Brewster Angle and Total Internal Reflection

Size: px
Start display at page:

Download "Brewster Angle and Total Internal Reflection"

Transcription

1 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, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 1

2 Polarized Light in the Universe Polarization indicates anisotropy not all directions are equal Typical anisotropies introduced by geometry (not everything is spherically symmetric) temperature gradients density gradients magnetic fields electrical fields Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 2

3 Polarized Light from the Big Bang Cosmic Microwave Background (CMB) is red-shifted radiation from Big Bang years ago age, geometry, density of universe from CMB intensity pattern first 0.1 seconds from polarization pattern of CMB inflation gravitational waves polarization signals polarization expected at (or below) 10 6 of intensity 13.7 billion year old temperature fluctuations from WMAP Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 3

4 Polarized Light due to Gravitational Waves Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 4

5 Watch Out for the Dust achieving sensitivity at the 10 6 level is difficult polarization due to galactic dust grains being aligned by galactic magnetic field BICEP2 results and Planck Dust Polarization Map Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 5

6 Scattering Polarization 1 Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 6

7 Scattering Polarization 2 Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 7

8 Unified Model of Active Galactic Nuclei Miller et al., 1991, ApJ 378, Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 8

9 The Power of Polarimetry 1 T Tauri in intensity MWC147 in intensity Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 9

10 The Power of Polarimetry 1 T Tauri in Linear Polarization Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl MWC147 in Linear Polarization ATI 2014, Lecture 5: Polarization 10

11 The Power of Polarimetry 2 R Cr B with HST in intensity R Cr B with ExPo in lin. pol. Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 11

12 Solar Magnetic Field Maps from Longitudinal Zeeman Effect Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 12

13 Planetary Scattered Light solar-system planets show scattering polarization much depends on cloud height can be used to study exoplanets ExPo, SPHERE, EPICS at Leiden Observatory Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 13

14 Polarization Plane Vector Wave ansatz E = E 0 e i( k x ωt) spatially, temporally constant vector E 0 lays in plane perpendicular to propagation direction k represent E 0 in 2-D basis, unit vectors e 1 and e 2, both perpendicular to k E 0 = E 1 e 1 + E 2 e 2. E 1, E 2 : arbitrary complex scalars damped plane-wave solution with given ω, k has 4 degrees of freedom (two complex scalars) additional property is called polarization many ways to represent these four quantities if E 1 and E 2 have identical phases, E oscillates in fixed plane Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 14

15 Summary of Fresnel Equations electric field amplitude transmission t s,p, reflection r s,p t s = t p = r s = r p = 2ñ 1 cos θ i ñ 1 cos θ i + ñ2 2 ñ2 1 sin2 θ i 2ñ 1 ñ 2 cos θ i ñ2 2 cos θ i + ñ 1 ñ2 2 ñ2 1 sin2 θ i ñ 1 cos θ i ñ2 2 ñ2 1 sin2 θ i ñ 1 cos θ i + ñ2 2 ñ2 1 sin2 θ i ñ 2 2 cos θ i ñ 1 ñ 2 2 ñ2 1 sin2 θ i ñ 2 2 cos θ i + ñ 1 ñ 2 2 ñ2 1 sin2 θ i reflectivity: R = r s,p 2, transmissivity: T = ñ 2 cos θ t ñ 1 cos θ i t s,p 2 Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 15

16 Brewster Angle r p = tan(θ i θ t ) tan(θ i +θ t ) = 0 when θ i + θ t = π 2 corresponds to Brewster angle of incidence of tan θ B = n 2 n 1 occurs when reflected wave is perpendicular to transmitted wave reflected light is completely s-polarized transmitted light is moderately polarized Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 16

17 Total Internal Reflection (TIR) Snell s law: sin θ t = n 1 n 2 sin θ i wave from high-index medium into lower index medium (e.g. glass to air): n 1 /n 2 > 1 right-hand side > 1 for sin θ i > n 2 n 1 all light is reflected in high-index medium total internal reflection transmitted wave has complex phase angle damped wave along interface Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 17

18 Phase Change on Total Internal Reflection (TIR) TIR induces phase change that depends on polarization complex ratios: r s,p = r s,p e iδs,p phase change δ = δ s δ p ( ) 2 tan δ cos θ i sin 2 θ i n2 2 = n 1 sin 2 θ i relation valid between critical angle and grazing incidence for critical angle and grazing incidence, phase difference is zero Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 18

