14. Matrix treatment of polarization
|
|
- Theodore Woods
- 6 years ago
- Views:
Transcription
1 14. Matri treatment of polarization This lecture Polarized Light : linear, circular, elliptical Jones Vectors for Polarized Light Jones Matrices for Polarizers, Phase Retarders, Rotators
2 (Linear) Polarization z E B E0 sin( kzt ) E 0 E z 0 0 E B 0 sin( kz t) B z 0 c This wave is an eample of a linearl polarized wave. We alwas define the direction of polarization as the direction of the oscillation of the Electric field vector (-direction in this case) In general, a linearl polarized wave traveling in the +z direction can be written as: in terms of components: E E0 cos sin( kzt) E E0 sin sin( kz t ) E z 0 E ˆ 0 ee sin( kz t ) ê is constant phase
3 질 문 6) Which equation correctl describes this electromagnetic wave? a) E = E o sin (kz + t) b) E = E o sin (kz - t) c) B = B o sin (kz - t) 7) In which direction is this wave polarized? a) b) c) z
4 질 문 At t = 0, z = 0, the electric field of an electromagnetic wave is oriented at an angle with respect to the -ais, as shown. A ê Which arrow indicates the direction of the magnetic field at the same location and instant of time? B (a) A (b) B This question cannot be answered unless the direction of propagation is specified: If the wave propagates in the +z direction, then B-field is along A If the wave propagates in the z direction, then B-field is along B
5 Consider a EM wave propagating along the z-direction. The comple amplitude is Two-element matri a 2 2 E% o, a b 1 b Jones vector
6 Linearl polarized lights E o ~ E o 0 1 a b If a 2 b 2 1, it is normalized form. E o 1 1 E o 1 0 E o 1 1 E 0 E0 Acos cos E 1 o 1b A, tan tan Eo Asin sin E0 a
7 Other Polarization States? Are there polarizations other than linear? Sure!! The general harmonic solution for a plane wave traveling in the +z-direction is: Linear Polarization E E E 0 sin( kz t ) E E sin( kz t ) 0 Circular Polarization E 0, E E o o tan Eo E o 2 (E 0 and E 0 are ±90 out of phase.)
8 (LCP) (RCP)
9 = 0, or, (RCP) (LCP)
10
11 Visualization Circular polarization stems from the intrinsic angular momentum ( spin ) of the photons that make up the beam. Note: If ou shine circularl polarized light onto an absorber, it will in principle start to rotate conservation of angular momentum!
12 Application: Light-Driven Micro Machines Fact 1: Small particles are attracted to regions of high E field gradient (induced dipole force) laser tweezers Fact 2: Because birefringent crstals convert linear circular polarization, the acquire angular momentum rotation Parts are onl 10m across! Uses: Biophsics: Manipulating DNA, proteins, etc. Microscopic fluid pumps
13
14 Eample
15
16
17 Usefulness of Jones vectors : two eamples
18 a b M c d Jones matri
19 Birefringence ( 복굴절 ) 현상이용 Quarter-wave plate (QWP) Half-wave plate (HWP)
20 Quarter-wave plate (QWP) Half-wave plate (HWP)
21 Wave Plates Birefringent crstals with precise thicknesses Crstal which produces a phase change of /2 quarter wave plate (a full wave plate produces a relative shift of 4 2 no effect). 2 Light polarized along the fast or slow ais merel travels through at the appropriate speed polarization is unchanged. Before QWP Light linearl polarized at 45 to the fast or slow ais will acquire a relative phase shift between these two components alter the state of polarization. The phase of the component along the fast ais is /2 out of phase with the component along the slow ais. E.g., E E E E E E E E sin( kz ) sin( kz ) 0 t 0 t sin( kz ) sin( kz t 2 After QWP 0 ) 0 t RCP Quarter Wave Plate summar: linear along fast ais linear linear at 45 to fast ais circular circular linear at 45 to fast ais
22
23
24 Usefulness of Jones matri
25 The operation of the polarizer or retarder on the electric field is described b M E% E% 0 0 For eample, a QWP converts linearl polarized light, when the light is at an angle of 45 to the SA of the QWP, to circularl polarized light 1 0 M ep % 1 1 % ep i / 4 1 i / 4 E0 ME0 0 i i A QWP will convert CP light back to LP light, but now rotated b ep i / 4 1 ep i / 4 0 i 2 i 2 1
Chapter 14 Matrix Treatment of Polarization
Chapter 4 Matri Treatment of Polarization Lecture Notes for Modern Optics based on Pedrotti & Pedrotti & Pedrotti Instructor: Naer Eradat Spring 29 5//29 Matri Treatment of Polarization Polarization Polarization
More informationPhys 322 Lecture 21. Chapter 8 Polarization
Phs 3 Lecture 1 Chapter 8 Polarization Plane of polarization Transverse M wave B Plane of polarization - plane defined b vector and k: Plane of polarization z: z t ˆi z, t ˆi coskz t, z Linearl (plane)
More informationJones vector & matrices
Jones vector & matrices Department of Physics 1 Matrix treatment of polarization Consider a light ray with an instantaneous E-vector as shown y E k, t = xe x (k, t) + ye y k, t E y E x x E x = E 0x e i
More information15. Polarization. Linear, circular, and elliptical polarization. Mathematics of polarization. Uniaxial crystals. Birefringence.
