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

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

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)

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

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

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

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:

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

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 ) !

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

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

Proposed compensator setups  for direct compensators:  for azimuthal compensators:

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

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

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

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

Numerical calculations- -the Wollastone compensator setup  The normalized intensity distribution for  =  - 2 f  0 

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

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

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!

Experimental results (1)  1 <  2 <  3

Experimental results (2)

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