19 Polarization Ellipse Polarization Ellipse Polarization E (t) = E 0 e i( k x ωt) E 0 = E 1 e iδ 1 e x + E 2 e iδ 2 e y wave vector in z-direction e x, e y : unit vectors in x, y E 1, E 2 : (real) amplitudes δ 1,2 : (real) phases Polarization Description 2 complex scalars not the most useful description at given x, time evolution of E described by polarization ellipse ellipse described by axes a, b, orientation ψ Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 19

20

21 Jones Formalism Jones Vectors E 0 = E x e x + E y e y beam in z-direction e x, e y unit vectors in x, y-direction complex scalars E x,y Jones vector e = ( Ex E y ) phase difference between E x, E y multiple of π, electric field vector oscillates in a fixed plane linear polarization phase difference ± π 2 circular polarization Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 21

22 Summing and Measuring Jones Vectors E 0 = E x e x + E y e y ( ) Ex e = E y Maxwell s equations linear sum of two solutions again a solution Jones vector of sum of two waves = sum of Jones vectors of individual waves if wave vectors k the same addition of Jones vectors: coherent superposition of waves elements of Jones vectors are not observed directly observables always depend on products of elements of Jones vectors, i.e. intensity I = e e = e x e x + e y e y Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 22

23 Jones matrices influence of medium on polarization described by 2 2 complex Jones matrix J ( ) e J11 J = J e = 12 e J 21 J 22 assumes that medium not affected by polarization state different media 1 to N in order of wave direction combined influence described by J = J N J N 1 J 2 J 1 order of matrices in product is crucial Jones calculus describes coherent superposition of polarized light Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 23

24 Linear Polarization ( 1 horizontal: 0 ( ) 0 vertical: 1 ( ) 45 1 : ) Circular Polarization ( ) 1 left: 2 1 i ( ) 1 right: 2 1 i Notes on Jones Formalism Jones formalism operates on amplitudes, not intensities coherent superposition important for coherent light (lasers, interference effects) Jones formalism describes 100% polarized light Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 24

25 Stokes and Mueller Formalisms Stokes Vector formalism to describe polarization of quasi-monochromatic light directly related to measurable intensities Stokes vector fulfills these requirements I = I Q U V = E x Ex + E y Ey E x Ex E y Ey E x Ey + E y Ex i ( E x Ey E y Ex ) = E E 2 2 E 2 1 E 2 2 2E 1 E 2 cos δ 2E 1 E 2 sin δ Jones vector elements E x,y, real amplitudes E 1,2, phase difference δ = δ 2 δ 1 I 2 Q 2 + U 2 + V 2 can describe unpolarized (Q = U = V = 0) light Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 25

26

27 Stokes Vector Interpretation I I = Q U = V degree of polarization P = intensity linear 0 linear 90 linear 45 linear 135 circular left right Q 2 + U 2 + V 2 1 for fully polarized light, 0 for unpolarized light summing of Stokes vectors = incoherent adding of quasi-monochromatic light waves I Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 27

28 Linear Polarization horizontal: vertical: : Circular Polarization left: right: Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 28

29 Mueller Matrices 4 4 real Mueller matrices describe (linear) transformation between Stokes vectors when passing through or reflecting from media I = M I, M = M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 N optical elements, combined Mueller matrix is M = M N M N 1 M 2 M 1 Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 29

30 Rotating Mueller Matrices optical element with Mueller matrix M Mueller matrix of the same element rotated by θ around the beam given by M(θ) = R( θ)mr(θ) with R (θ) = cos 2θ sin 2θ 0 0 sin 2θ cos 2θ Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 30

31 Vertical Linear Polarizer M pol (θ) = Horizontal Linear Polarizer M pol (θ) = Mueller Matrix for Ideal Linear Polarizer at Angle θ M pol (θ) = cos 2θ sin 2θ 0 cos 2θ cos 2 2θ sin 2θ cos 2θ 0 sin 2θ sin 2θ cos 2θ sin 2 2θ Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 31

32 Poincaré Sphere Relation to Stokes Vector fully polarized light: I 2 = Q 2 + U 2 + V 2 for I 2 = 1: sphere in Q, U, V coordinate system point on Poincaré sphere represents particular state of polarization graphical representation of fully polarized light Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 32

