Bounds for the degree of polarization.

A quantity of considerable interest in studies of polarized light is the degree of polarization of a beam of radiation. Every transformation of Stokes parameters described by a Mueller matrix may change the degree of polarization. The nature of this change, however, is not so obvious (see, e.g., Ref. 1). The main purpose of this Letter is to present simple upper and lower bounds for the change of the degree of polarization of a beam that occurs on interaction with matter, as described by a Mueller matrix. Such bounds can be used for testing optical devices and numerical techniques. We consider a quasi-monochromatic beam of radiation with Stokes parameters I , Q, U , and V (see, e.g., Refs. 2 and 3). We write these Stokes parameters as elements of a column vector I, called the Stokes vector, and define the degree of polarization as