Second-order nonlinear processes such as second-harmonic generation (SHG) require noncentrosymmetric structures. The development of second-order metamaterials, however, has been hampered by symmetry breaking due to sample defects and shape distortions. The resulting outcomes can be interpreted in terms of effective higher-multipole (magnetic and quadrupole) effects that strongly modify the radiative properties of the samples.
Czaplicki, R., Husu, H., Zdanowicz, M., Koskinen, K., Siikanen, R., Kauranen, M., Laukkanen, J., Lehtolahti, J., & Kuittinen, M. (2012). Metamaterials with tailorable nonlinear optical properties. Optics and Photonics News, 23(12), 34. https://doi.org/10.1364/OPN.23.12.000034