Maria Letizia De Marco

Dr Taizhi Jiang

Dr Jie Fang

Sabrina Lacomme

Yuebing Zheng

Alexandre Baron

Brian A Korgel

Dr Philippe Barois
email: philippe.barois@crpp.cnrs.fr

Dr Glenna L Drisko
email: glenna.drisko@icmcb.cnrs.fr

Dr Cyril Aymonier
email: cyril.aymonier@icmcb.cnrs.fr

Maria Letizia

De Marco

Dr M L De Marco

Dr B A Korgel Mcketta

Y Zheng Walker

Dr A Baron

Broadband forward light scattering by architectural design of core-shell silicon particles

Keywords: Visible light silicon resonators, core-shell, Huygens sources, directional light scattering

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Introduction

In conventional optics at visible-light frequencies, optical properties result solely from the electric polarization of matter. [START_REF] Landau | Electrodynamics of Continuous Media[END_REF] Metamaterials have emerged as a new class of materials designed to provide a companion magnetic polarization, whereby unparalleled light steering is anticipated. [START_REF] Shalaev | [END_REF] Commanding both electric and magnetic response to light opens the way to extraordinary properties such as cloaking, [3,4] negative refraction and perfect lensing, [START_REF] Shalaev | [END_REF]5] and broadband total transmission or reflection, [6][7][8] to name a few. The realization of metamaterials requires the design of resonant units (e.g. particles) exhibiting a strong magnetic response, ideally with a magnetic scattering efficiency larger than one, and of subwavelength size to preserve optical homogeneity. [9] High refractive index dielectric particles are appealing as they naturally sustain intense magnetic and electric Mie resonances, with low light absorption, [10][11][12] which is the limiting factor for plasmonic nanoparticles. [13] Crystalline silicon presents the best optimization of Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 3 refractive index and absorption coefficient in the visible among currently known materials. [14] However, spherical silicon particles exhibit well separated dipolar resonances, which results in wavelength dependent angular scattering, precluding their applications as Huygens sources.

Merging the two dipolar resonances is of considerable interest to enable high efficiency broadband forward scattering. [15] The electric and magnetic Mie resonances can be overlapped by reducing the refractive index, [16] employing clusters of particles, [17] introducing shape anisotropy [6,15] or designing a core-shell architecture. [18,19] Spherical core-shell particles are insensitive to the direction and polarization of the incident light and thus have advantages over anisotropic particles. Naraghi et al. theoretically proposed the first core-shell particle design composed of two dielectrics with different refractive indexes displaying either total forward scattering or near zero forward scattering by adjusting the core-to-shell radii ratio. [20] Tsuchimoto et al. demonstrated core-shell Si@SiO2 particles with a forward-to-backward scattering ratio five times higher than the bare Si particle, thanks to the coating SiO2 shell. [19] However, to date, no report exists for the bottom-up synthesis of silicon-based core-shell resonators active in the visible range.

Here, we demonstrate a colloidal synthesis involving the decomposition of bis(N,N'diisopropylbutylamidinato)dichlorosilane (silicon bisamidinate, a custom designed silicon coordination compound) with trisilane in supercritical n-hexane (Pc = 30.3 bar and Tc = 235 °C) to generate highly uniform core-shell Si nanoparticles with tunable optical electric and magnetic dipole resonances in the visible spectrum. The core size and shell thickness can be adjusted by simply changing the molar ratio between the two silane precursors. Measurements and simulations of the scattering properties show that these silicon-based core-shell particles exhibit strong magnetic scattering at visible frequencies and that the electric and magnetic dipolar resonances can be superimposed by tuning the core-to-shell ratio, thus validating the concept of a high index core encapsulated in a lower index shell to obtain total forward scattering. [19]

2.

Experimental Approach to Produce Silicon Core-shell Particles. fabrication. [21][22][23] The decomposition of trisilane in supercritical n-hexane yields monodisperse, submicrometer spherical particles of hydrogenated silicon. These particles exhibit well separated electric and magnetic dipole scattering in the near infrared spectrum. [22] Previously reported diameters range between 400 and 1000 nm. [21] Here, silicon particle size is reduced and a core-shell architecture is obtained by mixing trisilane with silicon bisamidinate in supercritical n-hexane (Figure 1A). Three different Si bisamidinate to trisilane molar ratios are investigated: 1/5, 1/20 and 1/40. Particles obtained from pure trisilane provide a control sample to assess the role of the Si bisamidinate coordination compound on the size, architecture and optical properties of the particles.

Spherical, monodisperse particles are obtained with variable core and shell dimensions that depend on the ratio of the two precursors (Figure 1 B-J and S3 and Table S3 in Supporting Information). Particles made from only trisilane have a 10 nm diffuse layer with a significant amount of oxygen, whereas particles made from the two precursors have a core-shell architecture with a well-defined edge between a silicon core and a shell (Figure 1 B-I) containing silicon, oxygen and nitrogen (SiOxNy). The incorporated nitrogen originates from the thermal decomposition of the Si bisamidinate complex (Figure S4 in Supporting Information). The nitrogen-containing shell is most likely more porous, and thus prone to oxidation upon particle exposure to the ambient environment post-synthetically. While the shell thickness increases with increasing Si bisamidinate concentration, the core size decreases from 190 to 140 nm with increasing bisamidinate concentration (Figure 1J), probably resulting from more extensive oxidation with increased nitrogen content. The low index shell is thus obtained while simultaneously decreasing the core diameter to values that are favorable for visible light scattering.

Particles made with pure trisilane are consistently larger than the core-shell particles. Adding a small amount of Si bisamidinate significantly decreases the overall particle size, dropping the diameter from 370 nm for pure trisilane to below 200 nm for the 1/40 ratio (Figure S3 in Supporting Information). However, as more Si bisamidinate is added, the particle size increases, with the 1/5 ratio having nearly the same diameter as particles made from pure trisilane. We A narrow size distribution is important for a homogeneous optical response, where size dispersion was also dependent on the precursor ratio (Figure 1J). The error in size distributions in Figure 1J takes into account particles from multiple batches. Particles made from pure trisilane were highly uniform within a single batch, but the particle size from one batch to another could vary substantially. Adding Si bisamidinate led to higher batch-to-batch reproducibility, but slightly larger size dispersion within a batch. This supercritical synthesis technique produces milligrams of uniform particles in a single batch, while giving control over architectural design.

According to X-Ray diffraction (XRD) patterns, selected area electron diffraction (SAED) (Figure S5) and Raman scattering (Figure 1 K), all the different batches have the same bond order, regardless of the relative amount of Si bisamidinate added. The XRD pattern exhibits two broad signals at 28.5° and ~51°, which are typically associated with amorphous silicon. [24] However, Raman spectroscopy, which is more sensitive to short range order than both SAED and XRD, [21] indicates that silicon cores possess an intermediate bond order between amorphous silicon and crystalline silicon (Figure 1K), as all batches show a relatively sharp peak at ~500 cm -1 . In fact, fully amorphous silicon has a broad Raman shift at about 480 cm -1 , while the crystalline form has a sharp, intense Raman shift at 522 cm -1 . [21,[25][26][27] Intermediate bond order implies that the particles contain high-order inclusions, consisting of linear chains of ordered tetragonal silicon (chain-like objects) or of nanocrystalline domains of about 1-2 nm, embedded in the amorphous silicon matrix. [21,26] The Raman and XRD results are not in contrast, if we consider that the crystalline domains are very small and randomly oriented, and therefore subject to Scherrer broadening. [21,24] As for the SiOxNy coating shell, the absence of any additional peak in the XRD patterns confirms that the shell is completely amorphous.

Fourier Transformed Infrared (FTIR) spectroscopy (Figure 1 L) reveals the presence of Si-H and Si-OH in the particles, though their relative intensity varies with changing precursor ratio.