15. Polarization Linear, circular, and elliptical polarization Mathematics of polarization Uniaial crstals Birefringence Polarizers Notation: polarization near an interface Parallel ("p") polarization
More informationExperiment 5 Polarization and Modulation of Light
1. Objective Experiment 5 Polarization and Modulation of Light Understanding the definition of polarized and un-polarized light. Understanding polarizer and analzer definition, Maluse s law. Retarding
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 32 Polarization of Light Spring 2015 Semester Matthew Jones Types of Polarization Light propagating through different materials: One polarization component can
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 informationWaves, Polarization, and Coherence
05-0-4 Waves, Polarization, and Coherence Lecture 6 Biophotonics Jae Gwan Kim jaekim@gist.ac.kr, X 0 School of nformation and Communication ngineering Gwangju nstitute of Sciences and Technolog Outline
More informationChapter 4: Polarization of light
Chapter 4: Polarization of light 1 Preliminaries and definitions B E Plane-wave approximation: E(r,t) ) and B(r,t) are uniform in the plane ^ k We will say that light polarization vector is along E(r,t)
More information17. Jones Matrices & Mueller Matrices
7. Jones Matrices & Mueller Matrices Jones Matrices Rotation of coordinates - the rotation matrix Stokes Parameters and unpolarized light Mueller Matrices R. Clark Jones (96-24) Sir George G. Stokes (89-93)
More informationAssignment , 7.1, 7.2, 7.5, 7.11, 7.12, 7.15, TIR and FTIR
LC45-summer, 1 1. 1.1, 7.1, 7., 7.5, 7.11, 7.1, 7.15, 7.1 1.1. TIR and FTIR a) B considering the electric field component in medium B in Figure 1. (b), eplain how ou can adjust the amount of transmitted
More informationUnit 12 Study Notes 1 Systems of Equations
You should learn to: Unit Stud Notes Sstems of Equations. Solve sstems of equations b substitution.. Solve sstems of equations b graphing (calculator). 3. Solve sstems of equations b elimination. 4. Solve
More informationLab 9: Polarization Phy208 Spring 2008
Lab 9: Polarization Ph208 Spring 2008 Name Section This sheet is the lab document our TA will use to score our lab. It is to be turned in at the end of lab. To receive full credit ou must use complete
More informationECEN 4606, UNDERGRADUATE OPTICS LAB
ECEN 4606, UNDERGRADUATE OPTICS LAB Lab 6: Polarization Original: Professor McLeod SUMMARY: In this lab you will become familiar with the basics of polarization and learn to use common optical elements
More informationPolarization. Polarization. Physics Waves & Oscillations 4/3/2016. Spring 2016 Semester Matthew Jones. Two problems to be considered today:
4/3/26 Physics 422 Waves & Oscillations Lecture 34 Polarization of Light Spring 26 Semester Matthew Jones Polarization (,)= cos (,)= cos + Unpolarizedlight: Random,, Linear polarization: =,± Circular polarization:
More informationPOLARISATION. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion.
