In this paper we review metamaterials fabricated from self-rolling strained metal-semiconductor layer systems. These systems relax their strain upon release from the substrate by rolling up into microtubes with a cross-section similar to a rolled-up carpet. We show that the walls of these microtubes represent three-dimensional optical metamaterials which so far could be used, for example, for the realization of broadband hyperlenses, fishnet metamaterials, or optically active three-dimensional metamaterials utilizing the unique possibility to stack optically active semiconductor heterostructures and metallic nanostructures. Furthermore, we discuss THz metamaterials based on arrays of rolled-up metal semiconductor microtubes and helices. 1. Introduction While the concept of metamaterials, that is, tailoring the optical properties of a material to desired values by cleverly designing its subwavelength composites, is in principle scalable in frequency, the realization of three-dimensional metamaterials for optical frequencies remains one of the current challenges in the research area of metamaterials [1, 2]. Compared to the fabrication used in the pioneering works on metamaterials operating in the microwave regime [3–6], which were composed of millimeter-sized metallic structures produced with well-established printed circuit board techniques, the deliberate structuring on the nanoscale in three dimensions for the production of three-dimensional optical metamaterials is much more elaborate. Possible routes are, for example, stacking of single-layered metamaterials by repeating planar lithographic processing steps [7], focused ion beam milling of multilayers [8], multilayer deposition on patterned substrates [9, 10], galvanization in combination with three-dimensional laser interference lithography [11], or galvanization in combination with anodic oxidation [12]. Here we discuss three-dimensional metamaterials prepared by rolling up a single-layered metamaterial with multiple rotations into a radial stack, similar to rolling up a bilayer of biscuit and cream into a Swiss-roll cake. One possibility to follow this route is actively rolling up the layer system as demonstrated by Gibbons and colleagues, who rolled up a gold-polymer bilayer around a millimeter-sized glass rod and obtained a high quality radial multilayer system [13]. Another possibility is utilizing the concept of strain induced self-rolling of nanolayers which was pioneered by Prinz and coworkers for the InGaAlAs semiconductor system [14, 15] and since then adopted to various kinds of material
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