P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003), p. 57.

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber-optic tunable loop mirror using Berry's geometric phase," Opt. Lett. 25, 533-535 (2000).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber optic Sagnac interferometer for the observation of Berry's topological phase," J. Opt. Soc. Am. B 17, 1914-1919 (2000).

[Crossref]

R. Bhandari, "Polarization of light and topological phases," Phys. Rep. 281, 1-64 (1997).

[Crossref]

E. M. Frins and W. Dultz, "Direct observation of Berry's topological phase by using an optical fiber ring interferometer," Opt. Commun. 136, 354-356 (1997).

[Crossref]

R. Bhandari, "4π spinor symmetry-some new observations," Phys. Lett. A 180, 15-20 (1993).

[Crossref]

R. Bhandari, "Interferometry without beam splitters-a sensitive technique for spinor phases," Phys. Lett. A 180, 21-24 (1993).

[Crossref]

R. Bhandari, "Observation of Dirac singularities with light polarization--I, II," Phys. Lett. A 171, 262-270 (1992).

[Crossref]

R. Bhandari, "Evolution of light beams in polarization and direction," Physica B 175, 111-122 (1991).

[Crossref]

R. Bhandari, "Observation of nonintegrable geometric phase on the Poincaré sphere," Phys. Lett. A 133, 1-3 (1991).

[Crossref]

R. Bhandari, "SU(2) phase jumps and geometric phases," Phys. Lett. A 157, 221-225 (1991).

[Crossref]

J. Anandan, "Non-adiabatic non-abelian geometric phase," Phys. Lett. A 133, 171-175 (1988).

[Crossref]

Y. Aharonov and J. Anandan, "Phase change during a cyclic quantum evolution," Phys. Rev. Lett. 58, 1593-1596 (1987).

[Crossref]
[PubMed]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fiber," Phys. Rev. Lett. 57, 937-940 (1986).

[Crossref]
[PubMed]

R. Y. Chiao and W. S. Wu, "Manifestations of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).

[Crossref]
[PubMed]

F. Wilczek and A. Zee, "Appearance of gauge strucures in simple dynamical systems," Phys. Rev. Lett. 52, 2111-2114 (1984).

[Crossref]

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

[Crossref]

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

Y. Aharonov and J. Anandan, "Phase change during a cyclic quantum evolution," Phys. Rev. Lett. 58, 1593-1596 (1987).

[Crossref]
[PubMed]

J. Anandan, "Non-adiabatic non-abelian geometric phase," Phys. Lett. A 133, 171-175 (1988).

[Crossref]

Y. Aharonov and J. Anandan, "Phase change during a cyclic quantum evolution," Phys. Rev. Lett. 58, 1593-1596 (1987).

[Crossref]
[PubMed]

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

[Crossref]

R. Bhandari, "Polarization of light and topological phases," Phys. Rep. 281, 1-64 (1997).

[Crossref]

R. Bhandari, "4π spinor symmetry-some new observations," Phys. Lett. A 180, 15-20 (1993).

[Crossref]

R. Bhandari, "Interferometry without beam splitters-a sensitive technique for spinor phases," Phys. Lett. A 180, 21-24 (1993).

[Crossref]

R. Bhandari, "Observation of Dirac singularities with light polarization--I, II," Phys. Lett. A 171, 262-270 (1992).

[Crossref]

R. Bhandari, "Evolution of light beams in polarization and direction," Physica B 175, 111-122 (1991).

[Crossref]

R. Bhandari, "Observation of nonintegrable geometric phase on the Poincaré sphere," Phys. Lett. A 133, 1-3 (1991).

[Crossref]

R. Bhandari, "SU(2) phase jumps and geometric phases," Phys. Lett. A 157, 221-225 (1991).

[Crossref]

R. Y. Chiao and W. S. Wu, "Manifestations of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).

[Crossref]
[PubMed]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fiber," Phys. Rev. Lett. 57, 937-940 (1986).

[Crossref]
[PubMed]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber optic Sagnac interferometer for the observation of Berry's topological phase," J. Opt. Soc. Am. B 17, 1914-1919 (2000).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber-optic tunable loop mirror using Berry's geometric phase," Opt. Lett. 25, 533-535 (2000).

[Crossref]

E. M. Frins and W. Dultz, "Direct observation of Berry's topological phase by using an optical fiber ring interferometer," Opt. Commun. 136, 354-356 (1997).

