Fig. 1 Resonant modes in h-BN nanodiscs in the RS2 band.

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Fig. 1 Resonant modes in h-BN nanodiscs in the RS2 band. Resonant modes in h-BN nanodiscs in the RS2 band. (A) In-plane and out-of-plane relative permittivity of h-BN; the two colored bands are the RS1 band (where εz < 0) and the RS2 band (where εx,y < 0). (B) Fundamental propagation mode supported by a 50-nm-thin h-BN on 285-nm SiO2 on Si in the RS2 band. The electric field and the local charge density in h-BN are shown. (C) Numerical calculation of the mode effective index as a function of frequency. (D) h-BN is patterned to create particles with size 10 to 50 times smaller than the free space wavelength, which shows several resonant modes in the RS2 band that can be imaged via near-field techniques such as SNOM and PiFM. Confinement is possible owing to the hyperbolic dispersion of this material, which ensures high confinement both vertically and laterally. (E) Charge density for the first modes supported by an h-BN disc in the RS2 band, computed analytically from Eqs. 2 and 3. Modes are listed according to the values of the integers s and n appearing in Eq. 3. The solution for s = 0, n = 1 is the constant solution, which represents the total charge, here assumed to be 0 due to charge neutrality. Michele Tamagnone et al. Sci Adv 2018;4:eaat7189 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).