Coupling of reciprocal vectors and corresponding degeneracy effect in a dual-periodic optical superlattice

A dual-periodic structure for quasi-phase matching cascaded optical parametric interactions is proposed. Due to the coupling of reciprocal vectors between the original and imposed periodic sequence, the reciprocal vectors and the corresponding effective nonlinear coefficients is no longer the simple combination of two periodic structures. The new analytical expression of the effective nonlinear coefficients is deduced and given. The degeneracy phenomena and the novel extinction rule resulting from the coupling of reciprocal vectors are found and investigated. The corresponding physical nature is also discussed.