Chapter 9 Electro-Optics
|
|
- Gladys Garrett
- 5 years ago
- Views:
Transcription
1 Chapter 9 Electro-Optics Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory Principles of Optical Imaging Electrical and Computer Engineering, UIUC
2 Electro Optics 1 st order effect: w 1 Pi ii jjrijkej ( ) Ek () i i i i j ijk j k ( ) 4 Dx n n r13ey EDc n ner133ez EDC Dy n n r13e xedc 4 r kdp 53 Dz ne Ez D n E n n r E E DC DC 11O z Chapter 9: Electro Optics
3 Electro Optics 4 n n r63e Dc 4 ij n r63edc n ne ' ij W( ) W( ) cos sin n cos sin sin cos n sin cos n ij n ; 4 n e b i 4 n r63 Ez ( DC) biaxial crystal Chapter 9: Electro Optics 3
4 Modulators Eg KDP(tetra 4m ) r 41, r 5, r 63 only three nonzero elements n KDP x n ; 1 1 n n n n n n n n x y n 1 n n 1 r n n r63ez ( DC) Chapter 9: Electro Optics 4
5 Modulators ( n n ') d n r E ( DC ) d 3 x y 63 z n V V n r 3 63 linearize T V T sin 4 sin s Add QW V Chapter 9: Electro Optics 5
6 Modulators Let V V sin t m m T sin sin m m t cos sin 1 sin sin m m t m m t 1 1T 1 sin t m m m m linear Chapter 9: Electro Optics 6
7 Quadratic (Kerr) ( ) 1 i ii jj ijk j k e P s E ( ) E ( DC ) E ( DC ) Chapter 9: Electro Optics 7
8 Applications of EO longitudinal modulators transverse For LiNiO 3 : 1 3 nx n n r 13 E 1 3 ny n n r13e 1 3 nz ne ne r33e 3 v nl n rv 13 V 3 v n r Ed 13 Phase mod(indep. of polariz.) Chapter 9: Electro Optics 8
9 Chapter 9 Acousto-optics Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory Principles of Optical Imaging Electrical and Computer Engineering, UIUC
10 Acousto optics optics i j i ijklsklej jkl x 1 6 ac wave: z S13 S P n n p S E U ( z, t) xa cos( t kz) Chapter 9: Acousto optics 1
11 Chapter 1: Introduction 11
12 Acousto optics optics K k K k 1 k k1 nk sin k / K / K sin B ; Bragg angle
13 Acousto optics optics small ( k k ) Doppler Shift Δk Δv Kvs Quantum mechanics k' k ' conservation of momentum conservation of energy Chapter 9: Acousto optics 13
14 Anisotropic media k' k k ' n-different ' - negative k'sin ' ksin ; ' n' n sin ' sin ; n sin ' sin n' n' k wavelength of sound Chapter 9: Acousto optics 14
15 Anisotropic Ex: C k ' k -(e) k ' - scattered in prop. Plane (o) k ' (o) n sin ' e sin n' n ' n n e ', n n e e n n n n Chapter 9: Acousto optics 15 e
16 Small angle Scattering I scatt I inc sin ( L L ) 3/ k ( nn 1 ) ep ijke S e 4 cos cos 1 i ke j Kin. Energy/ V = ½ W total I ac v s 1 v U U s vs u vs [ U ] I ac t 1 3 vs S U S z U Chapter 9: Acousto optics 16
17 Small angle Scattering S 3/ ac 3 Small cos 1 1 s I I ac k ( nn 1 ) I P 3 v 4 cos cos v s M 6 n p v p 3 s table 3/ 3 k ( nn 1 ) v s M I ac n vs MI ac Chapter 9: Acousto optics 17
18 Small angle Scattering Detuning: sin B k sin sin 1 ; B k k sin k sin 1 1 ( Bragg) k sin ( ) k 1 cos 1 1 k cos 1 ( ) k(cos 1cos ) k sin B I scat sin L 1 ; I inc 1 s 1 Chapter 9: Acousto optics 18
19 Finite Beams A B nw ; L ; f f size of acoustic beam 1 ; L nv cos 4v cos s s s -Full v nw w s 1 ; W or nvs cos ( ) f L! Not overlap with undiffracted order 1 Chapter 9: Acousto optics 19
20 N N spots f nw W f N nv s cos v s B f ; cond B nv s f f n L nv s f L Chapter 9: Acousto optics
Chapter 9 Electro-Optics
Chapter 9 Electro-Optics Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging Electrical
More information11/29/2010. Propagation in Anisotropic Media 3. Introduction. Introduction. Gabriel Popescu
Propagation in Anisotropic Media Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging
