Abstract

The dielectric property of the anisotropic optical medium is ascertained by considering the polarized photon as a two-component spinor of spherical harmonics. The geometric phase of a single-polarized photon has been evaluated in two ways: the phase two-form of the dielectric matrix through a twist and the Pancharatnam phase by changing the angular momentum of the incident polarized photon over a closed triangular path on the extended Poincaré sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies.

© 2006 Optical Society of America

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  3. M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London Ser. A 392, 45-57 (1984).
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  6. M. V. Berry, Proceedings of a NATO Advanced Research Workshop on Fundamental Aspects of Quantum Theory (NATO, 1985).
  7. R. Simon and N. Mukunda, "Universal SU(2) gadget for polarization optics," Phys. Lett. A 138, 474-480 (1989).
  8. R. Bhandari, "Observation of non-integrable geometric phase on the Poincaré sphere," Phys. Lett. A 157, 221-225 (1989).
  9. S. C. Tiwari, "Geometric phase in optics and angular momentum of light," J. Mol. Spectrosc. 51, 2297-2304 (2004).
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2004 (3)

S. C. Tiwari, "Geometric phase in optics and angular momentum of light," J. Mol. Spectrosc. 51, 2297-2304 (2004).

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

R. A. Bertlmann, K. Dustberger, Y. Hasegawa, and B. C. Hiesmayr, "Berry phase in entangled systems: a proposed experiment with single neutrons," Phys. Rev. A 69, 032112-032118 (2004).

2003 (1)

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

1997 (1)

D. Banerjee, "Polarization matrix and geometric phase," Phys. Rev. E 56, 1129-1134 (1997).

1993 (1)

S. J. van Enk, "Geometric phase, transformations of Gaussian light beams and angular momentum transfer," Opt. Commun. 102, 59-64 (1993).

1989 (2)

R. Simon and N. Mukunda, "Universal SU(2) gadget for polarization optics," Phys. Lett. A 138, 474-480 (1989).

R. Bhandari, "Observation of non-integrable geometric phase on the Poincaré sphere," Phys. Lett. A 157, 221-225 (1989).

1987 (1)

M. V. Berry, "The adiabatic phase and Pancharatnam phase for polarized light," J. Mod. Opt. 34, 1401-1407 (1987).

1986 (1)

S. Ramaseshan and R. Nityananda, "The interference of polarized light as an early example of Berry phase," Curr. Sci. 55, 1225-1226 (1986).

1984 (1)

M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London Ser. A 392, 45-57 (1984).

1956 (1)

S. Pancharatnam, "Generalized theory of interference and its application," Proc. Indian Acad. Sci. Sect. A 44, 247-262 (1956).

1948 (1)

1941 (1)

Bandyopadhyay, P.

P. Bandyopadhyay, Geometry, Topology and Quantization (Kluwer, 1996).

Banerjee, D.

D. Banerjee, "Polarization matrix and geometric phase," Phys. Rev. E 56, 1129-1134 (1997).

D. Banerjee, "The study of geometric phase in twisted crystal," arXiv:physics/0408068 v1 2004.

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

Berry, M. V.

M. V. Berry, "The adiabatic phase and Pancharatnam phase for polarized light," J. Mod. Opt. 34, 1401-1407 (1987).

M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London Ser. A 392, 45-57 (1984).

M. V. Berry, Proceedings of a NATO Advanced Research Workshop on Fundamental Aspects of Quantum Theory (NATO, 1985).

M. V. Berry, "Quantum adiabatic anholonomy," in Anomalies, Phases, and Defects, M. Bregola, G. Marmo, and G. Morandi, eds. (Bibliopolis, 1990).

Bertlmann, R. A.

R. A. Bertlmann, K. Dustberger, Y. Hasegawa, and B. C. Hiesmayr, "Berry phase in entangled systems: a proposed experiment with single neutrons," Phys. Rev. A 69, 032112-032118 (2004).

Bhandari, R.

R. Bhandari, "Observation of non-integrable geometric phase on the Poincaré sphere," Phys. Lett. A 157, 221-225 (1989).

Courtial, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

Crawford, R. R.

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

Dustberger, K.

R. A. Bertlmann, K. Dustberger, Y. Hasegawa, and B. C. Hiesmayr, "Berry phase in entangled systems: a proposed experiment with single neutrons," Phys. Rev. A 69, 032112-032118 (2004).

Franke-Arnold, S.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

Galvez, E. J.

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

Hasegawa, Y.

R. A. Bertlmann, K. Dustberger, Y. Hasegawa, and B. C. Hiesmayr, "Berry phase in entangled systems: a proposed experiment with single neutrons," Phys. Rev. A 69, 032112-032118 (2004).

Hiesmayr, B. C.

R. A. Bertlmann, K. Dustberger, Y. Hasegawa, and B. C. Hiesmayr, "Berry phase in entangled systems: a proposed experiment with single neutrons," Phys. Rev. A 69, 032112-032118 (2004).

Jones, R. C.

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

Mukunda, N.