33 Polarizers polarizer: optical element that produces polarized light from unpolarized input light linear, circular, or in general elliptical polarizer, depending on type of transmitted polarization linear polarizers by far the most common large variety of polarizers Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 33

34 Jones Matrix for Linear Polarizers Jones matrix for linear polarizer: ( px 0 J p = 0 p y ) 0 p x 1 and 0 p y 1, real: transmission factors for x, y-components of electric field: E x = p x E x, E y = p y E y p x = 1, p y = 0: linear polarizer in +Q direction p x = 0, p y = 1: linear polarizer in Q direction p x = p y : neutral density filter Mueller Matrix for Linear Polarizers M p = Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 34

35 Mueller Matrix for Ideal Linear Polarizer at Angle θ M pol (θ) = 1 2 Poincare Sphere 1 cos 2θ sin 2θ 0 cos 2θ cos 2 2θ sin 2θ cos 2θ 0 sin 2θ sin 2θ cos 2θ sin 2 2θ polarizer is a point on the Poincaré sphere transmitted intensity: cos 2 (l/2), l is arch length of great circle between incoming polarization and polarizer on Poincaré sphere Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 35

36 Wire Grid Polarizers parallel conducting wires, spacing d λ act as polarizer electric field parallel to wires induces electrical currents in wires induced electrical current reflects polarization parallel to wires polarization perpendicular to wires is transmitted rule of thumb: d < λ/2 strong polarization d λ high transmission of both polarization states (weak polarization) mostly used in infrared Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 36

37 Polaroid-type Polarizers developed by Edwin Land in 1938 Polaroid sheet polarizers: stretched polyvynil alcohol (PVA) sheet, laminated to sheet of cellulose acetate butyrate, treated with iodine PVA-iodine complex analogous to short, conducting wire cheap, can be manufactured in large sizes Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 37

38 Crystal-Based Polarizers crystals are basis of highest-quality polarizers precise arrangement of atom/molecules and anisotropy of index of refraction separate incoming beam into two beams with precisely orthogonal linear polarization states work well over large wavelength range many different configurations calcite most often used in crystal-based polarizers because of large birefringence, low absorption in visible many other suitable materials Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 38

39 Retarders or Wave Plates retards (delays) phase of one electric field component with respect to orthogonal component anisotropic material (crystal) has index of refraction that depends on polarization Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 39

40 Retarder Properties does not change intensity or degree of polarization characterized by two (not identical, not trivial) Stokes vectors of incoming light that are not changed by retarder eigenvectors of retarder depending on polarization described by eigenvectors, retarder is linear retarder circular retarder elliptical retarder linear, circular retarders are special cases of elliptical retarders circular retarders sometimes called rotators since they rotate the orientation of linearly polarized light linear retarders by far the most common type of retarder Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 40

41 Jones Matrix for Linear Retarders linear retarder with fast axis at 0 characterized by Jones matrix ( ) ( ) e iδ 0 e i δ 2 0 J r (δ) =, J 0 1 r (δ) = 0 e i δ 2 δ: phase shift between two linear polarization components (in radians) absolute phase does not matter Mueller Matrix for Linear Retarder M r = cos δ sin δ 0 0 sin δ cos δ Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 41

42 Quarter-Wave Plate on the Poincaré Sphere retarder eigenvector (fast axis) in Poincaré sphere points on sphere are rotated around retarder axis by amount of retardation Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 42

43 Variable Retarders sensitive polarimeters requires retarders whose properties (retardance, fast axis orientation) can be varied quickly (modulated) retardance changes (change of birefringence): liquid crystals Faraday, Kerr, Pockels cells piezo-elastic modulators (PEM) fast axis orientation changes (change of c-axis direction): rotating fixed retarder ferro-electric liquid crystals (FLC) Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 43

44 Liquid Crystals liquid crystals: fluids with elongated molecules at high temperatures: liquid crystal is isotropic at lower temperature: molecules become ordered in orientation and sometimes also space in one or more dimensions liquid crystals can line up parallel or perpendicular to external electrical field Christoph U. Keller, Leiden University, ATI 2014, Lecture 5: Polarization 44

45 Liquid Crystal Retarders dielectric constant anisotropy often large very responsive to changes in applied electric field birefringence δn can be very large (larger than typical crystal birefringence) liquid crystal layer only a few µm thick birefringence shows strong temperature dependence Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2014, Lecture 5: Polarization 45

