Abstract
The refractive index is the fundamental property of all optical materials and dictates Snell's law, propagation speed, wavelength, diffraction, energy density, absorption and emission of light in materials. Experimentally realized broadband refractive indices remain <40, even with intricately designed artificial media. Herein, we demonstrate a measured index >1,800 resulting from a mesoscopic crystal with a dielectric constant greater than three million. This gigantic enhancement effect originates from the space-filling curve concept from mathematics. The principle is inherently very broad band, the enhancement being nearly constant from zero up to the frequency of interest. This broadband giant-refractive-index medium promises not only enhanced resolution in imaging and raised fundamental absorption limits in solar energy devices, but also compact, power-efficient components for optical communication and increased performance in many other applications.
Highlights
The refractive index is the fundamental property of all optical materials and dictates Snell’s law, propagation speed, wavelength, diffraction, energy density, absorption and emission of light in materials
A dielectric constant over three million and a refractive index 41,800 were experimentally measured in microwave frequencies, and an index of 20 was numerically verified near the optical communication wavelengths for a scaled down structure
While an isotropic version can be designed by adding vertical connections and reducing the aspect ratio, the extreme anisotropy of the current design is naturally ideal for applications involving deep sub-wavelength resolution image transfer (Supplementary Fig. 10), similar to the case of artificial media with hyperbolic dispersion[17,18,19,20]
Summary
The refractive index is the fundamental property of all optical materials and dictates Snell’s law, propagation speed, wavelength, diffraction, energy density, absorption and emission of light in materials. The dielectric constant does not diverge on resonance due to various resonance broadening mechanisms that makes g a non-zero value As one minimizes these broadening factors, the resulting index becomes larger at the design frequency; but at the same time, it becomes more frequency dispersive and the index deviates severely even for slightly different frequencies. The experimentally measured values remained o40 (refs 8,9) as several practical and theoretical constraints impose upper bounds on the enhancement These include lateral fabrication resolution, dielectric breakdown and a more fundamental limitation, which is the breakdown of classical material models at sub-nanometre size gaps[10]. As the enhancement principle is based on quasi-static boundary conditions, almost constant enhancement occurs for many orders of magnitude of frequencies, making this design potentially suitable for applications that require very broad bandwidth as well
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