How Thin Multilayer Hyperbolic Metamaterial Can Be?

The capability to support optical waves with large wavevectors (high-k) is one of the principle features of hyperbolic metamaterials (HMMs). These waves play the key role in HMM applications such as imaging, sensing and lifetime engineering. To predict HMMs behavior a simple and convenient analytical effective medium approximation (EMA) is widely used. Theoretically, EMA is applicable to a deeply subwavelength unit cell of implicitly infinite periodic structures. So, in order to confidently use the EMA for the practical implementation HMMs, the question is what are constrains on the thickness, i.e. number of periods, of a realistic design to claim the validity of the EMA conclusions. We fabricated a series of stacks with 1, 2, … 10 periods of 10 nm gold – 10 nm alumina layers of exceptional quality keeping the roughness root mean square well below 1 nm. Characterization supported by modeling shows that starting from four periods, the multilayers properties are reasonably good expressed through EMA.