Non-linear photonic crystals enable control over quadratic non-linear optical interactions ^[1] and allow to create functional optical devices e.g. frequency converters, switches, beam shapers and optical amplifiers. However, the miniaturization of these devices is limited by the properties and ease of integration of the nonlinear crystals available in nature.

Recently a new family of nanostructured plasmonic optical materials, so-called metamaterials (MM), with artificial effective tunable nonlinearities, were demonstrated as well ^[2]. Controlling their nonlinear output can open a whole new area for potential fundamental research and development of efficient, active, integrated and ultra-compact nonlinear optical devices.

 Here we demonstrate experimentally a new family of functional metamaterial-based nonlinear photonic crystals. We use nonlinear MM based on plasmonic nano-resonators, and modulate their quadratic nonlinearity in different regions by geometric manipulations which impose π phase shift on the locally generated nonlinear signal. This modulation mimics domain inversion in conventional nonlinear photonic crystals.  We use it to demonstrate engineered nonlinear one-dimensional and two-dimensional diffraction and all-optical scanning, enabling ultra-wide angular scan of the nonlinear output from the MM. In addition we demonstrate intense focusing of the nonlinear signal directly from the MM by designing a non-linear Fresnel Zone plate, resulting in nearly two orders of magnitude enhanced intensity.

As these NLMPCs are two-dimensional, we also demonstrate by simulations an increased efficiency as a result of stacking of multiple MM layers into a three-dimensional structure, and by tuning the geometrical parameters of the structure.

[1] V. Berger, Phys. Rev. Lett. 81, 4136 (1998).

[2] M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737–748 (2012).