The intensity of the SiOx bond stretching (at ~ 1050 cm -1 ) [21,28] and of the Oy-SiHx bond wagging (at ~ 880 cm -1 ) [29] increases with respect to the SiHx bond stretching (~ 2100 cm -1 ) [21,28] and bending (~ 660 cm -1 ) [28] for increasing molar ratios. Nucleation may occur through an intermolecular reaction between trisilane and the bisamidinate silane complex. Silicon hypervalent centers have enhanced Lewis acidity by both attachment of strong electron withdrawing groups and by ring strain, [30] with reports of super Lewis acidity in such silanes. [31] The silicon bisamidinate complex contains two chlorine atoms that collectively withdraw electron density from one side of the complex and two 4-membered rings from the other side. It is thus reasonable to believe that this complex is electrophilic. On the other hand, trisilane decomposes through 1,2-H-shifts to form disilane and silylene (R2Si:) at 250 °C. [32] Silylene is a Lewis base and a nucleophile, [33] and is thus apt to react immediately with the electron depleted bisamidinate complex to form a new adduct, which may act as a nucleus for the growth of the silicon-based particles. Probably, the amidinate ligand, liberated at low temperature upon the reaction between the silicon bisamidinate complex and trisilane, and other nitrogen-containing degradation products, are incorporated into the architecture near the end of the reaction when the reaction temperature is highest, the trisilane concentration begins to dwindle and the reaction kinetics slow. Dark field single particle scattering shows that the scattering properties of individual particles are affected by particle size and morphology. [34] Figure 2 A-D shows a series of dark field images of four different particles resulting from different Si bisamidinate to trisilane ratios, each one representative of its batch, along with the dark field scattering spectra and the simulations performed using Mie theory (experimental details described in the Methods section). [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF] The scattering spectrum of a spherical core-shell particle is fully determined by the Mie theory if the following information is know: the refractive index of the particle and of its environment, the radii of the core and of the shell. The refractive index of individual particles can be retrieved through the best match of the calculated and measured scattering spectra. Knowing the outer diameter from scanning electron microscopy (SEM) measurements, we varied the shell thickness -within the experimental uncertainty given by the STEM-EDX analysis-and the refractive indexes of the core and the shell (Figure 2 E-H, Table S2 in Supporting Information).

The unknown effective refractive indexes of the core and the shell are assumed to be homogeneous. Four unknown functions of the wavelength are thus to be determined, namely the real and imaginary parts of both the core and the shell, linked two by two by the Kramers-Kronig relation. In order to build the appropriate trial functions, we define the core as a composite material made of a ternary mixture of crystalline silicon, amorphous silicon and a low refractive index medium (equivalent to that of water) and we use the simple Maxwell-Garnett mixing rule to estimate the value of the effective indexes (see Equation 1). The Maxwell-Garnett effective permittivity εeff of the core, made of 2 different inclusions of permittivity ε1,2 and volume fraction f1,2, in a host medium of permittivity εh reads: [START_REF] Sihvola | Subsurface Sensing Technologies and Applications[END_REF]

M eff h mh m m1 eff h m h 22 f             (1)
The dispersion of the real and imaginary parts of the refractive indexes is obtained by the square root of the effective permittivity. The choice of amorphous and crystalline silicon comes from Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron for the presence of low index inclusions, including a certain degree of hydrogenation, arising from the bottom-up synthesis method. [21,22] The fractions of amorphous silicon and low index medium control the imaginary and real parts of the effective indexes respectively, while the Maxwell-Garnett rule guarantees the Kramers-Kronig relationship. Thus, the number of free parameters reduces to two constants, namely the volume fractions of amorphous silicon and low index medium. The refractive index of the shell is also estimated by applying the Maxwell-Garnett rule to a two-component mixture made of low-index inclusions in silica. The resulting effective refractive index is slightly lower than the index of silica, arising from microporosity and the presence of nitrogen. Let it be clear that this model is only a convenient tool to construct a physical effective index and should not be taken as a structural model.

The scattering profile, red-shifting as particle size increases (Figure 2 A-D), is well reproduced by the simulation. The dark field experimental scattering spectra are displayed (Figure 2 E-H) with the computed scattering from the optimized refractive indexes (Figure 2 I-J). The particle obtained with pure trisilane shows dipolar and quadrupolar resonances in the visible spectrum, with magnetic dipole resonance at about 800 nm. This indicates that the size of the core of pure trisilane particles is noticeably larger than that of the silicon cores in the core-shell particles.

Moreover, even if these particles do not show a sharp core-shell boundary, the presence of a shell with a thickness of 70 nm had to be considered in order to obtain the best match between the experimental and simulated spectra. The simulations of core-shell particles show that the magnetic and electric dipole partially overlap in the visible spectrum. The broadband superposition of the magnetic and electric resonances is due to the presence of the low-index shell. The thicker the shell, the higher the ratio between the intensity of the magnetic and electric dipole resonance. Indeed, it has been predicted that a thicker shell increases the intensity of the forward scattering. [19] Bare silicon particles with the same radius and refractive index as the Si cores of the core-shell particles, present well separated dipoles in absence of a low index coating shell (Figure 2L).

In complement to single particle dark field spectroscopy, we studied the scattering from an ensemble of dispersed particles by polarization-resolved static light scattering (SLS), in order Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 11 to assess the quality and homogeneity of batches made by bottom-up synthesis. The case of a colloidal suspension of isotropic scatterers has been solved by Sharma. [START_REF] Sharma | [END_REF] SLS analyzes the polarization of the scattered light at a scattering angle of 90°. Briefly, the magnetic dipole and the electric quadrupole scatter polarized light parallel to the scattering plane (axial scattering) while the electric dipole and the magnetic quadrupole scatter polarized light perpendicular to the scattering plane (transverse scattering), [16,38] therefore, the contribution of the magnetic dipole to the total scattering can be separated from the electric dipole based on their polarization.

Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron Axial and transverse scattering were simulated using the scattering matrix formalism and the Mie theory [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF] (Figure 3F-I). The size distribution of each batch was considered (Figure 3 E), as monodispersity sharpens the scattering peaks and maximizes the scattering efficiency. The monodispersity of the sample with a 1/5 ratio is illustrated in the insert of Figure 3 E, for which the particle size distribution is below 5%. As dark field data indicate that the shell of the particles synthesized with bisamidinate has a refractive index of about 1.42 ±0.01 (Figure 2 K), we chose to perform SLS measurements in chloroform, a solvent with a matching refractive index of about 1.45 at optical frequencies. The contribution of the shell to scattering hence vanishes and the scattering reduces to the contribution of bare silicon cores. The particles considered have a radius Rc = R-t, where R is the total particle radius and t is the average shell thickness. The index matching of the coating shell is not as good for the pure trisilane particles, in this case we neglected the presence of the diffuse shell and considered these particles as composed of pure silicon with a very thin passivation layer.

As in the case of the single particle dark field scattering, the refractive index and absorption coefficient of the silicon cores were constructed with the Maxwell-Garnett mixing rule (details are reported in Table S3, in Supporting Information). The refractive indexes and extinction Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 13 coefficients obtained from SLS (Figure 3 J-K) are in good agreement with the values obtained from the dark field scattering for the core-shell particles (Figure 2 I-J). Let us note that the refractive indexes obtained-mostly above 3.0-albeit lower than the index of pure, compact silicon, are among the highest indexes reported in the visible spectrum. The absorption coefficient k is an intermediate value between those of amorphous and crystalline silicon. Dark field and SLS analyses both confirm these particles display high refractive index and low absorption.

In order to further compare the SLS and dark field results, the optical response of an average single particle was calculated in air using the refractive indexes and absorption coefficients retrieved from SLS (Figure S6 I-L in Supporting Information) and the average particle size for the silicon cores. The coating shell was considered using the average shell thickness obtained by STEM-EDX and the refractive indexes obtained from dark field simulations. Both SLS and dark field simulations indicate that the ratio between the magnetic dipole and electric dipole intensity approaches 1 with increasing bisamidinate concentration (Figure 3L and S6 in Supporting Information). The average simulated spectra for the core-shell particles have much in common with the single particle simulated spectra. These converging results validate the core-shell model, giving confidence in the effective refractive index values and attesting to the uniformity of the particles within a batch.

