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EDAYATHANKUDY G S PILLAY ARTS AND SCIENCE COLLAGE Wave Optics

EDAYATHANKUDY G S PILLAY ARTS AND SCIENCE COLLAGE Wave Optics. W.CHRISTPHER IMMANWELL. Spherical Wave, Image Formation, and Huygens’ Principle. Wavefront: a surface over which the phase of a wave is constant. Huygens’ Principle. Linear Polarization. Circular/Elliptical Polarization.

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EDAYATHANKUDY G S PILLAY ARTS AND SCIENCE COLLAGE Wave Optics

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  1. EDAYATHANKUDY G S PILLAY ARTS AND SCIENCE COLLAGEWave Optics W.CHRISTPHER IMMANWELL

  2. Spherical Wave, Image Formation, and Huygens’ Principle Wavefront: a surface over which the phase of a wave is constant Huygens’ Principle

  3. Linear Polarization

  4. Circular/Elliptical Polarization

  5. Unpolarized Light and Polarizer

  6. Liquid Crystal Display (LCD)

  7. 3D Imaging by Polarizers

  8. Reflection and Transmittance of Polarized Lights Fresnel equations: Note: p-polarization: E-field  plane of incidence s-polarization: E-field  plane of incidence

  9. Goos-Haenchen Shift

  10. Optical Transfer Matrix to Analyze Three-layer Film

  11. Optical Transfer Matrix to Analyze Three-layer Film (Cont’)

  12. Antireflection Film Antireflection Coatings on Solar Cells

  13. High-reflectance Film

  14. High-reflectance Film (Cont’)

  15. Interference Young’s Experiment Interference — superposition of two light wave result in bright and dark fringes Conditions for Interference: • same polarization • same frequency • constant phase relationship (coherence)

  16. Conditions for Interference Bright fringes:  = 0, 2, 4,…(in phase) Dark fringes:  = , 3, 5, …(out of phase) If 1 = 2 = 

  17. Fabry-Perot Interferometer

  18. Fabry-Perot Interferometer (Cont’)

  19. Fabry-Perot Interferometer (Cont’) GaAs’s natural cleavage plane is (1,1,0)-plane. Si’s and Ge’s natural cleavage plane are (1,1,1)-plane.

  20. Mach-Zehnder Interferometer

  21. Recording process Reconstructionprocess Holography/Hologram

  22. 3D Hologram Videos

  23. Michelson Interferometer

  24. Sagnac Effect and Ring Interferometer N: Fringe number

  25. Interferences of Coherent/Incoherent Waves • Coherence: All component electromagnetic waves are in phase or in the same phase difference. • Interference ofcoherent waves: Waves of different frequencies interfere to form a pulse if they are coherent. • Interference ofincoherent waves: Spectrally incoherent light interferes to form continuous light with a randomly varying phase and amplitude.

  26. Fresnel (Near-field) Diffraction

  27. Fraunhofer (Far-field) Diffraction

  28. Fraunhofer Diffraction Pattern of a Rectangular Aperture

  29. Fraunhofer Diffraction Pattern of a Circular Aperture

  30. Resolving Power of Imaging Systems Rayleigh criterion

  31. Minimum resolvable angular: D: diameter of open aperture : wavelength of light source Note: if < min, images cannot be resolved Minimum resolvable separation: where =h/d1 For objective lens, numerical aperture NA=sin1 Resolution Limit • Rayleigh criterion  two object point can be resolved by the lens of an optical system

  32. Resolution of Human Eye Resolving power of human eye  0.3 mrad Resolution limit of human eye  0.075mm

  33. Fourier Transform by a Convex Lens

  34. Optical Fourier Transform Fourier Plane Input Plane FTL f f a(x,y) A(u,v)

  35. Optical Signal Processing

  36. Examples of Optical Signal Processing

  37. Examples of Optical Signal Processing (Cont’)

  38. Fourier Optics and Its applications Optical Computing

  39. Phase Contrast Microscopy

  40. Appendix 4-1 Coherence

  41. Coherence Function Mutually coherent: point sources u1(t1, x1, y1, z1) and u2(t1, x2, y2, z2) maintain a fixed phase relation Mutual coherence function: Normalized mutual coherence function: (complex degree of coherence or degree of correlation) where 11() and 22() are the self-coherence functions of u1(t) and u2(t)

  42. Demonstration of Coherence Visibility of fringe: extended source interference pattern If I1 = I2= I (best condition),  =  12()  i.e., visibility of the fringe is a measure of the degree of coherence

  43. Spatial Coherence extended source Intensity distribution of the resultant fringe of two points on the extended source: extended source

  44. Measurement of Spatial Coherence

  45. Temporal Coherence Visibility of the fringe is a measure of the degree of temporal coherence 11() at same point Coherence length of the light source

  46. Measurement of Temporal Coherence

  47. Appendix 4-2 Fourier Transform

  48. Fourier Transform Pairs

  49. Basic Theorems of Fourier Transforms

  50. Basic Theorems of Fourier Transforms (Cont’)

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