[Crossref]

E. M. Frins and W. Dultz, "Direct observation of Berry's topological phase by using an optical fiber ring interferometer," Opt. Commun. 136, 354-356 (1997).

[Crossref]

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003), p. 57.

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

P. Senthilkumaran, "Berry's phase fiber loop mirror characteristics," J. Opt. Soc. Am. B 22, 505-511 (2005).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber-optic tunable loop mirror using Berry's geometric phase," Opt. Lett. 25, 533-535 (2000).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber optic Sagnac interferometer for the observation of Berry's topological phase," J. Opt. Soc. Am. B 17, 1914-1919 (2000).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber optic Sagnac interferometer for the observation of Berry's topological phase," J. Opt. Soc. Am. B 17, 1914-1919 (2000).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber-optic tunable loop mirror using Berry's geometric phase," Opt. Lett. 25, 533-535 (2000).

[Crossref]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fiber," Phys. Rev. Lett. 57, 937-940 (1986).

[Crossref]
[PubMed]

F. Wilczek and A. Zee, "Appearance of gauge strucures in simple dynamical systems," Phys. Rev. Lett. 52, 2111-2114 (1984).

[Crossref]

R. Y. Chiao and W. S. Wu, "Manifestations of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).

[Crossref]
[PubMed]

F. Wilczek and A. Zee, "Appearance of gauge strucures in simple dynamical systems," Phys. Rev. Lett. 52, 2111-2114 (1984).

[Crossref]

E. M. Frins and W. Dultz, "Direct observation of Berry's topological phase by using an optical fiber ring interferometer," Opt. Commun. 136, 354-356 (1997).

[Crossref]

P. Senthilkumaran, G. Thursby, and B. Culshaw, "Fiber-optic tunable loop mirror using Berry's geometric phase," Opt. Lett. 25, 533-535 (2000).

[Crossref]

A. Tavrov, R. Bohr, M. Totzeck, and H. Tiziani, "Achromatic nulling interferometer based on a geometric spin-redirection phase," Opt. Lett. 27, 2070-2072 (2002).

[Crossref]

J. Anandan, "Non-adiabatic non-abelian geometric phase," Phys. Lett. A 133, 171-175 (1988).

[Crossref]

R. Bhandari, "Observation of nonintegrable geometric phase on the Poincaré sphere," Phys. Lett. A 133, 1-3 (1991).

[Crossref]

R. Bhandari, "SU(2) phase jumps and geometric phases," Phys. Lett. A 157, 221-225 (1991).

[Crossref]

R. Bhandari, "4π spinor symmetry-some new observations," Phys. Lett. A 180, 15-20 (1993).

[Crossref]

R. Bhandari, "Interferometry without beam splitters-a sensitive technique for spinor phases," Phys. Lett. A 180, 21-24 (1993).

[Crossref]

R. Bhandari, "Observation of Dirac singularities with light polarization--I, II," Phys. Lett. A 171, 262-270 (1992).

[Crossref]

R. Bhandari, "Polarization of light and topological phases," Phys. Rep. 281, 1-64 (1997).

[Crossref]

R. Y. Chiao and W. S. Wu, "Manifestations of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).

[Crossref]
[PubMed]

F. Wilczek and A. Zee, "Appearance of gauge strucures in simple dynamical systems," Phys. Rev. Lett. 52, 2111-2114 (1984).

[Crossref]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fiber," Phys. Rev. Lett. 57, 937-940 (1986).

[Crossref]
[PubMed]

Y. Aharonov and J. Anandan, "Phase change during a cyclic quantum evolution," Phys. Rev. Lett. 58, 1593-1596 (1987).

[Crossref]
[PubMed]

R. Bhandari, "Evolution of light beams in polarization and direction," Physica B 175, 111-122 (1991).

[Crossref]

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

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

[Crossref]

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003), p. 57.

After submitting this manuscript we became aware of the work of Tavrov et al. , in which they use the geometric spin redirection phase due to out-of-plane propagation of light to realize an achromatic π-phase shift between the two beams of an astronomical interferometer for "nulling interferometry." In our judgement, the linear phase shift between the beams for circular polarization shown in Fig. 2(a) and the highly nonlinear phase shift for linear polarization shown in Fig. 2(b) of their paper correspond approximately to the curves A and C shown in Fig. of this paper.

When the Jones matrix of a halfwave plate is written without the factor i as done in and in some texbooks on optics, it implies an isotropic phase factor exp(±iπ/2) multiplying the SU(2) part. This must be removed before applying the considerations of Section .