coherencecoherenceoptics.hanyang.ac.kr/~shsong/5-coherence.pdf · 2016-08-31 · coherencecoherence...
TRANSCRIPT
CoherenceCoherenceCoherence
This is based on
Chapter 10. Statistical Optics, Fundamentals of PhotonicsBahaa E. A. Saleh, Malvin Carl Teich
and
Lecture Note on Laser Technology and OpticsProf. Matti Kaivola
Optics and Molecular Materials, Helsinki University of Technologyhttp://omm.hut.fi/optics/l_o/2005/
and
Coherence and Fringe LocalizationT. D. Milster and N. A. Beaudry
Optical Sciences Center, University of Arizonawww.optics.arizona.edu/milster
CoherenceCoherenceCoherenceCoherence is a measure of the correlation between the phases measured at
different (temporal and spatial) points on a wave
Coherence theory is a study of the correlation properties of random light which is also known as the statistical optics.
Coherence theoryCoherence theoryCoherence theoryCoherence and Fringe Localization, T. D. Milster and N. A. Beaudry,
Coherence as StatisticsCoherence as StatisticsCoherence as Statistics
Statistical Properties of Random LightStatistical Properties of Random LightStatistical Properties of Random Light
Second order average of a function
Mutual coherence functionMutual coherence functionMutual coherence function
Mutual coherence function
Degree of CoherenceDegree of CoherenceDegree of Coherence
CoherenceCoherenceandand
VisibilityVisibility
Young’s double pinhole interferometer (YDPI)
Temporal Coherence Temporal Coherence Temporal Coherence
See the next example
( ) ( ) and ( ) ( )G gτ τ τ γ τ= Γ =
1 2r r=
The temporal autocorrelation meansthe time average at the same position
Note, we use both notations of
Degree of Temporal CoherenceDegree of Temporal CoherenceDegree of Temporal Coherence
Coherence Time and LengthCoherence Time and LengthCoherence Time and Length
Coherence lengthc cl cτ=
Coherence time
Coherence length
Note, it is different from ½ width, 1/e width, …
Later, we will similarly define the spectral width
Temporal CoherenceTemporal CoherenceTemporal Coherence
1/c aveτ τ ν= = Δ
2/ /c cl c cτ ν λ λ= = Δ = Δ
Actually, what is the definition of Δv , why is satisfied the relation ?
Coherence Time and Spectral WidthCoherence Time and Spectral WidthCoherence Time and Spectral WidthFundamentals of Photonics, Bahaa E. A. Saleh, Malvin Carl Teich
where,
Coherence Time and Spectral WidthCoherence Time and Spectral WidthCoherence Time and Spectral Width
FWHM (full width at half maximum)
Δt Δv = 1
Example : A wave comprising a random sequence of finite wave train.
Note, it is not a monochromatic wave
A truncated monochromatic waveIs not monochromatic, any more.
Example 10.1-1. A wave comprising a random sequence of wavepackets decaying exp.
Quasi-monochromatic wavesQuasiQuasi--monochromatic wavesmonochromatic waves
Now, start to investigate concretely a relation between the visibility and the coherence from a 2-wavelength light source up to a polychromatic light source.
A point source with two wavelengths A point source with two wavelengths Young’s double pinhole interferometer (YDPI)
OPD = vΔtd << zo
A point source with two wavelengths A point source with two wavelengths
T = 2π/ωm = nλeq /c, where 1 1 1 2
/ meq a b c n
ωλ λ λ
= − =
Now, under the constraint that d << zo
A point source with two wavelengths A point source with two wavelengths
Coherence length
λeq
λ
C.L. =2
1 1 12 2 2eq
cλλΔλ Δν
⎛ ⎞ ⎛ ⎞⎜ ⎟≈ = ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
and a b a bλ λ λ ν ν νΔ = − Δ = −
A Polychromatic light sourceA Polychromatic light source
3 λ’s
5 λ’s
V decreased
A Polychromatic light sourceA Polychromatic light source
Fringe visibility
A Polychromatic light sourceA Polychromatic light source
0o
o
dysinc sinc lz c c
c l=
Δν ΔνΔ
ΔΔν
⎛ ⎞ ⎛ ⎞⋅ = ⋅ =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠
⇒
Coherence length
Coherence time
oz cyd v
ΔΔ
= ⋅
oz cyd v
ΔΔ
= ⋅
Δv
Δvm
2Δl =
Spatial CoherenceSpatial CoherenceSpatial Coherence
Remind!
Spatial Coherence: point sourceSpatial Coherence: point sourceSpatial Coherence: point source
Spatial Coherence: two point sourceSpatial Coherence: two point sourceSpatial Coherence: two point source
lc ~ λ/θ
Basic Spatial CoherenceBasic Spatial Coherence
d
Basic Spatial CoherenceBasic Spatial Coherence
Basic Spatial CoherenceBasic Spatial Coherence
Basic properties of spatial coherence
Basic Spatial CoherenceBasic Spatial CoherenceNow, extend to a continuous source distribution (an ensemble of incoherent point sources)
ss s A
s
y dOPD yz
θ= ≡
Basic Spatial CoherenceBasic Spatial Coherence
Fringe visibility
Basic Spatial CoherenceBasic Spatial Coherence
Fringe visibility
van Cittert-Zernike Theorem :Degree of Spatial Coherence is Fourier Transform (or, Fraunhofer Diffraction Pattern) of the source irradiance distribution Appendix I
Example: Spatial coherence length from a circular source
Lc ~ λ/θ
sOPDs
θs
θs
Since and ss
s
y dOPDz
= As
dz
θ =
ss
y SOPDf
⇒ =
ASf
θ⇒ =
Concept of Coherent areaConcept of Coherent area
A = 1 mm d = 3 mm
λ = 500 nm
l
V = 0
Terminology Used in Coherence TheoryTerminology Used in Coherence TheoryRemind!
Define the normalized mutual coherence function, or complex degree of coherence
Terminology Used in Coherence TheoryTerminology Used in Coherence Theory
Normalized mutual coherence functionComplex degree of coherence
Making Light Coherent Making Light Incoherent
Spatial Filter forSpatial Coherence
Wavelenth Filterfor Temporal Coherence
Ground Glass toDestroy Spatial Coherence
Move it toDestroy Temporal Coherence
Control of CoherenceControl of CoherenceControl of Coherence
Appendix IAppendix IAppendix I
Chuck DiMarzioNortheastern University
van Cittert-Zernike Theorem for Spatial Coherence
Summary of van Cittert-Zernike Theorem for Spatial Coherence
Van Cittert-Zernike Theorem: 1
Chuck DiMarzio, Northeastern University
Van Cittert-Zernike Theorem: 2
Chuck DiMarzio, Northeastern University
Van Cittert-Zernike Theorem: 3
Chuck DiMarzio, Northeastern University
Van Cittert-Zernike Theorem: 4
Chuck DiMarzio, Northeastern University
Van Cittert-Zernike Theorem: 5
Source Irradiance
Far-Field Correlation Function
Chuck DiMarzio, Northeastern University