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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Diagonal coherent-state representation for polarized light

C. L. Mehta, Manoj Kumar Sharma

Published Oct 15, 1974• 14 citations
Publisher

Abstract

We consider the transformation properties of the density operator as well as its diagonal coherent-state representation when a plane monochromatic light is passed through a compensator followed by a rotator. Special cases of unpolarized and polarized light are considered and the general form of the density operator and its coherent-state representation is determined.

DOI
10.1103/physrevd.10.2396

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Presented at•Jan 1, 2003•1 citation
We consider the transformation properties of the density operator as well as its diagonal coherent-state representation when a plane monochromatic light is passed through a compensator followed by a rotator. Special cases of unpolarized and polarized light are considered and the general form of the density operator and its coherent-state representation is determined.
By making use of the diagonal coherent state representation of an optical field, together with the operator relations between dynamic variables at the input and output of a beam splitter, we have derived a general relation between density operators of input and output states. As an illustration of the general procedure we consider two orthogonally polarized photons at the beam splitter input and derive the output state. We show that in the special case in which the reflectivities and transmissivities of the beam splitter are equal, this state exhibits certain features of the well-known singlet state for orthogonally polarized photons.
The invariance properties of the double-integral and diagonal representations of operators in terms of the coherent states are examined. It is shown that a unique diagonal representation always exists for bounded operators, hence for every density operator, and for unbounded operators which are polynomials in the boson creation and annihilation operators. The associated weight function $P(\ensuremath{\alpha})$ is a generalized function in the space ${Z}^{\ensuremath{'}}$. The physical significance of this result is discussed, with particular emphasis on the diagonal representation of the density operator of arbitrary radiation fields. A general formula for the weight function $P(\ensuremath{\alpha})$ is derived and is used to calculate the particular form of the weight function for several radiation fields of interest.
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.