Non-Hermitian metasurface with non-trivial topology

Abstract

The synergy between topology and non-Hermiticity in photonics holds immense potential for next-generation optical devices that are robust against defects. However, most demonstrations of non-Hermitian and topological photonics have been limited to super-wavelength scales due to increased radiative losses at the deep-subwavelength scale. By carefully designing radiative losses at the nanoscale, we demonstrate a non-Hermitian plasmonic-dielectric metasurface in the visible with non-trivial topology. The metasurface is based on a fourth order passive parity-time symmetric system. The designed device exhibits an exceptional concentric ring in its momentum space and is described by a Hamiltonian with a non-Hermitian $Z_3$ topological invariant of V = -1. Fabricated devices are characterized using Fourier-space imaging for single-shot k-space measurements. Our results demonstrate a way to combine topology and non-Hermitian nanophotonics for designing robust devices with novel functionalities.

Keywords: exceptional concentric ring; metasurface; non-Hermitian; plasmonics; topological photonics.

Figure 1:

Ground plane system: coupling between horizontal and vertical modes unlocks topological effects. (a) Scanning electron microscope image of non-Hermitian metasurface (scale bar: 1 μm). Silicon nanocylinders (radius = 120 nm, height = 120 nm) are arranged in a hexagonal lattice (lattice constant = 600 nm) on a silica spacer layer (variable thickness) and aluminum layer. (b) The metasurface contains horizontal and vertical photonic modes coupled to their respective image charges in the aluminum ground plane (κ _h, κ _v). Horizontal and vertical modes can couple to each other by varying the angle of incidence of excitation (κ _θ ). (c) Real part of eigenvalues for representative 4 × 4 Hamiltonian of the coupled system, showing exceptional lines (marked in red). (d) Cross sections of real part of eigenvalues, holding either κ _h or κ _θ constant. The exceptional concentric ring (red, labeled) and PT-symmetric (yellow) phases are accessible by varying either parameter (κ _h, κ _θ ) independently.

Figure 2:

Full-wave simulations of non-Hermitian metasurfaces reveal non-trivial topology. Absorption peaks extracted from full-wave simulations while varying the out-of-plane angle (θ) from 0° to 30° and in-plane angle (ϕ) from 30° (M point) to 60° (K point) for (a) spacer = 0 nm and (b) spacer = 120 nm. For spacer = 120 nm, an exceptional concentric ring feature is observed. (c) Simulated mode frequencies of the 4 resonator system as the in-plane angle is tuned. For spacer = 120 nm and out-of plane incident angle of 26°, the system undergoes a transition from PT-symmetric (yellow) to exceptional concentric ring (ECR, red) phases.

Figure 3:

Experiments for Fourier-space imaging for bandstructure measurements. (a) Metasurface sample characterization setup using a Bertrand lens to image the Fourier-plane onto the spectrometer CCD. A tungsten lamp illuminates the sample. (b) Example of a single-shot measurement of the angle-dependent normalized absorption spectrum.

Figure 4:

Experimental characterization of non-Hermitian metasurfaces (a) simulated device excited by a normally incident plane wave. Coupling between photonic and plasmonic horizontal modes is tuned by the silica spacer thickness, revealing a PT-phase transition and exceptional point for a 65 nm spacer. Inset: Schematic showing excited horizontal modes and no coupling to vertical modes. (b) Simulation and (c) experimental characterization of metasurfaces excited by normally incident light, confirming the presence of an exceptional point. (d) Simulation and (e) experimental characterization of angle-dependent absorption spectrum show qualitative agreement. Absorption for an in-plane angle of 25° in the PT-symmetric regime (spacer = 30 nm) is plotted.