Extremely High Refractive Index Terahertz Metamaterial
(From L to R) Bumki Min, Muhan Choi and Seung Hoon Lee
Author: Bumki Min
Affiliation: Department of Mechanical Engineering and KAIST Institute for Optical Science and Technology, Korea Advanced Institute of Science and Technology, South Korea
For the past ten years, researchers in the field of metamaterials have been focusing on the demonstration of negative refractive index, as the negative side of the index could not be reached with naturally existing materials. Partly due to this overwhelming enthusiasm over the negative refractive index, the positive side of the index spectra has not been seriously explored, though the range of positive index in natural materials was still very limited.
The key idea behind the realization of high refractive index is quite simple [1-3]. From a perspective on artificial atoms (or molecules), we need to increase the dipole moment of an artificial atom, that can be induced by incident light. Though simple in its structure, I-shaped metallic patches proposed in this work possess all the requirements for the high refractive index. By periodically arranging I-shaped metallic patches with narrow gaps in-between, we can increase the capacitance of the constituting subwavelength-scale capacitors (I-shaped metallic patches). As the gap closes, the capacitance diverges rapidly and this leads to the huge accumulation of charges at the end of the I-shaped metallic patches. This huge accumulation of charges, in turn, results in extreme polarization density, and therefore the huge effective permittivity.
However, there is another problem to solve. We have to minimize the diamagnetic effect that gives rise to the decrease in effective permeability. This can be achieved simply by thinning the metallic structure and by decreasing the metallic volume fraction.
Figure 1: (left) Unit cell structure of the high-index metamaterial made of a thin I-shaped metallic patch symmetrically embedded in a dielectric material. (middle) Optical micrographs of the fabricated single, double, and triple layer metamaterials. (right) Photograph of a flexibility test for the fabricated metamaterials.
To confirm the theoretical prediction, the measurement of complex refractive index of the proposed high index metamaterials was performed with terahertz time-domain spectroscopy (THz-TDS). The experimentally-obtained refractive indices (real parts) of metamaterials having different gap width (from 80 nm to 30 μm) are plotted in Fig.1. For the sample with the smallest gap width, we obtained the peak refractive index of 38.64 and the quasi-static limiting value greater than 20.
So far, we couldn’t test metamaterials with smaller gap-width than this, but it will be interesting to see what will happen to the refractive index -- once the gap width becomes smaller than the thickness of metallic patches. If the gap width becomes smaller than the thickness of metallic patch, the increase of refractive index with respect to the reduction in gap will be more pronounced, since the subwavelength capacitor enters into the regime of parallel plate capacitor.
In addition, it is worthwhile to note that the overall refractive index is proportional to the refractive index of the substrate. For the present work, we have used a relatively low refractive index dielectric (polyimide whose real index is around 1.8) as a substrate. We expect that higher refractive index will be achieved with the use of higher index natural materials as substrates.
Figure 2: Frequency dependent effective refractive indices of single layer metamaterials with varying gap widths. Inset shows the scanning electron micrographs of a nanogap (~80 nm) high-index metamaterial.
While the proposed I-shaped metallic patch structure has shown the proof of concept, it exhibits polarization dependency owing to the structural anisotropy of the unit cell. In order to access the feasibility of isotropic high index metamaterials, we have fabricated two different types of 2D isotropic high index metamaterials and conducted additional experiments and analyses to verify the polarization independency (See Fig.3). Although the structures are different, the underlying physics is the same: Maintain small gap width for large capacitance and thin metallic patch for negligible diamagnetism.
Figure 3: (left) Polarization-angle-resolved effective refractive index for a single layer hexagonal high index metamaterial. Here, the gap width is 1.5 μm and the thickness is 1.82 μm. (right) Polarization-angle-resolved effective refractive index for a single layer window-type high index metamaterial. Here, the gap width is 1.5 μm and the thickness is 1.82 μm.
High refractive index metamaterials might provide a new way of achieving subwavelength resolution in an imaging system. Subwavelength imaging is being investigated through the utilization of negative index metamaterials (or singly negative materials). In contrast to this “perfect (or super) lens” concept, it might be possible to build a huge NA (numerical aperture) lens that provides the subwavelength-scale resolving power. In the design of high refractive index lens, spatially-varying gradient index can be obtained simply by controlling the gap between unit cells, thereby making it possible to fabricate a very thin flat metamaterial lens. However, among its limitations are the short focal length of high index lens and the working distance, which should be investigated more carefully in near future.
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 M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index”, Nature 470, 369 (2011). Abstract.