We present a theory which explains how to achieve an enhancement of nonlinear effects in a thin layer of nonlinear medium by involving a planar periodic structure specially designed to bear a trapped-mode resonant regime. In particular, the possibility of a nonlinear thin metamaterial to produce the bistable response at a relatively low input intensity due to a large quality factor of the trapped-mode resonance is shown. Also a simple design of an all-dielectric lowloss silicon-based planar metamaterial which can provide an extremely sharp resonant reflection and transmission is proposed. The designed metamaterial is envisioned for aggregating with a pumped active medium to achieve an enhancement of quantum dots luminescence and to produce an all-dielectric analog of a 'lasing spaser'.Keywords: metamaterial, trapped-mode, nonlinear optics, bistability, luminescence
IntroductionOne of the current trends in the theory of metamaterials is the development of two-dimensional planar periodic systems (metasurfaces, metamaterials) constructed in the form of arrays of resonant metallic or dielectric particles, which are arranged periodically on a thin (compared with the wavelength) dielectric layer. It is known that such planar metamaterials can create an environment whose electromagnetic characteristics are similar to those achieved in the traditional cavity resonators, but, unlike the latter, planar structures can have a much smaller size.