Polarization of light: Fourth-order effects and polarization-squeezed states

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Abstract
The polarization properties of a monochromatic beam of light are ordinarily determined by three numbers, for example, the Stokes parameters. However, three numbers are no longer sufficient when intensity fluctuations in the polarized modes (or the correlation between them) are recorded. It is shown that in this case nine parameters, which can be arranged into 3×3 matrices, must be prescribed. The transformation properties of these matrices under polarization converters and the invariants of the matrices are analyzed. Specifically, the fourth-order polarization P 4 is introduced. Several examples are examined of light with “hidden” polarization—light which is not polarized in the ordinary sense (P 2=0) but is polarized in fourth order (P 4≠0)—as well as “polarization-squeezed” light in which the quantum fluctuations of the Stokes parameters are suppressed.

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