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

Transcription

1 Optics and Optical Design Chapter 6: Polarization Optics Lectures Cord Arnold / Anne L Huillier

2 Polarization of Light

3 Arbitrary wave vs. paraxial wave

4 One component in x direction y x z

5 Components in x and y direction y x z

6 Components in x and y direction y x z

7 Circular polarization y x z

8 Elliptic polarization y x z

9 Importance of polarization for light matter interaction Reflection/transmission at boundaries Absorption (e.g. polarizers) Light scattering Refractive index in anisotropic materials Interaction with molecules => The polarization state can be manipulated by certain media, e.g. Anisotropic, optical active, liquid crystals, and magnetooptic materials.

10 Polarization helix

11 The polarization ellipse

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14 Polarization quiz E t, z 3cos t - z/c eˆ x y x Linear polarization in x

15 E Polarization quiz t, z 3cos t - z/cˆ 3sin t - z/c ˆ y e x e y x Circular polarization

16 E Polarization quiz t, z 3cos t - z/cˆ 2cos t - z/c ˆ y e x e y x Linear polarization at angle -33.7

17 E Polarization quiz, 4 t z 3cos t - z/ceˆ x 3cost - z/c eˆ y y x 2R arctan 2 1 R 2 cos 4 45 Elliptic polarization

18 E Polarization quiz, 4 t z 3cos t - z/ceˆ x cost - z/c eˆ y y x 2R arctan 2 1 R 2 cos 14 Elliptic polarization

19 Orientation and ellipticity angles y Orientation angle 0 3 5, , 2 2 x Ellipticity angle

20 Poincaré sphere

21 Jones vectors

22 Polarizer

23 Wave retarders (wave plates)

24 Conclusions for wave retarders A λ/4 plate at 45 transforms linear polarization into circular polarization; elliptic otherwise. Circularly polarized light is transformed into linear polarization at 45 to the crystal axes, independent of the orientation of the plate. A λ/2 plate turns linear polarization by twice the angle θ to the plate, but maximum 90. Left circular polarization in transferred into right and vice versa, independent of the orientation of the plate.

25 Reflection and refraction

26 Reflection and refraction at a boundary TE Transverse Electric orthogonal (s)enkrecht TM Transverse Magnetic parallel (p)arallel

27 Boundary conditions

28 Fresnel equations

29 TE polarization external reflection Example n 1, n n n 1 2

30 TE polarization internal reflection Example n 1.5, n2 1 1 c Total internal reflection Critical angle for total internal reflection c sin 1 n n 2 1 n n 1 2

31 TM polarization external reflection Example n 1, n B Brewster angle Brewster angle (TM reflection vanishes) B tan 1 n n 2 1 n n 1 2

32 TM polarization internal reflection Example n 1.5, n2 1 1 Brewster TIR n n 1 2

33 External Overview Internal TE TM

34 Power reflectance

35 Application < > polarization by reflection

36 Application < > polarization filters in photography Source:

37 Application < > polarization change by total internal reflection Fresnel-Rhomb If n 1 =1.5 and n 2 =1 and θ 1 =47.6 or 55.5, the Fresnel-Rhomb transfers incoming linear polarization at 45 to circular by two internal reflections.

38 Optics in anisotropic media

39 Isotropic < > anisotropic

40 The index ellipsoid, impermeability tensor, indicatrix Biaxial: Uniaxial: Isotropic: All refractive indices are different n 1 n 2 n 3 Two refractive indices are identical, n 1 = n 2 =n o (ordinary refractive index) and n 3 = n e (extraordinary refractive index) n e >n o => positive uniaxial n e <n o => negative uniaxial The z-axis of a uniaxial crystal is the optic axis. The index ellepsoid is a sphere.

41 Propagation along a principal axis Nothing happens to linear polarization, if the light travels along a principal axis of the crystal and the direction of polarization is along another principal axis.

42 Propagation along a principal axis A linearly polarized wave with angle of polarization not along a principal axis is not a normal mode of the system. The polarization state changes upon propagation.

43 Propagation along an arbitrary direction

44 Finding the optical axes for biaxial crystals z OA n 3 OA The optic axes of a crystal are defined as direction in which a travelling wave suffers no birefringence. n 2 n2 n2 Without loss of generality we assume n 1 < n 2 <n 3. n 1 x Biaxial crystals obviously have two optical axes. y n 2 Uniaxial crystals have one optic axis along the direction of the extraordinary refractive index n e.

45 Propagation along an arbitrary direction of an uniaxial crystal Special case uniaxial crystal: n 1 = n 2 =n o

46 Propagation in an arbitrary direction in a uniaxial crystal Special case uniaxial crystal: n 1 = n 2 =n o H k D E D E, and Ordinary wave: Extraordinary wave: H k D D E and

47 Propagation in an arbitrary direction in a uniaxial crystal H E S H E S E k H H E k H k D D H k 2 1 0

48 Double refraction

49 Optical activity < > Circular birefringence Image source: Wikipedia

50 Faraday effect

51 Optics of liquid crystals

52 Optics of liquid crystals Orientation of a twisted nematic liquid crystal Propagation of light in a twisted nematic liquid crystal

53 Common elements to manipulate polarization

54 Polarizer

55 Applications of anisotropic media < > polarization beamsplitter no ne n o n o n o n e n o n e n o n e n e n e

56 Twistec nematic liquid crystal switch

57 Applications of anisotropic materials: Wave retarders Optic axis n e n o Uniaxial crystals: n 1 =n 2 =n o, n 3 =n e n o Example: λ/2-plate

58 Applications of anisotropic materials: Intensity control

59 Applications of anisotropic materials: Polarization rotators and optical isolators