EXPERIMENTAL-DETERMINATION OF A TOPOLOGICAL INVARIANT IN A PATTERN OFOPTICAL SINGULARITIES

Topological invariants which control the organization and the evolutio n of ensembles of singularities may be evidenced in-optical caustics. Our physical model is the optical pattern produced by light deflected through a nematic liquid crystal. We determine experimentally the Eule r number of the critical set associated with the caustic and we identi fy the umbilics. We develop a method that enables us to determine the index of the umbilics and to distinguish between the two types of hype rbolic umbilics. We are then able to check, for the first time, the va lue of the topological invariant predicted by the recent Chekanov theo ry.