Nonunitary squeezing and biorthogonal scalar products in polarization optics

Abstract

The polarization vectors of monochromatic electromagnetic fields can be transformed by multiplying them by 2 ? 2 matrices representing, respectively, retardation plates, rotators and partial polarizers. The present description of partial polarizers is related to a two-dimensional Lorentz algebra SU(1,1) leading to nonunitary squeezing as the present SU(1,1) algebra includes non-Hermitian operators in addition to the Hermitian ones. The present analysis exploits the use of similarity transformations which are more general than the unitary transformations used usually in quantum mechanics. By performing a similarity transformation on a set of Hermitian physical operators the transformed operators are Hermitian with respect to new scalar product defined by the use of a new metric. It is shown that such transformations can be implemented experimentally by the use of polarization optics and the metric obtained in such transformations is analysed.