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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 11 — Nov. 1, 2011
  • pp: 2279–2283

Three-dimensional polarization states of monochromatic light fields

R. M. A. Azzam  »View Author Affiliations

JOSA A, Vol. 28, Issue 11, pp. 2279-2283 (2011)

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The 3 × 1 generalized Jones vectors (GJVs) [ E x E y E z ] t (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3 × 3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E s = T E i , is briefly introduced. In such a matrix transformation, E i and E s are the 3 × 1 GJVs of the incident and scattered waves and T is the 3 × 3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.

© 2011 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(260.5430) Physical optics : Polarization
(260.6970) Physical optics : Total internal reflection
(350.7420) Other areas of optics : Waves

ToC Category:
Physical Optics

Original Manuscript: July 14, 2011
Revised Manuscript: September 14, 2011
Manuscript Accepted: September 16, 2011
Published: October 13, 2011

R. M. A. Azzam, "Three-dimensional polarization states of monochromatic light fields," J. Opt. Soc. Am. A 28, 2279-2283 (2011)

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