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Cheng Zhang1 Nina Hong2 Chengang Ji3 Wenqi Zhu1 Xi Chen3 Amit Agrawal1 Zhong Zhang3 Tom E. Tiwald2 Stefan Schoeche2 James N. Hilfiker2 L. Jay Guo3 Henri J. Lezec1

1, National Institute of Standards and Technology, Gaithersburg, Maryland, United States
2, J. A. Woollam Co., Lincoln, Nebraska, United States
3, University of Michigan-Ann Arbor, Ann Arbor, Michigan, United States

Hyperbolic metamaterials (HMMs) are highly anisotropic structures that exhibit metallic (i.e., Re (ε) < 0) and dielectric (i.e., Re (ε) > 0) response along orthogonal directions. They have been utilized to demonstrate various phenomena, including broadband light absorption, enhanced spontaneous emission, asymmetric light transmission, engineered thermal radiation, and sub-diffraction imaging. The key to the array of rich phenomena enabled by HMMs is their highly anisotropic permittivity. HMMs reported to date are often described by numerically calculated permittivity tensors based on effective medium theory (EMT), which utilizes constituent metal and dielectric permittivities reported in the literature or measured by spectroscopic ellipsometry. However, the accuracy of calculation is limited by the known precision of experimental layer thicknessness and local permittivities, as well as non-modelled effects such as layer roughness, strain, and inter-layer diffusion.

In this work, we demonstrate how both the in-plane and out-of-plane effective permittivities of an HMM operating at ultraviolet, visible, and near-infrared frequencies can be accurately extracted using a coupling-prism-enabled spectroscopic ellipsometry technique based on total internal reflection (TIR). For reference, this technique is compared to two other spectroscopic ellipsometry methods commonly used to date for HMM characterization, namely (1) interference enhancement (IE), in which reflection-mode ellipsometry exploits a substrate decorated with a silicon oxide layer to enhance light-HMM interaction, and (2) reflection plus transmission (R+T), which adds normal-incidence transmittance spectroscopy to standard reflection-mode ellipsometry. Although both IE and R+T techniques have been successfully used for characterizing isotropic thin absorbing films, we show here that neither method is able to robustly extract HMM out-of-plane effective permittivity. In contrast, the TIR method is demonstrated to provide robust permittivity extraction having well-converged fitting parameters. In particular, measurement sensitivity is improved compared to both the IE and R+T cases via prism-mediated enhancement of the out-of-plane electric field inside the HMM. The TIR technique requires neither modification of the HMM sample itself nor substantial re-configuration of a standard ellipsometer, and can therefore serve as a reliable and easy-to-adopt technique for the characterization of both HMMs and a variety of other anisotropic metamaterials.

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