ECEG105/ECEU646 Optics for Engineers Course Notes Part 5: Polarization

Transcription

1 ECEG105/ECEU646 Optics for Engineers Course Notes Part 5: Polarization Prof. Charles A. DiMarzio Northeastern University Fall 2008 Sept

2 Wave Nature of Light Failure of Raytracing Zero-λ Approximation Incoherent Process Empirical Wave Thy. Huygens Principle Derives Geom. Optics Backward Wave Maxwell s Equations Vector Wave Equation Polarization Scalar Wave Field Fresnel-Kirchoff Integral No Backward Wave Fresnel: Sum Fields

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 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 Polarized Light Starting Point Maxwell s Equations Homogeneous Medium Isotropic Medium Solution Plane Waves Transverse Fields y E Eigenstates y x or y x General Solution z x

6 Some Mechanisms of Interaction Dielectric Interface Oblique Incidence Scattering Material Properties Linear Birefringence Circular Birefringence, AKA Optical Activity

7 Linear Polarization x E θ y

8 Circular Polarization x E -y ωt

9 Unpolarized Light EV EH

10 Polarizing Components

11 Fresnel Reflection Boundary Conditions Dnormal= ε0enormal Dnormal ε0enormal ε0etangential Dtangential Dtangential= ε0etangential

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 Er Hr Er Ei Hi Et Ht Hr Hi Ei Ht Et

13 Polarization Labels Example M3 M2 Side View Laser (vertical polarization) M2 E M3 E M1 End View M1 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? + Dec

14 S-Polarization (1)

15 S-Polarization (2)

16 Fresnel Coefficient Summary Example Fresnel Reflection: Air to Glass, n=1.5 1 τp 0.5 ρp 0 τs ρs , θangle, Degrees

17 Special Angles Critical Angle (medium to air) Angle, Degrees 70 Brewster s Angle (air to medium) sin θ c = n Brewster s Angle (medium to air) 2 3 n, Index of refraction n

18 Summary of Reflectivities

19 Power Coefficients Poynting Vector Fresnel Reflection: Air to Water, n= TS TP R, T, db RS -15 RP , θangle, Degrees

20 Total Internal Reflection Topics for Later in the Course

21 Fresnel Reflection Examples (1) Air to Glass Air to ZnSe (IR) Fresnel Reflection: Air to Glass, n= TP 0.8 TP 0.8 TS TS 0.6 R, T R, T RS Fresnel Reflection: Air to ZnSE in IR, n=2.4 RP , θangle, Degrees 80 RS RP θ, Angle, Degrees

22 Fresnel Reflection Examples (2) Glass to Air Phase Glass to Air Amplitude Fresnel Reflection: Glass, n=1.5, to Air TP 150 TS Phase, Degrees R, T Fresnel Reflection: Glass, n=1.5, to Air RP 20 RS RP RP θ, Angle, Degrees TS TP RS θ, Angle, Degrees

23 Complex Index 4061ppt ppt

24 Fresnel Reflection for a Metal Fresnel Reflection: Air to Metal, n=4+3i Imaginary Part s R 0.6 p Fresnel Reflection: Air to Metal, n=4+3i deg 0 deg(p) 0 deg(s) , θangle, Degrees Real Part

25 Device Applications Device Input in Eigenvectors of Device Output End Views

26 Brewster Plates Fresnel Reflection: Air to Ge in IR, n= R, T , θangle, Degrees

27 Tent Polarizers

28 Wire Grid Polarizers

29 Polaroid H Sheets (H42 would be perfect )

30 S Reflection > P Reflection? July Dec How Do Polarized Sunglasses Work? What is the Underlying Assumption?

31 Birefringence Model nx kx ny ky

32 Waveplates (1)

33 Waveplates (2) (16.24µm)

34 Optical Activity Device

35 Fresnel Rhomb Phase, Degrees Functions as QWP True Phase Shift rather than Time Delay Broadband: Limited only by material Dispersion Fresnel Reflection: Glass, n=1.5, to Air Deg RP RS θ, Angle, Degrees

36 Jones Matrices Example: Polarizer Device Input Output End Views

37 Rotation of Coordinates x y x y

38 Alternative Basis Sets

39 Other Transforms Tramsform to Eigenstates of a Fiber may be complicated, but useful In Out

40 Some Jones Matrices Rotation of Coordinates (No Polarization Change) Physical Rotation of Polarization 2 Malus Law, Cos θ

41 Components at Arbitrary Angles 4061ppt5-24 Rotate Coordinates Rotate Back Do it

42 Maltese Cross (1) Polarizer Fast Lens Polarizer Green Light + What is the Orientation of the Polarizers in Each Photo Below? Why must the lens be fast to show this effect?

43 Maltese Cross (2) Photo at right taken with vertical polarizer over flash and horizontal polarizer over camera

44 Rotation Example M3 Side View Laser (30-deg. polarization) M2 M2 E M3 E M1 End View M1 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 + Dec

45 Partial Polarization Im b a=c LHC unpolarized 45 deg Re pol -45 RHC b

46 Coherency Matrices (1)

47 Coherency Matrices (2) Device Input Output End Views

48 Stokes Parameters 4061ppt

49 Stokes Vectors, Mueller Matrices

50 A Depolarizer? What s That? 4061ppt5-35?

51 The Poincaré Sphere Graphical Representation of Stokes -45 Parameters X DOP is Radius Vs= I M S C RHC C/I Y 45 M/I S/I LHC