More information8. Propagation in Nonlinear Media
8. Propagation in Nonlinear Media 8.. Microscopic Description of Nonlinearity. 8... Anharmonic Oscillator. Use Lorentz model (electrons on a spring) but with nonlinear response, or anharmonic spring d
More information7 Optical modulators. 7.1 Electro-optic modulators Electro-optic media
7.1 Electro-optic modulators 7.1.1 Electro-optic media In a linear anisotropic medium, the electric displacement field D and the electric field strength E are related to each other through the electric
More information(Introduction) Linear Optics and Nonlinear Optics
18. Electro-optics (Introduction) Linear Optics and Nonlinear Optics Linear Optics The optical properties, such as the refractive index and the absorption coefficient are independent of light intensity.
More informationECE 185 ELECTRO-OPTIC MODULATION OF LIGHT
ECE 185 ELECTRO-OPTIC MODULATION OF LIGHT I. Objective: To study the Pockels electro-optic (EO) effect, and the property of light propagation in anisotropic medium, especially polarization-rotation effects.
More informationNon-linear Optics II (Modulators & Harmonic Generation)
Non-linear Optics II (Modulators & Harmonic Generation) P.E.G. Baird MT2011 Electro-optic modulation of light An electro-optic crystal is essentially a variable phase plate and as such can be used either
More informationInnovation and Development of Study Field. nano.tul.cz
Innovation and Development of Study Field Nanomaterials at the Technical University of Liberec nano.tul.cz These materials have been developed within the ESF project: Innovation and development of study
More informationChapter 9 - Polarization
Chapter 9 - Polarization Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging Electrical
More informationSummary of Fourier Optics
Summary of Fourier Optics Diffraction of the paraxial wave is described by Fresnel diffraction integral, u(x, y, z) = j λz dx 0 dy 0 u 0 (x 0, y 0 )e j(k/2z)[(x x 0) 2 +(y y 0 ) 2 )], Fraunhofer diffraction
More informationRef. p. 110] 7.1 Modulators 85
Ref. p. 0] 7. Modulators 85 7. Modulators B. Kuhlow 7.. Introduction Modulation of light is used for a number of applications including the impression of information onto optical beams, Q-switching of
More informationWave Turbulence and Condensation in an Optical Experiment
Wave Turbulence and Condensation in an Optical Experiment S. Residori, U. Bortolozzo Institut Non Linéaire de Nice, CNRS, France S. Nazarenko, J. Laurie Mathematics Institute, University of Warwick, UK
More informationStructure of Surfaces
Structure of Surfaces C Stepped surface Interference of two waves Bragg s law Path difference = AB+BC =2dsin ( =glancing angle) If, n =2dsin, constructive interference Ex) in a cubic lattice of unit cell
More informationLecture 4: Anisotropic Media. Dichroism. Optical Activity. Faraday Effect in Transparent Media. Stress Birefringence. Form Birefringence
Lecture 4: Anisotropic Media Outline Dichroism Optical Activity 3 Faraday Effect in Transparent Media 4 Stress Birefringence 5 Form Birefringence 6 Electro-Optics Dichroism some materials exhibit different
More informationOptical Imaging Chapter 5 Light Scattering
Optical Imaging Chapter 5 Light Scattering Gabriel Popescu University of Illinois at Urbana-Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical
More informationUltracold atoms and molecules
