Discriminating States of Polarization

Equiprobable incoherent mixtures of two totally polarized states of light whose associated three-dimensional Jones vectors are mutually orthogonal are called discriminating states and constitute a peculiar type of state that plays a key role in the characteristic decomposition of a generic state into a totally polarized state, a totally unpolarized state, and a discriminating state. In general, discriminating states are three-dimensional, in the sense that the strengths of the three components of the electric field are nonzero for any Cartesian reference frame considered. In the limiting case that the electric field evolves in a fixed plane, the discriminating state is said to be regular and corresponds to a two-dimensional unpolarized state. The special features of discriminating states cover, e.g., their possible synthesis from infinite pairs of mutually orthogonal states as well as their transverse spin. The nature and properties of discriminating states are comprehensively analyzed based on their associated intrinsic Stokes parameters, which leads to meaningful interpretations in terms of the associated polarization ellipsoids and spin vectors.