POLARISATION Light is a transverse electromagnetic wave. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion. If the E field
More informationLight Waves and Polarization
Light Waves and Polarization Xavier Fernando Ryerson Communications Lab http://www.ee.ryerson.ca/~fernando The Nature of Light There are three theories explain the nature of light: Quantum Theory Light
More information6 Properties of polarized light - polarimetry
6 Properties of polarized light - polarimetr Supervisors : J.Geandrot, O.Frantz This practical work aims to stud some phenomena caused b the transversalit of light : dichroism, birefingence, rotating power.
More informationPOLARIZATION OF LIGHT
POLARIZATION OF LIGHT OVERALL GOALS The Polarization of Light lab strongly emphasizes connecting mathematical formalism with measurable results. It is not your job to understand every aspect of the theory,
More informationLab 10: Polarization Phy248 Spring 2009
Lab 10: Polarization Ph248 Spring 2009 Name Section This sheet is the lab document our TA will use to score our lab. It is to be turned in at the end of lab. To receive full credit ou must use complete
More informationPolarized sunglasses. Polarization
Polarized sunglasses 3 4 : is a propert of the wave of light that can oscillate with certain orientation; the wave ehibits polarization which has onl one possible polarization, namel the direction in which
More informationPolarized optical wave in optical fiber communication system
IOSR Journal of Applied Phsics (IOSR-JAP) e-issn: 2278-4861.Volume 9, Issue 5 Ver. IV (Sep. - Oct. 2017), PP 09-14 www.iosrjournals.org Polarized optical wave in optical fiber communication sstem Dinesh
More informationManipulation of circular polarised electromagnetic waves by artificial periodic structures (Invited Paper)
Manipulation of circular polarised electromagnetic waves b artificial periodic structures (Invited Paper) Zelenchuk, D., & Fusco, V. (215). Manipulation of circular polarised electromagnetic waves b artificial
More informationQuantum state measurement
Quantum state measurement Introduction The rotation properties of light fields of spin are described by the 3 3 representation of the 0 0 SO(3) group, with the generators JJ ii we found in class, for instance
More informationVector Basics. Lecture 1 Vector Basics
Lecture 1 Vector Basics Vector Basics We will be using vectors a lot in this course. Remember that vectors have both magnitude and direction e.g. a, You should know how to find the components of a vector
More informationPolarization of Light and Birefringence of Materials
Polarization of Light and Birefringence of Materials Ajit Balagopal (Team Members Karunanand Ogirala, Hui Shen) ECE 614- PHOTONIC INFORMATION PROCESSING LABORATORY Abstract-- In this project, we study
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 informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 32 Electromagnetic Waves Spring 2016 Semester Matthew Jones Electromagnetism Geometric optics overlooks the wave nature of light. Light inconsistent with longitudinal
More informationVector Calculus Review
Course Instructor Dr. Ramond C. Rumpf Office: A-337 Phone: (915) 747-6958 E-Mail: rcrumpf@utep.edu Vector Calculus Review EE3321 Electromagnetic Field Theor Outline Mathematical Preliminaries Phasors,
More informationPhysics 101 Lecture 2 Vectors Dr. Ali ÖVGÜN
Phsics 101 Lecture 2 Vectors Dr. Ali ÖVGÜN EMU Phsics Department www.aovgun.com Coordinate Sstems qcartesian coordinate sstem qpolar coordinate sstem Januar 21, 2015 qfrom Cartesian to Polar coordinate
More informationChiroptical Spectroscopy
Chiroptical Spectroscopy Theory and Applications in Organic Chemistry Lecture 2: Polarized light Masters Level Class (181 041) Mondays, 8.15-9.45 am, NC 02/99 Wednesdays, 10.15-11.45 am, NC 02/99 28 Electromagnetic
More information: Imaging Systems Laboratory II. Laboratory 6: The Polarization of Light April 16 & 18, 2002
