray diffraction X-ray image from the hand of Albert von Koelliker, taken in Wikipedia
7 Maxwell Equations in vacuum Contributions from: Charles Augustin de Coulomb Hans Christian Örsted Carl Friedrich Gauss Jean Baptiste Biot André Marie Ampére Michael Faraday Unified by James Clerk Maxwell in 1861 as set of twenty equations. The current form, termed Maxwell Equations, was compressed by using vector notation by Oliver Heavyside in 1884.
8 Maxwell Equations in a source free medium
9 Boundary conditions
10 Different types of media Linear: Nondispersive: Homogeneous: If P(r,t) is linearly related to Ԑ(r,t). The response is instantaneous. The polarization P(r,t) does not depend on earlier times. The relation between P and Ԑ is no function of space. Isotropic: The relation between P and Ԑ is independent of the direction of Ԑ. Spatially nondispersive: The relation between P and Ԑ is local.
11 Linear, nondispersive, homogeneous, isotropic, sourcefree media
12 Anisotropic, linear, nondispersive media The susceptibility tensor χ can have up to nine independent elements χ ji.
13 Dispersive media
14 Monochromatic electromagnetic waves Introduce monochromatic fields All fields and flux densities can be written in their monochromatic versions accordingly.
15 Transverse electromagnetic (TEM) plane wave E is orthogonal to H. Both are orthogonal to the direction of propagation k.
16 Vectorial spherical wave
17 Example: focusing of vectorial waves
18 Vectorial solutions of the Helmholtz Equation
19 Absorption and dispersion
20 Transmission bands for common materials in optics
21 Implications of dispersion
22 Refractive index for different isotropic materials and crystals
23 The resonant medium
24 The resonant medium
25 Multi resonance media
26 Sellmeier Equation for the refractive index far from resonance
27 Kramers Kronig Relations The Kramers-Kronig relations relate mathematically the real and imaginary parts of the susceptibility to each other. Knowing one determines the other and vice versa.
28
29 h t for t and ht is real for t (causal funtion) Causal response function H exp jt h t dt cost h t j sint hdt t Signum function Noncausal odd function h t signum t h t h t o o Causal response function
30 Frequency space imaginary part of a causal response function Frequency space real part of a causal response function H SIGNUM H o H o Real part Imaginary part The real and imaginary parts are related because they originate from the same function and they contain the same information!
31 The Drude Model for conductive media ω<ω p ω>ω p ω=ω p The effective permittivity is negative, β(ω) is imaginary. Light cannot propagate. => Perfect mirror. The effective permittivity is positive. Light can propagate. The refractive index is below 1. β(ω)=. Light cannot propagate. But one can resonantly excite plasma waves. Plasmons!
32 Pulse propagation in dispersive media
33 Dispersive media The field moves in respect to the envelope due to the difference of phase and group velocity The pulse spreads due to group velocity dispersion (GVD)
34 Electric field (a.u.) Temporal and spectral representation of laser pulses and the time bandwidth product Pulsed plane wave t At expj t U FWHM Carrier frequency Pulse envelope (spectrally broad) Time Fourier transform Spectral power (a.u.) Frequency Electric field (a.u.) FWHM FWHM.44 Time-bandwidth product (Gaussian pulse) Spectral power (a.u.) Time Frequency
35 Plane wave propagation ~ A A Laser pulses in dispersive media ~ z, Az, exp j 1 z, t F Az, ~ 1 F F Az, t z Spectral plane wave propagator exp j z Each frequency component evolves with a different wave number Wave number expansion around a carrier ω : c n ' 1! ' '! Group velocity v g 1/ ' Group velocity dispersion s s ' Inverse of a speed '' Inverse of an acceleration m m ' 1 v g, '' Group velocity and group velocity dispersion (GVD) result from dispersion.
