Light beams with general direction and polarization: Global description and geometric phase
We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S{sup 2} of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S{sup 2}×C{sup 2}∖(0), the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S{sup 2}×S{sup 2} which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana’s mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP{sup 2}, two dimensional complex projective space, which does notmore »
 Authors:

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 TIFR Centre for Interdisciplinary Sciences, 21, Brundavan colony, Narsingi, Hyderabad 500 089 (India)
 (India)
 Raman Research Institute, Sadashivanagar, Bangalore 560 080 (India)
 Publication Date:
 OSTI Identifier:
 22233547
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Annals of Physics (New York); Journal Volume: 341; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; BEAMS; DIAGRAMS; FOURDIMENSIONAL CALCULATIONS; GEOMETRY; INTEGRALS; MONOCHROMATIC RADIATION; POLARIZATION; SPACE; SPIN; STOKES PARAMETERS; VECTORS