Plasmonic bound states in the continuum to tailor light-matter coupling

Abstract

Plasmon resonances play a pivotal role in enhancing light-matter interactions in nanophotonics, but their low-quality factors have hindered applications demanding high spectral selectivity. Here, we demonstrate the design and 3D laser nanoprinting of plasmonic nanofin metasurfaces, which support symmetry-protected bound states in the continuum up to the fourth order. By breaking the nanofins’ out-of-plane symmetry in parameter space, we achieve high-quality factor (up to 180) modes under normal incidence. The out-of-plane symmetry breaking can be fine-tuned by the nanofins’ triangle angle, opening a pathway to precisely control the ratio of radiative to intrinsic losses. This enables access to the under-, critical, and over-coupled regimes, which we exploit for pixelated molecular sensing. We observe a strong dependence of the sensing performance on the coupling regime, demonstrating the importance of judicious tailoring of light-matter interactions. Our demonstration provides a metasurface platform for enhanced light-matter interaction with a wide range of applications.

3D-nanoprinted plasmonic nanofin metasurfaces with high-quality factor resonances can achieve enhanced light-matter interaction.

INTRODUCTION

Controlling and enhancing light-matter interaction is the foundation of nanophotonics. Over the last decades, surface plasmons have attracted much attention due to their subwavelength confinement of light, which can be exploited to remarkably enhance light-matter interactions. Plasmon resonances in the form of localized and propagating modes at metal-dielectric interfaces have been extensively used for plasmon-enhanced sensing (1, 2), fluorescence (3, 4) and Raman spectroscopy (5, 6), photoacoustics (7, 8), photocatalysis (9, 10), photovoltaics (11, 12), and nonlinear optics (13, 14), to name a few. However, these plasmon resonances typically feature low-quality factors (Q-factors) of around 10 due to the intrinsic loss in metals (15), which has limited their practical use as many applications demand high spectral selectivity. Although arrays of metallic nanostructures may support narrow surface lattice resonances (SLRs) with roughly 10-fold Q-factor improvement (15), they are extremely sensitive to both structural disorders and illumination conditions. Furthermore, they typically demand very large structured areas and embedment in a homogeneous medium (16–18).

Meanwhile, bound states in the continuum (BICs) were introduced to nanophotonics. Originating from quantum mechanics (19, 20), BICs are modes with an infinite Q-factor in an open system, which cannot couple to any radiation channel propagating outside the system (21–23). Small perturbations can destroy pure BICs and result in quasi-BIC modes with finite Q-factors, which become accessible to the far field. Among different types of BICs, symmetry-protected BICs have gained, by far, the most attention. To date, they have been mostly realized in low-loss dielectric metasurfaces using in-plane symmetry-broken geometries (24–27). For many photonic applications such as optical sensing (28), energy conversion (29), and light emission (30), not only high Q-factors but also strong near-field enhancement accompanied by a high coupling efficiency is essential. The latter is critical for maximizing light-matter interactions but cannot be obtained by lossless dielectric metasurfaces due to their mismatch between the radiative and intrinsic losses (31). Most of the impinging energy is not coupled to the resonant metasurfaces and hence lost in the form of reflection (32, 33). Although symmetry-protected BICs were recently observed in plasmonic metasurfaces (34–37), they rely on symmetry breaking in momentum space via oblique incident angles, rendering them not suitable for most applications. Therefore, it remains a great challenge to achieve a metasurface platform simultaneously supporting tunable high Q-factors at normal incidence and high light-matter coupling.

