Understanding Conoscopic
Interferometers
Pengqian Wang
Department of Physics
Western Illinois University
March 18, 2013
1
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.
2
In This Talk
1. Principle of conoscopic interferometers.
2. Simulation and observation of the
interference patterns.
3. Visualization of the isochromatic
interference fringes by spinningpolarizers.
3
Principle of conoscopic
interferometers
4
Experimental setup of a
conoscopic interferometer
Lens 1
Light
source
Polarizer
LiNbO3
Crystal
Lens 2
HV
Analyzer
Viewing
Screen
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
Power
source
Polarizer
Laser
Monitor
Viewing
screen
Lens
Lens
LiNbO3
crystal
Analyzer
CCD
Camera
6
Light propagation in an
anisotropic medium
• 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.
s
D2
n2
n1
D1
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.
Lens
j
Viewing
screen
d
Crystal
Analyzer
8
Principle of conoscopic
interferometers-2
For a given light propagation direction in the crystal
the final light intensity on the viewing screen is
I | E0 cosj sin j  E0 sin j cosj  eid |2
 I 0 sin 2j sin
2
2
d
2
.
j = orientation of the two eigenmodes for
the given light propagation direction
d = phase shift between the two eigenmodes
y
E0 (Input)
D2
Eigenmodes
j
D1
Ex
-Exeid
(Output)
x
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Simulation and observation
of the interference patterns
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Simulating the interference patterns:
Isogyres and isochromates
sin 2 2j sin 2
d
2

Interference pattern =
sin 2 2j

Isogyres
×
sin 2
d
2
Isochromates
Optic
axes
=
×
• The isogyres are dark fringes
• The isochromates are bright
where the two eigenmodes
fringes where the optical path
coincide with the transmission
length difference matches the
axes of the polarizers.
wavelength.
11
Conoscopic interference patterns:
simulation vs. experiment
Simulation:
Experiment:
V=0
V=Vp
V=2Vp
V=3Vp
Conoscopic interference patterns of LiNbO3 at different external voltages.
The optic plane is 45º to the polarizers.
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Visualization of the
isochromates
13
Isogyres and isochromates:
entangled fingerprints of crystals
14
Visualizing the isochromates by
spinning polarizer and analyzer
1
2 d
I  I 0 sin 2(j  t ) sin
 I 0 sin
2 2
2
2
t =0
t =p/8
2
t =p/4
d
t =3p/8
t =p/2
Average =
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Spinning-polarizer and spinning-analyzer
conoscopic interferometer: experimental apparatus
Polarizer
Motor
Light
source
Analyzer
Lens
Lens
Viewing
screen
LiNbO3
crystal
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Visualizing the isochromates:
experimental result
Conventional
interferometer:
Optic plane is 45º
to the polarizers.
Spinning-polarizer
spinning-analyzer
Interferometer:
V=0
V=Vp
V=2Vp
V=3Vp
Conoscopic interference patterns of LiNbO3 at different external voltages.
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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
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