Rolled-Up Three-Dimensional Metamaterials with a Tunable Plasma Frequency in the Visible Regime Stephan Schwaiger, Markus Bro ¨ll, Andreas Krohn, Andrea Stemmann, Christian Heyn, Yuliya Stark, Daniel Stickler, Detlef Heitmann, and Stefan Mendach * Institut fu ¨r Angewandte Physik und Zentrum fu ¨r Mikrostrukturforschung, Universita ¨t Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany (Received 20 October 2008; revised manuscript received 30 January 2009; published 24 April 2009) We propose and realize a novel concept of a self-organized three-dimensional metamaterial with a plasma frequency in the visible regime. We utilize the concept of self-rolling strained layers to roll up InGaAs=GaAs=Ag multilayers with multiple rotations. The walls of the resulting tubes represent a radial superlattice with a tunable layer thickness ratio and lattice constant. We show that the plasma frequency of the radial superlattice can be tuned over a broad range in the visible and near infrared by changing the layer thickness ratio in good agreement with an effective metamaterial description. Finite difference time domain simulations reveal that the rolled-up radial superlattices can be used as hyperlenses in the visible. DOI: 10.1103/PhysRevLett.102.163903 PACS numbers: 42.70.a, 78.67.n Metamaterials based on artificial building blocks with a size and lattice constant smaller than the wavelength of the transmitted electromagnetic waves have gained consider- able interest in the science community since the beginning of this century. Many new effects, e.g., negative refraction, superlensing, or object cloaking, have been demonstrated for metamaterials working in the microwave regime [1–5]. To explore the visible regime it is required that the artificial building blocks be scaled down to the order of 100 nm. Commonly planar lithographic techniques are used to ob- tain such small dimensions [6–8]. To construct three- dimensional materials, the planar processing step is re- peated until the desired thickness is obtained [9,10]. Hyperlenses [11,12] for ultraviolet light have been created by using this sequential method for alternating layers of Ag and Al 2 O 3 [13]. Recent alternative approaches for three- dimensional metamaterials in the visible are based on direct laser writing [14] and atomic layer deposition [15]. In this Letter we show that the concept of self-rolling strained multilayers [16,17] can be utilized to create three- dimensional metamaterials by rolling up planar metal and semiconductor films with multiple rotations. The walls of the resulting tubes represent high quality three- dimensional radial superlattices (RSLs) with accurately tunable unit cells and lattice constants [18,19]. We perform transmission measurements on RSLs which consist of (In)GaAs and Ag [Fig. 1(b)] and explain our results within the framework of an effective metamaterial approximation. We demonstrate that the effective plasma frequency of the RSLs can be shifted over a broad range in the visible and near infrared by changing the ratio between Ag and (In) GaAs layer thickness. By means of finite difference time domain simulations we show that our RSLs might be used as hollow fluid fillable [20] hyperlenses working in this frequency regime. The RSLs are prepared as follows: Initially a GaAs buffer layer (100 nm) is grown on a GaAs substrate using molecular beam epitaxy, followed by an AlAs sacrificial layer (40 nm), a strained In 20 Ga 80 As layer (17 nm), and a GaAs layer (17 nm). Subsequently an Ag layer is de- posited on the semiconductor by thermal evaporation. In this work we varied the Ag layer thickness for different samples between 17 and 25 nm. The exact thickness of the Ag layers was measured with an atomic force microscope. The strained layer system is released from the substrate by selectively etching away the AlAs sacrificial layer and minimizes its strain energy by rolling up into a tube. Details of the lithographic process used can be found in Ref. [21]. In good agreement with continuum strain theory [22] we obtain outer tube radii of r tube ¼ 2 m to r tube ¼ 3 m [Fig. 1(a)]. For transmission measurements through the tube walls we developed a transmission setup as shown in Fig. 2(a). To realize a light source which can be placed inside the microtubes we use a tapered multimode glass fiber with a core diameter of 65 m and a tip diameter of less FIG. 1 (color online). (a) Sketch of the microtube. The AlAs sacrificial layer is removed by selective etching. The released strained multilayer of In 20 Ga 80 As=GaAs=Ag relaxes and rolls up into a microtube. (b) The wall of the tube represents a RSL that consists of alternating layers of metal and semiconductor. PRL 102, 163903 (2009) PHYSICAL REVIEW LETTERS week ending 24 APRIL 2009 0031-9007= 09=102(16)=163903(4) 163903-1 Ó 2009 The American Physical Society