Here, we demonstrate the design and three-dimensional (3D) laser nanoprinting of a plasmonic nanofin metasurface (PNM) supporting multiple out-of-plane symmetry-protected BICs, which we use for pixelated molecular sensing in different coupling regimes. The PNM consists of an array of identical 3D triangular nanofin building blocks fabricated in a polymer matrix and coated with gold (Fig. 1A). By breaking the out-of-plane symmetry of the nanofins through the triangle angle α (defined in Fig. 1B), the nanofin transforms from a rod-like to a triangular structure supporting symmetry-protected quasi-BICs. The first- and second-order modes feature Q-factors of up to 105 and 180, respectively. We show that the excitation efficiency (represented by the absorption) and the Q-factor of the PNM can be flexibly tailored through α in parameter space (Fig. 1C). Precise engineering of the ratio of radiative to intrinsic losses allows tuning of the PNM from the under-coupling (UC) to critical coupling (CC) to the over-coupling (OC) regime. Consequently, we constructed a coupling-tailored PNM array that covers all coupling regimes to perform pixelated molecular sensing (Fig. 1D). The broad wavelength coverage in the mid-infrared (MIR) wavelength region, which is necessary for our surface-enhanced infrared absorption spectroscopy (SEIRAS) method, was achieved by scaling the size of the PNMs in small steps. We demonstrate that molecular analytes can introduce negative, positive, or no modulations to the quasi-BICs depending on the coupling efficiency between light and the used PNM pixels (Fig. 1E). In addition to high Q-factors and field enhancements, our results suggest that, for maximal sensitivity, the radiative decay rate of the resonant metasurface needs to be tailored as well.

Fig. 1. Principle of PNMs and their coupling-tailored sensing capabilities.

(A) Schematic illustration of a PNM unit cell consisting of standing polymer triangles covered in an optically dense layer of gold on a SiO₂ substrate. (B) A symmetric, standing dipolar rod featuring a dipole moment p₁ normal to the incoming electric field E; thus, no coupling is possible. Transforming the rod into a triangle allows coupling of its dipole moment p₂ to E, controlled by the asymmetry parameter α. (C) Tuning α allows for precise control over the radiative loss of the PNMs, capable of tailoring the absorbance from zero to unity. The UC, CC, and OC regimes are marked with different colors. (D) Schematic illustration of a coupling-tailored PNM array for molecular sensing, which consists of size-scaled PNM units in different coupling conditions. (E) Absorbance-modulated sensing based on the coupling-tailored PNM array, in which the analyte’s signal appears as envelope of the scaled PNM resonances. The sensitivity strongly depends on the coupling regime, with the lowest sensitivity around the CC condition and the highest in the UC and OC regime with negative and positive modulations, respectively.

RESULTS

Design of BIC-enhanced plasmonic metasurfaces

All investigated structures are based on arrays of vertically oriented, gold-coated triangles defined by their height h, diameter d, triangle angle α, and periodicity Λ (fig. S1). The gold layer is optically opaque (with thickness >40 nm), yielding zero transmittance and a simplified relation between absorbance A and reflectance R as A = 1 − R. A numerical analysis of different coating thicknesses reveals a minimal required gold thickness of 30 nm in the MIR (fig. S2). To investigate the photonic behavior of the PNM, we numerically studied the out-of-plane symmetry breaking in both momentum (k-) and parameter space by tilting the incident light (θ = 0 − 25°) on a symmetric rod structure and breaking the structural symmetry (α = 0 − 25°) under normal incidence, respectively. The MIR absorption spectra of a PNM with h = Λ = 3.5 μm and d = 0.7 μm reveal three high Q-factor modes (Fig. 2A). At the Γ point, where both excitation and structure are symmetric (θ = α = 0°), the two modes around 6 to 8.5 μm and 5 μm vanish, and the PNM acts like a gold mirror with unity reflectance. This indicates the existence of two symmetry-protected BICs at 8.3 μm (BIC1) and 4.8 μm (BIC2), which can be turned into leaky quasi-BICs by breaking their inversion symmetry either in momentum or parameter space. We attributed the third mode around 3 to 4 μm to an in-plane SLR that does not vanish at the Γ point but features an accidental BIC at α = 18° and a Q-factor of up to 1300 (fig. S3). As our experiments discussed below show, the SLR is drastically quenched because of its instability regarding fabrication and measurement imperfections.

Fig. 2. Numerical analysis of symmetry-protected BICs in momentum and parameter space.

(A) Transverse magnetic (TM) absorbance spectrum of a symmetric (α = 0°) PNM in momentum space illuminated by light under an incident angle θ and of a PNM under symmetric excitation (θ = 0°) in parameter space with a triangle angle α. Three modes are visible in both spaces, which we attribute to first- and second-order symmetry-protected BICs (BIC1 and BIC2) and a SLR (from long to short wavelengths, respectively). (B to D) Electric and magnetic field vectors (arrows) and intensities (in blue and red, respectively) of BIC1, BIC2, and the SLR. The fields were extracted according to the sketched cutting planes, and all correspond to the CC condition of each mode, marked as red lines in (A). (E) Maximal absorbance (gray), Q-factor (blue), and maximal field enhancement (red) of BIC1 in momentum (θ) and parameter (α) space. (F) PNM system illustrated as a single resonator coupled to one radiative and one intrinsic channel. (G) Nanofin sketch indicating the in-plane projection p_x of the nanofin’s dipole p. p_x is proportional to the asymmetry factor tanα. (H) The numerically obtained maximal absorbance (gray) is compared to the TCMT analytical model (black), assuming an inverse quadratic relation between the radiative Q-factor and an asymmetry factor tanα (blue).

