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Phase conjugation and four-wave mixing in a colloidal medium

We demonstrate phase conjugation by means of degenerate four-wave mixing from a colloidal crystal. The nonlinear medium is provided by a periodic spatial refractive index grating created in a colloidal suspension of dielectric microparticles trapped in the intensity distribution of two nearly copropagating interfering laser beams. Phase conjugation is achieved for a probe beam carrying orbital angular momentum as evidenced by the inversion of the topological charge of a phase singularity within the beam. The e ciency and nonlinear parameters of the colloidal crystal as well as its lattice properties are measured and compared to theoretical predictions and previous experimental work.