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

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

Polarimetry in the E-ELT era. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Fundamentals of Polarized Light

Polarimetry in the E-ELT era. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Fundamentals of Polarized Light Polarimetry in the E-ELT era Fundamentals of Polarized Light 1 Polarized Light in the Universe 2 Descriptions of Polarized Light 3 Polarizers 4 Retarders Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl

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

Typical anisotropies introduced by geometry (not everything is spherically symmetric) temperature gradients magnetic fields electrical fields

Typical anisotropies introduced by geometry (not everything is spherically symmetric) temperature gradients magnetic fields electrical fields Lecture 6: Polarimetry 1 Outline 1 Polarized Light in the Universe 2 Fundamentals of Polarized Light 3 Descriptions of Polarized Light Polarized Light in the Universe Polarization indicates anisotropy

More information

Lecture 4: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Outline

Lecture 4: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Outline Lecture 4: 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

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

Electromagnetic Waves Across Interfaces

Electromagnetic Waves Across Interfaces Lecture 1: Foundations of Optics Outline 1 Electromagnetic Waves 2 Material Properties 3 Electromagnetic Waves Across Interfaces 4 Fresnel Equations 5 Brewster Angle 6 Total Internal Reflection Christoph

More information

Wave Propagation in Uniaxial Media. Reflection and Transmission at Interfaces

Wave 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 information

Lecture 6: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Hanle Effect. Outline

Lecture 6: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Hanle Effect. Outline Lecture 6: Polarimetry 2 Outline 1 Polarizers and Retarders 2 Polarimeters 3 Scattering Polarization 4 Zeeman Effect 5 Hanle Effect Christoph U. Keller, Utrecht University, C.U.Keller@uu.nl Solar Physics,

More information

Lecture 4: Anisotropic Media. Dichroism. Optical Activity. Faraday Effect in Transparent Media. Stress Birefringence. Form Birefringence

Lecture 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 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

Polarized Light. Second Edition, Revised and Expanded. Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A.

Polarized Light. Second Edition, Revised and Expanded. Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A. Polarized Light Second Edition, Revised and Expanded Dennis Goldstein Air Force Research Laboratory Eglin Air Force Base, Florida, U.S.A. ш DEK KER MARCEL DEKKER, INC. NEW YORK BASEL Contents Preface to

More information

PMARIZED LI6HT FUNDAMENTALS AND APPLICATIONS EBWABD COLLETT. Measurement Concepts, Inc. Colts Neck, New Jersey

PMARIZED LI6HT FUNDAMENTALS AND APPLICATIONS EBWABD COLLETT. Measurement Concepts, Inc. Colts Neck, New Jersey PMARIZED LI6HT FUNDAMENTALS AND APPLICATIONS EBWABD COLLETT Measurement Concepts, Inc. Colts Neck, New Jersey Marcel Dekker, Inc. New York Basel Hong Kong About the Series Preface A Historical Note iii

More information

3.4 Elliptical Parameters of the Polarization Ellipse References

3.4 Elliptical Parameters of the Polarization Ellipse References Contents Preface to the Second Edition Preface to the First Edition A Historical Note Edward Collett iii v xiii PART 1: THE CLASSICAL OPTICAL FIELD Chapter 1 Chapter 2 Chapter 3 Chapter 4 Introduction

More information

Chap. 2. Polarization of Optical Waves

Chap. 2. Polarization of Optical Waves Chap. 2. Polarization of Optical Waves 2.1 Polarization States - Direction of the Electric Field Vector : r E = E xˆ + E yˆ E x x y ( ω t kz + ϕ ), E = E ( ωt kz + ϕ ) = E cos 0 x cos x y 0 y - Role :

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

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

Polarizers and Retarders

Polarizers and Retarders Phys 531 Lecture 20 11 November 2004 Polarizers and Retarders Last time, discussed basics of polarization Linear, circular, elliptical states Describe by polarization vector ĵ Today: Describe elements

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

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

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

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

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

Calculating Thin Film Stack Properties

Calculating Thin Film Stack Properties Lecture 5: Thin Films Outline 1 Thin Films 2 Calculating Thin Film Stack Properties 3 Fabry-Perot Tunable Filter 4 Anti-Reflection Coatings 5 Interference Filters Christoph U. Keller, Leiden University,