Advanced Experimental Techniques Ultracold atoms and molecules Steven Knoop s.knoop@vu.nl VU, June 014 1 Ultracold atoms laser cooling evaporative cooling BEC Bose-Einstein condensation atom trap: magnetic
More information18. Active polarization control
18. Active polarization control Ways to actively control polarization Pockels' Effect inducing birefringence Kerr Effect Optical Activity Principal axes are circular, not linear Faraday Effect inducing
More informationPart 5 ACOUSTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA
Part 5 ACOUSTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA Review of Fundamentals displacement-strain relation stress-strain relation balance of momentum (deformation) (constitutive equation) (Newton's Law)
More informationElectromagnetism II Lecture 7
Electromagnetism II Lecture 7 Instructor: Andrei Sirenko sirenko@njit.edu Spring 13 Thursdays 1 pm 4 pm Spring 13, NJIT 1 Previous Lecture: Conservation Laws Previous Lecture: EM waves Normal incidence
More informationF85/F86 - Grundpraktikum Optik (Photonics)
F85/F86 - Grundpraktikum Optik (Photonics) R. Folman, S. Manz, T. Fernholz, L. Feenstra Motivation Solid state light manipulation devices (Photonics) have become a basic tool for scientific research as
More informationTHE WAVE EQUATION (5.1)
THE WAVE EQUATION 5.1. Solution to the wave equation in Cartesian coordinates Recall the Helmholtz equation for a scalar field U in rectangular coordinates U U r, ( r, ) r, 0, (5.1) Where is the wavenumber,
More informationNonlinear effects in optical fibers - v1. Miguel A. Muriel UPM-ETSIT-MUIT-CFOP
Nonlinear effects in optical fibers - v1 Miguel A. Muriel UPM-ETSIT-MUIT-CFOP Miguel A. Muriel-015/10-1 Nonlinear effects in optical fibers 1) Introduction ) Causes 3) Parameters 4) Fundamental processes
More informationNonlinear Effects in Optical Fiber. Dr. Mohammad Faisal Assistant Professor Dept. of EEE, BUET
Nonlinear Effects in Optical Fiber Dr. Mohammad Faisal Assistant Professor Dept. of EEE, BUET Fiber Nonlinearities The response of any dielectric material to the light becomes nonlinear for intense electromagnetic
More informationAcoustooptic Devices. Chapter 10 Physics 208, Electro-optics Peter Beyersdorf. Document info ch 10. 1
Acoustooptic Devices Chapter 10 Physics 208, Electro-optics Peter Beyersdorf Document info ch 10. 1 Overview Raman-Nath Diffraction (chapter 9) AO Modulators AO deflectors Bandwidth Figures of Merit ch
More informationTopological phases of matter give rise to quantized physical quantities
Quantized electric multipole insulators Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017). Quantized electric multipole insulators. Science, 357(6346), 61 66. Presented by Mark Hirsbrunner, Weizhan
More informationStrongly correlated systems in atomic and condensed matter physics. Lecture notes for Physics 284 by Eugene Demler Harvard University
Strongly correlated systems in atomic and condensed matter physics Lecture notes for Physics 284 by Eugene Demler Harvard University September 18, 2014 2 Chapter 5 Atoms in optical lattices Optical lattices
More informationLiquid Crystals IAM-CHOON 1(1100 .,4 WILEY 2007 WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION. 'i; Second Edition. n z
Liquid Crystals Second Edition IAM-CHOON 1(1100.,4 z 'i; BICENTCNNIAL 1 8 0 7 WILEY 2007 DICENTENNIAL n z z r WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents Preface xiii Chapter 1.
