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The coupled-wave equations of three-wave interactions are generalized into three dimensions. The reciprocal lattice vectors (RLVs) of three-dimensional (3D) nonlinear photonic crystals (NPCs) which show some unique properties are analyzed in detail as compared to those in one- and two-dimensional cases. It is proposed as an example that the cross-distributing conical harmonic beams can be obtained from the 3D NPC by intentionally using the proper RLVs. Some other possible applications are suggested at the end of discussion.
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Chen et al. (2009) studied this question.
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