Strong Optical Coupling of Lattice Resonances in a Top-down Fabricated Hybrid Metal–Dielectric Al/Si/Ge Metasurface

Optical metasurfaces enable the manipulation of the light–matter interaction in ultrathin layers. Compared with their metal or dielectric counterparts, hybrid metasurfaces resulting from the combination of dielectric and metallic nanostructures can offer increased possibilities for interactions between modes present in the system. Here, we investigate the interaction between lattice resonances in a hybrid metal–dielectric metasurface obtained from a single-step nanofabrication process. Finite-difference time domain simulations show the avoided crossing of the modes appearing in the wavelength-dependent absorptance inside the Ge upon variations in a selected geometry parameter as evidence for strong optical coupling. We find good agreement between the measured and simulated absorptance and reflectance spectra. Our metasurface design can be easily incorporated into a top-down optoelectronic device fabrication process with possible applications ranging from on-chip spectroscopy to sensing.

In the coupled, lossless oscillator model, the energies  ± of the coupled modes (solid white lines in Fig. S2 (a)) are given by where  () and  () are the energies of the uncoupled collective lattice modes as a function of etching depth  (Fig. S2 (b)) and the coupling strength  is a fit parameter that is adjusted so that the energies  ± provide a good fit to the upper and lower branches of the resonance energies of the coupled system.In our case, while the dependence of  on the etching depth is negligible,  () shows a non-linear dependence on  that we fit as follows: The energies  () and  () are shown in Fig. S2 (b) as dashed lines.The solid lines in Fig. S2 (a) show results for  ± according to Eq. ( 1) and with  = 40 meV.As a result, we obtain a normal mode splitting Δ = 2 = 80 meV for our system.Figure S6: (a) A comparison of the absorptance spectra shows pronounced changes in peak height and width for the hybrid metasurface (solid line) as compared to the dielectric metasurface (dashed line).A fit to the absorptance for the dielectric metasurface without the Al using two Gaussian peaks for the overlapping EQ and MQ contributions is shown in (b).All spectra were obtained for an etching depth of 0 nm into the bottom Si layer.

Comparison of measured and simulated reflectance spectra for p-polarized light
Figure S7: A comparison of measured (solid lines) and simulated (dashed lines) reflectance spectra under different angles of incidence and using p-polarized light shows good agreement in the positions of the main peaks and dips, while the narrow peaks in a wavelength range of 1000 -1150 nm are not well seen in the measured spectra as a result of fabrication inhomogeneities.

Figure S2 :
Figure S2: Absorptance in the Ge of the (a) hybrid and (b) the dielectric metasurface (without Al cap) as a function of energy and etching depth.Solid lines indicate fit results to the coupled resonances, while dashed lines indicate the positions of the uncoupled resonances.

Figure S3 :
Figure S3: Electric (magnetic) fields in a y-(x-)normal cross section of the dielectric metasurface, i.e.where the top Al disk has been omitted.The fields obtained at a wavelength of 1310 nm and etching depth of 50 nm ((a) and (b); red border) as well as at a wavelength of 1310 nm and etching depth of 15 nm ((c) and (d); green border) show characteristics of an electric quadrupole resonance.The fields at a wavelength of 1065 nm and etching depth of 50 nm ((e) and (f); blue border) as well as at a wavelength of 1264 nm and etching depth of 15 nm ((g) and (h); orange border) show characteristics of a magnetic quadrupole resonance.

Figure S4 :
Figure S4: Simulated absorptance spectra as a function of changes in thicknesses of (a) the top Si disk, (b) the Ge disk and (c) the Al disk.Both changes in the thickness of the top Si disk and of the Ge disk lead to avoided crossing of resonances, while the Al thickness leaves the positions of the absorptance peaks unchanged once it exceeds 10 nm.

Figure S5 :
Figure S5: Simulated absorptance spectra as a function of changes in the lateral geometry parameters (a) disk diameter and (b) lattice pitch.While a change in lattice pitch also induces avoided crossing of resonances, a change in disk diameter shifts the absorption peaks but leaves their spectral separation largely unchanged.