The Importance of Surface Roughness on The Reflection from Epsilon-Near-Zero Substrates

Recent multiple applications and characteristics related to epsilon-near-zero (ENZ) media at infrared, visible and even ultraviolet frequencies have positioned them as a very active field of research. The performance of ENZ technologies is ultimately limited to material loss, which has been studied in detail, and the impact of surface roughness, which has attracted much less attention. In this work, the reflectivities of several silicon carbide (SiC) samples with different levels of artificially-induced roughness have been investigated numerically and experimentally. Samples have been treated via deep reactive ion etching (DRIE), and subsequently measured with a Fourier transform infrared spectroscopy (FTIR) microscope. The posterior characterization of the surface roughness of the samples focuses on the measurements made via atomic force microscopy (AFM).<br/><br/>Due to the dispersion of SiC, our samples enable a direct comparison of the impact of surface roughness on ENZ media, plasmonic-like systems and dielectric media, all within the same sample. The smoothest samples reveal near-perfect reflective behaviours, while the samples with more level of roughness shows a heavy decrease of the reflectivity, especially in the region between 10.3 μm and 12.55 µm. As a polar dielectric, its response at infrared frequencies exhibits this reflection band defined by the longitudinal and transversal optical phonons and a negative permittivity, it has been named Reststrahlen Band. Roughly, lower negative permittivities allow plasmonic-type effects, such as surface phonon polaritons. In consequence, the reflection band is strongly affected by the roughness. As long as the permittivity reaches high negative values, which are related to smaller skin-depths leading to hard interaction, this influence of the surface wave phenomena is decreased. The dielectric zone and the ENZ point (ε=0) are affected as well. However, it is found that the ENZ range is particularly robust against surface roughness.<br/><br/>We numerically validate our conclusions by using the full-wave solver Comsol Multiphysics. In a first approximation, the surface roughness was characterized by the sum of three waves and subsequently averaged with different periods in transversal electric (TE) polarization. Secondly, 15 AFM profiles were introduced manually and later their reflectivities calculated and averaged. Both calculations show a very precise approach to the measured reflectivities.