Efficient forward light scattering requires superimposed dipoles. [16,19] As the Si bisamidinate to trisilane molar ratio used in the reaction was increased, the two dipolar maxima coalesced: the magnetic dipole blue shifts while the electric dipole position remains fixed (Figure 3M).

Theoretical studies have shown that dipole coalescence may result from a refractive index contrast on the order of 2 between a homogeneous particle and the ambient medium. [16] Here we demonstrate experimentally that coating a high-index particle (n>3) with a low index dielectric shell superimposes the dipoles, while keeping a high scattering efficiency, in agreement with the findings of Tsuchimoto and co-authors. [19] Figure 4 shows intensity maps of the electric and magnetic fields computed for the 1/5 amidinate to trisilane particle at  = 619 nm, where de electric and magnetic dipolar scattering coincide in the far field as shown in Figure 2G. In this example, the core radius is 75 nm and Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron S2 in Supporting Information). The maxima of the resonant magnetic and electric fields are located in the core and in the shell respectively. The center of the core corresponds to a magnetic maximum and an electric minimum, whereas the electric maximum is located in the shell along the forward direction. Similar maps computed across the visible range show that the localization of the fields does not change much with wavelength (see Figure S7 in Supporting Information). This computation shows how, by tuning the coreshell morphology, the two dipole resonances can coexist within the particle. The polar plots in Figure 5 illustrate the spectacular superiority of the core-shell architecture over a plain silicon sphere for the production of Huygens sources. The scattering diagrams of the non-coated silicon sphere of radius 75 nm demonstrates equal forward and backward scattering at 500 and 600 nm, where the electric and magnetic dipoles respectively dominate. Almost total backward scattering is observed at 550 nm, where ED and MD are opposite, and relatively weak total forward scattering is seen at 656 nm, where the electric and magnetic dipoles coincide. On the other hand, over the same range, the scattering diagrams of the core-Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 15 shell particle, computed for the 1/5 amidinate to trisilane particle described in Figure 2G, exhibits intense broadband forward scattering from 500 nm to 750 nm with a scattering efficiency consistently above 1.3, and a maximum of 2.8 at 600 nm.

Conclusions

The potency of the bottom-up chemical approach is in its versatility. This first large-scale bottom-up synthesis of core-shell silicon-based nanospheres surpasses materials produced by top-down methods. The size and the shell thickness are controlled by changing the relative concentration of two molecular precursors. The richness of the core-shell architecture allows a fine tuning of Mie resonances in the visible spectrum. SLS and single particle scattering show that the two resonances tend to overlap as the shell thickness increases, fulfilling the conditions of a Huygens source. For a shell thickness similar to the core diameter, not only do the two Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 16 resonances occur throughout the same broad wavelength range, but the magnetic and electric dipolar modes have nearly the same amplitude. Over a broad range of visible frequencies, the core-shell particle outperforms the pure silicon particle both in intensity and directionality of forward These properties are crucial for the development of metasurfaces composed of broadband Huygens sources. Moreover, regarding the strength of the dipolar magnetic Mie resonances, these particles are suitable for the fabrication of a bulk artificial material with effective magnetic permeability significantly different from 1 in the visible.

Methods

Materials.

Trisilane was purchased from Voltaix, and stored in a glovebox (oxygen level < 0.1 ppm). N,N′-diisopropylcarbodiimide (99%), silicon tetrachloride (99%), butyl-lithium (2.5 M in hexane), n-hexane (anhydrous 95%), chloroform, and absolute ethanol were purchased from Sigma-Aldrich and used without further purification. Toluene and THF were dried using an Innovative Technology solvents purification system, then oxygen was removed by three freezepump-thaw cycles. The purified solvents were stored over 3 Å molecular sieves in an argon filled glovebox.

Synthesis of bis(N,N'-diisopropylbuyl)dichlorosilane.

The synthesis of bis(N,N'diisopropylbutyl)dichlorosilane, [(iPr-N)2C(C4H9)]2SiCl2 (2), was carried out under inert atmosphere, using Schlenk techniques to protect reactants and products from moisture and oxygen, by modifying previously published protocols. [39,40] The bis(N,N'diisopropylbuyl)dichlorosilane, or silicon bisamidinate for simplicity, has been prepared by a two-step synthesis (see reaction scheme in Figure S1 in Supporting Information). Butyl-lithium (13 mL, 0.032 mol) was added to a solution of of N,N′-diisopropylcarbodiimide (5 mL, 0.032 mol) in THF (80 mL) at -30 °C under magnetic agitation. This reaction yields the compound lithium (N,N'-diisopropylbutylamidinate), [(iPrN)2C(CH3)]Li•THF (1). Typically, the product (1) was not isolated and purified. The reaction was stirred overnight at room temperature to ensure complete reaction. Then, SiCl4 (1.86 mL, 0.016 mol) was added at -78 °C. The solution was stirred at room temperature for 18 h. The solvent was evaporated and substituted with toluene (60 mL). The solution was filtered, and silicon bisamidinate was crystallized from the filtrate by slow evaporation of the toluene.

Silicon bisamidinate was stored at -15 °C, under an argon atmosphere, to avoid premature degradation, as it is extremely sensitive to moisture and thermally labile. Supercritical synthesis of the silicon core-shell particles. The supercritical synthesis was carried out in a 10 mL titanium (alloy grade 2) batch reactor, purchased from High Pressure equipment (HiP) (part number 210617). This kind of reactor can withstand a maximum pressure and temperature of 345 bar (5000 psi) and 600 °C. The synthesis protocol was similar to what has been reported previously about the supercritical synthesis of silicon nanoparticles. [21][22][23] The reactor was loaded and sealed in a nitrogen filled glove box (O2 < 0.1 ppm) with n-hexane (5.6 mL), trisilane (5 µL, 40.2 µmol) and a variable amount of silicon bisamidinate (caution: trisilane is pyrophoric and must be handled with extreme care under inert atmosphere). The molar ratios, concentration and number of moles of silicon bisamidinate and trisilane used in the reactions are summarized in Table S1 in Supporting Information. The reactor was placed in a ceramic heating block, that was preheated to 510 °C, using a dummy reactor. Supercritical synthesis was carried out at 460 °C and 300 bar, for a duration of 10 min. After 10 min, the reactor was removed from the heating block and placed in an ice bath to quench the reaction.

Once the reactor cooled to room temperature, it was opened and the products collected under Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 18 air. The resulting product was centrifuged at 8000 rpm for 5 min, to precipitate the nanoparticles and discard the solvent. This cycle was repeated three more times, using chloroform to wash the products.

The nanoparticles were stored in a nitrogen-filled glovebox as a dry powder to avoid any further oxidation. The supercritical reaction yields about 2.0 -2.7 mg of dry particles, which correspond to a mass yield of about 50% (only in the case of the 1/5 silicon bisamidinate to trisilane ratio, the mass yield was about 30%).

Each experiment was repeated at least twice (for 1/40 and 1/5 ratio) or three times (for pure trisilane and 1/20 ratio) to ensure reproducibility in terms of particles size and dispersion. SEM characterization. SEM images were acquired using a Zeiss Supra 40 VP SEM, with an accelerating voltage of 5 keV. The samples were prepared by drop-casting a colloidal suspension of Si nanoparticles in chloroform onto the polished face of p-doped silicon wafer.

STEM-EDX characterization.

Selected area diffraction scattering (SAED), bright and dark field TEM imaging and elemental mapping of the Si particles were carried out using a Talos F200S G2 TEM (ThermoFisher, Eindhoven), using an accelerating voltage of 200 kV. Energy dispersive X-Ray spectroscopy (STEM-EDX) analysis and TEM imaging were performed on cross-sectioned particles. The samples were prepared by including free-standing particles in the form of a dry powder into an epoxy resin (Epon 812; Delta Microscopies, Toulouse, France) using beam capsule conical tips. The polymerization of the resin was carried out at 60 °C over a period of 24-48 hours.

