1. July 2003 Chuck DiMarzio, Northeastern University 11270-05-1 ECEG105/ECEU646 Optics for Engineers Course Notes Part 5: Polarization Prof. Charles A. DiMarzio Northeastern University Fall 2008 Sept 2008

2. July 2003 Chuck DiMarzio, Northeastern University 11270-05-2 Wave Nature of Light Failure of Raytracing –Zero- Approximation –Incoherent Process Empirical Wave Thy. –Huygens’ Principle Derives Geom. Optics Backward Wave –Fresnel: Sum Fields Maxwell’s Equations –Vector Wave Equation –Polarization –Scalar Wave Field –Fresnel-Kirchoff Integral No Backward Wave

3. July 2003 Chuck DiMarzio, Northeastern University 11270-05-3 Some Wave Phenomena Diffraction –Limiting Spot Size –Slits –Gratings –Fourier Optics Waveguides & Fibers Interference –Interferometry –Beat Signals –Fabry-Perot Resonator –Thin Films Polarization –Birefringence –Partial Polarization –E/O Effect Non-Linear Optics –Frequency Multiplying –Wave Mixing

4. July 2003 Chuck DiMarzio, Northeastern University 11270-05-4 Remaining Topics Polarized Light –Jones, Mueller, Coherency Matrices –Poincare Sphere –Fresnel Reflection Interference –Interferometers, Optical Testing, Laser Cavities, Thin Films, Doppler Laser Radar Diffraction –Kirchoff Integral, Fraunhoffer, Fresnel –Gratings, Gaussian Beams, Fourier Optics Radiometry Materials –Birefringence –Non-Linearity

5. July 2003 Chuck DiMarzio, Northeastern University 11270-05-5 Polarized Light Starting Point –Maxwell’s Equations –Homogeneous Medium –Isotropic Medium Solution –Plane Waves –Transverse Fields Eigenstates General Solution x y x y or x y z E

6. July 2003 Chuck DiMarzio, Northeastern University 11270-05-6 Some Mechanisms of Interaction Dielectric Interface –Oblique Incidence –Scattering Material Properties –Linear Birefringence –Circular Birefringence, AKA Optical Activity

7. July 2003 Chuck DiMarzio, Northeastern University 11270-05-7 Linear Polarization  E x y

8. July 2003 Chuck DiMarzio, Northeastern University 11270-05-8 Circular Polarization tt E x -y

9. July 2003 Chuck DiMarzio, Northeastern University 11270-05-9 Unpolarized Light EVEV EHEH

10. July 2003 Chuck DiMarzio, Northeastern University 11270-05-10 Polarizing Components

11. July 2003 Chuck DiMarzio, Northeastern University 11270-05-11 Fresnel Reflection Boundary Conditions D normal = D tangential =  0 E tangential  0 E normal D normal D tangential  0 E normal  0 E tangential

12. July 2003 Chuck DiMarzio, Northeastern University 11270-05-12 Polarization Labels Plane of Incidence –Normal & Incident Ray P-Polarization (TM) –E Parallel to Plane of Incidence S-Polarization (TE) –E Senkrecht = Perpendicular to Plane of Incidence ErEr EiEi EtEt HiHi HrHr HtHt ErEr EiEi EtEt HiHi HrHr HtHt

13. July 2003+ © Chuck DiMarzio, Northeastern University 11270-05-13 Polarization Labels Example Beam Path: –“North” to M1, Up to M2, “West” to M3, “South” Is the Output After M3 Polarized Verticaly or Horizontaly or Something Else? Is the Polarzation S or P at M1? At M2? At M3? Laser (vertical polarization) Dec 2004 Side View End View M1 M3 M2 M1 M2 M3 E E

14. July 2003 Chuck DiMarzio, Northeastern University 11270-05-14 S-Polarization (1)

15. July 2003 Chuck DiMarzio, Northeastern University 11270-05-15 S-Polarization (2)

16. July 2003 Chuck DiMarzio, Northeastern University 11270-05-16 Fresnel Coefficient Summary Example 020406080 -0.5 0 0.5 1 Fresnel Reflection: Air to Glass, n=1.5 , Angle, Degrees ss pp ss pp

17. July 2003 Chuck DiMarzio, Northeastern University 11270-05-17 Special Angles 1234 10 20 30 40 50 60 70 80 90 n, Index of refraction Angle, Degrees Critical Angle (medium to air) Brewster’s Angle (air to medium) Brewster’s Angle (medium to air)

18. July 2003 Chuck DiMarzio, Northeastern University 11270-05-18 Summary of Reflectivities

19. July 2003 Chuck DiMarzio, Northeastern University 11270-05-19 Power Coefficients 020406080 -20 -15 -10 -5 0 Fresnel Reflection: Air to Water, n=1.33 , Angle, Degrees R, T, dB RS RP TS TP |Poynting Vector|

20. July 2003 Chuck DiMarzio, Northeastern University 11270-05-20 Total Internal Reflection Topics for Later in the Course

21. July 2003 Chuck DiMarzio, Northeastern University 11270-05-21 Fresnel Reflection Examples (1) Air to ZnSe (IR)Air to Glass 020406080 0 0.2 0.4 0.6 0.8 1 Fresnel Reflection: Air to Glass, n=1.5 , Angle, Degrees R, T 020406080 0 0.2 0.4 0.6 0.8 1 Fresnel Reflection: Air to ZnSE in IR, n=2.4 , Angle, Degrees R, T RS RP TS TP RS RP TS TP