To elaborate more on the physical origin of the different resonances, we inspected their mode profiles at the points of maximum absorption in parameter space marked by red lines in Fig. 2A. The corresponding electric and magnetic field distributions of BIC1, BIC2, and the SLR are shown in Fig. 2 (B to D), respectively. The two symmetry-protected quasi-BIC modes exhibit out-of-plane dipolar profiles of the first (BIC1) and second (BIC2) order, showing electric field vectors perpendicular to the excitation and circulating magnetic field vectors around the nanofins (Fig. 2, B and C). Intuitively, these out-of-plane dipoles cannot couple to incoming light at the Γ point with the scalar product of the nanofins’ dipole moment and the impinging electric field being zero, as illustrated in Fig. 1B. Note that the gold layer on top of the substrate plays a crucial role by reducing the radiative decay channels to one (reflection). In contrast to the out-of-plane BIC modes, the mode profile of the SLR in Fig. 2D resembles an in-plane electric dipole with strong electric fields between neighboring nanofins and an out-of-plane circulating magnetic field around them. To study the effect of asymmetry on the light-matter coupling, Fig. 2E shows the absorbance maximum, the Q-factor, and the surface field enhancement of BIC1 for the asymmetry parameters θ and α, revealing an almost mirror symmetric behavior for the two symmetry breaking strategies. By adjusting θ or α, these mode properties can be easily controlled, resulting in maximal Q-factors in parameter space of 105 for BIC1 (blue curve in Fig. 2E) and 180 for BIC2 (fig. S4) and a maximum surface field enhancement of 750 and 1.98 × 10³, respectively. The latter values and their strong dependency on the assumed nanofin tip shape are further discussed in note S1. In the following, we focus on symmetry breaking in parameter space, which allows for direct multiplexing of PNMs with different asymmetries on the same device without changing the measurement conditions, making it more desirable for practical applications.

For a resonant cavity, the Q-factor is typically composed of two parts (31), the radiative Q_rad and the intrinsic Q_int, which are associated with the radiative γ_rad and intrinsic γ_int losses, respectively. The Q-factor can be defined as $Q={(\frac{1}{Q_{\mathrm{rad}}}+\frac{1}{Q_{\mathrm{int}}})}^{-1}=$ $\frac{{\omega }_0}{2({\gamma }_{\mathrm{rad}}+{\gamma }_{\mathrm{int}})}$, where ω₀ is the angular frequency of the resonance. It is common for dielectric metasurfaces (with a negligible γ_int ≈ 0) to have a diverging Q-factor around the BIC condition, namely, $Q\approx Q_{\mathrm{rad}}=\frac{{\omega }_0}{{\gamma }_{\mathrm{rad}}}\to \mathrm{\infty }$ for γ_rad → 0. This leads to the for BICs typical relation between the Q-factor and a structural asymmetry factor AF: Q⁻¹ ∝ AF² (27). In contrast to dielectric systems, we must separate the radiative and intrinsic losses in our PNMs for which we use temporal coupled-mode theory (TCMT). We model our PNM with a single resonator coupled to one radiative and one intrinsic channel (Fig. 2F), as described in note S2 in more detail. Accordingly, the absorbance A of the PNM at the resonance frequency can be expressed as

$$A=\frac{4{\gamma }_{\mathrm{rad}}{\gamma }_{\mathrm{int}}}{{({\gamma }_{\mathrm{rad}}+{\gamma }_{\mathrm{int}})}^{2^{\cdot }}}$$ (1)

