4. Wave Optics

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4. Wave Optics
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Spherical Wave, Image Formation, and Huygens
Principle
Wavefront a surface over which the phase of a
wave is constant
Huygens Principle
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Linear Polarization
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Circular/Elliptical Polarization
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Unpolarized Light and Polarizer
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Liquid Crystal Display (LCD)
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3D Imaging by Polarizers
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• Reflection and Transmittance of Polarized Lights

Note p-polarization E-field ?? plane of
incidence s-polarization E-field ? plane of
incidence
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Goos-Haenchen Shift
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Optical Transfer Matrix to Analyze Three-layer
Film
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Optical Transfer Matrix to Analyze Three-layer
Film (Cont)
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Antireflection Film
Antireflection Coatings on Solar Cells
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High-reflectance Film
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High-reflectance Film (Cont)
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Interference
Youngs Experiment

• Interference superposition of two light wave
  result in bright and dark fringes
• Conditions for Interference
• same polarization
• same frequency
• constant phase relationship (coherence)

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• Conditions for Interference

If ?1 ?2 ?
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Fabry-Perot Interferometer
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Fabry-Perot Interferometer (Cont)
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Fabry-Perot Interferometer (Cont)
GaAss natural cleavage plane is (1,1,0)-plane.
Sis and Ges natural cleavage plane are
(1,1,1)-plane.
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Mach-Zehnder Interferometer
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Holography/Hologram
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3D Hologram Videos
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Michelson Interferometer
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Sagnac Effect and Ring Interferometer

• N Fringe number

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Interferences of Coherent/Incoherent Waves

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

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Fresnel (Near-field) Diffraction
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Fraunhofer (Far-field) Diffraction
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Fraunhofer Diffraction Pattern of a Rectangular
Aperture
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Fraunhofer Diffraction Pattern of a Circular
Aperture
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Resolving Power of Imaging Systems
Rayleigh criterion
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Resolution Limit

• Rayleigh criterion ? two object point can be
  resolved by the lens of an optical system

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Resolution of Human Eye
Resolving power of human eye ? 0.3
mrad Resolution limit of human eye ? 0.075mm
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Fourier Transform by a Convex Lens
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• Optical Fourier Transform

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Optical Signal Processing
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Examples of Optical Signal Processing
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Examples of Optical Signal Processing (Cont)
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Fourier Optics and Its applications

• Optical Computing

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Phase Contrast Microscopy
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Appendix 4-1 Coherence
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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)
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• Demonstration of Coherence

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
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• Spatial Coherence

extended source
Intensity distribution of the resultant fringe of
two points on the extended source
extended source
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Measurement of Spatial Coherence
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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
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Measurement of Temporal Coherence
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Appendix 4-2 Fourier Transform
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Fourier Transform Pairs
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Basic Theorems of Fourier Transforms
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Basic Theorems of Fourier Transforms (Cont)
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Application of Fourier Transform-Distinguishing
Similar Signals
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Appendix 4-3 Phase Transform Function of a Lens
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Usage of a Thin Lens? Phase Transformation
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Phase Transform Function of a Lens
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Phase Transform Function of a Lens