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Chapter 5 Polarization

Chapter 5 Polarization. 物理科学与技术学院. 5.1 polarized light and natural light 、 degree of polarization 偏振光与自然光、偏振度 5.2 polarization by reflection and refraction 、 Brewster ’ s law 由反射和折射获得偏振光 布儒斯特定律 5.3 double refraction in uniaxial crystal 单轴晶体的双折射现象

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Chapter 5 Polarization

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  1. Chapter 5Polarization 物理科学与技术学院

  2. 5.1 polarized light and natural light、degree of polarization 偏振光与自然光、偏振度 5.2 polarization by reflection and refraction、Brewster’s law 由反射和折射获得偏振光 布儒斯特定律 5.3 double refraction in uniaxial crystal 单轴晶体的双折射现象 5.4 Huygen’s explanation of double refraction by wavefront 用波面的概念解释双折射现象 5.5 polarization prism and analyser Malus law 偏振棱镜和偏振片 马吕斯定律 5.6 elliptically and circularly polarized light wave plate 椭圆偏振光与圆偏振光 波片

  3. 5.8 detection of the state of polarization 偏振态的实验检验 5.9 interference of polarized light 偏振光的干涉 5.10 photoelastic effect and electro-optical effect 光弹性效应和电光效应 5.11 rotation of the plane of linearly polarized light 线偏振光沿晶体光轴传播时振动面的旋转

  4. electricvector opticalvector 光矢量 5.1 polarized light and natural light、 degree of polarization longitudinalwave 纵波 Preface —the light is propagated as longitudinal. 波的振动方向对传播方向具有对称性。 transverse wave 横波 —the light is propagated as transverse. 波的振动方向对传播方向没有对称性 偏振。 5.1.1 polarization and polarized light according tofrequency: { monochromatic单色光 nonmonochromatic复色光 state of polarization 偏振态 — state of the vibration on the propagation of light. 在垂直于光传播方向的平面内光矢量的振动状态。

  5. sort of state of polarization 偏振态的分类 natural light unpolarized 自然光 polarized light 完全偏振光 partial polarized light 部分偏振光 circularly polarized light 圆偏振光 elliptically polarized light 椭圆偏振光 linearly polarized light 平面偏振光(线偏振光) left handed 左旋 right handed 右旋 left handed 左旋 right handed 右旋 Monochromatic light is used to discuss the state of polarization

  6. · E y E Ey  x · · · · · Ex 5.1.2 natural light and polarized light自然光与偏振光 1. linearly polarized light 平面偏振光(线偏振光) light travels towards to you resolve into two component vibrations are perpendicular to plane of paper vibrations are parallel to plane of paper

  7. incoherent resolvent · · · 2.natural light自然光 a natural beam can be resolved into two incoherent components , which are perpendicular to each other with equal magnitude

  8. incoherent resolve · · · · · · · · 5.1.3 partially polarized light and degree of polarization polarized+unpolarized 最常讨论的部分偏振光可看成是自然光和线偏振光的混合, 天空的散射光和水面的反射光就是这种部分偏振光,它可以分解如下: degree of polarization偏振度 unpolarized P = 0 degree of polarization polarized P = 1 partially polarized 0<P<1

  9. 5.2 polarization by reflection and refraction、Brewster’s law 5.2.1 Brewster’s angle 布儒斯特角 unpolarizedpartial polarized rp=0 polarized, have no parallel component when write as i10 i10——Brewster’s angle 5.2.2 linearly polarized light by refraction 由折射获得偏振光 transmitted light is polarized ,the vibration being in plane of incidence a pile of glass plates玻璃堆 Laser-tube cavity 激光器谐振腔 Brewster window布儒斯特窗

  10. · P · · · · · i1 i1' n1 · · S n2 i2 · 5.2.3 explanation of polarization by reflection and refraction unpolarized beam is not incident at Brewster’s angle incident with : Reflected and refracted natural light are partially polarized light 自然光反射和折射后成为部分偏振光

