Parameters for polarization gradients in three-dimensional electromagnetic standing waves

The electric field polarization structure of three-dimensional monochromatic electromagnetic fields is investigated, with particular reference to the three-dimensional standing waves that are commonly used in laser cooling. Two parameters are introduced for describing the polarization at a field point, one of which is a generalization of the Stokes ellipticity parameter while the other describes the rotation of linear polarization (or the polarization ellipse) for small displacements. The two parameters are shown to be simply related to the density and flux of intrinsic angular momentum (spin) in the field. Additional parameters are introduced to provide measures of the polarization gradients on straight line trajectories in three-dimensional standing waves and the implications for laser cooling are discussed.