Zero-index metamaterials (ZIMs) offer exotic optical properties such as uniform spatial phase and infinite wavelength, as well as photonic applications including super-coupling and omnidirectional phase matching in nonlinear optics.
Here we present an on-chip ZIM consisting of a square array of air-holes in a 220-nm-thick silicon-on-insulator (SOI) wafer. This design enables mass production of ZIM-based photonic devices at low cost and high fidelity using standard CMOS fabrication technology.
To transition from the high-aspect ratio inverse case of silicon pillars under transverse magnetic (TM) polarization, our design is instead intended for a transverse electric (TE) polarization because of TE modes are, in general, better confined than TM modes for a given thin film. Furthermore, the larger volume fraction of silicon provided by the air-holes structure improves the confinement as compared with the silicon-pillars structure. We optimized the design to obtain a zero index corresponding to a finite impedance of 0.8 at 1550 nm. The bandstructure of the metamaterial shows a Dirac-cone dispersion at the center of the Brillouin zone at 1550 nm. These results indicate that this metamaterial possesses an impedance-matched, isotropic zero index at 1550 nm.
To experimentally verify that the metamaterial has a zero index, we fabricated a right-triangular prism measuring twenty unit cells across. The measured effective index of this prism crosses zero linearly at 1630 nm and shows positive and negative indices at short and longer wavelengths, respectively, indicating a Dirac-cone induced zero index. This measurement is in excellent agreement with the result of full-wave simulation.