Second order nonlinear processes in photonic crystals

We show that the second order parametric nonlinear interaction from waves that are counter propagating may be perfectly phase matched in the framework of a photonic crystal. We observe that the large momentum mismatch of such parametric process is compensated because of the interfaces present in the nonlinear photonic crystal considered, which separate a linear from a nonlinear material. The numerical results presented indicate that such nonlinear photonic crystals could be a very good material to consider the observation of backward parametric oscillation without mirror feedback. In the search for a material capable of holding such type of oscillation, we have performed second harmonic generation experiments using several nonlinear colloidal crystals. We compared the efficiency between such different nonlinear crystals obtained by binding different types of organic nonlinear molecules onto the surface of a polystyrene particle.