The resin containing the particles was then sectioned using a diamond knife (Diatome, Biel-Bienne, Switzerland) on an ultramicrotome (EM UCT, Leica Microsystems, Vienna, Austria).

Ultrathin sections (70 nm) were placed on copper grids with a carbon membrane for observation. Raman scattering. Raman spectra were collected with an Xplora spectrometer by Horiba, equipped with a confocal microscope. Samples were prepared by drop casting Si nanoparticles suspended in chloroform onto a glass microscope slide. An objective lens with a magnification of 50X was used to observe the sample and choose the measurement area. A 100X objective lens was employed to focus the laser beam on the selected spot. The spectra were run using a 532 nm excitation wavelength, using a filter to reduce the laser power to 50% of the total power. A 1800T grating was used to separate the scattered light into its components. Baseline subtraction was performed on each spectrum, using a linear baseline. Five measurements in five different zones were collected for each sample, to assess the reproducibility of the measurement and the uniformity of the sample.

X-Ray diffraction. Powder X-Ray diffraction spectra were performed using a Rigaku Spider diffractometer operated at 40 kW and 40 mA, with a Cu anode (λ=1.54 Å).

Nuclear magnetic resonance. Proton nuclear magnetic resonance spectra ( 1 H NMR) of the silicon bisamidinate were acquired using a Bruker Advance III-HD 400 MHz SB spectrometer (Wissembourg, France) equipped with a 5 mm broadband SmartProbe at 25 °C in C6D6. [START_REF] Landau | Electrodynamics of Continuous Media[END_REF] H-NMR spectra were acquired at 400.13 MHz using a single pulse sequence (π/2 pulse width of 10 µs, recycling delay of 2 s, acquisition time of 1.6 s, spectral window of 25 ppm and 24 scans).

Dark field single particle scattering. Dark field scattering spectra of particles were measured using an inverted microscope (Ti-E, by Nikon) operating in transmission mode, equipped with a halogen light source (12V, 100 W), a CCD camera and spectrograph (by Andor), an oil objective (100x) and a dark field condenser. [34] Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 20 Samples were drop-cast from dilute suspensions of particles in ethanol onto a microscope glass slide. The slide was placed between the dark field condenser and the oil objective. Scattered light was collected through the objective with the spectrometer, while dark field images of the particles were collected using the CCD camera. The aperture number of the oil objective was 0.5, while the aperture number of the dark field condenser was 1.43-1.20.

DF measurements were carried out on 10 particles in each batch to check the uniformity of the observations. An excellent reproducibility was obtained within each batch.

Static light scattering. Polarization resolved static light scattering was carried out using a custom-built set-up. The scattering matrix formalism linking the incident field Ei to the scattered field Escat (Equation 2) was used. [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF] The plane was defined by the directions of the incident and scattered fields, forming the scattering plane. The subscripts // and  signify the field components parallel (axial) and perpendicular (transverse) to the scattering plane respectively. For isotropic scatterers, such as spheres, the off-diagonal elements of the scattering matrix are zero.

S S iq

                    E E E E (2)
Theta (θ) is the scattering angle and phi (φ) is the angle between the scattering plane and the direction of the polarization of incident light (see Figure S2). At a scattering angle θ of 90°, the odd and even scattering modes are separate: the S1 element cumulates the scattering contribution of the electric dipole, magnetic quadrupole, electric octupole, etc. while the S2 element contains the contribution of the magnetic dipole, electric quadrupole, magnetic octupole, etc. [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF][START_REF] Sharma | [END_REF]38,41] The experimental geometry is shown in Figure S2 in Supporting Information. The light source is a super continuum laser (SuperK EXB-6 with SuperKSplit filter from NKT Photonics) emitting from 440 to 900 nm. The incident beam was linearly polarized by a Glan-Taylor polarizer (Thorlabs GL5-A) and the polarization angle phi was controlled by the rotation of a multipole scattering and EM coupling between particles was negligible, so that the scattering of all particles added up, weighted by their probability of occurrence. The probability P(Ri) of particle occurrence with a certain radius, Ri, was estimated from the histograms reported in As mentioned in the main text, the presence of the coating shell was neglected, since it has a refractive index very close to the refractive index of chloroform (Figure 2K). [START_REF] Polyanskiy | Refractive Index.INFO, Refractive index database[END_REF]48] Therefore, the size distribution of the silicon cores was considered for the computation of the axial and transverse scattering cross-section (Equation 9 and 10). [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF] The silicon cores size distribution was calculated by subtracting the average shell thickness, t, calculated thanks to the STEM-EDX characterization (see Table S3 in Supporting Information) from each value of the total radius Ri (reported in the histograms in Figure 3). By doing so, the size histograms were shifted to smaller values by a factor 2t. The average shell thickness and size distribution were experimentally known, and were considered as constant parameters during the simulations. The dispersion of the refractive index and absorption coefficient of the silicon cores were optimized for each batch, in order to obtain the best simulations of the experimental spectra, using the Maxwell-Garnett mixing rule (Equation 1).

These values were then used to calculate the scattering efficiency of an isolated core-shell particle in vacuum, having total radius, R, and shell thickness, t equal to the average values for

7 Figure 1 .

 71 Figure 1. Synthetic route towards optically-resonant core-shell particles. (A) Scheme representing the supercritical synthesis of core-shell silicon particles in a batch reactor heated to 460 °C. STEM-EDX mapping of the cross section of silicon particles realized with (B and F) pure trisilane, (C and G) 1/40, with (D and H) 1/20, and (E and I) 1/5 Si bisamidinate to trisilane molar ratio, respectively. The size of the scale bars represents 500 nm for the images B-E and 200 nm for the images F-I. (J) The core size and shell thickness of the particles depend on the molar ratio between the two precursors. (K) Raman and (L) infrared spectra of the different batches of particles, where δ represents the bending modes and ν the stretching modes.

Figure 2 .

 2 Figure 2. Light scattering properties of single particles. Dark field images of one particle representative of each batch: (A) 1/40 ratio (Ø=150 nm), (B) 1/20 ratio (Ø=262 nm), (C) 1/5 ratio (Ø=380 nm), and (D) pure trisilane (Ø=392 nm). The size of the scale bars represents 1 µm. The insets are SEM images of the measured particle, where the size of the scale bars

Figure 3 .

 3 Figure 3. Optical properties of batches of silicon particles. SEM pictures of batches of particles realized with different molar ratios: (A) 1/40, (B) 1/20, and (C) 1/5, and (D) with pure trisilane. The size of the scale bars represents 1 µm. (E) Histograms showing the diameter dispersion of different batches of particles of Figure 3 A-D, the inset shows the size distribution of the 1/5 sample. Experimental (solid lines) and simulated (dotted lines) axial (red) and transverse (blue) scattering of colloidal suspensions of particles produced with (F) 1/40, (G) 1/20, and (H) 1/5 ratios and (I) pure trisilane. (J) Refractive index and (K) absorption coefficient obtained from the SLS simulations. (L) Comparison of the MD/ED ratio between the dark field and the SLS data as the molar ratio increases and (M) the position of the maxima of the ED and MD resonances as a function of the Si bisamidinate relative concentration. The trends shown in (L) and (M) are extracted from the simulations in Figure 2 E-H and S5 I-L in Supporting Information.

Figure 4 :

 4 Figure 4: Electric field (left) and magnetic field (right) intensity maps computed for the 1/5 amidinate to trisilane particle described in Figure 2G at  = 619 nm, where the electric and magnetic dipolar far-field scattering coincide. The polarization is set perpendicular to the shown cutaway. The inner and outer black circles represent the core-shell and shell-free space interfaces respectively. The color scale maps the intensities as a percentage of the maximum in each case.

