Signal representation on the angular Poincaré sphere, based on second-order moments

摘要

Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensionalnoptical signal is proposed, which is associated with the angular Poincaré sphere. Vortex-free (or zero-twist)noptical beams arise on the equator of this sphere, while beams with a maximum vorticity (or maximum twist)nare located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for thendegree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beamnpropagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, ansystem that does not operate between conjugate planes is needed, with the gyrator as the prime representativenof such a system. A direct way is derived to find an optical system (consisting of a lens, a magnifier, a rotator,nand a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form. © 2010 OpticalnSociety of America