Hamilton’s theory of turns and a new geometrical representation for polarization optics |
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Authors: | R Simon N Mukunda ECG Sudarshan |
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Institution: | (1) Centre for Theoretical Studies, Indian Institute of Science, 560 012 Bangalore, India;(2) Present address: The Institute of Mathematical Sciences, C.I.T. Campus, 600 113 Madras, India;(3) Department of Physics, University of Texas at Austin, 78712 Austin, Texas, USA |
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Abstract: | Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics.
While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems
are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are
both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan
geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the
solid angle on the Poincaré sphere, is established. |
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Keywords: | Polarization optics geometrical phases theory of turns Poincaré sphere Pancharatnam phase |
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