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Non-Hermitian metasurfaces for the best of plasmonics and dielectrics

Frank Yang, Alexander Hwang, Chloe Doiron, and Gururaj V. Naik

Open Access Open Access

Abstract

Materials and their geometry make up the tools for designing nanophotonic devices. In the past, the real part of the refractive index of materials has remained the focus for designing novel devices. The absorption, or imaginary index, was tolerated as an undesirable effect. However, a clever distribution of imaginary index of materials offers an additional degree of freedom for designing nanophotonic devices. Non-Hermitian optics provides a unique opportunity to take advantage of absorption losses in materials to enable unconventional physical effects. Typically occurring near energy degeneracies called exceptional points, these effects include enhanced sensitivity, unidirectional invisibility, and non-trivial topology. In this work, we leverage plasmonic absorption losses (or imaginary index) as a design parameter for non-Hermitian, passive parity-time symmetric metasurfaces. We show that coupled plasmonic-photonic resonator pairs, possessing a large asymmetry in absorptive losses but balanced radiative losses, exhibit an optical phase transition at an exceptional point and directional scattering. These systems enable new pathways for metasurface design using phase, symmetry, and topology as powerful tools.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)
Fig. 1.
Fig. 1. Overview of passive PT-symmetric metasurfaces. (a) Basic model of coupled resonators and eigenvalue spectrum, showing PT phase transition. Schematic of a passive PT-symmetric metasurface consisting of (b) silicon nanocylinder array coupled to a metal ground plane, (c) an array of silicon nanocylinder dimers. A 1 nm thin layer of titanium is added to the bottom layer to induce loss.

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Fig. 2.
Fig. 2. Localized modes with high quality factor. (a) scattering and absorption cross sections of single silicon cylinder with height $=$ 120 nm and radius $=$ 80 nm, where radiative losses limit achievable Q factors. Right: XY-plane field profiles of magnetic (Re[Hy], green border) and electric (Re[Ex], brown border) dipole modes, (b) schematic of hexagonal array of silicon cylinders with periodicity a $=$ 600 nm, height $=$ 120 nm, and radius $=$ 120 nm, (c) reflectance of array for normally incident, x-polarized input and radius from 80 nm to 200 nm, showing crossing of electric and magnetic dipole modes, (d) TM and TE bandstructure showing flat band near $\Gamma$ point for silicon resonator array (periodicity a $=$ 600 nm, height $=$ 120 nm, and radius $=$ 120 nm).

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Fig. 3.
Fig. 3. Plane-wave excitation of different PT-symmetric metasurfaces (a) ground plane system and (d) coupled resonator system schematics, (b, e) absorption spectra showing passive PT-symmetry as spacer thickness D is decreased, (c, f) XZ-plane electric field profiles in PT-symmetric and PT-broken regimes.

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Fig. 4.
Fig. 4. Coupled resonator system: asymmetric scattering of quantum emitters Radiative Purcell enhancement for x-polarized dipoles (a) on the lossless or (b) on the lossy sides of the metasurface.

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Fig. 5.
Fig. 5. Ground plane system: coupling between horizontal and vertical modes unlocks topological effects (a) schematic showing coupling between vertical and horizontal modes and their image charges, (b) eigenvalue surface for 4x4 Hamiltonian given in Eqn. 2, with $\omega _0 = 10$, $\kappa _2 = \kappa _1/4$, $\gamma =1$, (c) Real part of eigenvalues for constant vertical-horizontal coupling ($\kappa _\theta = 0.5$), (d) Real part of eigenvalues for constant plasmonic-photonic coupling ($\kappa _1 = 3.5$).

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Equations (2)

Equations on this page are rendered with MathJax. Learn more.

H ^ = [ ω 0 κ κ ω 0 + i γ ]
H ^ = [ ω 0 κ 1 κ θ 0 κ 1 ω 0 + i γ 0 κ θ κ θ 0 ω 0 κ 2 0 κ θ κ 2 ω 0 + i γ ]
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