Figure 5 .

 5 Figure 5. Angular dependence of the scattering cross section for a core-shell and a bare silicon particle. Top row: Polar plots of the differential scattering efficiency computed for the coreshell particle shown in Figure 2G (blue lines) and a reference crystalline silicon sphere of radius 75 nm (red lines) at λ = 500 nm, 550 nm, 600 nm, 656 nm, 700 nm and 750 nm from left to right. Radial units are steradian -1 . Center and bottom rows: 3D scattering diagrams of the coreshell particle (blue) and the silicon reference (red), all shown at the same scale. Unpolarized incident light comes from the left in all diagrams.

1 H

 1 NMR (1) (400 MHz, C6D6, 25°C): δ 0.9489 (t, 3H, 3 JHH 7.20 Hz, CH3(CH2)4C), δ 1.3271 (d, 12H, 3 JHH 6.64 Hz, i Pr-CH3), δ 1.4047 (m, 4H THF, CH2), δ 1.40 (m, 2H CH3CH2CH2CH2C), δ Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 17 1.6152 (m, 2H, CH3CH2CH2CH2C), δ 2.3910 (m, 2H, CH3(CH2)2CH2C), δ 3.5795 (m, 4H THF, CH2O), δ 3.7236 (m, 2H, (CH3)2CH).

1 H NMR ( 2 )

 2 (400 MHz, C6D6, 25°C): δ 0.7662 (t, 6H, 3 JHH 7.4424 Hz, Bu-CH3), δ 1.0995 (d, 6H, 3 JHH 6.5221 Hz, i Pr-CH3), δ 1.133( m, 4H, 3 JHH , CH3CH2 (CH2)2C), δ 1.3851 (d, 6H, 3 JHH 6.6822, i Pr-CH3), δ 1.38 (m, 4H, CH3CH2CH2CH2C), δ 1.5964 (d, 6H, 3 JHH 7.0023 Hz, i Pr-CH3), δ 1.6313 (d, 6H, 3 JHH 6.8822 Hz, i Pr-CH3), δ 2.0084 (m, 4H, CH3(CH2)2CH2C), δ 3.5014 (sept. 2H, 3 JHH 6.7622 Hz, i Pr-CH), δ 4.1844 (sept. 2H, 3 JHH 8.9229 Hz, i Pr-CH).

FTIR spectroscopy .

 spectroscopy Fourier transform infrared (FTIR) spectra of the particles were collected using a Bruker Vertex 70 FTIR. A colloidal solution of particles in chloroform was drop-cast onto a double polished silicon wafer support. The sample was then placed in the optical path of Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 19 the beam. During the measurement, a stream of nitrogen was flushed through the IR chamber in order to evacuate CO2 and water. The infrared spectra have been normalized with respect the Si-Hx stretching mode (~2100 cm -1 ).

Figure 3E .

 3E Figure 3E. The histograms were built by measuring the size of 200 particles for each batch and distributing the sizes in bins of width 8 nm.The scattering cross sections for the transverse (S1) and axial (S2) scattering,

  , A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 10 the Raman results, which indicate intermediate bond order. The low index medium accounts

  , A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 12

  , A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 14 the shell thickness is 115 nm (Table

Acknowledgements

Benoît Cormary helped with the bisamadinate precursor synthesis. MLDM and GLD were supported by the LabEx AMADEus (ANR-10-LABX-42) in the framework of IdEx Bordeaux (ANR-10-IDEX-03-02), i.e. the Investissements d'Avenir program of the French government managed by the Agence Nationale de la Recherche. B.A.K. and T.J. acknowledge financial support of this work from the Robert A. Welch Foundation (F-1464) and the National Science Foundation through the Center for Dynamics and Control of Materials, an NSF MRSEC under Cooperative Agreement No. DMR-1720595. J.F. and Y.Z. acknowledge the financial support of the National Science Foundation (NSF-ECCS-2001650), and the National Institute of General Medical Sciences of the National Institutes of Health (DP2GM128446). STEM-EDX imaging was performed on the Bordeaux Imaging Center, member of the FranceBioImaging national infrastructure (ANR-10-INBS-04).

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))

Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915

Article Published in : De, M. L., Jiang, T., Fang, J., Lacomme, S., Zheng, Y., Baron, A., Korgel, B. A., Barois, P., Drisko, G. L., Aymonier, C., Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles. Adv. Funct. Mater. 2021, 2100915. https://doi.org/10.1002/adfm.202100915 21 tandem Fresnel rhombohedrum acting as an achromatic half-wave retarder (Thorlabs FR600HM).

The sample consisted of a colloidal suspension of silicon particles in chloroform placed in a fused silica cuvette. The scattered light was collected at θ=90° with respect to the direction of incident light, using a Minispectrometer (Hamamatsu C10083CA) fed with a collimated optical fiber. A second Glan-Taylor polarizer (Thorlabs GL10-A), placed between the sample and the detector, analysed the scattered light with parallel (axial) or perpendicular (transverse) polarization. Scattering spectra were collected over a 360° rotation of the φ angle at intervals of 10°. The intensities measured along the transverse and axial directions are the following:

(3)

Where I0(λ) is the spectral irradiance of the incident beam, Nscat represents the number of particles in the scattering volume, q is the wave number (2π/λ). The solid angle δΩ represents the detection window, T(λ) is the transmittance of the suspension and g(λ , δΩ) is an unknown function of the instrument, dependent on the spectral power of the source, the sensitivity of the detector and the transmittance and reflectance of all the optical elements.

The experimental axial and transverse scattering have been fitted for each wavelength with functions of the type A∥+ B∥sin²(φ) and A⊥+ B⊥cos²(φ), respectively. The background signals A∥ and A⊥ measure a residual anisotropy of the scatterers [START_REF] Gomez-Grana | 2016 10th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS)[END_REF] which were below 10% in most of the tested samples.

The differential scattering cross section of the transverse even modes (i.e. mostly ED and MQ in silicon particles) and axial odd modes (i.e. mostly MD and EQ) were obtained by normalizing the parameters B⊥ and B// by the parameter Bref of a known reference sample. A colloidal suspension of silica (SiO2) beads with diameter of 120 nm was used. In this size range, silica does not exhibit any Mie resonance, and, most importantly, its scattering cross section was simply calculated from the Mie theory. [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF]38,[START_REF] Many | [END_REF] Article Published in :

Where Nref and Nscat are the number of particles in the scattering volume for the SiO2 reference and the silicon sample respectively. The concentration ratio Nref/Nscat, which could not be determined with sufficient accuracy, was accounted for with an unknown scaling constant K.

Since the colloidal suspensions containing sample and reference must be highly diluted to prevent multiple scattering, the transmittances T(λ) of the sample and Tref(λ) of the reference, were simply the transmittance of the pure solvent so that the transmittance ratio appearing in Equation 5 and 6 equaled 1.

Maxwell-Garnett model. The Maxwell-Garnett model [START_REF] Sihvola | Subsurface Sensing Technologies and Applications[END_REF] (Equation 1) was used to build the effective permeability of the silicon core and of the shell. The complex effective refractive index N = n + ik, is the square root of the effective permittivity. Effective permittivity was constructed by considering the particles to be composed of a mixture of crystalline silicon, amorphous silicon and low index inclusions (refractive index equivalent to water). The index dispersion for amorphous and crystalline silicon were obtained from the data collected by Pierce and Spicer [44] and Aspnes and Studna [45] respectively, available on an online database. [START_REF] Polyanskiy | Refractive Index.INFO, Refractive index database[END_REF] To simulate the presence of low index impurities, included within the particles, a refractive index equal to water was used [START_REF] Daimon | [END_REF] .This model allows the volume fraction, fm, of c-Si, a-Si and low index impurities to be adjusted in order to obtain the best agreement between simulations and experiments, [START_REF] Sihvola | Subsurface Sensing Technologies and Applications[END_REF] while respecting the Kramers-Kronig conditions.