151-232: Imaging Systems Laboratory II Laboratory 6: The Polarization of Light April 16 & 18, 22 Abstract. In this lab, we will investigate linear and circular polarization of light. Linearly polarized
More informationIntroduction to Polarization
Phone: Ext 659, E-mail: hcchui@mail.ncku.edu.tw Fall/007 Introduction to Polarization Text Book: A Yariv and P Yeh, Photonics, Oxford (007) 1.6 Polarization States and Representations (Stokes Parameters
More informationQuantum Information through Angular momentum of Photon
Quantum Information through Angular momentum of Photon Dipti Banerjee# and Dipan Sinha* Department of Physics Vidyasagar College for Women, 39, Sankar Ghosh Lane, Kolkata-76 Abstract The angular momentum
More informationNewton s Laws of Motion, Energy and Oscillations
Prof. O. B. Wright, Autumn 007 Mechanics Lecture Newton s Laws of Motion, Energy and Oscillations Reference frames e.g. displaced frame x =x+a y =y x =z t =t e.g. moving frame (t=time) x =x+vt y =y x =z
More information2. Waves and the Wave Equation
2. Waves and the Wave Equation What is a wave? Forward vs. backward propagating waves The one-dimensional wave equation Phase velocity Reminders about complex numbers The complex amplitude of a wave What
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 informationPart III. Interaction with Single Electrons - Plane Wave Orbits
Part III - Orbits 52 / 115 3 Motion of an Electron in an Electromagnetic 53 / 115 Single electron motion in EM plane wave Electron momentum in electromagnetic wave with fields E and B given by Lorentz
More informationOptical Measurement of microscopic torques
Preprint of: T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop Optical Measurement of microscopic torques Journal of Modern Optics 48, 405-413 (001) Optical Measurement of microscopic torques
More informationroth t dive = 0 (4.2.3) divh = 0 (4.2.4) Chapter 4 Waves in Unbounded Medium Electromagnetic Sources 4.2 Uniform plane waves in free space
Chapter 4 Waves in Unbounded Medium 4. lectromagnetic Sources 4. Uniform plane waves in free space Mawell s equation in free space is given b: H rot = (4..) roth = (4..) div = (4..3) divh = (4..4) which
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 informationLecture 11: Polarized Light. Fundamentals of Polarized Light. Descriptions of Polarized Light. Scattering Polarization. Zeeman Effect.
Lecture 11: Polarized Light Outline 1 Fundamentals of Polarized Light 2 Descriptions of Polarized Light 3 Scattering Polarization 4 Zeeman Effect 5 Hanle Effect Fundamentals of Polarized Light Electromagnetic
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 informationElectromagnetic Waves & Polarization
Course Instructor Dr. Raymond C. Rumpf Office: A 337 Phone: (915) 747 6958 E Mail: rcrumpf@utep.edu EE 4347 Applied Electromagnetics Topic 3a Electromagnetic Waves & Polarization Electromagnetic These
More informationEigenvectors and Eigenvalues 1
Ma 2015 page 1 Eigenvectors and Eigenvalues 1 In this handout, we will eplore eigenvectors and eigenvalues. We will begin with an eploration, then provide some direct eplanation and worked eamples, and
More informationBasic Mathematics and Units
Basic Mathematics and Units Rende Steerenberg BE/OP Contents Vectors & Matrices Differential Equations Some Units we use 3 Vectors & Matrices Differential Equations Some Units we use 4 Scalars & Vectors
More informationRadio Propagation Channels Exercise 2 with solutions. Polarization / Wave Vector
/8 Polarization / Wave Vector Assume the following three magnetic fields of homogeneous, plane waves H (t) H A cos (ωt kz) e x H A sin (ωt kz) e y () H 2 (t) H A cos (ωt kz) e x + H A sin (ωt kz) e y (2)
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 25 Propagation of Light Spring 2013 Semester Matthew Jones Midterm Exam: Date: Wednesday, March 6 th Time: 8:00 10:00 pm Room: PHYS 203 Material: French, chapters
More informationPan Pearl River Delta Physics Olympiad 2005