22. July 2003 Chuck DiMarzio, Northeastern University 11270-05-22 Fresnel Reflection Examples (2) Glass to Air Amplitude Glass to Air Phase 020406080 0 0.2 0.4 0.6 0.8 1 Fresnel Reflection: Glass, n=1.5, to Air , Angle, Degrees R, T RS RP TS TP 020406080100 -200 -150 -100 -50 0 50 100 150 200 Fresnel Reflection: Glass, n=1.5, to Air , Angle, Degrees Phase, Degrees RP RS TS TP RP

23. July 2003 Chuck DiMarzio, Northeastern University 11270-05-23 Complex Index 4061ppt5-47 4061ppt5-48

24. July 2003 Chuck DiMarzio, Northeastern University 11270-05-24 Fresnel Reflection for a Metal -0.500.51 -0.5 0 0.5 1 Fresnel Reflection: Air to Metal, n=4+3i Real Part Imaginary Part 0 deg(p) 0 deg(s) 90 deg 020406080 0 0.2 0.4 0.6 0.8 1 Fresnel Reflection: Air to Metal, n=4+3i , Angle, Degrees R p s

25. July 2003 Chuck DiMarzio, Northeastern University 11270-05-25 Device Applications Device Input in Eigenvectors of Device Output End Views

26. July 2003 Chuck DiMarzio, Northeastern University 11270-05-26 Brewster Plates 020406080 0 0.2 0.4 0.6 0.8 1 Fresnel Reflection: Air to Ge in IR, n=4 , Angle, Degrees R, T

27. July 2003 Chuck DiMarzio, Northeastern University 11270-05-27 Tent Polarizers

28. July 2003 Chuck DiMarzio, Northeastern University 11270-05-28 Wire Grid Polarizers

29. July 2003 Chuck DiMarzio, Northeastern University 11270-05-29 Polaroid H Sheets (H42 would be “perfect”)

30. July 2003+ © Chuck DiMarzio, Northeastern University 11270-05-30 S Reflection > P Reflection? Dec 2004 How Do Polarized Sunglasses Work? What is the Underlying Assumption?

31. July 2003 Chuck DiMarzio, Northeastern University 11270-05-31 Birefringence Model nxnx kxkx nyny kyky

32. July 2003 Chuck DiMarzio, Northeastern University 11270-05-32 Waveplates (1)

33. July 2003 Chuck DiMarzio, Northeastern University 11270-05-33 Waveplates (2) (16.24  m)

34. July 2003 Chuck DiMarzio, Northeastern University 11270-05-34 Optical Activity Device

35. July 2003 Chuck DiMarzio, Northeastern University 11270-05-35 Fresnel Rhomb 020406080100 -200 -150 -100 -50 0 50 100 150 200 Fresnel Reflection: Glass, n=1.5, to Air , Angle, Degrees Phase, Degrees RS RP 45 Deg Functions as QWP –True Phase Shift rather than Time Delay –Broadband: Limited only by material Dispersion

36. July 2003 Chuck DiMarzio, Northeastern University 11270-05-36 Jones Matrices Device Input Output End Views Example: Polarizer

37. July 2003 Chuck DiMarzio, Northeastern University 11270-05-37 Rotation of Coordinates x y x’ y’

38. July 2003 Chuck DiMarzio, Northeastern University 11270-05-38 Alternative Basis Sets

39. July 2003 Chuck DiMarzio, Northeastern University 11270-05-39 Other Transforms Tramsform to Eigenstates of a Fiber may be complicated, but useful In Out

40. July 2003 Chuck DiMarzio, Northeastern University 11270-05-40 Some Jones Matrices Malus Law, Cos 2  Rotation of Coordinates (No Polarization Change) Physical Rotation of Polarization

41. July 2003 Chuck DiMarzio, Northeastern University 11270-05-41 Components at Arbitrary Angles Do it Rotate Back Rotate Coordinates 4061ppt5-24

42. July 2003+ © Chuck DiMarzio, Northeastern University 11270-05-42 Maltese Cross (1) What is the Orientation of the Polarizers in Each Photo Below? Polarizer Fast Lens Green Light Why must the lens be fast to show this effect?

43. July 2003+ © Chuck DiMarzio, Northeastern University 11270-05-43 Maltese Cross (2) Photo at right taken with vertical polarizer over flash and horizontal polarizer over camera.

44. July 2003+ © Chuck DiMarzio, Northeastern University 11270-05-44 Rotation Example Beam Path: –“North” to M1, Up to M2, “West” to M3, “South” What is the Polarization after M3? –Suppose Mirrors Are Metal, n=4+3i, at 45 Degrees Laser (30-deg. polarization) Dec 2004 Side View End View M1 M3 M2 M1 M2 M3 E E

45. July 2003 Chuck DiMarzio, Northeastern University 11270-05-45 Partial Polarization a=c Re b Im b 45 deg pol -45 LHC RHC unpolarized

46. July 2003 Chuck DiMarzio, Northeastern University 11270-05-46 Coherency Matrices (1)

47. July 2003 Chuck DiMarzio, Northeastern University 11270-05-47 Coherency Matrices (2) Device Input Output End Views

48. July 2003 Chuck DiMarzio, Northeastern University 11270-05-48 Stokes Parameters 4061ppt5-31

49. July 2003 Chuck DiMarzio, Northeastern University 11270-05-49 Stokes Vectors, Mueller Matrices

50. July 2003 Chuck DiMarzio, Northeastern University 11270-05-50 A Depolarizer? What’s That? ? 4061ppt5-35

51. July 2003 Chuck DiMarzio, Northeastern University 11270-05-51 The Poincaré Sphere Graphical Representation of Stokes Parameters DOP is Radius C/I S/I M/I RHC X 45  -45  Y LHC IMSCIMSC Vs=Vs=