More informationGuided Acoustic Wave Brillouin Scattering (GAWBS) in Photonic Crystal Fibers (PCFs)
Guided Acoustic Wave Brillouin Scattering (GAWBS) in Photonic Crystal Fibers (PCFs) FRISNO-9 Dominique Elser 15/02/2007 GAWBS Theory Thermally excited acoustic fiber vibrations at certain resonance frequencies
More informationCold atoms in optical lattices
Cold atoms in optical lattices www.lens.unifi.it Tarruel, Nature Esslinger group Optical lattices the big picture We have a textbook model, which is basically exact, describing how a large collection of
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 informationChap. 4. Electromagnetic Propagation in Anisotropic Media
Chap. 4. Electromagnetic Propagation in Anisotropic Media - Optical properties depend on the direction of propagation and the polarization of the light. - Crystals such as calcite, quartz, KDP, and liquid
More informationConcepts for Specific Heat
Concepts for Specific Heat Andreas Wacker 1 Mathematical Physics, Lund University August 17, 018 1 Introduction These notes shall briefly explain general results for the internal energy and the specific
More informationFourier Approach to Wave Propagation
Phys 531 Lecture 15 13 October 005 Fourier Approach to Wave Propagation Last time, reviewed Fourier transform Write any function of space/time = sum of harmonic functions e i(k r ωt) Actual waves: harmonic
More informationThe Interaction of Acoustic Phonons and Photons in the Solid State
University of Tennessee, Knoxville Trace: Tennessee Research and Creative Exchange University of Tennessee Honors Thesis Projects University of Tennessee Honors Program Spring 5-2007 The Interaction of
More informationElectromagnetic Properties of Materials Part 2
ECE 5322 21 st Century Electromagnetics Instructor: Office: Phone: E Mail: Dr. Raymond C. Rumpf A 337 (915) 747 6958 rcrumpf@utep.edu Lecture #3 Electromagnetic Properties of Materials Part 2 Nonlinear
More informationPhonons I - Crystal Vibrations (Kittel Ch. 4)
Phonons I - Crystal Vibrations (Kittel Ch. 4) Displacements of Atoms Positions of atoms in their perfect lattice positions are given by: R 0 (n 1, n 2, n 3 ) = n 10 x + n 20 y + n 30 z For simplicity here
More informationOptical Lattices. Chapter Polarization
Chapter Optical Lattices Abstract In this chapter we give details of the atomic physics that underlies the Bose- Hubbard model used to describe ultracold atoms in optical lattices. We show how the AC-Stark
More informationOPTI 511L Fall A. Demonstrate frequency doubling of a YAG laser (1064 nm -> 532 nm).
R.J. Jones Optical Sciences OPTI 511L Fall 2017 Experiment 3: Second Harmonic Generation (SHG) (1 week lab) In this experiment we produce 0.53 µm (green) light by frequency doubling of a 1.06 µm (infrared)
More informationOptics, Optoelectronics and Photonics
Optics, Optoelectronics and Photonics Engineering Principles and Applications Alan Billings Emeritus Professor, University of Western Australia New York London Toronto Sydney Tokyo Singapore v Contents
More informationDeep Inelastic Scattering (DIS) Un-ki Yang Dept. of Physics and Astronomy Seoul National University Un-ki Yang - DIS
Deep Inelastic Scattering (DIS) Un-ki Yang Dept. of Physics and Astronomy Seoul National University ukyang@snu.ac.kr Un-ki Yang - DIS 1 Elastic and Inelastic scattering Electron-Proton Scattering P Electron-proton
More informationPH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5
PH575 Spring 2009 Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 Spring 2009 POP QUIZ Phonons are: A. Fermions B. Bosons C. Lattice vibrations D. Light/matter interactions PH575 Spring 2009 POP QUIZ
More informationAcoustooptic Bragg Diffraction in 2-Dimensional Photonic Crystals
Acoustooptic Bragg Diffraction in 2-Dimensional Photonic Crystals Z.A. Pyatakova M.V. Lomonosov Moscow State University, Physics Department zoya.pyatakova@gmail.com Abstract. The paper shows that silicon-based
More information12. Nonlinear optics I
1. Nonlinear optics I What are nonlinear-optical effects and why do they occur? Maxwell's equations in a medium Nonlinear-optical media Second-harmonic generation Conservation laws for photons ("Phasematching")
More information3.5 Cavities Cavity modes and ABCD-matrix analysis 206 CHAPTER 3. ULTRASHORT SOURCES I - FUNDAMENTALS
206 CHAPTER 3. ULTRASHORT SOURCES I - FUNDAMENTALS which is a special case of Eq. (3.30. Note that this treatment of dispersion is equivalent to solving the differential equation (1.94 for an incremental
