Abstract
We describe anon-abelian Berry phase in polarization optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarized light. The analogy permits a simple optical realization of the non-abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.
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References
M V Berry,Proc. R. Soc. A392, 45 (1984)
F Wilczek and A Zee,Phys. Rev. Lett. 52, 2111 (1984)
Y Aharonov and J Anandan,Phys. Rev. Lett. 58, 1593 (1987)
J Samuel and R Bhandari,Phys. Rev. Lett. 60, 2339 (1988)
A Shapere and F Wilczek,Geometric phases in physics (World Scientific, Singapore, 1989)
R Bhandari and J Samuel,Phys. Rev. Lett. 60, 211 (1988)
R Simon, H J Kimble and E C G Sudarshan,Phys. Rev. Lett. 61, 19 (1988)
T H Chyba, L J Wang, L Mandel and R Simon,Opt. Lett. 13, 562 (1988)
P Hariharan and M Roy,J. Mod. Opt. 39, 1811 (1992)
M V Berry and S Klein,J. Mod. Opt. 43, 165 (1996)
P Hariharan, Hema Ramachandran, K A Suresh and J Samuel,The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections RRI-96-18,J. Mod. Opt. (to appear)
H Mathur,Phys. Rev. Lett. 67, 3325 (1991)
R Shankar and H Mathur,Phys. Rev. Lett. 73, 1565 (1994)
J Samuel,Phys. Rev. Lett. 76, 717 (1996)
L H Thomas,Philos. Mag. 3, 1 (1927)
J D Jackson,Classical electrodynamics (Wiley Eastern Limited, New Delhi, 1978)
H Urbantke,Am. J. Phys. 58, 747 (1990)
R Penrose and W Rindler,Spinors and Spacetime (Cambridge University Press, Cambridge, 1984) vol. I
See the remark attributed to R Nityananda on page 245 in the article by S Ramaseshan inEssays on Particles and Fields edited by R R Daniel and B V Sreekantan (Indian Academy of Sciences, Bangalore, 1989)
G N Ramachandran and S Ramaseshan, Crystal Optics inHandbuch der Physik (Springer, Berlin, 1961) vol. 25, part I
If one forms the (impure) density matrixρ=u 0+u.σ, the components (u 0, u) have an optical interpretation in terms of the Stokes [19] parameters (I, Q, U, V) of a partially polarized light beam described by that density matrix
S Pancharatnam,Proc. Indian Acad. Sci. A44, 247 (1956); reprinted inCollected works of S Pancharatnam (Oxford University Press, London, 1975)
S Ramaseshan and R Nityananda,Curr. Sci. (India) 55, 1225 (1986)
M V Berry,J. Mod. Opt. 34, 1401 (1987)
G S Ranganath, K A Suresh, S R Rajagopalan and U D Kini,Pramana Special Supplement 1, 353 (1975)
M Kitano and T Yabuzaki,Phys. Lett. A142, 321 (1989)
A Zee,Phys. Rev. A38, 1 (1988)
R Tycko,Phys. Rev. Lett. 58, 2281 (1987)
M V Berry,J. Phys. A18, 15 (1985)
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Samuel, J., Sinha, S. Thomas rotation and polarized light: A non-abelian geometric phase in optics. Pramana - J Phys 48, 969–975 (1997). https://doi.org/10.1007/BF02847456
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DOI: https://doi.org/10.1007/BF02847456