36 Group velocity and group index ', ' ' 1 ', n n N N c n n c v n n c n n c n c c c g Depends on the change of the refractive index in respect to the wavelength Group index The speed of a pulse is determined by the rate of change of the refractive index Refractive index for a typical material
37 Group velocity dispersion (GVD) 3 '' '' '' n c D c c Refractive index for fused silica GVD is proportional n ( ), that is the curvature of n( ). 3 ' ', ' ' n c D n c D GVD for fused silica z D z D D D Estimation for dispersive pulse broadening
38 Pulse broadening in dispersive media
39 Dispersive media n<1 n>1 N>1 => v g <v p N>1 => v g <v p Anomalous dispersion Anomalous dispersion Normal dispersion
Summary of Beam Optics
Summary of Beam Optics Gaussian beams, waves with limited spatial extension perpendicular to propagation direction, Gaussian beam is solution of paraxial Helmholtz equation, Gaussian beam has parabolic
More informationElectromagnetic optics!
1 EM theory Electromagnetic optics! EM waves Monochromatic light 2 Electromagnetic optics! Electromagnetic theory of light Electromagnetic waves in dielectric media Monochromatic light References: Fundamentals
More informationOverview in Images. S. Lin et al, Nature, vol. 394, p , (1998) T.Thio et al., Optics Letters 26, (2001).
Overview in Images 5 nm K.S. Min et al. PhD Thesis K.V. Vahala et al, Phys. Rev. Lett, 85, p.74 (000) J. D. Joannopoulos, et al, Nature, vol.386, p.143-9 (1997) T.Thio et al., Optics Letters 6, 197-1974
More information3 Constitutive Relations: Macroscopic Properties of Matter
EECS 53 Lecture 3 c Kamal Sarabandi Fall 21 All rights reserved 3 Constitutive Relations: Macroscopic Properties of Matter As shown previously, out of the four Maxwell s equations only the Faraday s and
More informationLecture 3 Fiber Optical Communication Lecture 3, Slide 1
Lecture 3 Optical fibers as waveguides Maxwell s equations The wave equation Fiber modes Phase velocity, group velocity Dispersion Fiber Optical Communication Lecture 3, Slide 1 Maxwell s equations in
More informationEE485 Introduction to Photonics. Introduction
EE485 Introduction to Photonics Introduction Nature of Light They could but make the best of it and went around with woebegone faces, sadly complaining that on Mondays, Wednesdays, and Fridays, they must
More informationCHAPTER 9 ELECTROMAGNETIC WAVES
CHAPTER 9 ELECTROMAGNETIC WAVES Outlines 1. Waves in one dimension 2. Electromagnetic Waves in Vacuum 3. Electromagnetic waves in Matter 4. Absorption and Dispersion 5. Guided Waves 2 Skip 9.1.1 and 9.1.2
More informationLecture 21 Reminder/Introduction to Wave Optics
Lecture 1 Reminder/Introduction to Wave Optics Program: 1. Maxwell s Equations.. Magnetic induction and electric displacement. 3. Origins of the electric permittivity and magnetic permeability. 4. Wave
More informationOPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626
OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona kkieu@optics.arizona.edu Meinel building R.626 Important announcements Homework #1 assigned, due Jan. 29 Normal class on
More informationOPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626
OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona kkieu@optics.arizona.edu Meinel building R.626 Announcements Mid-term exam on Monday, March 6 th Review Properties of light
More informationOPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626
OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona kkieu@optics.arizona.edu Meinel building R.626 Announcements Mid-term exam will be on Feb 27 th, 2PM, room 307 (open books/notes)
More informationOPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626
OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona kkieu@optics.arizona.edu Meinel building R.626 Announcements No class Monday, Feb 26 Mid-term exam will be on Feb 28 th
More informationElectromagnetic fields and waves
