Rolled-Up Three-Dimensional Metamaterials with a Tunable Plasma Frequency in the Visible Regime

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 $\mathrm{InGaAs}/\mathrm{GaAs}/\mathrm{Ag}$ 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.

Figure 1

(a) Sketch of the microtube. The AlAs sacrificial layer is removed by selective etching. The released strained multilayer of ${\mathrm{In}}_{20}{\mathrm{Ga}}_{80}\mathrm{As}/\mathrm{GaAs}/\mathrm{Ag}$ 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.

Figure 2

(a) Scanning electron microscope image of the tip of the fiber and sketch of the setup. The patterns in the tip metallization are prepared by focused ion beams. The fiber is manipulated by an $XYZ$ piezostack. The signal is collected by a microscope objective and measured with a CCD. Intensity measurements on selected areas (cf. red circle) are performed using software based apertures. (b) Microscope image of the fiber in front of the microtube. The light, which is coupled into the fiber, is scattered through the holes in the tip metallization (red circle). (c) The fiber tip is manipulated into the microtube, and the light is transmitted through the RSL.

Figure 3

Measured transmission data (symbols) of an $(\mathrm{In})\mathrm{GaAs}/\mathrm{Ag}$ radial superlattice together with the corresponding transfer matrix calculations for perpendicular incidence on a flat multilayer (solid lines). For most data points the error bars are smaller than the symbols. The thickness of the $\mathrm{InGaAs}/\mathrm{GaAs}$ layer was $d_{(\mathrm{In})\mathrm{GaAs}}=34\mathrm{nm}$ for all samples, and the Ag-layer thickness was varied. Circles, $\eta <0.03$ ($d_{\mathrm{Ag}}<1\mathrm{nm}$) with 5 rotations and $d_{\mathrm{tot}}\approx 170\mathrm{nm}$; squares, $\eta =0.5$ ($d_{\mathrm{Ag}}=17\mathrm{nm}$) with 4 rotations and $d_{\mathrm{tot}}=204\mathrm{nm}$; triangles, $\eta =0.56$ ($d_{\mathrm{Ag}}=19\mathrm{nm}$) with 4 rotations and $d_{\mathrm{tot}}=212\mathrm{nm}$; rhombuses, $\eta =0.65$ ($d_{\mathrm{Ag}}=22\mathrm{nm}$) with 6 rotations and $d_{\mathrm{tot}}=336\mathrm{nm}$. The arrows point to the center of the respective plasma edge (cf. Fig. 4).

Figure 4

Plasma frequency of RSL metamaterial with different layer thickness ratios $\eta$. The solid line gives the values of ${\omega }_p$ calculated with the effective metamaterial approximation, i.e., Eq. (1). The red squares are experimental values for ${\omega }_p$ characterized by the center position of the measured plasma edges. The uncertainty of the center position is indicated by error bars.

Figure 5

Finite difference time domain simulations (Lumerical FDTD-solutions) on hyperlenses working at visible frequencies based on rolled-up $\mathrm{Ag}/(\mathrm{In})\mathrm{GaAs}$ RSLs. Two dipoles with a distance of 250 nm are placed at the inner perimeter of the RSL. The dipoles emit at ${\lambda }_p=685\mathrm{nm}$ with $H$ polarized along the RSL axis. The value of $H_z$ represents the wave field normalized to the dipole sources and is given by a logarithmic color plot. (a) RSL with $\eta =0.65$, $d_{\mathrm{Ag}}=4\mathrm{nm}$, $d_{(\mathrm{In})\mathrm{GaAs}}=6\mathrm{nm}$, 25 rotations, $r_{\mathrm{inner}}=0.380\mu \mathrm{m}$, $r_{\mathrm{outer}}=0.630\mu \mathrm{m}$, $V=1.7$. (b) RSL with $\eta =0.65$, $d_{\mathrm{Ag}}=22\mathrm{nm}$, $d_{(\mathrm{In})\mathrm{GaAs}}=34\mathrm{nm}$, six rotations, $r_{\mathrm{inner}}=1.500\mu \mathrm{m}$, $r_{\mathrm{outer}}=1.836\mu \mathrm{m}$, $V=1.2$.