  11. 书P.206 解: 例5-1 自然光以入射角i投射到水面上,使发射光成为完全偏振光。现有一块玻璃浸于水中,如光从玻璃面反射也为完全偏振光,试求水面与玻璃面之间的夹角。

  12. unpolarized i n1 n2 re anisotropic ro e o o { O ray is at plane of incidence { e E ray is not always at plane of incidence 5.3 double refraction in uniaxial crystal 5.3.1 ordinary ray and extraordinary ray 1. double refraction a ray of light is refracted by a crystal, it gives two refracted rays 自然光入射到各向异性介质中, 折射光分成两束的现象。 2.ordinary ray and extraordinary ray寻常(o)光和非寻常(e)光 obey laws of refraction 遵从折射定律 usually,not obey laws of refraction一般不遵从折射定律

  13. e  · · · · · ·  o 偏振片 calcite 方解石 e o calcite方解石 rotate calcite round the incident ray as an axis vibrations of two refracted rays are perpendicular to each other 双折射的两束光振动方向相互垂直

  14. calcite 折射现 双 折射现 象 Phenomenon of double refraction

  15. image by E ray 纸面 双 折 射 光 纸面 纸面 paper 纸面 光 双 折 射 双 折 射 双 折 射 光 光 光 光 光 光 光 光 image by o ray calcite image of o ray remains stationary o光的像不动, when calcite is rotated, image of e ray rotates with the rotation of crystal光的像围绕 o光的像旋转

  16. 78° A 102° B optic axis 5.3.2 optic axis 光轴 1. optic axis光轴 a direction, not a line ,along which the double refraction is absent特定的方向,晶体中光沿这个方向传播时,不发生双折射现象。 Crystallised CaCO3(Iceland spar) 方解石晶体(冰洲石) Extraordinary ray { propagation along optic axisn()=no propagation perpendicular to optic axisn()=ne

  17. 78° A 102° B { uniaxial crystal单轴晶体:calcite方解石、quartz石英 biaxial crystal双轴晶体:云毋、sulfur硫磺、topaz黄玉 5.3.3 principal section主截面 a plane , which contains the optic axis and the normal of the crystal face, is called principal section 晶体光轴与晶体表面法线构成的平面叫主截面 normal for every point there are three principal section note the difference from the definition in Chinese textbook P.207 optic axis

  18. · principal plane of o ray · · · o ray optic axis principal plane主平面 a plane , which contains the optic axis and the ray of light, is called principal plane principal plane of the ordinary ray principal plane of the extraordinary ray principal plane of e ray e ray optic axis vibration of o ray is perpendicular to its principal plane o光的振动方向垂直于o光的主平面 vibration of e ray is parallel to its principal plane usually, vibrations of o ray and e ray are not perpendicular to each other e光的振动方向平行于e光的主平面

  19. · · I calcite · · · o e · special case: optic axis in the plane of incidencethe principal planes of o ray and e ray coincidevibrations of o ray and e ray are perpendicular to each other comments: general, the angle between two principal planes is very small, the vibrations of o ray and e ray are almost normal 5.3.4 relative intensity of o ray and e ray o光与e光的相对光强 special case: normal incidence principal section a. incidence of natural light optic axis

  20. Ao θ Ae b.incidence of linearly polarized light rotating the crystal round incident ray introduces the rotation of principal section θ changes θ=0 ,I0=0, Ie=I θ=90,I0=I ,Ie=0

  21. z z x x ~ 5.4 Huygen’s explanation of double refraction by wavefront in crystal the wavefront of o ray is sphericalo光波面是球面 in crystal the wavefront of e ray is an ellipsoid of revolution e光波面是旋转椭球面 varies with the direction in crystal n varieswith the different vibration direction velocity of light varies Opic axis uniaxial :symmetry of revolution around optic axis vibration is normal to z: vibration is parallel to z: other direction vibration between

