Abstract

The exact formula for calculating the geometric phase in an elliptical polariscope with arbitrary oriented elliptically birefringent nondichroic medium has been presented. The visualization of the obtained results using the Poincaré sphere representation allows the prediction of the effect of the setup geometry on the final result.

© 2012 Optical Society of America

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References

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  1. http://science.jrank.org/pages/2655/Eye.html .
  2. S. Pancharatnam, “Generalized theory of interference and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).
  3. M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
    [CrossRef]
  4. G. D. Love, “The unbounded nature of geometrical and dynamical phases in polarization optics,” Opt. Commun. 131, 236–240 (1996).
    [CrossRef]
  5. R. Bhandari, “SU (2) phase jump and geometrical phases,” Phys. Lett. A 157, 221–225 (1991).
    [CrossRef]
  6. T. H. Chyba, L. J. Wang, L. Mandel, and R. Simon, “Measurement of the Pancharatnam phase for a light beam,” Opt. Lett. 13, 562–564 (1988).
    [CrossRef]
  7. E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
    [CrossRef]
  8. Y. Ben-Aryeh, “Berry and Pancharatnam topological phases of atomic and optical systems,” J. Opt. B 6, R1–R18 (2004).
    [CrossRef]
  9. A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14, 4208–4220 (2006).
    [CrossRef]
  10. J. Courtial, “Wave plates and the Pancharatnam phase,” Opt. Commun. 171, 179–183 (1999).
    [CrossRef]
  11. P. Kurzynowski, W. A. Woźniak, and M. Szarycz, “Geometric phase: two triangles on the Poincaré sphere,” J. Opt. Soc. Am. A 28, 475–482 (2011).
    [CrossRef]
  12. P. Kurzynowski and W. A. Woźniak, “Geometric phase for dichroic media,” J. Opt. Soc. Am. A 28, 1949–1953 (2011).
    [CrossRef]
  13. D. Goldstein, “The Stokes polarization parameters,” in Polarized Light, Revised and Expanded (Dekker, 1993), pp. 31–64.
  14. D. Goldstein, “The Mueller matrices for polarizing components,” in Polarized Light, Revised and Expanded (Dekker, 1993), pp. 65–86.

2011 (2)

2006 (1)

2004 (1)

Y. Ben-Aryeh, “Berry and Pancharatnam topological phases of atomic and optical systems,” J. Opt. B 6, R1–R18 (2004).
[CrossRef]

2003 (1)

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

1999 (1)

J. Courtial, “Wave plates and the Pancharatnam phase,” Opt. Commun. 171, 179–183 (1999).
[CrossRef]

1996 (1)

G. D. Love, “The unbounded nature of geometrical and dynamical phases in polarization optics,” Opt. Commun. 131, 236–240 (1996).
[CrossRef]

1991 (1)

R. Bhandari, “SU (2) phase jump and geometrical phases,” Phys. Lett. A 157, 221–225 (1991).
[CrossRef]

1988 (1)

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[CrossRef]

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).

Ben-Aryeh, Y.

Y. Ben-Aryeh, “Berry and Pancharatnam topological phases of atomic and optical systems,” J. Opt. B 6, R1–R18 (2004).
[CrossRef]

Berry, M. V.

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[CrossRef]

Bhandari, R.

R. Bhandari, “SU (2) phase jump and geometrical phases,” Phys. Lett. A 157, 221–225 (1991).
[CrossRef]

Biener, G.

Chyba, T. H.

Courtial, J.

J. Courtial, “Wave plates and the Pancharatnam phase,” Opt. Commun. 171, 179–183 (1999).
[CrossRef]

Crawford, P. R.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Galvez, E. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Goldstein, D.

D. Goldstein, “The Stokes polarization parameters,” in Polarized Light, Revised and Expanded (Dekker, 1993), pp. 31–64.

D. Goldstein, “The Mueller matrices for polarizing components,” in Polarized Light, Revised and Expanded (Dekker, 1993), pp. 65–86.

Haglin, P. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Hasman, E.

Kleiner, V.

Kurzynowski, P.

Love, G. D.

