ECEG105/ECEU646 Optics for Engineers Course Notes Part 5: Polarization Prof. Charles A. DiMarzio Northeastern University Fall 2008 Sept 2008 11270-05-1
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 11270-05-2
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 11270-05-3
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 11270-05-4
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 11270-05-5
Some Mechanisms of Interaction Dielectric Interface Oblique Incidence Scattering Material Properties Linear Birefringence Circular Birefringence, AKA Optical Activity 11270-05-6
Linear Polarization x E θ y 11270-05-7
Circular Polarization x E -y ωt 11270-05-8
Unpolarized Light EV EH 11270-05-9
Polarizing Components 11270-05-10
Fresnel Reflection Boundary Conditions Dnormal= ε0enormal Dnormal ε0enormal ε0etangential Dtangential Dtangential= ε0etangential 11270-05-11
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 11270-05-12
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 2004 11270-05-13
S-Polarization (1) 11270-05-14
S-Polarization (2) 11270-05-15
Fresnel Coefficient Summary Example Fresnel Reflection: Air to Glass, n=1.5 1 τp 0.5 ρp 0 τs ρs -0.5-1 0 20 40 60, θangle, Degrees 11270-05-16 80
Special Angles 90 80 Critical Angle (medium to air) Angle, Degrees 70 Brewster s Angle (air to medium) 60 50 40 30 20 sin θ c = n2 10 1 Brewster s Angle (medium to air) 2 3 n, Index of refraction n1 11270-05-17 4
Summary of Reflectivities 11270-05-18
Power Coefficients Poynting Vector Fresnel Reflection: Air to Water, n=1.33 0 TS TP R, T, db -5-10 RS -15 RP -20 0 20 40 60, θangle, Degrees 80 11270-05-19
Total Internal Reflection Topics for Later in the Course 11270-05-20
Fresnel Reflection Examples (1) Air to Glass Air to ZnSe (IR) Fresnel Reflection: Air to Glass, n=1.5 1 1 TP 0.8 TP 0.8 TS TS 0.6 R, T R, T 0.6 0.4 0.4 RS 0.2 0 0 Fresnel Reflection: Air to ZnSE in IR, n=2.4 RP 20 40 60, θangle, Degrees 80 RS 0.2 0 0 RP 20 40 60 θ, Angle, Degrees 80 11270-05-21
Fresnel Reflection Examples (2) Glass to Air Phase Glass to Air Amplitude Fresnel Reflection: Glass, n=1.5, to Air 1 200 TP 150 TS Phase, Degrees 0.8 100 R, T 0.6 0.4 0.2 0 0 Fresnel Reflection: Glass, n=1.5, to Air RP 20 RS RP 50 0-50 -100 RP -150 40 60 80 θ, Angle, Degrees -200 0 20 TS TP RS 40 60 80 θ, Angle, Degrees 11270-05-22 100
Complex Index 4061ppt5-47 4061ppt5-48 11270-05-23
Fresnel Reflection for a Metal Fresnel Reflection: Air to Metal, n=4+3i 1 1 0.8 Imaginary Part s R 0.6 p 0.4 0.2 0 0 Fresnel Reflection: Air to Metal, n=4+3i 0.5 0 90 deg 0 deg(p) 0 deg(s) -0.5 20 40 60, θangle, Degrees 80-1 -1-0.5 0 0.5 Real Part 11270-05-24 1
Device Applications Device Input in Eigenvectors of Device Output End Views 11270-05-25
Brewster Plates Fresnel Reflection: Air to Ge in IR, n=4 1 0.8 R, T 0.6 0.4 0.2 0 0 20 40 60, θangle, Degrees 80 11270-05-26
Tent Polarizers 11270-05-27
Wire Grid Polarizers 11270-05-28
Polaroid H Sheets (H42 would be perfect ) 11270-05-29
S Reflection > P Reflection? July Dec 2003+ 2004 How Do Polarized Sunglasses Work? What is the Underlying Assumption? 11270-05-30
Birefringence Model nx kx ny ky 11270-05-31
Waveplates (1) 11270-05-32
Waveplates (2) (16.24µm) 11270-05-33
Optical Activity Device 11270-05-34
Fresnel Rhomb 200 150 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 100 50 0 45 Deg -50-100 RP -150-200 0 20 RS 40 60 80 θ, Angle, Degrees 11270-05-35 100
Jones Matrices Example: Polarizer Device Input Output End Views 11270-05-36
Rotation of Coordinates x y x y 11270-05-37
Alternative Basis Sets 11270-05-38
Other Transforms Tramsform to Eigenstates of a Fiber may be complicated, but useful In Out 11270-05-39
Some Jones Matrices Rotation of Coordinates (No Polarization Change) Physical Rotation of Polarization 2 Malus Law, Cos θ 11270-05-40
Components at Arbitrary Angles 4061ppt5-24 Rotate Coordinates Rotate Back Do it 11270-05-41
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? 11270-05-42
Maltese Cross (2) Photo at right taken with vertical polarizer over flash and horizontal polarizer over camera. + 11270-05-43
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 2004 11270-05-44
Partial Polarization Im b a=c LHC unpolarized 45 deg Re pol -45 RHC 11270-05-45 b
Coherency Matrices (1) 11270-05-46
Coherency Matrices (2) Device Input Output End Views 11270-05-47
Stokes Parameters 4061ppt5-31 11270-05-48
Stokes Vectors, Mueller Matrices 11270-05-49
A Depolarizer? What s That? 4061ppt5-35? 11270-05-50
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 11270-05-51