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Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws

Abstract

Metamaterials allow for extraordinary electromagnetic properties that are not attainable in nature1,2,3,4,5,6,7,8,9. Indefinite media with hyperbolic dispersion, in particular, have found intriguing applications10,11,12,13. The miniaturization of optical cavities increases the photon density of states and therefore enhances light–matter interactions for applications in modern optoelectronics. However, scaling down the optical cavity is limited to the diffraction limit and by the reduced quality factor. Here, we experimentally demonstrate an optical cavity made of indefinite metamaterials that confines the electromagnetic field to an extremely small space. The experiments reveal that indefinite cavities demonstrate anomalous scaling laws: cavities with different sizes can resonant at the same frequency, and a higher-order resonance mode oscillates at a lower frequency. We also demonstrate a universal fourth power law for the radiation quality factor of the wave vector. Cavities with sizes down to λ/12 are realized with ultrahigh optical indices (up to 17.4), a feature that is critically important for many applications14,15,16,17,18.

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Figure 1: Schematic of multilayer indefinite metamaterial structure and its hyperboloid IFC.
Figure 2: FDTD-calculated IFC of the multilayer metamaterial and mode profiles of indefinite optical cavities.
Figure 3: SEM images and measured transmission spectra of indefinite optical cavities with different sizes.
Figure 4: Radiation quality factor as a function of the resonating wave vector of a cavity mode.

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Acknowledgements

The authors acknowledge funding support from the US Department of Energy under contract no. DE-AC02-05CH11231 through Materials Sciences Division of Lawrence Berkeley National Laboratory (LBNL). J.S.R. acknowledges a fellowship from the Samsung Scholarship Foundation, Republic of Korea.

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Contributions

X.D.Y. and J.Y. performed numerical simulations. J.S.R. fabricated and SEM-imaged device samples. X.D.Y. carried out optical measurements. X.D.Y., X.B.Y. and X. Z. analysed the experimental data. X.D.Y., X.B.Y. and X.Z. wrote the manuscript. X.Z. and X.B.Y. guided the research. All authors contributed to discussions.

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Correspondence to Xiang Zhang.

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The authors declare no competing financial interests.

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Yang, X., Yao, J., Rho, J. et al. Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws. Nature Photon 6, 450–454 (2012). https://doi.org/10.1038/nphoton.2012.124

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