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

Polarization of Light

Polarization of Light Polarization of Light A light beam which has all of the wave oscillations in a single plane of space is said to have total plane polarization. Light with an equal amount of oscillations in all directions

More information

Lecture 2: Thin Films. Thin Films. Calculating Thin Film Stack Properties. Jones Matrices for Thin Film Stacks. Mueller Matrices for Thin Film Stacks

Lecture 2: Thin Films. Thin Films. Calculating Thin Film Stack Properties. Jones Matrices for Thin Film Stacks. Mueller Matrices for Thin Film Stacks Lecture 2: Thin Films Outline Thin Films 2 Calculating Thin Film Stack Properties 3 Jones Matrices for Thin Film Stacks 4 Mueller Matrices for Thin Film Stacks 5 Mueller Matrix for Dielectrica 6 Mueller

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

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

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

Lecture 8 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell

Lecture 8 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell Lecture 8 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell 1. Scattering Introduction - Consider a localized object that contains charges

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

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

Chapter 1 - The Nature of Light

Chapter 1 - The Nature of Light David J. Starling Penn State Hazleton PHYS 214 Electromagnetic radiation comes in many forms, differing only in wavelength, frequency or energy. Electromagnetic radiation comes in many forms, differing

More information

Optics of Liquid Crystal Displays

Optics of Liquid Crystal Displays Optics of Liquid Crystal Displays Second Edition POCHIYEH CLAIRE GU WILEY A John Wiley & Sons, Inc., Publication Contents Preface Preface to the First Edition xiii xv Chapter 1. Preliminaries 1 1.1. Basic

More information

Polarized and unpolarised transverse waves, with applications to optical systems

Polarized and unpolarised transverse waves, with applications to optical systems 2/16/17 Electromagnetic Processes In Dispersive Media, Lecture 6 1 Polarized and unpolarised transverse waves, with applications to optical systems T. Johnson 2/16/17 Electromagnetic Processes In Dispersive

More information

Calculating Thin Film Stack Properties. Polarization Properties of Thin Films

Calculating Thin Film Stack Properties. Polarization Properties of Thin Films Lecture 6: Thin Films Outline 1 Thin Films 2 Calculating Thin Film Stack Properties 3 Polarization Properties of Thin Films 4 Anti-Reflection Coatings 5 Interference Filters Christoph U. Keller, Utrecht

More information

What is polarization?

What is polarization? Polarimetry What is polarization? Linear polarization refers to photons with their electric vectors always aligned in the same direction (below). Circular polarization is when the tip of the electric vector

More information

FUNDAMENTALS OF POLARIZED LIGHT

FUNDAMENTALS OF POLARIZED LIGHT FUNDAMENTALS OF POLARIZED LIGHT A STATISTICAL OPTICS APPROACH Christian Brosseau University of Brest, France A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New York - Chichester. Weinheim. Brisbane

More information

Lab #13: Polarization

Lab #13: Polarization Lab #13: Polarization Introduction In this experiment we will investigate various properties associated with polarized light. We will study both its generation and application. Real world applications

More information

Light for which the orientation of the electric field is constant although its magnitude and sign vary in time.

Light for which the orientation of the electric field is constant although its magnitude and sign vary in time. L e c t u r e 8 1 Polarization Polarized light Light for which the orientation of the electric field is constant although its magnitude and sign vary in time. Imagine two harmonic, linearly polarized light

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

POLARIZATION FUNDAMENTAL OPTICS POLARIZATION STATES 1. CARTESIAN REPRESENTATION 2. CIRCULAR REPRESENTATION. Polarization. marketplace.idexop.

POLARIZATION FUNDAMENTAL OPTICS POLARIZATION STATES 1. CARTESIAN REPRESENTATION 2. CIRCULAR REPRESENTATION. Polarization. marketplace.idexop. POLARIZATION POLARIZATION STATS Four numbers are required to describe a single plane wave Fourier component traveling in the + z direction. These can be thought of as the amplitude and phase shift of the

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

Physics 313: Laboratory 8 - Polarization of Light Electric Fields

Physics 313: Laboratory 8 - Polarization of Light Electric Fields Physics 313: Laboratory 8 - Polarization of Light Electric Fields Introduction: The electric fields that compose light have a magnitude, phase, and direction. The oscillating phase of the field and the