Electromagnetic fields and waves Maxwell s rainbow Outline Maxwell s equations Plane waves Pulses and group velocity Polarization of light Transmission and reflection at an interface Macroscopic Maxwell
More informationElectrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Electro Dynamic
Electrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Name Electro Dynamic Instructions: Use SI units. Short answers! No derivations here, just state your responses clearly. 1. (2) Write an
More informationLecture 4 Fiber Optical Communication Lecture 4, Slide 1
ecture 4 Dispersion in single-mode fibers Material dispersion Waveguide dispersion imitations from dispersion Propagation equations Gaussian pulse broadening Bit-rate limitations Fiber losses Fiber Optical
More informationOverview in Images. 5 nm
Overview in Images 5 nm K.S. Min et al. PhD Thesis K.V. Vahala et al, Phys. Rev. Lett, 85, p.74 (000) J. D. Joannopoulos, et al, Nature, vol.386, p.143-9 (1997) S. Lin et al, Nature, vol. 394, p. 51-3,
More informationBasics of electromagnetic response of materials
Basics of electromagnetic response of materials Microscopic electric and magnetic field Let s point charge q moving with velocity v in fields e and b Force on q: F e F qeqvb F m Lorenz force Microscopic
More informationE E D E=0 2 E 2 E (3.1)
Chapter 3 Constitutive Relations Maxwell s equations define the fields that are generated by currents and charges. However, they do not describe how these currents and charges are generated. Thus, to find
More informationLinear pulse propagation
Ultrafast Laser Physics Ursula Keller / Lukas Gallmann ETH Zurich, Physics Department, Switzerland www.ulp.ethz.ch Linear pulse propagation Ultrafast Laser Physics ETH Zurich Superposition of many monochromatic
More informationX-Ray Interaction with Matter: Absorption, Scattering and Refraction
X-Ray Interaction with Matter: Absorption, Scattering and Refraction David Attwood University of California, Berkeley 1 The short wavelength region of the electromagnetic spectrum n = 1 δ + iβ δ, β
More informationOptics and Optical Design. Chapter 6: Polarization Optics. Lectures 11-13
Optics and Optical Design Chapter 6: Polarization Optics Lectures 11-13 Cord Arnold / Anne L Huillier Polarization of Light Arbitrary wave vs. paraxial wave One component in x-direction y x z Components
More information1 Fundamentals of laser energy absorption
1 Fundamentals of laser energy absorption 1.1 Classical electromagnetic-theory concepts 1.1.1 Electric and magnetic properties of materials Electric and magnetic fields can exert forces directly on atoms
More informationCourse Secretary: Christine Berber O3.095, phone x-6351,
IMPRS: Ultrafast Source Technologies Franz X. Kärtner (Umit Demirbas) & Thorsten Uphues, Bldg. 99, O3.097 & Room 6/3 Email & phone: franz.kaertner@cfel.de, 040 8998 6350 thorsten.uphues@cfel.de, 040 8998
More informationSinfonia. Professor Hong Guo 1
Sinfonia Professor Hong Guo (hongguo@pku.edu.cn) IQE@EE.EECS.PKU CREAM@IQE.EE.EECS.PKU 1 CREAM@IQE.EE.EECS.PKU 2 CREAM@IQE.EE.EECS.PKU 3 CREAM@IQE.EE.EECS.PKU 4 CREAM@IQE.EE.EECS.PKU 5 CREAM@IQE.EE.EECS.PKU
More informationElectromagnetic (EM) Waves
Electromagnetic (EM) Waves Short review on calculus vector Outline A. Various formulations of the Maxwell equation: 1. In a vacuum 2. In a vacuum without source charge 3. In a medium 4. In a dielectric
More informationElectromagnetic Theory for Microwaves and Optoelectronics
Keqian Zhang Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Translated by authors With 259 Figures Springer Contents 1 Basic Electromagnetic Theory 1 1.1 Maxwell's Equations 1 1.1.1
More informationChap. 1 Fundamental Concepts
NE 2 Chap. 1 Fundamental Concepts Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820) Faradays
More informationfiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Content-ELECTRICITY AND MAGNETISM 1. Electrostatics (1-58) 1.1 Coulomb s Law and Superposition Principle 1.1.1 Electric field 1.2 Gauss s law 1.2.1 Field lines and Electric flux 1.2.2 Applications 1.3
