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Journal of Optics

Experimental determination of the refractive index of metamaterials

Michael G. Nielsen, Anders Pors, Ole Albrektsen, Morten Willatzen, Sergey I. Bozhevolnyi

Published Apr 15, 2011• 10 citations
Publisher

Abstract

We present a simple experimental technique based on diffraction for determining the complex refractive index of metamaterials, and demonstrate it with metamaterials that consist of detuned electrical dipoles (DEDs), mimicking the dressed-state picture of electromagnetically induced transparency (EIT). The metamaterials are realized by fabricating lithographically defined gold nanorods on a silica substrate, covered with a ~ 15 µm thick polymer layer, and feature EIT-like transmission spectra with transparency windows centered at wavelengths near ~ 800 nm. The refractive indices are determined for wavelengths where the DED metamaterials exhibit enhanced transmission. Thereby, we experimentally demonstrate normal dispersion in the transmission window and estimate the group refractive index to ~ 3.6. Furthermore, finite-element simulations are conducted on a monolayer of DED unit cells, which similarly exhibit the EIT-like behavior in terms of enhanced transmission revealed in the transmission spectra. Simulated transmission and reflection spectra are utilized for calculations of the real and imaginary parts of the metamaterial refractive index, showing consistent trends with those obtained experimentally.

DOI
10.1088/2040-8978/13/5/055106

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We present a simple experimental technique based on diffraction for determining the complex refractive index of metamaterials, and demonstrate it with metamaterials that consist of detuned electrical dipoles (DEDs), mimicking the dressed-state picture of electromagnetically induced transparency (EIT). The metamaterials are realized by fabricating lithographically defined gold nanorods on a silica substrate, covered with a ~ 15 µm thick polymer layer, and feature EIT-like transmission spectra with transparency windows centered at wavelengths near ~ 800 nm. The refractive indices are determined for wavelengths where the DED metamaterials exhibit enhanced transmission. Thereby, we experimentally demonstrate normal dispersion in the transmission window and estimate the group refractive index to ~ 3.6. Furthermore, finite-element simulations are conducted on a monolayer of DED unit cells, which similarly exhibit the EIT-like behavior in terms of enhanced transmission revealed in the transmission spectra. Simulated transmission and reflection spectra are utilized for calculations of the real and imaginary parts of the metamaterial refractive index, showing consistent trends with those obtained experimentally.
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In this work, using finite-difference time-domain method, we propose and numerically demonstrate a novel way to achieve electromagnetically induced transparency (EIT) phenomenon in the reflection spectrum by stacking two different types of coupling effect among different elements of the designed metamaterial. Compared with the conventional EIT-like analogues coming from only one type of coupling effect between bright and dark meta-atoms on the same plane, to our knowledge the novel approach is the first to realize the optically active and precise control of the wavelength position of EIT-like phenomenon using optical metamaterials. An on-to-off dynamic control of the EIT-like phenomenon also can be achieved by changing the refractive index of the dielectric substrate via adjusting an optical pump pulse. Furthermore, in near infrared region, the metamaterial structure can be operated as an ultra-high resolution refractive index sensor with an ultra-high figure of merit (FOM) reaching 3200, which remarkably improve the FOM value of plasmonic refractive index sensors. The novel approach realizing EIT-like spectral shape with easy adjustment to the working wavelengths will open up new avenues for future research and practical application of active plasmonic switch, ultra-high resolution sensors and active slow-light devices.
Electromagnetically induced transparency (EIT)-like effects in silver, gold, and aluminum metamaterials consisting of dipole resonators and quadrupole resonators were demonstrated at visible wavelengths. Optical characteristics of the metamaterials could be controlled by the gap distance between the two resonators. EIT-like effects were observed at wavelengths between 603 and 789 nm, 654 and 834 nm, and 462 and 693 nm for the silver, gold, and aluminum EIT metamaterials, respectively. At wavelengths longer than around 650 nm, the silver metamaterials had better EIT-like features. At wavelengths shorter than around 650 nm, on the other hand, the aluminum metamaterials showed promising EIT-like results.
We investigate numerically an analog of electromagnetically induced transparency (EIT) in an all-dielectric metamaterial-waveguide (ADMW) that consists of a two-dimensional silicon rod array on quartz slab waveguide. The EIT-like response is achieved by the destructive interference between a broad magnetic resonance and a narrow guide mode resonance. By tailoring the guided mode through the thickness of the slab waveguide or the lattice period of the metamaterial, an EIT-like transmission window is achieved with both high Q-factor (>104) and high transmission (>94%). And the group refractive index at the EIT-like resonance of the ADMW can be up to several thousands. These results demonstrate that the proposed ADMW has potential applications in low-loss slow-light based devices, bio-chemical sensing, and optical modulations.