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Physical Review A

Density Operator of Unpolarized Radiation

Hari Prakash, Naresh Chandra

Published Aug 1, 1971• 67 citations
Publisher

Abstract

The general form of the density operator for unpolarized radiation is obtained. It is shown that if two orthogonally polarized components of unpolarized radiation are statistically independent, the radiation is necessarily chaotic. It is also shown that the procedure currently being used for studying interactions of unpolarized radiation is not correct, and that Stokes's parameters do not correctly specify the unpolarized state of radiation.

DOI
10.1103/physreva.4.796

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American Journal of Physics•May 1, 1970•52 citations
The general form of the density operator for unpolarized radiation is obtained. It is shown that if two orthogonally polarized components of unpolarized radiation are statistically independent, the radiation is necessarily chaotic. It is also shown that the procedure currently being used for studying interactions of unpolarized radiation is not correct, and that Stokes's parameters do not correctly specify the unpolarized state of radiation.
We give a general definition of unpolarized light that rests on invariance properties rather than specific values of second-order field correlations or, equivalently, the Stokes parameters. It turns out that to require invariance with respect to rotation around the propagation axis and symmetry with respect to left- and right-handed circular polarization is not sufficient to fully characterize completely unpolarized light, such as natural light. Actually, a third requirement demanding invariance with respect to phase retardation is needed. Depending on whether it is satisfied or not, we speak of type I or type II unpolarized light, and we specify the general form of both classical distribution functions and density operators consistent with the respective conditions. \textcopyright{} 1996 The American Physical Society.
The mathematical structures of the theories of a two-level atom interacting with radiation and an electromagnetic wave interacting with a dielectric medium in which it is propagated as a plane wave are identical. The spin structure of the Jones operator in optics representing the polarizer, is obtained in its general form in terms of Stokes parameters and identified with the optical density operator with a spin structure identical with the density operator in the quantum mechanics of the atom. While the quantum dynamical equation of the atom can be reduced to the gyroscopic form, the correspondence law giving expression to the parallelism of the two processes leads to forms of the dynamical law in topics which are identical with those of the quantum theory of the atom.