More informationOPTI 501, Electromagnetic Waves (3)
OPTI 501, Electromagnetic Waves (3) Vector fields, Maxwell s equations, electromagnetic field energy, wave equations, free-space solutions, box modes, Fresnel equations, scalar and vector potentials, gauge
More informationChapter 9. Electromagnetic waves
Chapter 9. lectromagnetic waves 9.1.1 The (classical or Mechanical) waves equation Given the initial shape of the string, what is the subsequent form, The displacement at point z, at the later time t,
More informationElectromagnetic Theory for Microwaves and Optoelectronics
Keqian Zhang Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Second Edition With 280 Figures and 13 Tables 4u Springer Basic Electromagnetic Theory 1 1.1 Maxwell's Equations 1 1.1.1
More informationLasers and Electro-optics
Lasers and Electro-optics Second Edition CHRISTOPHER C. DAVIS University of Maryland III ^0 CAMBRIDGE UNIVERSITY PRESS Preface to the Second Edition page xv 1 Electromagnetic waves, light, and lasers 1
More informationOptics and Optical Design. Chapter 6: Polarization Optics. Lectures 11 13
Optics and Optical Design Chapter 6: Polarization Optics Lectures 11 13 Cord Arnold / Anne L Huillier Polarization of Light Arbitrary wave vs. paraxial wave One component in x direction y x z Components
More informationOptical Fiber Signal Degradation
Optical Fiber Signal Degradation Effects Pulse Spreading Dispersion (Distortion) Causes the optical pulses to broaden as they travel along a fiber Overlap between neighboring pulses creates errors Resulting
More informationPlasmonics: elementary excitation of a plasma (gas of free charges) nano-scale optics done with plasmons at metal interfaces
Plasmonics Plasmon: Plasmonics: elementary excitation of a plasma (gas of free charges) nano-scale optics done with plasmons at metal interfaces Femius Koenderink Center for Nanophotonics AMOLF, Amsterdam
More informationChapter Three: Propagation of light waves
Chapter Three Propagation of Light Waves CHAPTER OUTLINE 3.1 Maxwell s Equations 3.2 Physical Significance of Maxwell s Equations 3.3 Properties of Electromagnetic Waves 3.4 Constitutive Relations 3.5
More informationIMPRS: Ultrafast Source Technologies
IMPRS: Ultrafast Source Technologies Fran X. Kärtner & Thorsten Uphues, Bldg. 99, O3.097 & Room 6/3 Email & phone: fran.kaertner@cfel.de, 040 8998 6350 Thorsten.Uphues@cfel.de, 040 8998 706 Lectures: Tuesday
More informationIntroduction to Electromagnetic Theory
Introduction to Electromagnetic Theory Lecture topics Laws of magnetism and electricity Meaning of Maxwell s equations Solution of Maxwell s equations Electromagnetic radiation: wave model James Clerk
More informationElectromagnetic Waves Across Interfaces
Lecture 1: Foundations of Optics Outline 1 Electromagnetic Waves 2 Material Properties 3 Electromagnetic Waves Across Interfaces 4 Fresnel Equations 5 Brewster Angle 6 Total Internal Reflection Christoph
More informationClassical Electrodynamics
Classical Electrodynamics Third Edition John David Jackson Professor Emeritus of Physics, University of California, Berkeley JOHN WILEY & SONS, INC. Contents Introduction and Survey 1 I.1 Maxwell Equations
More informationNonlinear optics: a back-to-basics primer Lecture 1: linear optics
Guoqing (Noah) Chang, October 9, 15 Nonlinear optics: a back-to-basics primer Lecture 1: linear optics 1 Suggested references Robert W. Boyd, Nonlinear optics (8) Geoffrey New, Introduction to nonlinear
More informationPhysics of Light and Optics
Physics of Light and Optics Justin Peatross and Harold Stokes Brigham Young University Department of Physics and Astronomy All Publication Rights Reserved (2001) Revised April 2002 This project is supported
More informationDescribe the forces and torques exerted on an electric dipole in a field.