  22. principal plane----contains the optic axis and the ray of light o ray----vibration is normal to principal plane at any direction,vibration is normal to optic axis wavefront is spherical—— o ray has same velocity at any direction e ray----vibration is parallel to principal plane vibration is normal to z propagation along z propagation is normal to z vibration is parallel to z wavefront is an ellipsoid of revolution—— e ray has different velocity at different direction

  23. { ve<vo quartz石英 positive crystal正晶体 ve>vo negative crystal负晶体 calcite方解石 · · · · · · · cΔt · · · · · optic axis 5.4.2propagation direction of o ray and e ray in uniaxial crystal a. optic axis in the plane of incidence, oblique incidence B i D A voΔt veΔt re r0 o e

  24. · · · · · · · · 晶体 光轴 · · · · · · · · · · o o e e b. optic axis is normal to the surface, normal incidence no separation no double refraction optic axis same velocity c. optic axis is parallel to the surface, normal incidence double refraction happens no separation but different velocity

  25. optic axis • • • • • e o o o e e • • • • d. optic axis is normal to the plane of incidence,normal incidence · · · · double refraction happens optic axis • • • same as “c ”case e. optic axis is normal to the plane of incidence, oblique incidence

  26. 5.5 polarization prism and analyser Malus law 5.5.1 polarization prism偏振棱镜 1 .Nicol prism尼科耳棱镜 no=1.658 ne=1.486 nb=1.550 • • • e • • • Canada balsam 加拿大树胶 2.Wollaston prism 渥拉斯顿棱镜 e • • e • • • • • o o  • • • •

  27. • e • • • • • o examples: Calcite(negative crystal) (1) • • e no=1.658 ne=1.486 • • • o  • • • • (2) no=1.658 ne=1.486 nglass=1.5 glass • •  • • • • calcite

  28. 5.5.2 analyser (polarization plate)

  29. P2 P1 A1 · · ·  natural light I0 linear I A 2= A1cos P2   Malus law马吕斯定律(1809) 5.5.3 Malus law马吕斯定律 plane of transmission —— extinguish intensity vanishes 消光

  30. 例5-2 假定在两个静止的、理想的、正交的起偏器之间有另一个理想的起偏器以角速度w旋转,试证透射光的强度满足下列关系式: ★例5-3设一水晶棱镜的顶角A为60度,光轴与棱镜主截面垂直,钠光以最小偏向角的方向在棱镜中折射,用焦距为0.5m的透镜聚焦,no=1.54425,ne=1.5536,试求o光和e光两谱线的间隔为多少?

  31. 5.6 elliptically and circularly polarized light wave plate 5.6.1 description of elliptically and circularly polarized light 圆偏振光和椭圆偏振光的描述 a.definition { circularly polarized圆偏振光—— tip of the vector draws a circle elliptically polarized椭圆偏振——tip of the vector draws a ellipse { clockwise——right handed右旋 face to the ray counter-clockwise——left handed左旋 b.theory elliptically polarized light consists of two plane polarized rays with same frequency, orthogonal vibrations,traveling along same direction 椭圆偏振光可通过两列频率相同,振动方向相互垂直, 沿同一方向传播的线偏振光叠加得到。

  32. circularly polarized light consists of two plane polarized rays with same frequency, orthogonal vibrations of equal amplitude, phase difference of (2k+1)/2 ,traveling along same direction 圆偏振光可通过两频率相同,振动方向相互垂直,且振幅相同, 位相差(2k+1)/2,沿同一方向传播的线偏振光叠加得到。 amplitude linear polarized  =0, { discussion AxAy elliptically polarized  = /2 Ax=Ay circularly polarized  =其他值 obliqueelliptically polarized

  33. ½波片 ¼波片 5.6.2 wave plate波(晶)片 wave plate——a plate of doubly refracting uniaxial crystal, which optic axis is parallel to the surface. o ray and e ray travel along same direction with different velocities principal section nod——optical path of o ray d—thickness of plate ned——optical path of e ray optical path difference:  =(no- ne)d quarter wave plate phase difference: (半波片) half wave plate

