1 Understanding Conoscopic Interferometers Pengqian Wang Department of Physics Western Illinois University March 18, 2013

2 Conoscopic interferometers A conoscopic interferometer consists of an optically anisotropic specimen placed between two crossed linear polarizers and illuminated by a convergent light beam.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.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.

3 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.

4 Principle of conoscopic interferometers

5 Experimental setup of a conoscopic interferometer Light source Polarizer Lens 1 LiNbO 3 Crystal Lens 2 Analyzer Viewing Screen HV In a conoscopic interferometer an optically anisotropic material is placed between two crossed linear polarizers and is illuminated by a convergent light beam.

6 Conoscopic interferometers: experimental apparatus Laser Polarizer LiNbO 3 crystal Analyzer Monitor Power source Viewing screen CCD Camera Lens

7 Light propagation in an anisotropic medium D1D1 s D2D2 n2n2 n1n1 The index ellipsoid is used to analyze 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.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.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

8 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 .For a given light propagation direction in the crystal the vertically polarized incident light is decomposed into the two eigenmodes orientated at angle . The two eigenmodes gain a phase shift of  in the crystal.The two eigenmodes gain a phase shift of  in the crystal. After the crystal the two eigenmodes are projected onto the horizontal analyzer. An interference pattern is produced on the viewing screen.After the crystal the two eigenmodes are projected onto the horizontal analyzer. An interference pattern is produced on the viewing screen.   Analyzer Viewing screen Lens Crystal

9 Principle of conoscopic interferometers-2 For a given light propagation direction in the crystal the final light intensity on the viewing screen is y  x Eigen- modes D1D1 D2D2 E 0 (Input) ExEx -E x e i  (Output)  = orientation of the two eigenmodes for the given light propagation direction  = phase shift between the two eigenmodes

10 Simulation and observation of the interference patterns

11 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 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.The isochromates are bright fringes where the optical path length difference matches the wavelength. Interference pattern = Isogyres × Isochromates = ×Opticaxes

V=0V=V  V=2V  V=3V  12 Conoscopic interference patterns: simulation vs. experiment Conoscopic interference patterns of LiNbO 3 at different external voltages. The optic plane is 45º to the polarizers. Simulation: Experiment:

13 Visualization of the isochromates

14 Isogyres and isochromates: entangled fingerprints of crystals

15 Visualizing the isochromates by spinning polarizer and analyzer  t =  /8  t =0  t =  /4  t =3  /8  t =  /2 Average =

16 Spinning-polarizer and spinning-analyzer conoscopic interferometer: experimental apparatus Polarizer Analyzer Viewing screen Lens LiNbO 3 crystal Motor Light source

V=0V=V  V=2V  V=3V  17 Visualizing the isochromates: experimental result Conoscopic interference patterns of LiNbO 3 at different external voltages. Conventional interferometer: Optic plane is 45º to the polarizers. Spinning-polarizer spinning-analyzer Interferometer:

18 Summary Conoscopic interference patterns are decomposed into isogyres and isochromates.Conoscopic interference patterns are decomposed into isogyres and isochromates. We simulated the interference patterns. Our simulation agrees well with experimental observation.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.A spinning-polarizer and spinning-analyzer method is used to eliminate the isogyres and visualize the full isochromates.

19 THANK YOU