2, RWTH Aachen University, Aachen, , Germany
Polaritons in materials with free charge carriers (surface plasmon polaritons) or polar optic phonons (surface phonon polaritons) offer a route to beating the diffraction limit for compact mid- and far-infrared optoelectronics. The latter of these two quasi-particles has received intense scrutiny in recent years due to inherently low losses from phonon scattering, albeit at the limitation of relatively low spectral tunability. One particularly interesting class of polaritons are hyperbolic modes – which occur in highly anisotropic crystals, such as the 2D materials or artificial layered metamaterials. This phenomenon arises from the layered structure, with significantly different vibrational energies in- and out-of-plane directions. The techniques that have been used to study these modes involve nano-structuring, scattering type scanning nearfield optical microscopy (s-SNOM) and photothermal induced resonance (PTIR) techniques. Whilst highly successful these techniques have drawbacks, such as the complex effect of scattering from a nanoscale particle or tip which makes data analysis complex. As a result, accurately measuring the dielectric response of 2D crystals Is extremely difficult using these techniques, but the small size of samples precludes the use of infrared spectroscopic ellipsometry. Here we discuss how prism coupling techniques can be used to measure hyperbolic polaritons and extract dielectric function data from two dimensional crystals.
Specifically, we discuss how the choice of appropriate substrate is critical for successful measurements on two dimensional crystals such as hexagonal boron nitride. Prism coupling requires attenuated total reflection (ATR) between the boundary and substrate, but many low-index materials are not suitable for 2D material preparation. By using a combination of simulations and experiments, we show that by thickening the Si/SiO2 layers conventionally used for mechanical exfoliation of two dimensional materials, we can measure ATR spectra even on high index Si. The measured response is highly sensitive to the thickness of the flakes, as predicted by the dispersion of hyperbolic modes. Specifically, we are able to observe multiple dips in reflection, corresponding to different modes of identical wavevector. Finally, we comment on the repeatability of this technique under both varied measurement and different exfoliation conditions, including the importance of substrate adhesion. One major advantage of this approach is that by using an appropriate prism it is possible to access frequencies that are difficult to measure using both s-SNOM and PTIR techniques (for example the far-IR, where laser sources are limited). Furthermore, by comparison with numerical simulations it is possible to extract dielectric data, like spectroscopic ellipsometry. This can then inform the design of nanostructures to create efficient far-IR thermal emitters and optical components.