Surface Lattice Resonances in 3D Chiral Metacrystals for Plasmonic Sensing

Abstract Chiral lattice modes are hybrid states arising from the chiral plasmonic particles assembled in ordered arrays with opportune periodicity. These resonances exhibit dependence on excitation handedness, and their observation in plasmonic lattices is strictly related to the chiroptical features of the fundamental plasmonic unit. Here, the emergence of chiral surface lattice resonances (c‐SLRs) is shown in properly engineered arrays of nanohelices (NHs), fully three dimensional (3D) chiral nano‐objects fabricated by focused ion beam processing. By tuning the relative weight of plasmonic and photonic components in the hybrid mode, the physical mechanism of strong diffractive coupling leading to the emergence of the lattice modes is analyzed, opening the way to the engineering of chiral plasmonic systems for sensing applications. In particular, a coupling regime is identified where the combination of a large intrinsic circular dichroism (CD) of the plasmonic resonance with a well‐defined balance between the photonic quality factor (Q factor) and the plasmonic field enhancement (M) maximizes the capability of the system to discriminate refractive index (RI) changes in the surrounding medium. The results lay the foundation for exploiting CD in plasmonic lattices to high performance refractometric sensing.

. Comparison between the left and right-handed circularly polarized extinction spectra derived from transmission measurements of helix array (LP 460 nm) in oil (n=1.518) with different number of elements: 42x42 elements corresponding to a patterned area of 360 µm 2 (blue), 30x30 elements corresponding to a patterned area of 225 µm 2 (blue), and 20x20 elements corresponding to a patterned area of 100 µm 2 (light blue) showed in the left panel SEM image with scale bar 2 µm. The symbols with the same colors indicate similar spectral features (displayed in the legend) observed in both arrays.

S2. Effect of Lattice Period
Circularly polarized extinction spectra have been extracted from the central pixel of the measured extinction maps of the arrays of 30x30 elements with four different lattice periods (400nm, 430nm, 460nm, 490nm) displayed in the main text (figure 2). In periodic arrays of plasmonic chiral nanostructures, the chiral LSPRs can couple to the diffractive lattice modes of the array, generating the c-SLRs. This results in a peak in the extinction spectra (circle in figure S2a) preceded by a dip related to the linear dispersion of the (±1,0) RAs. The extinction intensity increases with LP, and it is found to be higher for RCP, when incident polarization matches the same handedness of the helices, while is lower when interacting with the opposite light handedness. When increasing LP, a redshift of the spectral features and a progressive spectral narrowing is observed. For LP 460nm and LP 490nm, two additional modes are observed, corresponding to the coupling with (±1,±1)RAs. This confirms that moving towards configurations different from the zero-detuning strong coupling regime, the CD increases [5] .

S3. Circularly Polarized Light Extinction Maps
In figure S3 we display the measured LCP, RCP extinction maps and the retrieved CD. The c-SLR onset is evident for both the two incident polarizations, but with different intensity due to a more efficient dipole excitation in RH structure from RCP incident light. This is confirmed in the CD maps where chiral SLR signatures can also be observed. Their angular dispersion in the maps can be clearly distinguished confirming the hybrid nature of the c-SLR. In addition to what discussed in the main text, we highlight that the lower polariton branch (UP) mode superimposes with the (±1,±1)RAs generating a new mode splitting ((±1,±1)RAs at 510 and MP at 560nm) for LP =490 nm. Figure S3. a-b. Experimentally measured energy-momentum extinction dispersions for LCP and RCP light for four different lattice periods (400 nm, 430 nm, 460 nm, 490 nm). c. Circular dichroism far-field maps as a function of LP calculated as the difference between RCP and LCP extinctions.

S4. Numerical simulations of the energy-momentum far field extinction dispersions
The simulated extinction far-field maps of figure S4 are retrieved under interaction with LCP and RCP light in oil environment for different lattice periods: 400nm, 430nm, 460nm, 490nm. They present a good agreement with what observed experimentally and reported in the main text. In particular, we observe a similar trend of the c-SLR with the LP variation with the experimental data. RCP extinction maps display higher intensity, suggesting a better spectral overlap when matching the polarization and the structural handedness, according to experimental data. Figure S4. RCP and LCP simulated far-field extinction maps evaluated in oil environment for different LPs. Figure S5 a,b,c display the Hopfield coefficients for the upper, lower and middle branches, respectively, referred to RCP incident light condition discussed in the main text ( figure 3 a). The plots describe how the photonic/plasmonic fraction of the hybrid mode changes with LP. The Hopfield coefficients (α) can be calculated as in [6] :

S5. Calculated Hopfield Coefficients
Where Δ is the detuning at a given lattice k-vector, Ω = √ ( 2 + 2 and g is the coupling coefficient, that is half the separation between the lower and upper branches at zero detuning. In the lower branch, for low LPs (<340nm) the hybrid mode is mostly plasmon-like. Increasing LP, the plasmon mode fraction decreases and the (±1,0) diffractive order mode weight becomes predominant. At LP = 340 nm, that is the zero detuning condition, the plasmonic and the (±1,0) diffractive order fractions are the same. Analogously, in the upper branch(figure S5b) for low LPs (<440nm) the mode is almost pure diffractive orders (DO)-like, while increasing LP, the diffractive order mode fraction decreases and the plasmon fraction increases; for higher LP, the latter value becomes predominant. The middle branch composition ( Figure S5c)

S6. Q-factor
The Q-factor of figure S6 was calculated from the experimental spectra acquired in water environment (n=1.3334) as: where λ corresponds to the spectral peak of c-SLRs, and Δλ is the full width at half maximum derived by the Gaussian fit of the SLR spectra. The measured Q-factor shows a clear increase with the lattice period, caused by a reduction of plasmonic content. It should be noted that the material composition of NH fabricated by FIBID is not purely metallic, thus explaining the low absolute values of measured c-SLR Qfactor.

S7. CD sensitivity to refractive index variations
The CD spectra of the samples with different lattice periods were collected in known refractive index (RI) environment. We considered glycerol−water mixtures with varying concentration from 0 to 20% (corresponding to a refractive index range between 1.333 and 1.358) [7] . All the spectra red-shift and, in particular, we focused on the shift of CD maxima, shown in the panels of figure S7, which were used to calculate the sensitivity values in nm/RIU shown in the main text, figure 4a. Figure S7 a-f. CD spectra of the NH arrays as a function of the surrounding refractive index environment (0%, 5%, 10%, 15% 20% of glycerol in water solution), zoomed at the relative resonance peaks measured for different lattice periods: a)LP 370nm, b)LP 400nm, c) LP 430nm, d) LP 460nm, e) c) LP 490nm, f) LP 520nm.

S8 Calculated Field enhancement
We have performed simulations of the field enhancement (M=E/E0), as a function of the LP, averaged at three different points along the nanohelix z-evolution, in particular at the bottom, center and top side. We found that the M value is maximized for LP=490nm, corresponding to a plasmonic fraction of 0.1. Figure S8. Calculated field enhancement as a function of LP= a) 420 nm, b) 490 nm, c) 550 nm.