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

: 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

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

Chap. 4. Electromagnetic Propagation in Anisotropic Media

Chap. 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 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

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

Phys 531 Lecture 27 6 December 2005

Phys 531 Lecture 27 6 December 2005 Phys 531 Lecture 27 6 December 2005 Final Review Last time: introduction to quantum field theory Like QM, but field is quantum variable rather than x, p for particle Understand photons, noise, weird quantum

More information

EM Waves. From previous Lecture. This Lecture More on EM waves EM spectrum Polarization. Displacement currents Maxwell s equations EM Waves

EM Waves. From previous Lecture. This Lecture More on EM waves EM spectrum Polarization. Displacement currents Maxwell s equations EM Waves EM Waves This Lecture More on EM waves EM spectrum Polarization From previous Lecture Displacement currents Maxwell s equations EM Waves 1 Reminders on waves Traveling waves on a string along x obey the

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

linear polarization: the electric field is oriented in a single direction circular polarization: the electric field vector rotates

linear polarization: the electric field is oriented in a single direction circular polarization: the electric field vector rotates Chapter 8 Polarimetry 8.1 Description of polarized radiation The polarization of electromagnetic radiation is described by the orientation of the wave s electric field vector. There are two different cases

More information

PRINCIPLES OF PHYSICAL OPTICS

PRINCIPLES OF PHYSICAL OPTICS PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction

More 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

Coherent Superposition of Mueller-Jones States: Synthesizing Mueller Matrices with an Ellipsometer

Coherent Superposition of Mueller-Jones States: Synthesizing Mueller Matrices with an Ellipsometer Coherent Superposition of Mueller-Jones States: Synthesizing Mueller Matrices with an Ellipsometer Ertan Kuntman, Mehmet A. Kuntman Oriol Arteaga SPECTROSCOPIC ELLIPSOMETRY FOCUS TOPIC Young s double slit

More information

Deviations from Malus Law

Deviations from Malus Law From: Steve Scott, Jinseok Ko, Howard Yuh To: MSE Enthusiasts Re: MSE Memo #18a: Linear Polarizers and Flat Glass Plates Date: January 16, 2004 This memo discusses three issues: 1. When we measure the

More information

REFLECTION AND REFRACTION

REFLECTION AND REFRACTION S-108-2110 OPTICS 1/6 REFLECTION AND REFRACTION Student Labwork S-108-2110 OPTICS 2/6 Table of contents 1. Theory...3 2. Performing the measurements...4 2.1. Total internal reflection...4 2.2. Brewster

More information

Chapter 6. Polarization Optics

Chapter 6. Polarization Optics Chapter 6. Polarization Optics 6.1 Polarization of light 6. Reflection and refraction 6.3 Optics of anisotropic media 6.4 Optical activity and magneto-optics 6.5 Optics of liquid crystals 6.6 Polarization

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

Lecture 4: Polarisation of light, introduction

Lecture 4: Polarisation of light, introduction Lecture 4: Polarisation of light, introduction Lecture aims to explain: 1. Light as a transverse electro-magnetic wave 2. Importance of polarisation of light 3. Linearly polarised light 4. Natural light

More information

Topic 4: Waves 4.3 Wave characteristics

Topic 4: Waves 4.3 Wave characteristics Guidance: Students will be expected to calculate the resultant of two waves or pulses both graphically and algebraically Methods of polarization will be restricted to the use of polarizing filters and

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

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

September 14, Monday 4. Tools for Solar Observations-II

September 14, Monday 4. Tools for Solar Observations-II September 14, Monday 4. Tools for Solar Observations-II Spectrographs. Measurements of the line shift. Spectrograph Most solar spectrographs use reflection gratings. a(sinα+sinβ) grating constant Blazed

More information

Fundamentals on light scattering, absorption and thermal radiation, and its relation to the vector radiative transfer equation

Fundamentals on light scattering, absorption and thermal radiation, and its relation to the vector radiative transfer equation Fundamentals on light scattering, absorption and thermal radiation, and its relation to the vector radiative transfer equation Klaus Jockers November 11, 2014 Max-Planck-Institut für Sonnensystemforschung

More information

OPTI 501, Electromagnetic Waves (3)