More informationQuantum Corrections for Monte Carlo Simulation
Quantum Corrections for Monte Carlo Simulation Brian Winstead and Umberto Ravaioli Beckman Institute University of Illinois at Urbana-Champaign Outline Quantum corrections for quantization effects Effective
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 information4: birefringence and phase matching
/3/7 4: birefringence and phase matching Polarization states in EM Linear anisotropic response χ () tensor and its symmetry properties Working with the index ellipsoid: angle tuning Phase matching in crystals
More informationIntroduction to solid state physics
PHYS 342/555 Introduction to solid state physics Instructor: Dr. Pengcheng Dai Professor of Physics The University of Tennessee (Room 407A, Nielsen, 974-1509) Chapter 5: Thermal properties Lecture in pdf
More informationElectro-optics. Chapter 7 Physics 208, Electro-optics Peter Beyersdorf. Document info
Electro-optics Chapter 7 Physics 208, Electro-optics Peter Beyersdorf Document info 1 Impermeability Tensor It is convenient to consider the inverse of the relative permitivity, which we call the impermeability
More information6.730 Physics for Solid State Applications
6.730 Physics for Solid State Applications Lecture 29: Electron-phonon Scattering Outline Bloch Electron Scattering Deformation Potential Scattering LCAO Estimation of Deformation Potential Matrix Element
More informationDiffraction of light by acoustic waves in liquids
International Letters of Chemistry, Physics and Astronomy Online: 13-9-19 ISSN: 99-3843, Vol. 4, pp 39-57 doi:1.185/www.scipress.com/ilcpa.4.39 1 SciPress Ltd., Switzerland Diffraction of light by acoustic
More informationName : Roll No. :.... Invigilator s Signature :.. CS/B.Tech (NEW)/SEM-2/PH-201/2013 2013 PHYSICS - I Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are
More informationWhere are the Fringes? (in a real system) Div. of Amplitude - Wedged Plates. Fringe Localisation Double Slit. Fringe Localisation Grating
Where are the Fringes? (in a real system) Fringe Localisation Double Slit spatial modulation transverse fringes? everywhere or well localised? affected by source properties: coherence, extension Plane
More informationPH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5
PH575 Spring 2014 Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 POP QUIZ Phonons are: A. Fermions B. Bosons C. Lattice vibrations D. Light/matter interactions PH575 POP QUIZ Phonon dispersion relation:
More informationMP464: Solid State Physics Problem Sheet
MP464: Solid State Physics Problem Sheet 1 Write down primitive lattice vectors for the -dimensional rectangular lattice, with sides a and b in the x and y-directions respectively, and a face-centred rectangular
More informationLecture 14 Dispersion engineering part 1 - Introduction. EECS Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku
Lecture 14 Dispersion engineering part 1 - Introduction EEC 598-2 Winter 26 Nanophotonics and Nano-scale Fabrication P.C.Ku chedule for the rest of the semester Introduction to light-matter interaction
More informationObservation of Bose-Einstein Condensation in a Dilute Atomic Vapor
Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell Science 14 Jul 1995; Vol. 269, Issue 5221, pp. 198-201 DOI:
More informationSupplementary Figure 1: SAW transducer equivalent circuit
Supplementary Figure : SAW transducer equivalent circuit Supplementary Figure : Radiation conductance and susceptance of.6um IDT, experiment & calculation Supplementary Figure 3: Calculated z-displacement
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 informationDecoherence in molecular magnets: Fe 8 and Mn 12
Decoherence in molecular magnets: Fe 8 and Mn 12 I.S. Tupitsyn (with P.C.E. Stamp) Pacific Institute of Theoretical Physics (UBC, Vancouver) Early 7-s: Fast magnetic relaxation in rare-earth systems (Dy
More informationGRATING CLASSIFICATION
GRATING CLASSIFICATION SURFACE-RELIEF GRATING TYPES GRATING CLASSIFICATION Transmission or Reflection Classification based on Regime DIFFRACTION BY GRATINGS Acousto-Optics Diffractive Optics Integrated
More informationLecture 12: Phonon heat capacity
Lecture 12: Phonon heat capacity Review o Phonon dispersion relations o Quantum nature of waves in solids Phonon heat capacity o Normal mode enumeration o Density of states o Debye model Review By considering
More informationflbc in Russia. PIWiREE COHORTS ARE NOT PULL- ING TOGETHER. SIGHTS AND SCENES IN ST. PETERSBURG.
