Second-order susceptibility phase matching

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

Moreover, the isolation of self-assembled LiNbOj powders using this route has added credibility to the methodology they were otherwise prepared by templating colloidal crystals of polyelectrolyte-coated spheres. The interest in LiNb03 inverse opals stems from the fact that they have a constant refractive index, but a spatially periodic second-order nonlinear susceptibility. Such nonlinear periodic structures allow for efficient qnasi-phase-matched second-order harmonic generation, which conld find applications where simultaneous conversion of multiple wavelengths is reqnired. Thns, in this chapter we will focus our... 

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