As qualitatively shown in Fig. 1B, coupling to the incident light depends on the in-plane component of the nanofin’s dipole moment. Because h remains constant for all asymmetries, the nanofin’s in-plane dipole moment is proportional to tanα, thus, we define AF as tanα (Fig. 2G), leading to ${\gamma }_{\mathrm{rad}}\propto {\mathrm{Q}}_{\mathrm{rad}}^{-1}\propto \mathrm{A}{\mathrm{F}}^2=$ $\tan {\alpha }^2$. The intrinsic loss of our PNM can be extracted from Fig. 2E at the CC condition, where γ_int = γ_rad and thus γ_int = ω₀ tan α_CC², with α_CC = 12°. This gives rise to an analytical solution for the absorbance of the PNM

$$A=\frac{4\tan {\alpha }^2\tan {\alpha }_{CC}{}^2}{{(\tan {\alpha }^2+\tan {\alpha }_{CC}{}^2)}^2}$$ (2)

Without any further fitting, our analytical and numerical results match very well (Fig. 2H). We find a nearly perfect agreement in the UC regime, while deviations remain below 10% in the OC regime, which might be attributed to the simplified asymmetry factor. The good agreement further confirms the relation of $Q_{\mathrm{rad}}^{-1}\propto A{F}^2$, proofing the symmetry-protected BIC nature of our modes. Moreover, the asymmetry factor provides a pathway to precisely control the radiative loss of the PNM to tailor light-matter coupling from the UC to the OC regime.

Fabrication and experimental verification

The PNMs, each with areas of 160 μm by 160 μm, were 3D laser–nanoprinted (two-photon polymerization) in liquid photoresist on a silica substrate (Fig. 3A). After removing the unpolymerized resist, gold was sputtered from four different angles (Fig. 3B). More details about the fabrication process are given in Methods. We fabricated PNMs with different α from the symmetric case of α = 0° to the highly asymmetric case with α = 26° in steps of 2°. The scanning electron microscopy images of our PNMs with α = 4 ° , 12 ° , and 22°, associated with the UC, CC, and OC regimes, respectively, are given in Fig. 3C. We find a good agreement between measured spectra (see Methods) of BIC1 and numerical results (Fig. 3D, fig. S5, and note S3). The inset in Fig. 3D shows CC around α = 12° with a maximum absorbance of 0.75 and a maximum Q-factor of 60. The small discrepancy between our experiments and simulations might result from an angular spread of the excitation source, imperfect linear polarization of light, finite PNM sizes, and fabrication deviations.

Fig. 3. Fabrication and experimental verification of higher-order BICs.

Schematic illustration of the two fabrication steps: (A) 3D laser nanoprinting in a dip-in configuration and (B) four-angle gold sputtering. (C) Scanning electron microscopy images of a PNM with Λ = h = 3.5 μm, d = 0.7 μm, and α = 12° in the top row and side-view images for α = 4°, 12°, and 22° in the bottom row (the size parameters defining the PNM structure are given in fig. S1). (D) Comparison of measured (colored) and simulated (gray) PNM spectra of BIC1 from symmetric (α = 0°) to highly asymmetric (α = 26°) structures. The inset shows corresponding amplitudes and Q-factors. (E) Ultrawide-scaled BIC1 spectra from the near-infrared (1.8 μm) to the MIR (10 μm) wavelength region.

Our 3D nanoprint lithography approach allows us to continuously scale all size parameters as demonstrated in Fig. 3E, where we sweep the BIC mode across a broad spectral range while keeping the Q-factor and amplitude of the resonance nearly constant. We tune critically coupled PNMs (α = 12°) with different scaling factors from 0.4 to 1.6 between 1.8 and 10 μm (near-infrared to MIR) limited only by the used detector (see Methods). Furthermore, scaling the height allows us to excite BIC modes up to the fourth order with even higher Q-factors of up to 84 (note S4 and fig. S6), which to our knowledge is, to date, the highest reported BIC order. We use the second-order BIC to perform refractive index sensing of a liquid (fig. S7). We achieved a large experimental figure of merit (FOM) of 70, which is defined as $\mathrm{FOM}=\frac{\mathrm{\Delta }\lambda }{{\lambda }_{\mathrm{res}}}$, where Δλ and λ_res represent the wavelength shift per refractive index unit and the resonance wavelength, respectively. Our experimental FOM is not the highest reported; however, it is competitive with recent refractive index sensing metasurfaces and even outperforms dielectric BICs (see table S2). While it is not necessary to tune the coupling strength of metasurfaces for refractive index sensing, it is desirable to ensure both high Q-factor and strong enhancement of the surface-confined electromagnetic fields of the metasurfaces, which occurs between the UC and CC regimes (Fig. 2E). Notably, for some fabricated PNMs, we can weakly couple light into the SLR (fig. S8); however, the signal modulation is very low, which further indicates its instability regarding finite sample sizes and excitation angles.