Learning Outcomes - PHYS 2015 Electric charges and forces: Describe the electrical nature of matter; Explain how an object can be charged; Distinguish between electrical conductors and insulators and the
More informationPhotonic/Plasmonic Structures from Metallic Nanoparticles in a Glass Matrix
Excerpt from the Proceedings of the COMSOL Conference 2008 Hannover Photonic/Plasmonic Structures from Metallic Nanoparticles in a Glass Matrix O.Kiriyenko,1, W.Hergert 1, S.Wackerow 1, M.Beleites 1 and
More informationMaxwell s equations and EM waves. From previous Lecture Time dependent fields and Faraday s Law
Maxwell s equations and EM waves This Lecture More on Motional EMF and Faraday s law Displacement currents Maxwell s equations EM Waves From previous Lecture Time dependent fields and Faraday s Law 1 Radar
More informationOverview - Previous lecture 1/2
Overview - Previous lecture 1/2 Derived the wave equation with solutions of the form We found that the polarization of the material affects wave propagation, and found the dispersion relation ω(k) with
More informationMEFT / Quantum Optics and Lasers. Suggested problems Set 4 Gonçalo Figueira, spring 2015
MEFT / Quantum Optics and Lasers Suggested problems Set 4 Gonçalo Figueira, spring 05 Note: some problems are taken or adapted from Fundamentals of Photonics, in which case the corresponding number is
More informationInvisible Random Media And Diffraction Gratings That Don't Diffract
Invisible Random Media And Diffraction Gratings That Don't Diffract 29/08/2017 Christopher King, Simon Horsley and Tom Philbin, University of Exeter, United Kingdom, email: cgk203@exeter.ac.uk webpage:
More informationUNIT I ELECTROSTATIC FIELDS
UNIT I ELECTROSTATIC FIELDS 1) Define electric potential and potential difference. 2) Name few applications of gauss law in electrostatics. 3) State point form of Ohm s Law. 4) State Divergence Theorem.
More informationUNIT-III Maxwell's equations (Time varying fields)
UNIT-III Maxwell's equations (Time varying fields) Faraday s law, transformer emf &inconsistency of ampere s law Displacement current density Maxwell s equations in final form Maxwell s equations in word
More informationIntroduction to Electromagnetism
Introduction to Electromagnetism Electric Field Lines If a charge feels an electrostatic force (Coulombic Force), it is said to be in an electric field. We like to represent electric fields with lines.
More informationPrinciples of Mobile Communications
Communication Networks 1 Principles of Mobile Communications University Duisburg-Essen WS 2003/2004 Page 1 N e v e r s t o p t h i n k i n g. Wave Propagation Single- and Multipath Propagation Overview:
More informationLecture Notes on Wave Optics (03/05/14) 2.71/2.710 Introduction to Optics Nick Fang
Outline: A. Electromagnetism B. Frequency Domain (Fourier transform) C. EM waves in Cartesian coordinates D. Energy Flow and Poynting Vector E. Connection to geometrical optics F. Eikonal Equations: Path
More informationHomework 1. Property LASER Incandescent Bulb
Homework 1 Solution: a) LASER light is spectrally pure, single wavelength, and they are coherent, i.e. all the photons are in phase. As a result, the beam of a laser light tends to stay as beam, and not
More informationSOFT X-RAYS AND EXTREME ULTRAVIOLET RADIATION
SOFT X-RAYS AND EXTREME ULTRAVIOLET RADIATION Principles and Applications DAVID ATTWOOD UNIVERSITY OF CALIFORNIA, BERKELEY AND LAWRENCE BERKELEY NATIONAL LABORATORY CAMBRIDGE UNIVERSITY PRESS Contents
More informationNote on Group Velocity and Energy Propagation
Note on Group Velocity and Energy Propagation Abraham Bers Department of Electrical Engineering & Computer Science and Plasma Science & Fusion Center Massachusetts Institute of Technology, Cambridge, MA
More informationScattering of ECRF waves by edge density fluctuations and blobs
