14. Matrix treatment of polarization

Size: px
Start display at page:

Download "14. Matrix treatment of polarization"

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 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 information

Phys 322 Lecture 21. Chapter 8 Polarization

Phys 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 information

Jones vector & matrices

Jones 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 information

15. Polarization. Linear, circular, and elliptical polarization. Mathematics of polarization. Uniaxial crystals. Birefringence.

15. 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 information

Experiment 5 Polarization and Modulation of Light

Experiment 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 information

Waves & Oscillations

Waves & 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 information

Chapter 9 - Polarization

Chapter 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 information

Waves, Polarization, and Coherence

Waves, 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 information

Chapter 4: Polarization of light

Chapter 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 information

17. Jones Matrices & Mueller Matrices

17. 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 information

Assignment , 7.1, 7.2, 7.5, 7.11, 7.12, 7.15, TIR and FTIR

Assignment , 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 information

Unit 12 Study Notes 1 Systems of Equations

Unit 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 information

Lab 9: Polarization Phy208 Spring 2008

Lab 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 information

ECEN 4606, UNDERGRADUATE OPTICS LAB

ECEN 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 information

Polarization. Polarization. Physics Waves & Oscillations 4/3/2016. Spring 2016 Semester Matthew Jones. Two problems to be considered today:

Polarization. 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 information

POLARISATION. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion.

POLARISATION. 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 information

Light Waves and Polarization

Light 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 information

6 Properties of polarized light - polarimetry

6 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 information

POLARIZATION OF LIGHT

POLARIZATION 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 information

Lab 10: Polarization Phy248 Spring 2009

Lab 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 information

Polarized sunglasses. Polarization

Polarized 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 information

Polarized optical wave in optical fiber communication system

Polarized 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 information

Manipulation of circular polarised electromagnetic waves by artificial periodic structures (Invited Paper)

Manipulation 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 information

Quantum state measurement

Quantum 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 information

Vector Basics. Lecture 1 Vector Basics

Vector 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 information

Polarization of Light and Birefringence of Materials

Polarization 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 information

4: birefringence and phase matching

4: 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 information

Waves & Oscillations

Waves & 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 information

Vector Calculus Review

Vector 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 information

Physics 101 Lecture 2 Vectors Dr. Ali ÖVGÜN

Physics 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 information

Chiroptical Spectroscopy

Chiroptical 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

: 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 information

Introduction to Polarization

Introduction 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 information

Quantum Information through Angular momentum of Photon

Quantum 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 information

Newton s Laws of Motion, Energy and Oscillations

Newton 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 information

2. Waves and the Wave Equation

2. 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 information

ECE 185 ELECTRO-OPTIC MODULATION OF LIGHT

ECE 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 information

Part III. Interaction with Single Electrons - Plane Wave Orbits

Part 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 information

Optical Measurement of microscopic torques

Optical 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 information

roth 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

roth 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 information

Phase Sensitive Faraday Rotation in. and various Diamagnetic liquid Samples

Phase 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

Lecture 11: Polarized Light. Fundamentals of Polarized Light. Descriptions of Polarized Light. Scattering Polarization. Zeeman Effect.

Lecture 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 information

Optics and Optical Design. Chapter 6: Polarization Optics. Lectures 11-13

Optics 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 information

Electromagnetic Waves & Polarization

Electromagnetic 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 information

Eigenvectors and Eigenvalues 1

Eigenvectors 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 information

Basic Mathematics and Units

Basic 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 information

Radio Propagation Channels Exercise 2 with solutions. Polarization / Wave Vector

Radio 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 information

Waves & Oscillations

Waves & 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 information

Pan Pearl River Delta Physics Olympiad 2005

Pan 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 information

Oscillations. Phys101 Lectures 28, 29. Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum

Oscillations. 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 information

1 f. result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by

1 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 information

Optics and Optical Design. Chapter 6: Polarization Optics. Lectures 11 13

Optics 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 information

The first change comes in how we associate operators with classical observables. In one dimension, we had. p p ˆ

The 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 information

Quarter wave plates and Jones calculus for optical system

Quarter 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 information

Optical measurement of microscopic torques

Optical 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 information

Lecture 5: Polarization. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Outline

Lecture 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 information

Course Updates. 2) This week: Electromagnetic Waves +

Course 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 information

4. Spontaneous Emission october 2016

4. 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 information

DIGITAL CORRELATION OF FIRST ORDER SPACE TIME IN A FLUCTUATING MEDIUM

DIGITAL 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 information

Brewster Angle and Total Internal Reflection

Brewster 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 information

Theory and Experiment

Theory 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 information

Supporting Information

Supporting 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 information

Periodic 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 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 information

Electricity&Magnetism Lecture 24. Electricity & Magne/sm Lecture 24, Slide 1

Electricity&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 information

Two conventions for coordinate systems. Left-Hand vs Right-Hand. x z. Which is which?

Two 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 information

Department of Physics and Astronomy University of Georgia

Department 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 information

Physics 101. Vectors. Lecture 2. h0r33fy. EMU Physics Department. Assist. Prof. Dr. Ali ÖVGÜN

Physics 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

[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 information

Phys 2310 Mon. Oct. 30, 2017 Today s Topics. Begin Modern Optics Ch. 2: The Nature of Polarized Light Reading for Next Time

Phys 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 information

Jones calculus for optical system

Jones 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 information

EE 5337 Computational Electromagnetics. Preliminary Topics

EE 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 information

Interaction-Free Ion-Photon Gates

Interaction-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 information

Physics I Keystone Institute Technology & Management Unit-II

Physics 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 information

Polarization and Related Antenna Parameters

Polarization 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 information

Chapter 33: ELECTROMAGNETIC WAVES 559

Chapter 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 information

OPTICAL TWEEZERS AND SPANNERS PHELIM DORAN Colin Phelan

OPTICAL 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 information

CREATING UNCONVENTIONALLY

CREATING 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 information

The 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. 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 information

16. More About Polarization

16. 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 information

Brewster Angle and Total Internal Reflection

Brewster 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 information

Chapter 15. Mechanical Waves

Chapter 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 information

Lecture 8: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Outline

Lecture 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 information

1 Lagrangian for a continuous system

1 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 information

ECE 6340 Intermediate EM Waves. Fall 2016 Prof. David R. Jackson Dept. of ECE. Notes 16

ECE 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 information

Scalars distance speed mass time volume temperature work and energy

Scalars 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 information

Light 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 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 information

Fresnel s law, theory of reflection

Fresnel 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 information

Requirements for scaleable QIP

Requirements 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 information

Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission

Dielectric 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 information

Chap. 5. Jones Calculus and Its Application to Birefringent Optical Systems

Chap. 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 information

Basic 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 & 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 information

Effects of birefringence on Fizeau interferometry that uses polarization phase shifting technique

Effects 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 information

Transformers. slide 1

Transformers. 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 information

Chapter 3. Theory of measurement

Chapter 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 information

Polarimetry. Dave McConnell, CASS Radio Astronomy School, Narrabri 30 September kpc. 8.5 GHz B-vectors Perley & Carilli (1996)

Polarimetry. 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 information

PH 222-2C Fall Electromagnetic Waves Lectures Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)

PH 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 information

Physics 9 Fall 2011 Homework 9 Fall October 28, 2011

Physics 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 information

Slow Photons in Vacuum as Elementary Particles. Chander Mohan Singal

Slow 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 information

Anyone who can contemplate quantum mechanics without getting dizzy hasn t understood it. --Niels Bohr. Lecture 17, p 1

Anyone 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