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Eigenmodes of X((2)) wave mixings: cross-induced second-order nonlinear refraction.

Eigenmodes of three-wave interactions in second-order [X((2))] nonlinear materials are explored that have a noenergy-exchange property between all the waves. They are shown to exhibit cross-induced nonlinear refraction and to be ideal candidates for amplitude-dependent phase control in X((2)) materials that emulate nonlinear refractive-index effects in third-order [X((3))] materials. It is shown that all these eigenmodes are spatially stable.