PSFC/JA-14-7 Scattering of ECRF waves by edge density fluctuations and blobs A. K. Ram and K. Hizanidis a June 2014 Plasma Science and Fusion Center, Massachusetts Institute of Technology Cambridge, MA
More informationNonlinear Optics (NLO)
Nonlinear Optics (NLO) (Manual in Progress) Most of the experiments performed during this course are perfectly described by the principles of linear optics. This assumes that interacting optical beams
More informationSupplementary Figure 1 Schematics of an optical pulse in a nonlinear medium. A Gaussian optical pulse propagates along z-axis in a nonlinear medium
Supplementary Figure 1 Schematics of an optical pulse in a nonlinear medium. A Gaussian optical pulse propagates along z-axis in a nonlinear medium with thickness L. Supplementary Figure Measurement of
More informationLecture notes 5: Diffraction
Lecture notes 5: Diffraction Let us now consider how light reacts to being confined to a given aperture. The resolution of an aperture is restricted due to the wave nature of light: as light passes through
More informationPhysics of Condensed Matter I
Physics of Condensed Matter I 1100-4INZ`PC Faculty of Physics UW Jacek.Szczytko@fuw.edu.pl Dictionary D = εe ε 0 vacuum permittivity, permittivity of free space (przenikalność elektryczna próżni) ε r relative
More informationLet us consider a typical Michelson interferometer, where a broadband source is used for illumination (Fig. 1a).
7.1. Low-Coherence Interferometry (LCI) Let us consider a typical Michelson interferometer, where a broadband source is used for illumination (Fig. 1a). The light is split by the beam splitter (BS) and
More informationLecture 15 February 23, 2016
MATH 262/CME 372: Applied Fourier Analysis and Winter 2016 Elements of Modern Signal Processing Lecture 15 February 23, 2016 Prof. Emmanuel Candes Scribe: Carlos A. Sing-Long, Edited by E. Bates 1 Outline
More informationOptical Solitons. Lisa Larrimore Physics 116
Lisa Larrimore Physics 116 Optical Solitons An optical soliton is a pulse that travels without distortion due to dispersion or other effects. They are a nonlinear phenomenon caused by self-phase modulation
More informationLECTURE 23: LIGHT. Propagation of Light Huygen s Principle
LECTURE 23: LIGHT Propagation of Light Reflection & Refraction Internal Reflection Propagation of Light Huygen s Principle Each point on a primary wavefront serves as the source of spherical secondary
More informationLecture 2 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell
Lecture Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell 1. Dispersion Introduction - An electromagnetic wave with an arbitrary wave-shape
More information26. The Fourier Transform in optics
26. The Fourier Transform in optics What is the Fourier Transform? Anharmonic waves The spectrum of a light wave Fourier transform of an exponential The Dirac delta function The Fourier transform of e
More information1. Reminder: E-Dynamics in homogenous media and at interfaces
0. Introduction 1. Reminder: E-Dynamics in homogenous media and at interfaces 2. Photonic Crystals 2.1 Introduction 2.2 1D Photonic Crystals 2.3 2D and 3D Photonic Crystals 2.4 Numerical Methods 2.5 Fabrication
More informationCHAPTER 2. COULOMB S LAW AND ELECTRONIC FIELD INTENSITY. 2.3 Field Due to a Continuous Volume Charge Distribution
CONTENTS CHAPTER 1. VECTOR ANALYSIS 1. Scalars and Vectors 2. Vector Algebra 3. The Cartesian Coordinate System 4. Vector Cartesian Coordinate System 5. The Vector Field 6. The Dot Product 7. The Cross
More information3.1 The Plane Mirror Resonator 3.2 The Spherical Mirror Resonator 3.3 Gaussian modes and resonance frequencies 3.4 The Unstable Resonator
Quantum Electronics Laser Physics Chapter 3 The Optical Resonator 3.1 The Plane Mirror Resonator 3. The Spherical Mirror Resonator 3.3 Gaussian modes and resonance frequencies 3.4 The Unstable Resonator
More informationTypical anisotropies introduced by geometry (not everything is spherically symmetric) temperature gradients magnetic fields electrical fields
