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1、光光 學(xué)學(xué)O OP PT TI IC CS S第五章第五章 光的偏振光的偏振Propagation of light in linear Propagation of light in linear anisotropic dielectrics (crystals)anisotropic dielectrics (crystals)第五章第五章 光的偏振光的偏振第一節(jié)第一節(jié) 偏振光的屬性偏振光的屬性第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射第三節(jié)第三節(jié) 偏振與散射和反射偏振與散射和反射第四節(jié)第四節(jié) 延遲器和起偏器延遲器和起偏器第五節(jié)第五節(jié) 旋光性旋光性第六節(jié)第六節(jié) 光調(diào)制光調(diào)制第七節(jié)第七節(jié)

2、偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述第五章第五章 光的偏振光的偏振第一節(jié)第一節(jié) 偏振光的屬性偏振光的屬性Nature of polarized light Linear polarization Circular polarization Elliptical polarization Random polarization Partial polarizationLinear Polarization)cos()cos(),(),(),(00tkzEjtkzEitzEtzEtzEyxyxLinear-polarized or plane-polarized light:The orientati

3、on of the E-field is constant.If = 0 or , thenE is linear polarized.第一節(jié)第一節(jié) 偏振光的屬性偏振光的屬性Circular PolarizationIf E0 x= E0y, = /2, thenE is left-circularly polarized.If E0 x= E0y, = - /2, thenE is right-circularly polarized.)cos()cos(),(),(),(00tkzEjtkzEitzEtzEtzEyxyx第一節(jié)第一節(jié) 偏振光的屬性偏振光的屬性Elliptical Polar

4、ization202000200202000cos22tansincos2)cos()cos(),(),(),(yxyxxxyyxxyyyxyxEEEEEEEEEEEEtkzEjtkzEitzEtzEtzE第一節(jié)第一節(jié) 偏振光的屬性偏振光的屬性State of PolarizationP P-state: Plane- or linear-polarizedR R-state: Right-circular-polarizedL L-state: Left-circular-polarizedE E-state: Elliptical-polarizedP = R LE = aR bL第一節(jié)第

5、一節(jié) 偏振光的屬性偏振光的屬性How to prove it?Angular Momentum of PhotonsLLEdtdLdtdE第一節(jié)第一節(jié) 偏振光的屬性偏振光的屬性The Jones VectorsHorizontalP-state01VerticalP-stateP-stateat +45oP-stateat -45oR-stateL-state1011211121i121i121001*hvvhRLLRLLRREEEEEEEEEEEE)(cos)()()(cos)()(00ttkxtEjtEttkxtEitEyyyxxxyxiyixyxeEeEtEtEE00)()(第一節(jié)第一節(jié)

6、 偏振光的屬性偏振光的屬性PolarizersBasic mechanism: Dichroism Birefringence Scattering Reflection Asymmetry第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Maluss Law22200cos)0(cos2)(IEcI第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Dichroism Wire-Grid PolarizerThe transmission axis of the grid is perpendicular to the wires.Dichroism refers to the selective absor

7、ption of one of the two orthogonal P-state components of an incident beam.第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Dichroism Dichroic CrystalsOrientation-dependent conductivity photon energy joule heat第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射The tansmitted light suffers polarization- (and wavelength-)dependent absorption dichroismDichrois

8、m PolaroidEach separate miniscule dichroic entity is known as a dichromophore. The dichromophores are of molecular dimensions. Polaroid is a very effective polarizer across the entire visible spectrum, but is somewhat less so at the blue end.第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Optical Anisotropy Dichroism & Birefr

9、ingence第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射birefringencedichroismBirefringence Calcite (I)3-fold symmetry第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射*Birefringence Calcite (II)第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射o-ray or e-ray ?EHu rpBirefringence Calcite (II)第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Birefringent CrystalsBirefringencen = ( ne no )vcvc/Negative uniaxial:op

10、tic axis is slow-axisPositive uniaxial:optic axis is fast-axis第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Birefringent Polarizers Glan-Faucault Prism第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射oennsin1Birefringent Polarizers Glan-Faucault Prism第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射oennsin1What about positive crystals?Birefringent Polarizers Wollaston Prism第二節(jié)第二

11、節(jié) 雙色性和雙折射雙色性和雙折射Birefringent Polarizers Wollaston Prism第二節(jié)第二節(jié) 雙色性和雙折射雙色性和雙折射Negative or positive crystal?Polarization by Scattering第三節(jié)第三節(jié) 偏振與散射和反射偏振與散射和反射EHu rpRayleigh scattering and electrical dipolesPolarization by Scattering第三節(jié)第三節(jié) 偏振與散射和反射偏振與散射和反射Fresnel Equations & Natural LightRandom polarizat