  34. o光  e光 Ae Ao' 2 A  Ao a. natural light is incident two components of incident light have unfixed phase difference  o and e rays have unfixed phase difference  emergent light is natural light b.plane polarized light is incident intensity ratio of o ray and e ray : sin2/cos2  phase difference: optic axis for half wave plate: incident linearly polarized light makes an angle of  with optic axis passing a half wave plate,the emergent light is still a linearly polarized light,which direction of polarization is rotated by 2

  35. y optic axis P wave plate A Ae x Ae A  Ao   elliptically Ao linear optic axis d d 5.6.3 production of elliptically and circularly polarized light 圆偏振光和椭圆偏振光的产生 a. linearly polarized light passes through a wave plate when the ray have traveled through the thickness d in crystal, a phase difference is introducted between o、e rays: general case----- product an elliptically polarized light

  36. special case ----- and product an circularly polarized light b. linearly polarized light passes through a quarter wave plate thickness of the wave plate circularly polarized light plane polarized light elliptically polarized light(normal)

  37. · · · P  c. production of elliptically and circularly polarized light from natural light incidence of natural light transmitted rays have no fixed phase difference-----natural light at first, the natural light must pass a polarizer to become a linearly polarized light natural light I0 usually, elliptically polarized light optic axis when =45° quarter wave plate circularly polarized

  38. 例5-4 一束圆偏振光,(1)垂直入射到1/4波片上,求透射光的 偏振态;(2)垂直入射到1/6波片上,求透射光的偏振态; 例5-5 一单色自然光通过尼科尔棱镜N1,N2和晶片C,其次序 如图示, N1的主截面水平,C对应于这波长的1/4波片,其主截面与竖直方向成30度,试问: (1)在N1和C之间,C和N2之间,以及从N2透射出来的光各是什么性质的光? (2)若入射光的强度为I0,则上述各部分的光的强度各是多少? 注:此例最好放到偏振光干涉之后讲

  39. · · · · · · · · Calculate the thickness of (i) a quarter wave plate and (ii) a half wave plate given that 5.7 detection of the state of polarization 偏振态的实验检验 5.7.1 Compensator Babinet’s Compensator Soleil’s Compensator

  40. incident light incident on a rotating polarizer intensity does not change intensity changes but never vanishes intensity changes and vanishes result result result case 2 case 3 either elliptically polarized or partially polarized either circularly polarized or unpolarized plane polarized 5.7.2 detection of the state of polarization case 1

  41. either circularly polarized or unpolarized case 2: original beam incident on a quarter wave plate unpolarized plane polarized incident on a rotating polarizer intensity changes and vanishes intensity does not vanish result result circularly polarized unpolarized

  42. either elliptically polarized or partially polarized case 3: original beam incident on a quarter wave plate, whose optic axis is parallel to max partially polarized plane polarized incident on a rotating polarizer intensity changes and vanishes intensity does not vanich result result partially polarized (linearly polarize +natural) circularly polarized

  43. 思考 ▲ 如何区分由自然光和椭圆偏振光组成的 部分偏振光与由自然光和线偏振光组成 的部分偏振光? ▲ 如何区分由自然光和圆偏振光组成的部分 偏振光与自然光?

  44. polarizerP1 wave plate C polarizerP2 interference  natural light optic axis d 5.8 interference of polarized light 偏振光的干涉 5.8.1 set up and intensity distribution偏振光干涉装置和强度分布 P1 C A1 A1e P2   A1o A2e after P1: A2o after P2:

  45. ' = phase difference: Interference intensity: { ——P1,P2 are at same side of optic axis  +  ——P1,P2 are at opposite side of optic axis

  46. P1,P2 are at same side of optic axis: —constructive interference —destructive interference P1,P2 are at opposite side of optic axis: —constructive interference —destructive interference if d is various,there are equal thickness fringes in screen

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