Molecular sensing based on a coupling-tailored PNM array

Typically, SEIRAS exploits the coupling of surface plasmon modes to weak MIR molecular vibrational absorption bands (28, 38). The molecules induce additional intrinsic loss to the resonator system, which dampens the plasmon mode around the absorption band, leading to a highly enhanced signal (39). It has been recognized that the field enhancement is the most critical feature for the sensitivity in SEIRAS (40, 41). To investigate the performance of our PNMs for molecular sensing, we designed and fabricated three coupling-tailored PNM arrays with α = 6 ° , 12°, and 20° covering the UC, CC, and OC coupling regimes, respectively. To fully recover the spectral fingerprint of an analyte, we implemented the pixelated sensing approach (24) in each array through finely scaling the size of all PNM sensing units (Fig. 4A). It should be mentioned that our achieved Q-factors for the fundamental BICs are more than adequate to spectrally resolve a plethora of common analyte molecules or mixtures (table S3 and note S5).

Fig. 4. Light-matter coupling-tailored molecular sensing.

(A) Illustration of three coupling-tailored PNM arrays, each with 8 by 8 size-scaled PNM units. (B) Analytical TCMT solution for the two-resonator system. The gray line denotes the α-dependent maximal absorbance of the unperturbed bright mode, while the colored line shows the perturbed signal with additional loss γ_int2 due to the molecules. The absorbance modulation (the difference between the two lines) is depicted in green, revealing areas of negative, nearly no, and positive modulation in the regions of UC, CC, and OC, respectively. At 13.3°, the absorbance remains completely constant. (C to E) Uncoated (gray) and 5-nm PMMA-coated (colored) absorbance spectra for the UC, CC, and OC sensors, respectively. (F to H) The corresponding sensing results with both simulations (curves) and experiments (dots) consistently showing that the PMMA analyte can introduce negative, no, and positive modulations depending on the coupling regime.

To analyze our results, we adapted our TCMT model (note S2) by adding a second, nonradiative resonator to represent weak molecular vibrations (Fig. 4B, inset). Hence, this dark resonator acts as an additional intrinsic loss channel of the PNM. The adapted absorbance A of the coupled PNM at the resonance frequency is given by

$$A=\frac{4{\gamma }_{\mathrm{rad}}({\gamma }_{\mathrm{int}}+{\gamma }_{\mathrm{int}2})}{{({\gamma }_{\mathrm{rad}}+{\gamma }_{\mathrm{int}}+{\gamma }_{\mathrm{int}2})}^2}$$ (3)

with ${\gamma }_{\mathrm{int}2}=\frac{{\mu }^2}{{\gamma }_{\mathrm{analyte}}}$ as the additional intrinsic loss channel due to the analyte, where μ and γ_analyte denote the coupling constant and the analyte’s intrinsic loss, respectively, both in the dimension of frequency. To study the effect of γ_int2, Fig. 4B compares the calculated absorbance maximum as a function of α with (colored spectrum) and without (gray spectrum; same as in Fig. 2E) the additional intrinsic loss channel based on Eq. 3. As an exemplary demonstration, we chose γ_int2 = 0.5γ_int in our calculations, which shows the stretching of the curve, shifting the CC from 12° to 15°.

Consequently, we show that the absorbance modulation depends strongly on the coupling regime of the PNMs. We chose polymethyl methacrylate (PMMA) as our analyte and investigate its prominent absorption line of around 5.75 μm. Our numerical study (Fig. 2, C to E) reveals a negative modulation for the UC regime and a positive modulation for the OC regime. Notably, we observe no and nearly no modulation at 13.3° and around the CC condition, respectively. This is in strong contrast to the intuitive assumption that the sensitivity for SEIRAS would be the highest at the CC position, where the field enhancement is the strongest. The envelopes of the simulated absorbance modulations in different coupling regimes were plotted in Fig. 4 (F to H) (lines), revealing a maximal modulation of around 15% (fig. S9 for normalized modulation). For our measurements, we spin-coated a thin layer of PMMA on the PNM arrays (Methods). Our experimental results (dots in Fig. 4, F to H) follow the same trend in different coupling regimes as the simulations. Hence, our demonstration explicitly proves that tailoring the coupling conditions of a high Q-factor metasurface is essential for high-performance molecular sensing.

