Holey structure has refractive index of -2 in the near-IR

Much recent press in the optics community has been devoted to metamaterials, which, with their potential for negative refraction, may enable lenses with exotic optical properties.

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Much recent press in the optics community has been devoted to metamaterials, which, with their potential for negative refraction, may enable lenses with exotic optical properties. The creation of a functional negative-refractive-index optical metamaterial for use at near-IR (and ultimately visible) wavelengths hinges on two developments, however. First, a fabrication process must be developed that is practical; and second, a geometry and combination of materials must be crafted that does not absorb most of the light (a problem for metamaterials’ resonant structures that contain metal).

A group at the University of New Mexico (UNM; Albuquerque, NM), well known for its research in interference lithography, is using the lithographic technique, in combination with a simplified but effective resonant-structure geometry, to tackle the first problem; in the process, they are at least partially solving the second problem as well. The structure, which consists of a glass substrate holding two holey gold films separated by an aluminum oxide dielectric layer, exhibits a negative refractive index around 2 µm that reaches -2 (see figure).1

Simple structure

The gold films have identical square arrays of holes with a period of 838 nm and a hole diameter of 360 nm. They are fabricated by interferometric lithography at a 355-nm wavelength; the inherently large-field interferometric approach results in a sample size of about 1 cm2. The separated metal layers interact resonantly, with the holes coupling these interactions to the surface-plasmon waves of the composite structure.

To determine the refractive index-both real (which determines refraction) and imaginary (which determines absorption)-the researchers measured the amplitude and phase of the structure’s reflection and transmission. Interferometric setups consisting of periodic separated stripes of the metamaterial determined phase (with silver filling in the blank areas for reflective measurements). The spectral measurements were performed with Fourier-transform IR spectroscopy at near-normal incidence with unpolarized light. Only the zeroth order emanating from the periodic-stripe structure was collected.

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A multilayer metamaterial structure consists of an aluminum oxide dielectric layer between two gold films perforated with a square array of holes (838-nm pitch; 360‑nm diameter) atop a glass substrate (top). For the specific polarization and propagation direction shown, the active regions for the electric (blue regions) and magnetic (green regions) responses are indicated. The structure, which exhibits a refractive index of -2 at 2 µm, is seen in a scanning-electron micrograph (bottom).
Click here to enlarge image

The spectral transmittance and reflectance data show several effects-for example, features at 1.3 µm stem from surface-plasmon waves at the interface of the gold and glass, while features at 2 µm arise from the intended inductive-capacitive-circuit resonance. The transmission and reflectance phase were extracted from the data, from which the metamaterial’s refractive index could be evaluated.

Calculations of the effective refractive index of the structure were compared to experimental measurements; the results matched well. The real portion of the refractive index reached down to -2 at the 2-µm resonant wavelength, down from approximately zero elsewhere in the spectrum. At the same wavelength, however, the imaginary part of the refractive index rose above 3-an indication of significant light absorption.

Since the submission of these results for publication, the group has been making continuous progress in designing and fabricating metamaterials with improved optical performance, says Steven Brueck, one of the researchers and the director of UNM’s Center for High Technology Materials. The low transmission in the region of negative index in the published results is because of the large impedance mismatch between the metamaterial and the surrounding air and glass claddings and the high imaginary part of the index, he notes.

A follow-up numerical study showed that reducing the linewidth of the metallic stripes responding to the electric field addresses these two problems simultaneously.2 The researchers have experimentally demonstrated a much higher transmission (over 40%) over the range of negative refraction, says Brueck, as well as an improved figure of merit (the real component divided by the imaginary component of the refractive index), which is relevant to the material loss. “We are now looking into extending these results with multiple stacks of metal/dielectric/metal to make a thicker metamaterial that also should have lower loss, according to the modeling results,” he says.

John Wallace


1. S. Zhang et al., Phys. Rev. Lett.95, 137404 (Sept. 23, 2005).

2. S. Zhang et al., Optics Express 13, 4922 (2005).

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