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On the limits of the effective description of hyperbolic materials in presence of surface waves

Hyperbolic materials are artificially engineered composite media which allow innovative optical properties that could lead to significant advances in numerous breakthrough technologies. However, these properties are conventionally studied by means of an effective medium theory. But this one is specifically well adapted to describe the optical behaviour of composite materials in the far field region. Here, we adress the question of the validity of such an approach in the near field region. We show that the presence of localized modes such as resonant surface waves drastically limits the validity of the effective description and requires revisiting the concept of homogenization in near-field. In particular we demonstrate from exact calculations that one can find surface modes in spectral regions where the effective medium theory predicts hyperbolic modes only. Hence, the presence of surface modes which are not accounted for in the effective medium theory can lead to physical misinterpretations in the description of hyperbolic materials and their related properties.