Dark field scattering simulation. The scattering spectra of the silicon particles were computed from the Mie theory which provides exact analytical expressions of the scattering efficiency by both homogeneous spheres and spherical core-shell structures. [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF] The control parameters were the size and refractive index of the core and the shell.

The single particle dark field scattering simulations were carried out considering both the angle of incident light (55-80°) and the cone of acceptance of scattered light, spanning from 0° to 30°. The angle of incident light, from 55° to 80°, was determined from the numerical aperture of the dark field condenser, while the angle of collection was determined from the numerical aperture of the oil immersion objective. The scattering spectra of single particles with total radius R, core radius Rc, and shell thickness t=R-Rc, were simulated. The variable m2 represent the contrast between the coating shell index and the medium, and the variable m1 is the contrast between the Si index core and the medium. In this case, the surrounding medium was defined as air.

The particle radius, R, is the only parameter known with accuracy from SEM measurements, and it is not varied during the simulation (see Figure 2 A-D). The shell thickness, t (or equivalently the core size, Rc) is optimized around the average values obtained from TEM-EDX (see Table S2 and S3 in Supporting Information for comparison between the optimized and average values).

The Si core refractive index and absorption coefficient, as well as the shell refractive index, were varied according to the Maxwell-Garnett model, by adjusting the volume fraction of crystalline and amorphous silicon, and of low index impurities (see subsection above). By optimizing the refractive index and absorption coefficient, as well as t, the best accord between simulated and experimental data could be obtained. The wavelength dispersions of the refractive index and absorption coefficient are presented in Figure 2 I-J, along with the wavelength dispersion of crystalline and amorphous silicon. The optimized t and Rc are presented in Table S2 (see Table S2 and S3 for comparison between the optimized and average values). The simulations of dark field scattering obtained by optimizing n, k, and t are presented in Figure S6 A-D along with the experimental dark field scattering. The optimized parameters were used for computing the total scattering efficiency, magnetic and electric dipoles and quadrupoles scattering efficiency of the single particle in air (Figure S6). The field maps shown in Figure 4 represent the exact Mie solution for a coated sphere computed as an expansion in vector spherical harmonics with the appropriate set of scattering coefficients. [START_REF] Bohren | Absorption and Scattering of Light from Small Particles[END_REF] Static light scattering simulation. In contrast with DF, static light scattering collects the scattering of an ensemble of particles suspended in the scattering volume. The statistic size distribution must therefore be taken into account. In the case of highly dilute suspension,

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.


Jean-Francois Korobelnik
email: jean-francois.korobelnik@chu-bordeaux.fr

Michael Larsen

Nicole Eter

Clare Bailey

Sebastian Wolf

Thomas Schmelter

Helmut Allmeier

Varun Chaudhary

Jean-Franc ¸ois Korobelnik

Jean-François Korobelnik

Professor Jean-François Korobelnik

Efficacy and Safety of Intravitreal Aflibercept Treat-and-Extend for Macular Edema in Central Retinal Vein Occlusion: The CENTERA Study

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Retinal vein occlusion is a common cause of vision loss in patients with chronic macular edema. 1 There are three different types of retinal vein occlusion, based on obstruction site: branch retinal vein occlusion, central retinal vein occlusion (CRVO), and hemi-retinal vein occlusion. [START_REF] Schmidt-Erfurth | Guidelines for the Management of Retinal Vein Occlusion by the European Society of Retina Specialists (EURETINA)[END_REF] CRVO is an obstruction of the main retinal vein at or posterior to the optic nerve head, [START_REF] Pulido | Retinal Vein Occlusions Preferred Practice Pattern(®) Guidelines[END_REF] it affects both men and women, and most commonly occurs in patients who are 60 years of age or older. [START_REF] Schmidt-Erfurth | Guidelines for the Management of Retinal Vein Occlusion by the European Society of Retina Specialists (EURETINA)[END_REF][START_REF] Klein | The epidemiology of retinal vein occlusion: the Beaver Dam Eye Study[END_REF] Although CRVO is usually unilateral, [START_REF] Klein | The epidemiology of retinal vein occlusion: the Beaver Dam Eye Study[END_REF] approximately 7.8% of patients with CRVO in one eye also have RVO in the fellow eye. [START_REF] Leitner | Bilateral Retinal Vein Occlusion[END_REF] CRVO leads to impaired venous drainage from the eye, which in turn may result in increased venous pressure, reduced arterial perfusion, and retinal ischemia. Retinal non-perfusion leads to an increase in vascular endothelial growth factor (VEGF), which increases vascular permeability, and can cause macular edema, retinal hemorrhage, and neovascularization. [START_REF] Noma | Vitreous levels of interleukin-6 and vascular endothelial growth factor in macular edema with central retinal vein occlusion[END_REF] Treatment of macular edema secondary to CRVO involves the administration of anti-VEGF agents, such as aflibercept and ranibizumab, which have become the standard of care. The efficacy and safety of intravitreal aflibercept (IVT-AFL) was assessed in two pivotal Phase 3 studies, COPERNICUS (NCT00943072) [START_REF] Boyer | Vascular endothelial growth factor Trap-Eye for macular edema secondary to central retinal vein occlusion: six-month results of the phase 3 COPERNICUS study[END_REF][START_REF] Brown | Intravitreal aflibercept injection for macular edema secondary to central retinal vein occlusion: 1-year results from the phase 3 COPERNICUS study[END_REF] and GALILEO (NCT01012973), [START_REF] Korobelnik | Intravitreal aflibercept injection for macular edema resulting from central retinal vein occlusion: One-year results of the Phase 3 GALILEO study[END_REF][START_REF] Holz | VEGF Trap-Eye for macular oedema secondary to central retinal vein occlusion: 6-month results of the phase III GALILEO study[END_REF] in which findings demonstrated that IVT-AFL was beneficial for the treatment of macular edema secondary to CRVO. In these studies, the mean change from baseline to Week 24 in best-corrected visual acuity (BCVA) was +17.3 and +18.0 letters for patients treated with IVT-AFL compared with -4.0 and +3.3 letters in patients who received sham injections, respectively. [START_REF] Boyer | Vascular endothelial growth factor Trap-Eye for macular edema secondary to central retinal vein occlusion: six-month results of the phase 3 COPERNICUS study[END_REF][START_REF] Holz | VEGF Trap-Eye for macular oedema secondary to central retinal vein occlusion: 6-month results of the phase III GALILEO study[END_REF] These studies demonstrate how, if left untreated, patients with macular edema secondary to CRVO lose visual acuity (VA) and have a poor prognosis. This was similarly shown in the CRUISE study (NCT00485836), in which mean change from baseline BCVA at Month 6 was +12.7 letters and +14.9 letters in the 0.3 mg and 0.5 mg ranibizumab groups, respectively, and +0.8 letters in the sham group. [START_REF] Brown | Ranibizumab for macular edema following central retinal vein occlusion: six-month primary end point results of a phase III study[END_REF] Both the COPERNICUS and GALILEO studies included pro re nata (PRN) dosing from Week 24 of treatment to investigate the possibility of extending the treatment interval beyond 4 weeks. Post-hoc assessment of the different dosing subgroups demonstrated some destabilization of the disease with PRN dosing. Although the deterioration seen during the study period was minor, possibly due to the regular monitoring schedule implemented in these trials, it is likely to progress over the expected longer-term treatment duration that is required in the real-world setting for patients with macular edema secondary to CRVO.