1 Jan. 29, 25 Morning Session (9 am 12 pm) Q1 (5 Two identical worms of length L are ling on a smooth and horizontal surface. The mass of the worms is evenl distributed along their bod length. The starting
More informationOscillations. Phys101 Lectures 28, 29. Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum
Phys101 Lectures 8, 9 Oscillations Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum Ref: 11-1,,3,4. Page 1 Oscillations of a Spring If an object oscillates
More information1 f. result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by
result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by amplitude (how far do the bits move from their equilibrium positions? Amplitude of MEDIUM)
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 informationThe first change comes in how we associate operators with classical observables. In one dimension, we had. p p ˆ
VI. Angular momentum Up to this point, we have been dealing primaril with one dimensional sstems. In practice, of course, most of the sstems we deal with live in three dimensions and 1D quantum mechanics
More informationQuarter wave plates and Jones calculus for optical system
2/11/16 Electromagnetic Processes In Dispersive Media, Lecture 6 1 Quarter wave plates and Jones calculus for optical system T. Johnson 2/11/16 Electromagnetic Processes In Dispersive Media, Lecture 6
More informationOptical measurement of microscopic torques
Preprint of: T. A. Nieminen, N. R. Heckenberg and H. Rubinsztein-Dunlop Optical measurement of microscopic torques Journal of Modern Optics 48, 405-413 (001) Changes: equation (7) corrected. Optical measurement
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 informationCourse Updates. 2) This week: Electromagnetic Waves +
Course Updates http://www.phys.hawaii.edu/~varner/phys272-spr1/physics272.html Reminders: 1) Assignment #11 due Wednesday 2) This week: Electromagnetic Waves + 3) In the home stretch [review schedule]
More information4. Spontaneous Emission october 2016
4. Spontaneous Emission october 016 References: Grynberg, Aspect, Fabre, "Introduction aux lasers et l'optique quantique". Lectures by S. Haroche dans "Fundamental systems in quantum optics", cours des
More informationDIGITAL CORRELATION OF FIRST ORDER SPACE TIME IN A FLUCTUATING MEDIUM
DIGITAL CORRELATION OF FIRST ORDER SPACE TIME IN A FLUCTUATING MEDIUM Budi Santoso Center For Partnership in Nuclear Technolog, National Nuclear Energ Agenc (BATAN) Puspiptek, Serpong ABSTRACT DIGITAL
More informationBrewster Angle and Total Internal Reflection
Lecture 4: Polarization Outline 1 Polarized Light in the Universe 2 Brewster Angle and Total Internal Reflection 3 Descriptions of Polarized Light 4 Polarizers 5 Retarders Christoph U. Keller, Utrecht
More informationTheory and Experiment
Theory and Experiment Mark Beck OXPORD UNIVERSITY PRESS Contents Table of Symbols Preface xiii xix 1 MATHEMATICAL PRELIMINARIES 3 1.1 Probability and Statistics 3 1.2 LinearAlgebra 9 1.3 References 17
More informationSupporting Information
Supporting Information Devlin et al. 10.1073/pnas.1611740113 Optical Characterization We deposit blanket TiO films via ALD onto silicon substrates to prepare samples for spectroscopic ellipsometry (SE)
More informationPeriodic Leaky-Wave Antennas for Orbital Angular Momentum Multiplexing System Master Thesis Final Presentation
Periodic Leaky-Wave Antennas for Orbital Angular Momentum Multiplexing System Master Thesis Final Presentation Amar Al-Bassam 23.06.2014 Outline I. INTRODUCTION II. CONCEPT OF GENERATION III. ELECTROMAGNETIC
More informationElectricity&Magnetism Lecture 24. Electricity & Magne/sm Lecture 24, Slide 1
Electricity&Magnetism Lecture 24 Electricity & Magne/sm Lecture 24, Slide 1 Optics Kit.............................................. Optics Bench Incandenscent Light Source Ray Table Ray Table Component
More informationTwo conventions for coordinate systems. Left-Hand vs Right-Hand. x z. Which is which?
