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A new phase difference compensation method for elliptically birefringent media Piotr Kurzynowski, Sławomir Drobczyński Institute of Physics Wrocław University of Technology Poland

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Scheme of presentation The literature background Compensators for linearly birefringent media Elliptically birefringent medium in the compensator setup A phase plate eliminating the medium ellipticity Numerical calculations The measurement procedure Experimental results Conclusions

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The literature background H.G. Jerrard, „Optical Compensators for Measurements of Elliptical Polarization”, JOSA, Vol.38 (1948) H. De Senarmont, Ann. Chim. Phys.,Vol.73 (1840) P. Kurzynowski, „Senarmont compensator for elliptically birefringent media”, Opt. Comm., Vol.171 (2000) J. Kobayashi, Y. Uesu, „A New Method and Apparatus ‘HAUP’ for Measuring Simultaneously Optical Activity and Birefringence of Crystals. I. Principles and Constructions”, J.Appl. Cryst., Vol.16 (1983) C.C. Montarou, T.K. Gaylord, „Two-wave-plate compensator for single-point retardation measurements”, Appl. Opt., Vol.43 (2004) P.Kurzynowski, W.A. Woźniak, „Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates”, Optik, Vol.113 (2002) M.A. Geday, W. Kaminsky, J.G. Lewis, A.M. Glazer, „Images of absolute retardance using the rotating polarizer method”, J. of Micr., Vol.198 (2000)

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Direct compensators for linearly birefringent media P P =0 A A =90 M f =45 -unknown C =-45 x -variable

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The phase shift compensation idea for direct compensators A rule: the total phase shift introduced by two media is equal to the difference phase shifts introduced by the medium M and the compensator C, because Transversal compensators (e.g. the Wollastone one): for some x 0 co-ordinate axis Inclined compensators (e.g. the Ehringhause one): for some inclination angle 0

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Azimuthal compensators for linearly birefringent media P P =0 /4 =0 A A -variable A0 =90 M f =45 -unknown

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The phase shift compensation idea for azimuthal compensators A rule: the quarter wave plate transforms the polarization state of the light after te medium M to the linearly one:

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Linearly birefringent medium in the compensator setup the Stokes vector V of the light after the medium M the light azimuth angle doesn’t change; the light ellipticity angle is equal to the half of the phase shift introduced by the medium M

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Elliptically birefringent medium in the compensator setup (1) the Stokes vector V of the light after the medium M but This is a rotation matrix R(2 f ) !

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Elliptically birefringent medium in the compensator setup (2) hence so

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Elliptically birefringent medium in the compensator setup (3) elimination of the f medium M ellipticity influence -the rotation matrix -the rotation matrix a linearly birefringent medium C with the azimuth angle =0 ° and introducing the phase shift -so if the medium C is introduced in the setup, the light azimuth angle doesn’t change if only =2· f

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Proposed compensator setups for direct compensators: for azimuthal compensators:

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The direct compensation setup M f =45 , f unknown P P =0 C =0 -variable C =-45 C -variable A A =90

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The azimuthal compensation setup M f =45 , f unknown P P =0 C =0 -variable /4 =0 A A -variable A0 =90

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The output light intensity distribution where for direct compensators or for azimuthal ones. generally where and

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Numerical calculations- -the Wollastone compensator setup The normalized intensity distribution for i = - 2 f 1 = 0 < 2 < 3

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Numerical calculations- -the Wollastone compensator setup The normalized intensity distribution for = - 2 f 0

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Numerical calculations- -the Wollastone compensator setup The normalized intensity distribution for = - 2 f =0

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The measurement procedure The direct compensators: a)the ellipticity angle f measurement the inclined (for example Ehringhause one) compensator C action the fringe visibility maximizing f b) the absolute phase shift measurement two-wavelength or white-light analysis of the intensity light distribution at the setup output

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The Senarmont configuration Two or one compensating plates? A quarter wave plate action is from mathematically point of wiev a rotation matrix R(90 ° ) So symbolically The new Senarmont setup configuration!

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Experimental results (1) 1 < 2 < 3

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Experimental results (2)

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Conclusions Due to the compensating plate C application there is possibility to measure in compensators setups not only the phase shift introduced by the medium but also its ellipticity The solution ( , f ) is univocal independently of medium azimuth angle f sign (±45 °) indeterminity A new (the last or latest?) Senarmont compensator setup has been presented

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