G. D. Love, “The unbounded nature of geometrical and dynamical phases in polarization optics,” Opt. Commun. 131, 236–240 (1996).
[CrossRef]

Mandel, L.

Niv, A.

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).

Pysher, M. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Simon, R.

Szarycz, M.

Sztul, H. I.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Wang, L. J.

Williams, R. E.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Wozniak, W. A.

J. Mod. Opt. (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[CrossRef]

J. Opt. B (1)

Y. Ben-Aryeh, “Berry and Pancharatnam topological phases of atomic and optical systems,” J. Opt. B 6, R1–R18 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

J. Courtial, “Wave plates and the Pancharatnam phase,” Opt. Commun. 171, 179–183 (1999).
[CrossRef]

G. D. Love, “The unbounded nature of geometrical and dynamical phases in polarization optics,” Opt. Commun. 131, 236–240 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

R. Bhandari, “SU (2) phase jump and geometrical phases,” Phys. Lett. A 157, 221–225 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 1–4 (2003).
[CrossRef]

Proc. Indian Acad. Sci. A (1)

S. Pancharatnam, “Generalized theory of interference and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).

Other (3)

http://science.jrank.org/pages/2655/Eye.html .

D. Goldstein, “The Stokes polarization parameters,” in Polarized Light, Revised and Expanded (Dekker, 1993), pp. 31–64.

D. Goldstein, “The Mueller matrices for polarizing components,” in Polarized Light, Revised and Expanded (Dekker, 1993), pp. 65–86.

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Figures (1)

Fig. 1.
Fig. 1.

Construction on the Poincaré sphere, which visualizes the geometric phase for elliptically birefringent medium placed inside the elliptical polariscope (see description in text).

Equations (23)

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W⃗out=A·B·P·W⃗in,
V⃗i=[MiCiSi],i=P,F,A.
Iout[1+(V⃗A·V⃗F)(V⃗P·V⃗F)]+cosγ·[(V⃗A·V⃗P)(V⃗A·V⃗F)(V⃗P·V⃗F)]+sinγ·[V⃗F·(V⃗A×V⃗P)],
IoutT·[1+K·cos(γ+φG)],
tanφG=V⃗F·(V⃗A×V⃗P)(V⃗P·V⃗A)(V⃗P·V⃗F)(V⃗F·V⃗A),
T=1+(V⃗P·V⃗F)(V⃗F·V⃗A),
K2=[(V⃗P·V⃗A)(V⃗P·V⃗F)(V⃗F·V⃗A)]2+[V⃗F·(V⃗A×V⃗P)]2[1+(V⃗P·V⃗F)(V⃗F·V⃗A)]2.
V⃗F=[100].
tanφG=SP/CPSA/CA1+SP/CP·SA/CA,
T=1+MP·MA,
K2=(CP2+SP2)(CA2+SA2)(1+MP·MA)2,
V⃗i=[MiCiSi]=[cos2αi·cos2ϑisin2αi·cos2ϑisin2ϑi]=[cos2βisin2βi·cosδisin2βi·sinδi],i=P,A,
φG=δPδA.
Ioutsin2(γ/2).
Ioutcos2(γ/2).
W⃗in=[1000]T.
B=[10000MF2Z+XCFMFZSFMFZYCF0MFCFZCF2Z+XSFCFZ+YMF0MFSFZ+YCFCFSFZYMFSF2Z+X],
P=12[1MPCPSPMPMP2MPCPMPSPCPCPMPCP2CPSPSPSPMPSPCPSP2],
A=12[1MACASAcos2αLcos2αL·MAcos2αL·CAcos2αL·SAsin2αLsin2αL·MAsin2αL·CAsin2αL·SA0000],
Iout1+aX+bY+cZ,
a=MA·MP+CA·CP+SA·SP,
b=MF(CA·SPSA·CP)CF(MA·SPSA·MP)+SF(MA·CPCA·MP),
c=MF·CF(MA·CP+CA·MP)+MF·SF(MA·SP+SA·MP)+CF·SF(CA·SP+CA·CP)+MF2·MA·MP+CF2·CA·CP+SF2·SA·SP.

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