DISCUSSION

We have designed a new PNM platform composed of 3D triangular nanofins supporting out-of-plane symmetry-protected BICs in parameter space. Tuning the triangle angle α of the nanofins allows us to precisely tailor the radiative decay rate and couple to the metasurface in different regimes. We have shown that the coupling efficiency of the PNMs, represented by the metasurface absorbance, can be flexibly tuned from zero to unity. We fabricated our metasurface structures based on 3D laser nanoprinting in liquid resist. Our PNMs exhibit high Q-factor BIC modes up to the fourth order, scaled from 1.8 to 10 μm. In addition, we have designed and fabricated coupling-tailored PNM arrays for pixelated molecular sensing. Our results unveil a strong dependency of the sensitivity on the asymmetry parameter of the PNMs, which was echoed from our TCMT calculations. We show that the additional intrinsic loss imposed by the molecular analyte can introduce negative, positive, or even no modulations on the BIC resonance. As a result, we have demonstrated the importance of controlling light-matter interaction in a coupled metasurface system for enhancing the detection sensitivity of molecular sensing. We believe that our demonstrated light-matter interaction-enhanced metasurface platform harnessing tunable high Q-factor plasmonic BICs paves the way for numerous applications for optical sensing (42), energy conversion (12), nonlinear photonics (14), surface-enhanced spectroscopy (5), quantum optics (43), and information technologies (44).

METHODS

All simulations were performed using the finite element solver CST Studio Suite (Simulia, Providence, USA) with adaptive mesh refinement and periodic boundary conditions. Because we assume an optically dense layer of gold, as discussed in fig. S2, the nanofins were simulated as solid gold triangles with no polymer core to reduce calculation time. We adapted the permittivity for gold and PMMA from (45) and (46), respectively, while we assume SiO₂ to have no dispersion with n = 1.5 and k = 0.

We printed the PNMs by using a Photonic Professional GT 3D (Nanoscribe, Germany) direct laser printer. A “dip-in” configuration was used with the substrate fixed upside down and liquid photoresist (IP-Dip, Nanoscribe, Germany) in between it and a 1.4 numerical aperture (NA), 63× oil immersion objective. A 780 nm femtosecond pulsed laser polymerizes the resist via two-photon absorption processes. The focus position of the laser is controlled via a galvo mirror in the xy plane and a piezo stage along the z axis. Afterward, the unpolymerized resist is removed by placing the substrate in a propylene glycol methyl ether acetate (PGMEA) bath (15 min). We further cleaned the samples in an isopropyl alcohol (IPA) bath (15 min) followed by a Novec 7000 bath (2 min). We used a Von Ardenne LS 320 S magnetron sputterer to sputter an adhesion layer of ≍5 nm chrome followed by ≍40 nm gold sputtered from four sides under an angle of 20°.

The measurements in Fig. 3E were performed with a HYPERION IImicroscope (Bruker) combined with a VORTEX 80V FTIR (Bruker). We used a 15× mirror objective and a liquid nitrogen cooled mercury cadmium telluride (LN-MCT) detector in reflection mode. For all other optical measurements, we used the spectral imaging MIR microscope Spero from Daylight Solutions Inc., USA, with a low 4× magnification objective (NA = 0.1) and a 2 mm² field of view. The system is equipped with four tunable quantum cascade lasers continuously covering the range between 5.6 and 10.5 μm. To extract the spectral data from each metasurface array, we used an edge detection algorithm to identify the corresponding pixels. We determined the position, rotation, and size of single metasurfaces by fitting a grid mask over all selected pixels. Next, we averaged the spectral data of all pixels within the detected area to reduce noise. For the molecular sensing in Fig. 4, we used a 1% solution (A1) of 495K PMMA in anisole and spin-coated the film with 5000 rpm (for 2 min) followed by a 1min bake at 120 °C.

Supplementary Materials

This PDF file includes:

Notes S1 to S6

Tables S1 to S3

Figs. S1 to S10

References