12、ion 2 orthogonal, incoherent, equal-amplitude P-states22/RRIIIRIIIirriiiminmaxminmaxIIIIVIIIVnpporDegree of polarization第三節(jié)第三節(jié) 偏振與散射和反射偏振與散射和反射Polarization by Reflection第三節(jié)第三節(jié) 偏振與散射和反射偏振與散射和反射Polarization by Reflection第三節(jié)第三節(jié) 偏振與散射和反射偏振與散射和反射(Phase) Retarders Wave Plates第四節(jié)第四節(jié) 延遲器與起偏器延遲器與起偏器)cos()cos

13、(),(),(),(00tkzEjtkzEitzEtzEtzEyxyxP P-state: Plane- or linear-polarizedR R-state: Right-circular-polarizedL L-state: Left-circular-polarizedE E-state: Elliptical-polarizedRetarders serve to change the state of polarization of an incident wave, by changing the relative phase of the two constituent P

14、-states.HorizontalP-state01VerticalP-stateP-stateat +45oP-stateat -45oR-stateL-state1011211121i121i121(Phase) Retarders Wave Platesopticaxisk第四節(jié)第四節(jié) 延遲器與起偏器延遲器與起偏器Negative uniaxial retarder: ne v Positive uniaxial retarder:ne no v/ nR): d-rotatory(nL nR): l-rotatory第五節(jié)第五節(jié) 旋光性旋光性A Classical Model of O

15、ptical Activity第五節(jié)第五節(jié) 旋光性旋光性Induced Optical EffectsOptical Modulators第六節(jié)第六節(jié) 光調(diào)制光調(diào)制Photoelasticity(mechanical birefringence, stress birefringence) The regions in which (n1-n2) is constant are known as isochromatic regions. Each region corresponds to a particular color.The plastic sample is put betwee

16、n crossed Polaroids.第六節(jié)第六節(jié) 光調(diào)制光調(diào)制The Faraday Effect1-cm flint glassB = 1000 gauss = ? = V (,T) B d第六節(jié)第六節(jié) 光調(diào)制光調(diào)制The Faraday Effect第六節(jié)第六節(jié) 光調(diào)制光調(diào)制RnRLnn LnRLnn l-rotatoryd-rotatoryBvfL-stateBvfR-stateLnBvfR-stateBvfL-stateRnThe Kerr Effectsn = K E2 = 2KlV2/d2Example:Nitrobenzene celld = 1 cml = 5 cm Hal

17、f-wave voltage?第六節(jié)第六節(jié) 光調(diào)制光調(diào)制The Pockels Effects = 2n03r63V/63302/2rnVKDPn0 = 1.51 = 633 nmHalf-wave voltage?第六節(jié)第六節(jié) 光調(diào)制光調(diào)制Transverse & LongitudinalLiquid Crystal),(2TVnd第六節(jié)第六節(jié) 光調(diào)制光調(diào)制Mathematical Descriptionof Polarization第七節(jié)第七節(jié) 偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述Stokes Parameters？t第七節(jié)第七節(jié) 偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述Stokes Paramete

18、rs？tI/2HP+R第七節(jié)第七節(jié) 偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述Stokes ParametersTyxyxTyxyxTyTxTyTxyyyxxxEESEESEESEESttkxtEitEttkxtEitE)sin(2)cos(2)(cos)()()(cos)()(003002202012020000Unpolarized:HorizontalP-state0011010101011001001100011001VerticalP-stateP-stateat +45oP-stateat -45oR-stateL-state02/123222123222120/)(SSSSVSSSS(co

19、mpletely polarized)(degree of polarization)第七節(jié)第七節(jié) 偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述Stokes ParametersTyxyxTyxyxTyTxTyTxyyyxxxEESEESEESEESttkxtEitEttkxtEitE)sin(2)cos(2)(cos)()()(cos)()(0030022020120200003210SSSSHomework: For time-independent amplitudes and phases, prove the equations, neglecting the common factor .20nc第七節(jié)第七節(jié) 偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述Jones Matrices & Mueller Matrices第七節(jié)第七節(jié) 偏振態(tài)的數(shù)學(xué)描述偏振態(tài)的數(shù)學(xué)描述Homework: 9.43; 9.48; 9.70-(a),(b)