# O E O KOE O F Y F O VO V NO 5 OE KEN ONY Y 2 9 OE NO 265 E K N F z 5 7 X ) $2 Q - EO NE? O - 5 OO Y F F 2 - P - F O - FEE > < 5 < P O - 9 #»»» F & & F $ P 57 5 9 E 64 } 5 { O $665 $5 $ 25 E F O 9 5 [
More informationThe laser oscillator. Atoms and light. Fabry-Perot interferometer. Quiz
toms and light Introduction toms Semi-classical physics: Bohr atom Quantum-mechanics: H-atom Many-body physics: BEC, atom laser Light Optics: rays Electro-magnetic fields: Maxwell eq. s Quantized fields:
More informationThe laser oscillator. Atoms and light. Fabry-Perot interferometer. Quiz
toms and light Introduction toms Semi-classical physics: Bohr atom Quantum-mechanics: H-atom Many-body physics: BEC, atom laser Light Optics: rays Electro-magnetic fields: Maxwell eq. s Quantized fields:
More informationDr. Tao Li
Tao Li taoli@nju.edu.cn Nat. Lab. of Solid State Microstructures Department of Materials Science and Engineering Nanjing University Concepts Basic principles Surface Plasmon Metamaterial Summary Light
More informationDiscrete diffraction in an optically induced lattice in photorefractive media with a quadratic electro-optic effect
OPTO-ELECTRONICS REVIEW 13(2), 93 102 7 th International Workshop on Nonlinear Optics Applications Discrete diffraction in an optically induced lattice in photorefractive media with a quadratic electro-optic
More informationAN1106 Maximizing AO Diffraction efficiency. Efficiency is typically defined as the ratio of the zero and first order output beams:
AN1106 Maximizing AO Diffraction efficiency Nov11 Efficiency is typically defined as the ratio of the zero and first order output beams: Absorber First Order Input q Bragg q Sep Zero Order Transducer Diffraction
More informationWhich of the following can be used to calculate the resistive force acting on the brick? D (Total for Question = 1 mark)
1 A brick of mass 5.0 kg falls through water with an acceleration of 0.90 m s 2. Which of the following can be used to calculate the resistive force acting on the brick? A 5.0 (0.90 9.81) B 5.0 (0.90 +
More informationReview of Semiconductor Physics
Solid-state physics Review of Semiconductor Physics The daunting task of solid state physics Quantum mechanics gives us the fundamental equation The equation is only analytically solvable for a handful
More informationx n cos 2x dx. dx = nx n 1 and v = 1 2 sin(2x). Andreas Fring (City University London) AS1051 Lecture Autumn / 36
We saw in Example 5.4. that we sometimes need to apply integration by parts several times in the course of a single calculation. Example 5.4.4: For n let S n = x n cos x dx. Find an expression for S n
More informationWave Propagation in Uniaxial Media. Reflection and Transmission at Interfaces
Lecture 5: Crystal Optics Outline 1 Homogeneous, Anisotropic Media 2 Crystals 3 Plane Waves in Anisotropic Media 4 Wave Propagation in Uniaxial Media 5 Reflection and Transmission at Interfaces Christoph
More informationHigh-Resolution. Transmission. Electron Microscopy
Part 4 High-Resolution Transmission Electron Microscopy 186 Significance high-resolution transmission electron microscopy (HRTEM): resolve object details smaller than 1nm (10 9 m) image the interior of
More information36. Nonlinear optics: (2) processes
36. Nonlinear optics: () processes The wave equation with nonlinearity Second-harmonic generation: making blue light from red light approximations: SVEA, zero pump depletion phase matching quasi-phase
More information5. Liquid Crystal Display
5. Liquid Crystal Display Twisted Nematic(TN) LC : Director is twisted by 90 o o o o Supertwisted Nematic(STN) LC : Director is twisted by 180, 40 or 70 Better contrast and viewing angle. Yeh; 5-1 5.1
