Hamilton’s theory of turns and a new geometrical representation for polarization optics
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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.
KeywordsPolarization optics geometrical phases theory of turns Poincaré sphere Pancharatnam phase
PACS Nos42·10 02·20 42·78
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