OPTI 501, Electromagnetic Waves (3) OPTI 501, Electromagnetic Waves (3) Vector fields, Maxwell s equations, electromagnetic field energy, wave equations, free-space solutions, box modes, Fresnel equations, scalar and vector potentials, gauge

More information

Electromagnetic fields and waves

Electromagnetic fields and waves Electromagnetic fields and waves Maxwell s rainbow Outline Maxwell s equations Plane waves Pulses and group velocity Polarization of light Transmission and reflection at an interface Macroscopic Maxwell

More information

Physics 214 Course Overview

Physics 214 Course Overview Physics 214 Course Overview Lecturer: Mike Kagan Course topics Electromagnetic waves Optics Thin lenses Interference Diffraction Relativity Photons Matter waves Black Holes EM waves Intensity Polarization

More information

PHY410 Optics Exam #3

PHY410 Optics Exam #3 PHY410 Optics Exam #3 NAME: 1 2 Multiple Choice Section - 5 pts each 1. A continuous He-Ne laser beam (632.8 nm) is chopped, using a spinning aperture, into 500 nanosecond pulses. Compute the resultant

More information

Polarized Light. Nikki Truss. Abstract:

Polarized Light. Nikki Truss. Abstract: Polarized Light Nikki Truss 9369481 Abstract: In this experiment, the properties of linearly polarised light were examined. Malus Law was verified using the apparatus shown in Fig. 1. Reflectance of s-polarised

More information

Interference, Diffraction and Fourier Theory. ATI 2014 Lecture 02! Keller and Kenworthy

Interference, Diffraction and Fourier Theory. ATI 2014 Lecture 02! Keller and Kenworthy Interference, Diffraction and Fourier Theory ATI 2014 Lecture 02! Keller and Kenworthy The three major branches of optics Geometrical Optics Light travels as straight rays Physical Optics Light can be

More information

OPSE FINAL EXAM Fall 2015 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT.

OPSE FINAL EXAM Fall 2015 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. CLOSED BOOK. Equation Sheet is provided. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like

More information

Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves

Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves Chapter 2 Electromagnetic Radiation Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves Electromagnetic waves do not need a medium to

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

Massachusetts Institute of Technology Physics 8.03SC Fall 2016 Homework 9

Massachusetts Institute of Technology Physics 8.03SC Fall 2016 Homework 9 Massachusetts Institute of Technology Physics 8.03SC Fall 016 Homework 9 Problems Problem 9.1 (0 pts) The ionosphere can be viewed as a dielectric medium of refractive index ωp n = 1 ω Where ω is the frequency

More information

Polarization Mode Dispersion

Polarization Mode Dispersion Unit-7: Polarization Mode Dispersion https://sites.google.com/a/faculty.muet.edu.pk/abdullatif Department of Telecommunication, MUET UET Jamshoro 1 Goos Hänchen Shift The Goos-Hänchen effect is a phenomenon

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

DEGREE OF POLARIZATION VS. POINCARÉ SPHERE COVERAGE - WHICH IS NECESSARY TO MEASURE PDL ACCURATELY?

DEGREE OF POLARIZATION VS. POINCARÉ SPHERE COVERAGE - WHICH IS NECESSARY TO MEASURE PDL ACCURATELY? DEGREE OF POLARIZATION VS. POINCARÉ SPHERE COVERAGE - WHICH IS NECESSARY TO MEASURE PDL ACCURATELY? DEGREE OF POLARIZATION VS. POINCARE SPHERE COVERAGE - WHICH IS NECESSARY TO MEASURE PDL ACCURATELY? Introduction

More information

Polarimetry Techniques. K. Sankarasubramanian ISRO Satellite Centre Bangalore India

Polarimetry Techniques. K. Sankarasubramanian ISRO Satellite Centre Bangalore India Polarimetry Techniques K. Sankarasubramanian ISRO Satellite Centre Bangalore sankark@isac.gov.in Outline Introduction Why Polarimetry? Requirements Polarization Basics Stokes Parameters & Mueller Matrices

More information

Lecture 19 Optical MEMS (1)

Lecture 19 Optical MEMS (1) EEL6935 Advanced MEMS (Spring 5) Instructor: Dr. Huikai Xie Lecture 19 Optical MEMS (1) Agenda: Optics Review EEL6935 Advanced MEMS 5 H. Xie 3/8/5 1 Optics Review Nature of Light Reflection and Refraction

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

Satellite Remote Sensing SIO 135/SIO 236. Electromagnetic Radiation and Polarization

Satellite Remote Sensing SIO 135/SIO 236. Electromagnetic Radiation and Polarization Satellite Remote Sensing SIO 135/SIO 236 Electromagnetic Radiation and Polarization 1 Electromagnetic Radiation The first requirement for remote sensing is to have an energy source to illuminate the target.