Lecture 6: Polarimetry 1 Outline 1 Polarized Light in the Universe 2 Fundamentals of Polarized Light 3 Descriptions of Polarized Light Polarized Light in the Universe Polarization indicates anisotropy
More informationECE 484 Semiconductor Lasers
ECE 484 Semiconductor Lasers Dr. Lukas Chrostowski Department of Electrical and Computer Engineering University of British Columbia January, 2013 Module Learning Objectives: Understand the importance of
More information37. 3rd order nonlinearities
37. 3rd order nonlinearities Characterizing 3rd order effects The nonlinear refractive index Self-lensing Self-phase modulation Solitons When the whole idea of χ (n) fails Attosecond pulses! χ () : New
More informationLight. November 101 Lect 11 1
Light What is light? To start, what are the observed properties of light? Describe the intrinsic properties of light light by itself. Later, what are the interactions of light? What happens when light
More informationAST 553. Plasma Waves and Instabilities. Course Outline. (Dated: December 4, 2018)
AST 553. Plasma Waves and Instabilities Course Outline (Dated: December 4, 2018) I. INTRODUCTION Basic concepts Waves in plasmas as EM field oscillations Maxwell s equations, Gauss s laws as initial conditions
More informationAntennas and Propagation. Chapter 2: Basic Electromagnetic Analysis
Antennas and Propagation : Basic Electromagnetic Analysis Outline Vector Potentials, Wave Equation Far-field Radiation Duality/Reciprocity Transmission Lines Antennas and Propagation Slide 2 Antenna Theory
More informationTheoretische Physik 2: Elektrodynamik (Prof. A-S. Smith) Home assignment 9
WiSe 202 20.2.202 Prof. Dr. A-S. Smith Dipl.-Phys. Ellen Fischermeier Dipl.-Phys. Matthias Saba am Lehrstuhl für Theoretische Physik I Department für Physik Friedrich-Alexander-Universität Erlangen-Nürnberg
More informationFundamentals of Modern Optics
Script Fundamentals of Modern Optics, FSU Jena, Prof. T. Pertsch, FoMO_Script_2014-10-19s.docx 1 Fundamentals of Modern Optics Winter Term 2014/2015 Prof. Thomas Pertsch Abbe School of Photonics Friedrich-Schiller-Universität
More informationJones calculus for optical system
2/14/17 Electromagnetic Processes In Dispersive Media, Lecture 6 1 Jones calculus for optical system T. Johnson Key concepts in the course so far What is meant by an electro-magnetic response? What characterises
More informationA Review of Basic Electromagnetic Theories
A Review of Basic Electromagnetic Theories Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820)
More informationELECTROMAGNETISM. Second Edition. I. S. Grant W. R. Phillips. John Wiley & Sons. Department of Physics University of Manchester
ELECTROMAGNETISM Second Edition I. S. Grant W. R. Phillips Department of Physics University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE Flow diagram inside front cover
More informationELECTROMAGNETIC FIELD
UNIT-III INTRODUCTION: In our study of static fields so far, we have observed that static electric fields are produced by electric charges, static magnetic fields are produced by charges in motion or by
More information9 The conservation theorems: Lecture 23
9 The conservation theorems: Lecture 23 9.1 Energy Conservation (a) For energy to be conserved we expect that the total energy density (energy per volume ) u tot to obey a conservation law t u tot + i
More informationPhysics for Scientists & Engineers 2
Light as Waves Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 41! In the previous chapter we discussed light as rays! These rays traveled in a straight line except when they were reflected
More informationPY3101 Optics. Overview. A short history of optics Optical applications Course outline. Introduction: Overview. M.P. Vaughan
Introduction: Overview M.P. Vaughan Overview A short history of optics Optical applications Course outline 1 A Short History of Optics A short history of optics Optics: historically the study of visible