More informationIntroduction to Condensed Matter Physics
Introduction to Condensed Matter Physics The Reciprocal Lattice M.P. Vaughan Overview Overview of the reciprocal lattice Periodic functions Reciprocal lattice vectors Bloch functions k-space Dispersion
More informationLOWELL. MICHIGAN, THURSDAY, AUGUST 16, Specialty Co. Sells to Hudson Mfg. Company. Ada Farmer Dies When Boat Tips
K N» N - K V XXXV - N 22 N 5 V N N q N 0 " " - x Q- & V N -" Q" 24-?? 2530 35-6 9025 - - K ; ) ) ( _) ) N K : ; N - K K ) q ( K N ( x- 89830 z 7 K $2000 ( - N " " K : K 89335 30 4 V N
More informationEffects of Various Uncertainty Sources on Automatic Generation Control Systems
Effects of Various Uncertainty Sources on Automatic Generation Control Systems D. Apostolopoulou, Y. C. Chen, J. Zhang, A. D. Domínguez-García, and P. W. Sauer University of Illinois at Urbana-Champaign
More informationQuantum Mechanics: Particles in Potentials
Quantum Mechanics: Particles in Potentials 3 april 2010 I. Applications of the Postulates of Quantum Mechanics Now that some of the machinery of quantum mechanics has been assembled, one can begin to apply
More informationAtomic Physics (Phys 551) Final Exam Solutions
Atomic Physics (Phys 551) Final Exam Solutions Problem 1. For a Rydberg atom in n = 50, l = 49 state estimate within an order of magnitude the numerical value of a) Decay lifetime A = 1 τ = 4αω3 3c D (1)
More information3. LATTICE VIBRATIONS. 3.1 Sound Waves
3. LATTIC VIBRATIONS Atoms in lattice are not stationary even at T 0K. They vibrate about particular equilibrium positions at T 0K ( zero-point energy). For T > 0K, vibration amplitude increases as atoms
More informationSupplementary Table 1. Parameters for estimating minimum thermal conductivity in MoS2
Supplementary Table 1. Parameters for estimating minimum thermal conductivity in MoS2 crystal. The three polarizations (TL1 TL2 and TA) are named following the isoenergydecomposition process described
More informationLecture 3 : Electrooptic effect, optical activity and basics of interference colors with wave plates
Lecture 3 : Electrooptic effect, optical activity and basics of interference colors with wave plates NW optique physique II 1 Electrooptic effect Electrooptic effect: example of a KDP Pockels cell Liquid
More information36. Nonlinear optics: χ(2) processes
36. Nonlinear optics: χ() processes The wave equation with nonlinearity Second-harmonic generation: making blue light from red light approximations: SVEA, zero pump depletion phase matching quasi-phase
More informationB 2 P 2, which implies that g B should be
Enhanced Summary of G.P. Agrawal Nonlinear Fiber Optics (3rd ed) Chapter 9 on SBS Stimulated Brillouin scattering is a nonlinear three-wave interaction between a forward-going laser pump beam P, a forward-going
More informationTime resolved optical spectroscopy methods for organic photovoltaics. Enrico Da Como. Department of Physics, University of Bath
Time resolved optical spectroscopy methods for organic photovoltaics Enrico Da Como Department of Physics, University of Bath Outline Introduction Why do we need time resolved spectroscopy in OPV? Short
More informationLOWELL, MICHIGAN, MAY 28, Every Patriotic American Salutes His Nation's Flag
/ U N K U Y N Y 8 94 N /U/ N N 3 N U NY NUN ;!! - K - - 93 U U - K K»- [ : U K z ; 3 q U 9:3 - : z 353 «- - - q x z- : N / - q - z 6 - x! -! K N - 3 - U N x >» } ( ) - N Y - q K x x x Y 3 z - x x - x 8
More informationLecture 5: Polarization. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Outline
