Substrate-thickness dependence of negative-index metamaterials at optical frequencies

Optical metamaterials have attracted intensive attention in recent years for their broad applications in superlenses, electromagnetic cloaking, and bio-sensing. Negative refractive index (NRI) metal-dielectric-metal fishnet metamaterials (MMs) are typically used for beyond-diffraction-limit imaging. However, there are few reports about the substrate-thickness dependence of NRI, which strongly affects the practical application. In our study, it is demonstrated that the membrane-based NRI MMs with a more negative index work better than the bulk substrate-based counterparts. In addition, a regular periodic vibration of NRI with the thickness of the membrane substrate was theoretically studied. The destructive interference of the thin film can explain this phenomenon. Furthermore, the proposed explanation was further proved by substituting the dielectric spacer with a larger permittivity. Therefore, an NRI structure on a membrane substrate with constructive interference can be a good choice in ultra-compact photoelectronic devices. This study can be a guide to the practical application of ultracompact NRI devices.