Ellipsometric Identification of Transition from a Layered Metal-Dielectric Film to a Hyperbolic Metamaterial

Hyperbolic metamaterials (HMMs) continue to be intriguing due to their applications in super-resolution imaging and spontaneous emission control. One of the successful realizations of HMMs is a layered metal-dielectric film. Despite the extensive knowledge in thin-film technology and the promises of HMM's applications, the scale-up and practical utilization of HMMs have not yet occurred. A general design approach is needed to predict the transition of a layered structure into an HMM. In this work, effective medium theory and the transfer matrix method are combined to determine the transition and validated by spectroscopic ellipsometry measurements on a predefined HMM structure made of silver and alumina. Four interdependent design parameters are explored: thicknesses of metal and dielectric layers, transition wavelength, and the minimum number of periods required for a layered metal-dielectric film to display hyperbolic dispersion. The findings are presented as a practical engineering design chart, similar to a state diagram, which can be extended to other combinations of materials.