More informationINTRODUCTION TO ELECTRODYNAMICS
INTRODUCTION TO ELECTRODYNAMICS Second Edition DAVID J. GRIFFITHS Department of Physics Reed College PRENTICE HALL, Englewood Cliffs, New Jersey 07632 CONTENTS Preface xi Advertisement 1 1 Vector Analysis
More informationMain Notation Used in This Book
Main Notation Used in This Book z Direction normal to the surface x,y Directions in the plane of the surface Used to describe a component parallel to the interface plane xoz Plane of incidence j Label
More informationAll-optical generation of surface plasmons in graphene
All-optical generation of surface plasmons in graphene T. J. Constant, 1, S. M. Hornett, 1 D. E. Chang, 2, and E. Hendry 1 1 Electromagnetic Materials Group, Department of Physics, College of Engineering,
More information10. OPTICAL COHERENCE TOMOGRAPHY
1. OPTICAL COHERENCE TOMOGRAPHY Optical coherence tomography (OCT) is a label-free (intrinsic contrast) technique that enables 3D imaging of tissues. The principle of its operation relies on low-coherence
More informationSupplementary Information for Negative refraction in semiconductor metamaterials
Supplementary Information for Negative refraction in semiconductor metamaterials A.J. Hoffman *, L. Alekseyev, S.S. Howard, K.J. Franz, D. Wasserman, V.A. Poldolskiy, E.E. Narimanov, D.L. Sivco, and C.
More informationMODERN OPTICS. P47 Optics: Unit 9
MODERN OPTICS P47 Optics: Unit 9 Course Outline Unit 1: Electromagnetic Waves Unit 2: Interaction with Matter Unit 3: Geometric Optics Unit 4: Superposition of Waves Unit 5: Polarization Unit 6: Interference
More informationSub-wavelength electromagnetic structures
Sub-wavelength electromagnetic structures Shanhui Fan, Z. Ruan, L. Verselegers, P. Catrysse, Z. Yu, J. Shin, J. T. Shen, G. Veronis Ginzton Laboratory, Stanford University http://www.stanford.edu/group/fan
More informationThe structure of laser pulses
1 The structure of laser pulses 2 The structure of laser pulses Pulse characteristics Temporal and spectral representation Fourier transforms Temporal and spectral widths Instantaneous frequency Chirped
More informationLecture cycle: Spectroscopy and Optics
Lecture cycle: Spectroscopy and Optics Thu. 13:00-15:00 / Room 1.003 15.11.2017 (Staudinger) Mischa Bonn Light-matter interaction overview I 30.11.2017 Mischa Bonn Light-matter interaction overview II
More information2.4 Properties of the nonlinear susceptibilities
2.4 Properties of the nonlinear susceptibilities 2.4.1 Physical fields are real 2.4.2 Permutation symmetry numbering 1 to n arbitrary use symmetric definition 1 2.4.3 Symmetry for lossless media two additional
More informationThermal Emission in the Near Field from Polar Semiconductors and the Prospects for Energy Conversion
Thermal Emission in the Near Field from Polar Semiconductors and the Prospects for Energy Conversion R.J. Trew, K.W. Kim, V. Sokolov, and B.D Kong Electrical and Computer Engineering North Carolina State
More informationOptical Spectroscopy of Advanced Materials
Phys 590B Condensed Matter Physics: Experimental Methods Optical Spectroscopy of Advanced Materials Basic optics, nonlinear and ultrafast optics Jigang Wang Department of Physics, Iowa State University
More information4. The interaction of light with matter
4. The interaction of light with matter The propagation of light through chemical materials is described by a wave equation similar to the one that describes light travel in a vacuum (free space). Again,
More informationPRINCIPLES OF PHYSICAL OPTICS
PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction
More informationEdward S. Rogers Sr. Department of Electrical and Computer Engineering. ECE318S Fundamentals of Optics. Final Exam. April 16, 2007.
Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE318S Fundamentals of Optics Final Exam April 16, 2007 Exam Type: D (Close-book + two double-sided aid sheets + a non-programmable
More information