The LEAVO study (ISRCTN13623634) compared IVT-AFL, bevacizumab, and ranibizumab using a PRN dosing regimen and introduced a threshold of treatment success for suspending treatment (>83 Early Treatment Diabetic Retinopathy Study [ETDRS] letters), which allowed a comparative assessment of the treatment burden associated with each treatment arm. [START_REF] Hykin | Clinical Effectiveness of Intravitreal Therapy With Ranibizumab vs Aflibercept vs Bevacizumab for Macular Edema Secondary to Central Retinal Vein Occlusion: A Randomized Clinical Trial[END_REF] Treatment with any of these three anti-VEGF agents resulted in improved and sustained VA when patients were monitored regularly and treated promptly (IVT-AFL, +15.1 letters; ranibizumab, +12.5 letters; and bevacizumab, +9.8 letters at Week 100). Notably, IVT-AFL was non-inferior to ranibizumab at Week 100.

Post-hoc analyses of COPERNICUS and GALILEO support the implementation of proactive treatment to prevent deterioration of functional and anatomic outcomes. Treat and extend (T&E) is a proactive, individualized dosing strategy, whereby the patient receives an injection at every visit. The treatment interval is decided at every visit and is gradually extended if functional and anatomic stability is maintained, and shortened if deterioration is observed, to minimize the risk of disease recurrence rather than in response to it. [START_REF] Freund | Treat-and-extend regimens with anti-VEGF agents in retinal diseases: A literature review and consensus recommendations[END_REF] Additionally, with T&E dosing regimens, the need for interim monitoring is minimized, which reduces the number of appointments per patient and minimizes the need for monitoring visits. [START_REF] Lanzetta | Fundamental principles of an anti-VEGF treatment regimen: optimal application of intravitreal anti-vascular endothelial growth factor therapy of macular diseases[END_REF] Decreasing the number of visits per patient reduces the treatment burden and the need for scheduling visits, thus benefiting both the patient and the healthcare providers.

To our knowledge, T&E dosing regimens have not been evaluated in large-scale studies of IVT-AFL for the treatment of macular edema secondary to CRVO. The aim of the CENTERA study was therefore to assess the efficacy and safety of IVT-AFL administered in a T&E dosing regimen in patients with macular edema secondary to CRVO. phase of the treatment). Starting at Week 8, the re-treatment interval was determined, and the frequency of injections could be adjusted by 2-week increments, to maintain stable functional and anatomic outcomes (the T&E phase of treatment).

The stability criteria were: no new cysts found on optical coherence tomography; BCVA within a ±5 letter "stability corridor" (defined as no more than a 5-letter gain since the last or second to last visit and no more than a 5-letter loss from best previous BCVA at any visit); and central retinal thickness (CRT) within a ±20% "stability corridor" (defined as no more than 20% thickness reduction since the last or second to last visit and no more than 20% thickening from best previous CRT at any visit). Values of BCVA and CRT outside of these "stability corridors" were considered to be "improvements" for higher BCVA values and lower CRT values, and "deteriorations" for lower BCVA values and higher CRT values.

From Week 8, at every treatment visit (and at Weeks 24, 52, and 76), the physician determined the stability status of each patient, and the following algorithm was used to determine the re-treatment interval: if the condition was stable (all stability criteria met), the treatment interval was extended by 2 weeks; if the condition was improving (no new cysts and improvement in at least one of the disease activity criteria [BCVA or CRT] with the other improving or stable), the treatment interval was maintained; and if the condition was deteriorating (new cysts and/or deterioration in at least one of the other disease activity criteria [BCVA or CRT]), the treatment interval was reduced by 2 weeks. Injections were not to be administered more frequently than every 4 weeks (minimum re-treatment interval).

Study Endpoints

The pre-determined co-primary endpoints were the proportion of patients who gained ≥15 letters from baseline to Week 76 and the proportion of patients with a mean treatment interval of ≥8 weeks from the last initiation phase visit to Week 76. These endpoints were met if significantly ≥40% of patients gained ≥15 letters and if significantly ≥50% of patients had a mean treatment interval of ≥8 weeks.

Secondary endpoints included mean change in BCVA and CRT from baseline to Weeks 24, 52, and 76, the number of injections from baseline to Week 76, and the mean treatment interval from baseline to Week 76. Other endpoints reported included the proportion of patients who lost <15 letters. The following post-hoc analyses were also conducted: the proportion of patients who achieved a last actual (defined as the length of the interval before study end [last]) and last intended treatment interval (defined as the next planned interval [next planned]) of ≥8 weeks and the proportion of patients who had a BCVA of ≥70 letters at all mandatory study visits. Safety was assessed throughout the study period. Adverse events (AEs) were treatment-emergent if they occurred or worsened after the first IVT-AFL dose and, at most, 30 days after the last dose. All AEs were reported in case-report forms and coded using Medical Dictionary for Regulatory Activities, version 22.0. An adjudication of AEs according to the Antiplatelet Trialists' Collaboration (APTC) criteria was also performed.

Statistical Analysis

Study success required that a gain of ≥15 letters at Week 76 was reached by significantly more than 40% of patients and that a mean treatment interval of ≥8 weeks was reached by significantly more than 50% of patients during the T&E phase. The exact one-sample binomial test was used to assess each of the co-primary efficacy variables at a significance level of 5% (two-sided test) using the full analysis set (FAS), and 95% confidence intervals (CIs) were provided. A sample size of 150 patients was calculated to provide a power of ≥90% to meet both co-primary endpoints, assuming a true probability for gaining ≥15 letters of 55% and a true probability to reach a mean treatment interval of ≥8 weeks of 65%. All other variables were analyzed by descriptive statistical methods, and frequency tables were generated for categorical data.

The safety analysis set included all enrolled patients who received IVT-AFL. The FAS included all enrolled patients who received IVT-AFL, had a baseline BCVA assessment, and had at least one post-baseline BCVA assessment. The primary efficacy analysis was conducted using the FAS. The per-protocol set (PPS) included all enrolled patients who received IVT-AFL, had a BCVA assessment at study baseline, had at least one BCVA assessment at Week 24 or later, and did not have a major protocol deviation.

The co-primary efficacy variable sensitivity analysis was conducted on the PPS.

Statistical evaluation was performed using Statistical Analysis System, v9.4 (SAS Institute Inc., Cary, NC, USA).

Results

Patients

Of the 244 patients who were enrolled, 162 completed screening and entered the treatment period. Two patients had no post-baseline assessments available and were not included in the FAS. Overall, 92.6% (n=150) of patients completed the study. The reasons for study discontinuation were death (n=4), withdrawal by patient (n=3), AEs (n=2), physician decision (n=2), and lost to follow-up (n=1). In total, 147 patients were included in the PPS (Figure 1).

The overall mean (standard deviation [SD]

) age was 66.2 (13.4) years, and 60.0% of patients were male (Table 1). At baseline, mean (SD) BCVA was 51.9 (16.9) letters and mean (SD) CRT was 759.9 (246.0) µm.

Treatment Exposure

Patients received a mean (SD) of 5.3 (0.7) (baseline to Week 24), 3.9 (1.3) (Weeks 24-52), and 3.0 (1.3) (Weeks 52-76) IVT-AFL injections. Of those who completed treatment (n=150), the mean treatment interval in the T&E phase was 7.6 (1.9) weeks, and the mean length of the last and next planned treatment interval was 9.3 (3.5) weeks and 9.7 (3.8) weeks, respectively. Overall, 25.6% (n=41) and 36.9% (n=59) of patients achieved a last and a next planned treatment interval of ≥12 weeks, respectively.

Efficacy

In total, 65.6% (n=105; 95% CI, 57.7-72.9, P <0.0001 [test against threshold of 40%]) of patients gained ≥15 letters from baseline to Week 76. Overall, 45.0% (n=72; 95% CI, 37.1-53.1, P = 0.8822 [test against threshold of 50%]) of patients achieved a mean treatment interval of ≥8 weeks during the T&E phase. Additionally, 63.1% (n=101) of patients achieved a last and 67.5% (n=108) a next planned treatment interval of ≥8 weeks.