R. Simon and N. Mukunda, "Universal SU(2) gadget for polarization optics," Phys. Lett. A 138, 474-480 (1989).

Nityananda, R.

S. Ramaseshan and R. Nityananda, "The interference of polarized light as an early example of Berry phase," Curr. Sci. 55, 1225-1226 (1986).

Padgett, M. J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

Pancharatnam, S.

S. Pancharatnam, "Generalized theory of interference and its application," Proc. Indian Acad. Sci. Sect. A 44, 247-262 (1956).

Pysher, M. J.

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

Ramachandran, G. N.

G. N. Ramachandran and S. Ramaseshan, Crystal Optics in Encyclopedia of Physics, S.Flugge, ed. (Springer-Verlag, 1961), Vol. 25, Part I.

Ramaseshan, S.

S. Ramaseshan and R. Nityananda, "The interference of polarized light as an early example of Berry phase," Curr. Sci. 55, 1225-1226 (1986).

G. N. Ramachandran and S. Ramaseshan, Crystal Optics in Encyclopedia of Physics, S.Flugge, ed. (Springer-Verlag, 1961), Vol. 25, Part I.

Simon, R.

R. Simon and N. Mukunda, "Universal SU(2) gadget for polarization optics," Phys. Lett. A 138, 474-480 (1989).

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

Sztul, H. I.

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

Tiwari, S. C.

S. C. Tiwari, "Geometric phase in optics and angular momentum of light," J. Mol. Spectrosc. 51, 2297-2304 (2004).

van Enk, S. J.

S. J. van Enk, "Geometric phase, transformations of Gaussian light beams and angular momentum transfer," Opt. Commun. 102, 59-64 (1993).

Vladimirski, V. V.

V. V. Vladimirski, "The rotation of a polarization plane for curved light ray." in Topological Phases in Quantum Theory, B.Markovski and S.I.Vinitsky, eds. (World Scientific, 1989).

Williams, R. E.

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

Curr. Sci. (1)

S. Ramaseshan and R. Nityananda, "The interference of polarized light as an early example of Berry phase," Curr. Sci. 55, 1225-1226 (1986).

J. Mod. Opt. (1)

M. V. Berry, "The adiabatic phase and Pancharatnam phase for polarized light," J. Mod. Opt. 34, 1401-1407 (1987).

J. Mol. Spectrosc. (1)

S. C. Tiwari, "Geometric phase in optics and angular momentum of light," J. Mol. Spectrosc. 51, 2297-2304 (2004).

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

S. J. van Enk, "Geometric phase, transformations of Gaussian light beams and angular momentum transfer," Opt. Commun. 102, 59-64 (1993).

Phys. Lett. A (2)

R. Simon and N. Mukunda, "Universal SU(2) gadget for polarization optics," Phys. Lett. A 138, 474-480 (1989).

R. Bhandari, "Observation of non-integrable geometric phase on the Poincaré sphere," Phys. Lett. A 157, 221-225 (1989).

Phys. Rev. A (1)

R. A. Bertlmann, K. Dustberger, Y. Hasegawa, and B. C. Hiesmayr, "Berry phase in entangled systems: a proposed experiment with single neutrons," Phys. Rev. A 69, 032112-032118 (2004).

Phys. Rev. E (1)

D. Banerjee, "Polarization matrix and geometric phase," Phys. Rev. E 56, 1129-1134 (1997).

Phys. Rev. Lett. (2)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric methods to measure orbital and spin or the total angular momentum of a single photon," Phys. Rev. Lett. 92, 013601-4 (2004).

E. J. Galvez, R. R. Crawford, H. I. Sztul, M. J. Pysher, and R. E. Williams, "Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum," Phys. Rev. Lett. 90, 203901-204100 (2003).

Proc. Indian Acad. Sci. Sect. A (1)

S. Pancharatnam, "Generalized theory of interference and its application," Proc. Indian Acad. Sci. Sect. A 44, 247-262 (1956).

Proc. R. Soc. London Ser. A (1)

M. V. Berry, "Quantum phase factors accompanying adiabatic changes," Proc. R. Soc. London Ser. A 392, 45-57 (1984).

Other (6)

M. V. Berry, Proceedings of a NATO Advanced Research Workshop on Fundamental Aspects of Quantum Theory (NATO, 1985).

V. V. Vladimirski, "The rotation of a polarization plane for curved light ray." in Topological Phases in Quantum Theory, B.Markovski and S.I.Vinitsky, eds. (World Scientific, 1989).

D. Banerjee, "The study of geometric phase in twisted crystal," arXiv:physics/0408068 v1 2004.

P. Bandyopadhyay, Geometry, Topology and Quantization (Kluwer, 1996).

M. V. Berry, "Quantum adiabatic anholonomy," in Anomalies, Phases, and Defects, M. Bregola, G. Marmo, and G. Morandi, eds. (Bibliopolis, 1990).

G. N. Ramachandran and S. Ramaseshan, Crystal Optics in Encyclopedia of Physics, S.Flugge, ed. (Springer-Verlag, 1961), Vol. 25, Part I.

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