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We present a new approach to dielectric metasurface design that relies on a single resonator per unit cell and produces robust, high quality-factor Fano resonances. Our approach utilizes symmetry breaking of highly symmetric resonator geometries, such as cubes, to induce couplings between the otherwise orthogonal resonator modes. In particular, we design perturbations that couple "bright" dipole modes to "dark" dipole modes whose radiative decay is suppressed by local field effects in the array. Our approach is widely scalable from the near-infrared to radio frequencies. We first unravel the Fano resonance behavior through numerical simulations of a germanium resonator-based metasurface that achieves a quality-factor of ~1300 at ~10.8 µm. Then, we present two experimental demonstrations operating in the near-infrared (~1 µm): a silicon-based implementation that achieves a quality-factor of ~350; and a gallium arsenide-based structure that achieves a quality-factor of ~600 -the highest near-infrared quality-factor experimentally demonstrated to date with this kind of metasurfaces. Importantly, large electromagnetic field enhancements appear within the resonators at the Fano resonant frequencies. We envision that combining high quality-factor, high field enhancement resonances with nonlinear and active/gain materials such as gallium arsenide will lead to new classes of active optical devices.Metasurfaces are currently the subject of intensive research worldwide since they can be tailored to produce a wide range of optical behaviors. However, metasurfaces generally exhibit broad spectral resonances, and it is difficult to obtain narrow (i.e. high quality-factor, Q) spectral features. Attaining such high-Q features from metasurfaces would greatly expand their application space, particularly in the areas of sensing, spectral filtering, and optical modulation. Early metasurfaces were fabricated from metals and exhibited particularly broad resonances at infrared and optical frequencies as a result of Ohmic losses. Dielectric resonator-based metasurfaces were introduced to overcome these losses and have enabled, among others, wave-front manipulation and cloaking devices, perfect reflectors, and ultrathin lenses [1-10] but, although absorptive losses were reduced, the metasurface resonances remained broad due to strong coupling with the external field (i.e. large radiation losses).Recently, new strategies based on "electromagnetically induced transparency" or "Fano resonances" have been developed that show great promise for achieving high-Q resonances [11][12][13][14][15]. In this approach, the resonator system is designed to support both "bright" and "dark" resonances. The incident optical field readily couples to the bright resonance, but cannot couple directly to the dark resonance. Through proper design, a weak coupling between the two resonances can be introduced, allowing energy from the incident wave to be indirectly coupled to the dark resonance. The metasurface transmission and reflection spectra resulting from ...

In this paper we describe a methodology for tailoring the design of metamaterial dielectric resonators, which represent a promising path toward low-loss metamaterials at optical frequencies. We first describe a procedure to decompose the far field scattered by subwavelength resonators in terms of multipolar field components, providing explicit expressions for the multipolar far fields. We apply this formulation to confirm that an isolated high-permittivity dielectric cube resonator possesses frequency separated electric and magnetic dipole resonances, as well as a magnetic quadrupole resonance in close proximity to the electric dipole resonance. We then introduce multiple dielectric gaps to the resonator geometry in a manner suggested by perturbation theory, and demonstrate the ability to overlap the electric and magnetic dipole resonances, thereby enabling directional scattering by satisfying the first Kerker condition. We further demonstrate the ability to push the quadrupole resonance away from the degenerate dipole resonances to achieve local behavior. These properties are confirmed through the multipolar expansion and show that the use of geometries suggested by perturbation theory is a viable route to achieve purely dipole resonances for metamaterial applications such as wave-front manipulation with Huygens' metasurfaces. Our results are fully scalable across any frequency bands where high-permittivity dielectric materials are available, including microwave, THz, and infrared frequencies.

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Abstract-The design of resonators with degenerate magnetic and electric modes usually requires the ability to perturb one or both types of modes in order to induce alignment of magnetic and electric properties. In this paper perturbation theory is used to identify different types of inclusions that can be used to realize fundamentalmode degeneracy in a rectangular dielectric resonator and thus, can ultimately be used in the design of negative-index metamaterials. For reasons associated with fabrication in the infrared-frequency regime, rectangular resonator designs are of particular interest.