Lecture 5: Polarization Outline 1 Polarized Light in the Universe 2 Descriptions of Polarized Light 3 Polarizers 4 Retarders Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2016,
More informationQuantum Mechanics. p " The Uncertainty Principle places fundamental limits on our measurements :
Student Selected Module 2005/2006 (SSM-0032) 17 th November 2005 Quantum Mechanics Outline : Review of Previous Lecture. Single Particle Wavefunctions. Time-Independent Schrödinger equation. Particle in
More information[D] indicates a Design Question
EP421 Assignment 4: Polarization II: Applications of Optical Anisotropy use of the Jones Calculus (Handed Out: Friday 1 November 2013 Due Back: Friday 8 November 2013) 1. Optic Axis of Birefringent Crystals
More informationSlow Photons in Vacuum as Elementary Particles. Chander Mohan Singal
Ref ETOP98 Slow Photons in Vacuum as Elementary Particles Chander Mohan Singal Department of Physics, Indian Institute of Technology-Delhi, Hauz Khas, New Delhi-1116, INDIA E-Mail: drcmsingal@yahoocom
More informationD-D NUCLEAR FUSION PROCESSES INDUCED IN POLYEHTYLENE BY TW LASER-GENERATED PLASMA
D-D NUCLEAR FUSION PROCESSES INDUCED IN POLYEHTYLENE BY TW LASER-GENERATED PLASMA L. Torrisi 1, M. Cutroneo, S. Cavallaro 1 and J. Ullschmied 3 1 Physics Department, Messina University, V.le S. D Alcontres
More informationINSTITUTE BECKMAN. K. Hess, Y. Liu, F. Oyafuso, W.C. Ng and B.D. Klein. The Beckman Institute University of Illinois at Urbana-Champaign
BECKMAN INSTITUTE K. Hess, Y. Liu, F. Oyafuso, W.C. Ng and B.D. Klein. The Beckman Institute University of Illinois at Urbana-Champaign Photo by Don Hamerman Typical VCSEL Structure and Electronic Mesh
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 informationOptical Spectroscopy. Steady State and Time Dependent Fluorescence Measurements. Kai Wen Teng. October 8 th PHYS 403 Fall 2013
Optical Spectroscopy Steady State and Time Dependent Fluorescence Measurements Kai Wen Teng October 8 th 2013 PHYS 403 Fall 2013 EM Spectrum of molecules Rotational Energy Infrared Vibrational Energy Near
More information# FIR. [ ] = b k. # [ ]x[ n " k] [ ] = h k. x[ n] = Ae j" e j# ˆ n Complex exponential input. [ ]Ae j" e j ˆ. ˆ )Ae j# e j ˆ. y n. y n.
[ ] = h k M [ ] = b k x[ n " k] FIR k= M [ ]x[ n " k] convolution k= x[ n] = Ae j" e j ˆ n Complex exponential input [ ] = h k M % k= [ ]Ae j" e j ˆ % M = ' h[ k]e " j ˆ & k= k = H (" ˆ )Ae j e j ˆ ( )
More information3A. Average specific heat of each free electron at constant volume
Solution of the theoretical problem 3 3A Average specific heat of each free electron at constant volume (1) Each free electron has 3 degrees of freedom According to the equipartition of energy theorem
More informationGrading. Class attendance: (1 point/class) x 9 classes = 9 points maximum Homework: (10 points/hw) x 3 HW = 30 points maximum
Grading Class attendance: (1 point/class) x 9 classes = 9 points maximum Homework: (10 points/hw) x 3 HW = 30 points maximum Maximum total = 39 points Pass if total >= 20 points Fail if total
More informationBreakup of Ring Beams Carrying Orbital Angular Momentum in Sodium Vapor
Breakup of Ring Beams Carrying Orbital Angular Momentum in Sodium Vapor Petros Zerom, Matthew S. Bigelow and Robert W. Boyd The Institute of Optics, University of Rochester, Rochester, New York 14627 Now
More informationPhase Sensitive Faraday Rotation in. and various Diamagnetic liquid Samples
Phase Sensitive Faraday Rotation in TERBIUM GALLIUM GARNET crystal and various Diamagnetic liquid Samples Supervisor: Dr. Saadat Anwar Siddiqi Co-Supervisor: Dr. Muhammad Sabieh Anwar Presented by: Aysha
More information