walters@buffalo.edu CSE 480/580 Lecture 2 Slide 3-D Transformations 3-D space Two conventions for coordinate sstems Left-Hand vs Right-Hand (Thumb is the ais, inde is the ais) Which is which? Most graphics
More informationDepartment of Physics and Astronomy University of Georgia
Department of Physics and Astronomy University of Georgia August 2007 Written Comprehensive Exam Day 1 This is a closed-book, closed-note exam. You may use a calculator, but only for arithmetic functions
More informationPhysics 101. Vectors. Lecture 2. h0r33fy. EMU Physics Department. Assist. Prof. Dr. Ali ÖVGÜN
Phsics 101 Lecture 2 Vectors ssist. Prof. Dr. li ÖVGÜN EMU Phsics Department h0r33f www.aovgun.com Coordinate Sstems qcartesian coordinate sstem qpolar coordinate sstem qfrom Cartesian to Polar coordinate
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 informationPhys 2310 Mon. Oct. 30, 2017 Today s Topics. Begin Modern Optics Ch. 2: The Nature of Polarized Light Reading for Next Time
Phys 3 Mon. Oct. 3, 7 Today s Topics Begin Modern Optics Ch. : The Nature of Polarized Light Reading for Next Time By Wed.: Reading this Week Begin Ch. of Modern Optics (. 8.) Nature of Polarized Light,
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 informationEE 5337 Computational Electromagnetics. Preliminary Topics
Instructor Dr. Raymond Rumpf (915) 747 6958 rcrumpf@utep.edu EE 5337 Computational Electromagnetics Lecture #3 Preliminary Topics Lecture 3These notes may contain copyrighted material obtained under fair
More informationInteraction-Free Ion-Photon Gates
Interaction-Free Ion-Photon Gates (Milan, May 17, 2007) Mladen Pavičić pavicic@grad.hr ; Web: http://m3k.grad.hr/pavicic University of Zagreb Interaction-Free Ion-Photon Gates p. 1/1 Early Interaction-Free
More informationPhysics I Keystone Institute Technology & Management Unit-II
Un-polarized light Ordinary light is a collection of wave trains emitted by atoms or group of atoms with coherent time no longer than 10-8 second. Each wave train has different orientation and phase of
More informationPolarization and Related Antenna Parameters
ANTENTOP- 01-007, # 009 Polarization and Related Antenna Parameters Feel Yourself a Student! Dear friends, I would like to give to ou an interesting and reliable antenna theor. Hours searching in the web
More informationChapter 33: ELECTROMAGNETIC WAVES 559
Chapter 33: ELECTROMAGNETIC WAVES 1 Select the correct statement: A ultraviolet light has a longer wavelength than infrared B blue light has a higher frequency than x rays C radio waves have higher frequency
More informationOPTICAL TWEEZERS AND SPANNERS PHELIM DORAN Colin Phelan
OPTICAL TWEEZERS AND SPANNERS PHELIM DORAN 97449067 & Colin Phelan 97081540 Contents: Chapter: Page: 1. Introduction. 2 2. The Physics. 3 3. Applications. 6 4. Appendix. 8 5. References. 9 Introduction:
More informationCREATING UNCONVENTIONALLY
CREATING UNCONVENTIONALLY POLARIZED BEAMS BY STRESS INDUCED BIREFRINGENCE Jacob Chamoun Cornell University Advisors: Dr. John Noe Dr. Marty Cohen October 25, 2010 OUTLINE Theory i. Birefringence ii. Cylindrical
More informationThe equations so far... Gauss Law for E Fields. Gauss Law for B Fields. B da. inside. d dt. n C 3/28/2018
The equations so far... Gauss Law for E Fields E da S n 1 Q inside Gauss Law for B Fields B da S n C Faraday s Law d E dl dt S B da n Ampere s Law B dl I C 3/8/18 1 Ampere s Law B dl I inside _ path No
More information16. More About Polarization
16. More About Polarization Polarization control Wave plates Circular polarizers Reflection & polarization Scattering & polarization Birefringent materials have more than one refractive index A special
More informationBrewster Angle and Total Internal Reflection
Lecture 5: Polarization Outline 1 Polarized Light in the Universe 2 Brewster Angle and Total Internal Reflection 3 Descriptions of Polarized Light 4 Polarizers 5 Retarders Christoph U. Keller, Leiden University,
More informationChapter 15. Mechanical Waves
Chapter 15 Mechanical Waves A wave is any disturbance from an equilibrium condition, which travels or propagates with time from one region of space to another. A harmonic wave is a periodic wave in which
More informationLecture 8: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Outline
Lecture 8: Polarimetry 2 Outline 1 Polarizers and Retarders 2 Polarimeters 3 Scattering Polarization 4 Zeeman Effect Christoph U. Keller, Utrecht University, C.U.Keller@uu.nl Observational Astrophysics
More information1 Lagrangian for a continuous system
Lagrangian for a continuous system Let s start with an example from mechanics to get the big idea. The physical system of interest is a string of length and mass per unit length fixed at both ends, and
More informationECE 6340 Intermediate EM Waves. Fall 2016 Prof. David R. Jackson Dept. of ECE. Notes 16
C 6340 Intermediate M Waves Fall 2016 Prof. David R. Jackson Dept. of C Notes 16 1 Polarization of Waves Consider a plane wave with both and components (,, z) = ( ˆ + ˆ ) e jkz Assume j0 = ae = a = j be
More informationScalars distance speed mass time volume temperature work and energy
Scalars and Vectors scalar is a quantit which has no direction associated with it, such as mass, volume, time, and temperature. We sa that scalars have onl magnitude, or size. mass ma have a magnitude
More informationLight and Matter. Thursday, 8/31/2006 Physics 158 Peter Beyersdorf. Document info
Light and Matter Thursday, 8/31/2006 Physics 158 Peter Beyersdorf Document info 3. 1 1 Class Outline Common materials used in optics Index of refraction absorption Classical model of light absorption Light
More informationFresnel s law, theory of reflection
Fresnel s law, theory of reflection LP Used concepts Electromagnetic theory of light, reflection coefficient, reflection factor, Brewster s law, law of refraction, polarisation, degree of polarisation.
