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Understanding Conoscopic Interferometers
Pengqian Wang
Department of Physics
Western Illinois University
March 18, 2013
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Conoscopic interferometers
• A conoscopic interferometer consists of an optically anisotropic specimen placed between two crossed linear polarizers and illuminated by a convergent light beam.
• Conoscopic interference patterns are used to identify minerals, to explore the structure of biological tissues, as well as to study the optical properties of crystals.
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In This Talk
1. Principle of conoscopic interferometers.
2. Simulation and observation of the interference patterns.
3. Visualization of the isochromatic interference fringes by spinning-polarizers.
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Principle of conoscopic interferometers
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Experimental setup of aconoscopic interferometer
Lightsource Polarizer
Lens 1LiNbO3
CrystalLens 2
AnalyzerViewingScreen
HV
In a conoscopic interferometer an optically anisotropic material is placed between two crossed linear polarizers and is illuminated by a convergent light beam.
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Conoscopic interferometers:experimental apparatus
Laser
Polarizer
LiNbO3 crystal
Analyzer
MonitorPowersource
Viewingscreen
CCDCamera
LensLens
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Light propagation in an anisotropic medium
D1
s
D2n2
n1
• The index ellipsoid is used to analyze light propagation in an anisotropic medium.
• A plane that contains the origin and is perpendicular to the light propagation direction intersects the index ellipsoid with an intersection ellipse.
• The two semi-axes of the intersection ellipse indicate the refractive indices and polarization directions of the two eigenmodes of the light waves.
Index ellipsoid
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Principle of conoscopic interferometers-1
• For a given light propagation direction in the crystal the vertically polarized incident light is decomposed into the two eigenmodes orientated at angle j.
• The two eigenmodes gain a phase shift of d in the crystal.
• After the crystal the two eigenmodes are projected onto the horizontal analyzer. An interference pattern is produced on the viewing screen.
jd
Analyzer
Viewing screen
Lens
Crystal
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Principle of conoscopic interferometers-2
For a given light propagation direction in the crystal the final light intensity on the viewing screen is
.2
sin2sin
|cossinsincos|
220
200
I
eEEI i
y
j
x
Eigen-modes
D1
D2
E0 (Input)
Ex-Exeid
(Output)
j = orientation of the two eigenmodes for the given light propagation direction d = phase shift between the two
eigenmodes
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Simulation and observation of the interference patterns
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Simulating the interference patterns: Isogyres and isochromates
• The isogyres are dark fringes where the two eigenmodes coincide with the transmission axes of the polarizers.
• The isochromates are bright fringes where the optical path length difference matches the wavelength.
2sin 2sin
2sin2sin 2222
Interference pattern = Isogyres × Isochromates
= ×
Opticaxes
V=0 V=Vp V=2Vp V=3Vp
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Conoscopic interference patterns:simulation vs. experiment
Conoscopic interference patterns of LiNbO3 at different external voltages. The optic plane is 45º to the polarizers.
Simulation:
Experiment:
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Visualization of the isochromates
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Isogyres and isochromates:entangled fingerprints of crystals
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Visualizing the isochromates byspinning polarizer and analyzer
2sin
2
1
2sin )(2sin 2
022
0
ItII
wt =p/8wt =0 wt =p/4 wt =3p/8 wt =p/2
Average =
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Spinning-polarizer and spinning-analyzerconoscopic interferometer: experimental apparatus
PolarizerAnalyzer Viewing
screenLensLens
LiNbO3 crystal
Motor
Lightsource
V=0 V=Vp V=2Vp V=3Vp
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Visualizing the isochromates: experimental result
Conoscopic interference patterns of LiNbO3 at different external voltages.
Conventionalinterferometer:
Optic plane is 45º to the polarizers.
Spinning-polarizer spinning-analyzer
Interferometer:
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Summary
• Conoscopic interference patterns are decomposed into isogyres and isochromates.
• We simulated the interference patterns. Our simulation agrees well with experimental observation.
• A spinning-polarizer and spinning-analyzer method is used to eliminate the isogyres and visualize the full isochromates.
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THANK YOU