Broadband operation of rolled-up hyperlenses

This work is related to an earlier publication [Schwaiger et al., Phys. Rev. Lett. 102, 163903 (2009)], where we demonstrated by means of fiber-based transmission measurements that rolled-up Ag-(In)GaAs multilayers represent three-dimensional metamaterials with a plasma edge which is tunable over the visible and near-infrared regime by changing the thickness ratio of Ag and (In)GaAs, and predicted by means of finite-difference time-domain simulations that hyperlensing occurs at this frequency-tunable plasma edge. In the present work we develop a method to measure reflection curves on these structures and find that they correspond to the same tunable plasma edge. We find that retrieving the effective parameters from transmission and reflection data fails, because our realized metamaterials exceed the single-layer thicknesses of $5\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, which we analyze to be the layer thickness limit for the applicability of effective parameter retrieval. We show that our realized structures nevertheless have the functionality of an effective metamaterial by supplying a detailed finite-difference time-domain study which compares light propagation through our realized structure (17-nm-thick Ag layers and 34-nm-thick GaAs layers) and light propagation through an idealized structure of the same total thickness but with very thin layers [2-nm-thick Ag layers and 4-nm-thick (In)GaAs layers]. In particular, our simulations predict broadband hyperlensing covering a large part of the visible spectrum for both the idealized and our realized structures.