More informationRequirements for scaleable QIP
p. 1/25 Requirements for scaleable QIP These requirements were presented in a very influential paper by David Divincenzo, and are widely used to determine if a particular physical system could potentially
More informationDielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission
DOI:.38/NNANO.25.86 Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission Amir Arbabi, Yu Horie, Mahmood Bagheri, and Andrei
More informationChap. 5. Jones Calculus and Its Application to Birefringent Optical Systems
Chap. 5. Jones Calculus and Its Application to Birefringent Optical Systems - The overall optical transmission through many optical components such as polarizers, EO modulators, filters, retardation plates.
More informationBasic Mathema,cs. Rende Steerenberg BE/OP. CERN Accelerator School Basic Accelerator Science & Technology at CERN 3 7 February 2014 Chavannes de Bogis
Basic Mathema,cs Rende Steerenberg BE/OP CERN Accelerator School Basic Accelerator Science & Technolog at CERN 3 7 Februar 014 Chavannes de Bogis Contents Vectors & Matrices Differen,al Equa,ons Some Units
More informationEffects of birefringence on Fizeau interferometry that uses polarization phase shifting technique
Effects of birefringence on Fizeau interferometr that uses polarization phase shifting technique Chunu Zhao, Dongel Kang and James H. Burge College of Optical Sciences, the Universit of Arizona 1630 E.
More informationTransformers. slide 1
Transformers an alternating emf V1 through the primary coil causes an oscillating magnetic flux through the secondary coil and, hence, an induced emf V2. The induced emf of the secondary coil is delivered
More informationChapter 3. Theory of measurement
Chapter. Introduction An energetic He + -ion beam is incident on thermal sodium atoms. Figure. shows the configuration in which the interaction one is determined b the crossing of the laser-, sodium- and
More informationPolarimetry. Dave McConnell, CASS Radio Astronomy School, Narrabri 30 September kpc. 8.5 GHz B-vectors Perley & Carilli (1996)
VLA @ 8.5 GHz B-vectors Perley & Carilli (1996) 10 kpc Polarimetry Dave McConnell, CASS Radio Astronomy School, Narrabri 30 September 2010 1 Electro-magnetic waves are polarized E H S = c/4π (E H) S E/M
More informationPH 222-2C Fall Electromagnetic Waves Lectures Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)
PH 222-2C Fall 2012 Electromagnetic Waves Lectures 21-22 Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 33 Electromagnetic Waves Today s information age is based almost
More informationPhysics 9 Fall 2011 Homework 9 Fall October 28, 2011
Physics 9 Fall 2011 Homework 9 Fall October 28, 2011 Make sure your name is on your homework, and please box your final answer. Because we will be giving partial credit, be sure to attempt all the problems,
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 informationAnyone who can contemplate quantum mechanics without getting dizzy hasn t understood it. --Niels Bohr. Lecture 17, p 1
Anone who can contemplate quantum mechanics without getting di hasn t understood it. --Niels Bohr Lecture 7, p Phsics Colloquium TODAY! Quantum Optomechanics Prof. Markus Aspelmeer, U. Vienna Massive mechanical
More information