DISCRETE SUPERPOSITIONS OF COHERENT STATES AND PHASE PROPERTIES OF ELLIPTICALLY POLARIZED-LIGHT PROPAGATING IN A KERR MEDIUM

The problem of the formation of discrete superpositions of coherent states when elliptically polarized light is propagating through a nonlinear Kerr medium is considered. It is shown that superpositions with any number of components can be obtained if the evolution time is taken as a fraction M/N of the period, where M and N are mutually ′ integers. Exact analytical formalae for finding the superposition coefficients are given. It is shown that the coupling between the two circularly polarized components of the elliptically polarized light caused by the asymmetry of the nonlinear properties of the medium can suppress the number of components in the superposition from N2 to N, if the asymmetry parameter takes appropriate values. The phase distribution function P( theta +, theta -) for the two-mode field is obtained according to the new Pegg-Barnett phase formalism. This function exhibits a well resolved, multi-peak structure clearly indicating the formation of the discrete superpositions of coherent states. Examples of the phase distribution function for several superposition states are illustrated graphically, showing in a very spectacular way the formation of such superpositions.