#### Document Type

Article

#### Publication Date

10-13-2011

#### Abstract

The 3×1 generalized Jones vectors (GJVs) [ExEyEz]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 Es=T Ei , is briefly introduced. In such a matrix transformation, Ei and Es 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.

#### Journal Name

Journal of the Optical Society of America A

#### Recommended Citation

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

## Comments

This paper was published in

Journal of the Optical Society of America Aand is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-11-2279. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.