Poutrina et al. developed an analytical approach allowing to relate a particular geometry of a metamaterial unit cell incorporating nonlinear elements to the effective nonlinear susceptibilities characterizing the resulting effective medium. The approach allows the prediction, analysis, and possible enhancement of the nonlinear response of a metacrystal, exploiting and proving a long-predicted concept of the increased nonlinear response in metamaterial structures. The theory shows an excellent agreement with the experimentally retrieved parameters and thus creates a link to further practical applications in design and optimization of nonlinear metamaterial-based devices.
Analysis of nonlinear electromagnetic metamaterials, Poutrina, E., Huang D., and Smith D. R. , New Journal of Physics, Volume 12, Number 9, p.093010, (2010)