Polarized direction

1. Part 3 Polarization of light Polarized direction

2. The electric field vector in electromagnetic wave are sensitive for most detectors. -- -vector is called light vector. §17-11 Polarization state of light • Electromagnetic wave is transverse wave • Polarized state:the oscillatingstate of light vector.  Natural light Classification  Plane polarized light Partially polarized light Elliptically polarized light  Circularly polarized light

3. 1. Natural light (Unpolarized light) • The amplitudes of light vectors along all directions at the plane which is perpendicular to the direction of propagation have same magnitude.

4. 2. Plane polarized light(线偏振光 or 平面偏振光) • The oscillating direction of light vector is always located in a fixed plane. Light vector Oscillating plane

5. 3. Partially polarized light(部分偏振光) • The amplitudes of light vectors along all directions at the plane which is perpendicular to the direction of propagation have different magnitude.

6. 4. Circularly or Elliptically polarized light (圆 or 椭圆偏振光) The end of the light vector moves with constant speed in a circle, or in an ellipse.

7. Poleroid Polarizing direction • I. Polarizing and polarization analyzing (起偏和检偏) • Polaroid (偏振片) §17-12 Polarization of light Law of Malus • Polarizing direction(偏振化方向)：permitting the light vector passing through.

8. analyzer polarizer • Polarizing--natural light  polarizer  plane polarized light • Polarization analyzing--to test whether the incident light is polarized.

9. II. Malus law A1, A2—amplitudes of the polarized light. ----Malus law

10. I2 I1  -1800 2700 1800 0 -900 900 Discussion：   =0 or =1800, I2=I1 -- maximum   =900 or =2700, I=0 --minimum

11. [Example] Two polarizing sheets are put parallely. Their polarized directions have the angle 300. Calculate when the natural light is incident on the polaroids normally, the intensity ratio of transmitting and incident light. (discuss two cases:  the polaroids have not absorption  the polaroids have 10% ratio of absorption.)

12. Solution ： no absorption Assume the intensity of incident natural light is I0 . The light is fully polarized after passing P1 . The polarized direction is parallel to P1 and the intensity is After I1 passes through P2 , its polarized direction is parallel to P2 and the intensity is

13.  the absorption ratio equals to 10%

14. I. Partially polarization phenomenon §17-13 Polarization by Reflection and Refraction • When a natural light is incident on a interface of two kinds of materials, its reflected light and refracted light are partially polarized light. • characteristic：for reflected light, the perpendicular component is larger than parallel component. Refracted light is converse.

15. Brewster angle 900 • When i equals to a special angle i0， the reflected light is fully polarized light with the polarized direction perpendicular to the incident plane. II. Brewster law In this case As ----Brewster Law

16. Notes When i= i0，the reflected light is fully polarized, the refracted light is partially polarized and has the maximum polarized degree.  The reflected light is of low intensity (15%), and the refracted light is of high intensity . Let a natural light passes through a stacking glass plates, the transmitted light is almost polarized.

17. 双折射 双 折 双 折 射 双 折 Calcite crystal I. Birefringence (Bi-refraction) phenomenon §17-14 Double refraction o-ray e-ray Ordinary light (o-ray): follows Refraction Law. Extraordinary light(e-ray): does notfollow Refraction Law.

18. When the crystal rotates round the incident light，o-ray is fixed and e-ray rotates round o-ray.

19. 1. Some concepts of crystallography • Optical axis：it represents a direction that there isno birefringence phenomenon when a light travels along this direction II. Characteristic of birefringence of light • Uniaxial crystal---it has one optical axis only ( calcite方解石、 quartz石英) • Biaxial crystal--- it has two optical axes (mica 云母 sapphire蓝宝石)

20. normal • Principal plane （主平面）：the plane formed by some ray (o-ray or e-ray) and optical axis. e-ray In the crystal. optical axis o-ray • If the optical axis is not at the incident plane, the principle planes of e-ray and o-ray are not coincide.

21. O-ray E-ray 2. Characteristics  O-ray and e-ray are plane polarized light. • The oscillating direction of o-rayits principle plane. The oscillating direction of e-ray its principle plane.

22. o.A.  When the optical axis is located in the incident plane, the principle planes of o-ray and e-ray coincide. The oscillating directions of o-ray and e-ray are perpendicular to each other.

23. Reason:The travel speed of o-ray in a birefringence crystal is homogeneous isotropic. The speed of e-ray is anisotropic. • O-ray：the wavefront is spherical surface. • E-ray： the wavefront is ellipic surface. III. Explanation of birefringence phenomenon positive crystal negative crystal

24. O.A. O.A. • The explanation of Huygens principle

25. O.A. O.A.

26. calcite crystal A cement from Canada tree IV. Application of birefringence Nicle polarizing prism

27. O.A.

28. O.A. Birefringence film polarizer natural light analyzer §17-15 The interference of polarized light偏振光的干涉 I. The interference principle of polarized light Polarized light Two coherent olarized lights

29. The polarized light behind P1 is separated into o-ray and e-ray after it passes through the birefringence film. The phase difference between o-rayande-rayis --their vibration directions  and  is constant. Their amplitudes are

30. Behind analyzer：o-ray and e-ray have their vibration components on the polarized direction of P2 : --equal amplitude, but opposite vibrating direction ( i.e. having extra phase difference .)

31. The phase difference between two coherent polarized lights is When the thick of birefringence film is different, the interference fringes appear. The interference fringes of the polarized lights produced by quartz crystal edge.

32. Mechanical stress --birefringence material analyzer polarizer II. Optical stress analysis

33. The experiment shows: k：proportion factor， p：stress when the internal stress of a material is not uniform, the interference fringes will appear behind P2.