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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