More information

UE SPM-PHY-S Polarization Optics

UE SPM-PHY-S Polarization Optics UE SPM-PHY-S07-101 Polarization Optics N. Fressengeas Laboratoire Matériaux Optiques, Photonique et Systèmes Unité de Recherche commune à l Université Paul Verlaine Metz et à Supélec Document à télécharger

More information

NAWAB SHAH ALAM KHAN COLLEGE OF ENGINEERING & TECHNOLOGY UNIT II-a POLARISATION

NAWAB SHAH ALAM KHAN COLLEGE OF ENGINEERING & TECHNOLOGY UNIT II-a POLARISATION NAWAB SHAH ALAM KHAN COLLEGE OF ENGINEERING & TECHNOLOGY UNIT II-a 1 POLARISATION SYLLABUS :Polarization: Introduction, Malus s law, double refraction, Nicol prism, Quarter wave and half wave plates. 1.

More information

4. Circular Dichroism - Spectroscopy

4. Circular Dichroism - Spectroscopy 4. Circular Dichroism - Spectroscopy The optical rotatory dispersion (ORD) and the circular dichroism (CD) are special variations of absorption spectroscopy in the UV and VIS region of the spectrum. The

More information

ELECTROMAGNETIC WAVES

ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES AND POLARIZATION ELECTROMAGNETIC WAVES Waves occur in a variety of physical contexts such as water waves produced by a stone dropped in a pond, w which travel along a plucked string,

More information

OPTICAL Optical properties of multilayer systems by computer modeling

OPTICAL Optical properties of multilayer systems by computer modeling Workshop on "Physics for Renewable Energy" October 17-29, 2005 301/1679-15 "Optical Properties of Multilayer Systems by Computer Modeling" E. Centurioni CNR/IMM AREA Science Park - Bologna Italy OPTICAL

More information

OPTICS LAB -ECEN 5606

OPTICS LAB -ECEN 5606 Department of Electrical and Computer Engineering University of Colorado at Boulder OPTICS LAB -ECEN 5606 Kelvin Wagner KW&K.Y. Wu 1994 KW&S.Kim 2007 Experiment No. 12 POLARIZATION and CRYSTAL OPTICS 1

More information

Matrices in Polarization Optics. Polarized Light - Its Production and Analysis

Matrices in Polarization Optics. Polarized Light - Its Production and Analysis Matrices in Polarization Optics Polarized Light - Its Production and Analysis For all electromagnetic radiation, the oscillating components of the electric and magnetic fields are directed at right angles

More information

Summary of Fourier Optics

Summary 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 information

Polarization Optics. N. Fressengeas

Polarization Optics. N. Fressengeas Polarization Optics N. Fressengeas Laboratoire Matériaux Optiques, Photonique et Systèmes Unité de Recherche commune à l Université de Lorraine et à Supélec Download this document from http://arche.univ-lorraine.fr/

More information

OPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT.

OPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. CLOSED BOOK. Equation Sheet is provided. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like

More information

POLARIZATION AND BIREFRINGENCE

POLARIZATION AND BIREFRINGENCE UNIT 3 POLARIZATION AND BIREFRINGENCE Name Lab Partner(s) Date Lab Section # TA signature Be sure to have your TA check your lab work and sign this sheet before you leave. Save it until the end of the

More information

Chapter 34. Electromagnetic Waves

Chapter 34. Electromagnetic Waves Chapter 34 Electromagnetic Waves The Goal of the Entire Course Maxwell s Equations: Maxwell s Equations James Clerk Maxwell 1831 1879 Scottish theoretical physicist Developed the electromagnetic theory

More information

Physics of Light and Optics

Physics of Light and Optics Physics of Light and Optics Justin Peatross and Harold Stokes Brigham Young University Department of Physics and Astronomy All Publication Rights Reserved (2001) Revised April 2002 This project is supported

More information