A sensitivity analysis of the co-primary efficacy variables conducted on the PPS provided similar results to the primary analysis on the FAS: 66.7% (n=98; 95% CI, 58.4-74.2) of patients gained ≥15 letters from baseline to Week 76 and 47.6% (n=70; 95% CI, 39.3-56.0) of patients achieved a mean treatment interval of ≥8 weeks during the T&E phase.

Clinically meaningful improvements in mean BCVA were observed at all mandatory visits. Mean (SD) BCVA was 51.9 (16.8) In a post-hoc analysis of the FAS, 13.8% (n=22) of patients had a baseline BCVA of ≥70 letters (20/40 Snellen equivalent), which increased to 66.9% (n=107) of patients at Week 76 (LOCF). Overall, 60.0% (n=96) of patients included in the FAS had a BCVA of ≥70 letters at all mandatory study visits (Weeks 24, 52, and 76).

Clinically meaningful improvements in mean CRT were observed at all mandatory visits. Mean (SD) CRT decreased from 759.9 (246.0) µm at baseline to 265.4 (57.9) µm at Week 76 (mean change: -496.1 [252.4] µm) (Figure 3).

Safety

In total, 80.9% (n=131) of patients reported at least one treatment-emergent AE (TEAE) during the study, and these were predominantly mild or moderate in severity (Table 2).

Overall, 55.6% (n=90) of patients reported ocular TEAEs in the study eye, the most common of which were reduced VA (14.8% [n=24]), increased intraocular pressure (12.3%

[n=20]), conjunctival hemorrhage (9.3% [n=15]), and retinal ischemia (9.3% [n=15]). No cases of endophthalmitis were reported. A listing of ocular TEAEs ≥1% in the study eye is reported in Supplemental Table 2.

Serious TEAEs were reported in 19.8% (n=32) of patients, and 4.9% (n=8) of patients experienced serious ocular TEAEs in the study eye. One case of intraocular inflammation (IOI), iridocyclitis, and one case of retinal artery occlusion (0.6% each) were assessed as serious TEAEs related to IVT-AFL. In total, there were four deaths reported; one patient had an APTC event (pulmonary embolism; the patient also experienced a lower respiratory tract infection and atrial flutter). The three other deaths reported were due to Bcell lymphoma, intestinal perforation, and pneumonia (n=1 each). Two deaths were treatment-emergent and none were assessed as being related to IVT-AFL.

Discussion

CENTERA was among the first studies to evaluate IVT-AFL administered in a T&E dosing regimen for the treatment of macular edema secondary to CRVO on a relatively large scale.

This study showed that IVT-AFL administered in a T&E dosing regimen improved functional and anatomic outcomes in patients with macular edema secondary to CRVO over 76 weeks. Overall, 66% of patients gained ≥15 letters from baseline to Week 76; conversely, the proportion of patients who achieved a mean treatment interval of ≥8 weeks between the last initiation phase visit and Week 76 did not reach statistical significance.

The robustness of these results was further demonstrated in a sensitivity analysis on the PPS.

Although fewer than half of patients achieved a mean treatment interval of ≥8 weeks, post-hoc analysis demonstrated that 63% and 68% of patients achieved a last and next planned treatment interval of ≥8 weeks, respectively. Functional and anatomic improvements were achieved with a mean of five injections (baseline to Week 24), four injections (Weeks 24-52), and three injections (Weeks 52-76). As expected with the T&E treatment paradigm, treatment burden was highest during the initiation phase and decreased over time. The downwards trend in the intensity of the treatment pattern through to the end of the study further supports the notion that a mean treatment interval of ≥8 weeks between the last initiation phase visit and Week 76 may have been met with the implementation of a longer observation period.

Clinically meaningful improvements in BCVA were observed at all mandatory study visits, with a mean change from baseline of +20 letters at Week 76. Results of a post-hoc analysis showed that, by Week 76, 67% of patients had a BCVA of ≥70 letters, which is a threshold for maintaining a driving license in many countries. Clinically meaningful improvements in anatomic outcomes were also observed at all mandatory study visits, with a mean change in CRT of -496 µm at Week 76. The majority of the reduction in CRT was seen following the first IVT-AFL injection (-462 µm at Week 4). It is also worth noting that 73% of patients were treated within 4 weeks of diagnosis. The safety profile of IVT-AFL was consistent with previous studies. [START_REF] Brown | Intravitreal aflibercept injection for macular edema secondary to central retinal vein occlusion: 1-year results from the phase 3 COPERNICUS study[END_REF][START_REF] Korobelnik | Intravitreal aflibercept injection for macular edema resulting from central retinal vein occlusion: One-year results of the Phase 3 GALILEO study[END_REF] Notably, there were no cases of endophthalmitis and only one case of IOI.

The functional and anatomic outcomes achieved in CENTERA using a T&E regimen similar to those seen in other studies of IVT-AFL with monthly or PRN dosing. [START_REF] Brown | Intravitreal aflibercept injection for macular edema secondary to central retinal vein occlusion: 1-year results from the phase 3 COPERNICUS study[END_REF][START_REF] Korobelnik | Intravitreal aflibercept injection for macular edema resulting from central retinal vein occlusion: One-year results of the Phase 3 GALILEO study[END_REF][START_REF] Hykin | Clinical Effectiveness of Intravitreal Therapy With Ranibizumab vs Aflibercept vs Bevacizumab for Macular Edema Secondary to Central Retinal Vein Occlusion: A Randomized Clinical Trial[END_REF][START_REF] Scott | Effect of Bevacizumab vs Aflibercept on Visual Acuity Among Patients With Macular Edema Due to Central Retinal Vein Occlusion: The SCORE2 Randomized Clinical Trial[END_REF] The mean change in BCVA from baseline to Week 24 was +20 letters in CENTERA, +17 letters in COPERNICUS, 7 +18 letters in GALILEO, 10 +19 letters in SCORE-2, [START_REF] Scott | Effect of Bevacizumab vs Aflibercept on Visual Acuity Among Patients With Macular Edema Due to Central Retinal Vein Occlusion: The SCORE2 Randomized Clinical Trial[END_REF] and +13 letters in LEAVO. [START_REF] Hykin | Clinical Effectiveness of Intravitreal Therapy With Ranibizumab vs Aflibercept vs Bevacizumab for Macular Edema Secondary to Central Retinal Vein Occlusion: A Randomized Clinical Trial[END_REF] The mean change in CRT from baseline to Week 52 was -481 µm in CENTERA, -413 µm in COPERNICUS, and -424 µm GALILEO [START_REF] Brown | Intravitreal aflibercept injection for macular edema secondary to central retinal vein occlusion: 1-year results from the phase 3 COPERNICUS study[END_REF][START_REF] Korobelnik | Intravitreal aflibercept injection for macular edema resulting from central retinal vein occlusion: One-year results of the Phase 3 GALILEO study[END_REF] .

The majority of patients in the CENTERA study had non-ischemic CRVO (93%). In the COPERNICUS [START_REF] Boyer | Vascular endothelial growth factor Trap-Eye for macular edema secondary to central retinal vein occlusion: six-month results of the phase 3 COPERNICUS study[END_REF] and VIBRANT [START_REF] Campochiaro | Intravitreal aflibercept for macular edema following branch retinal vein occlusion: the 24-week results of the VIBRANT study[END_REF] studies of IVT-AFL, a smaller proportion of patients had non-ischemic disease, 67.5% and 60.4%, respectively. In all three studies, patients showed improvement in functional and anatomic outcomes, therefore indicating that IVT-AFL therapy is effective in patients with both ischemic and non-ischemic CRVO.

The importance of differentiating fluid compartments is gaining increasing attention in neovascular age-related macular degeneration (nAMD), whereby fluid compartments have been shown to have differential effects on functional outcomes [START_REF] Jaffe | Macular Morphology and Visual Acuity in Year Five of the Comparison of Age-related Macular Degeneration Treatments Trials[END_REF] . It is feasible that tolerance of anti-VEGF resistant fluid in specific compartments (such as subretinal fluid) may allow extension of intervals while maintaining good functional outcomes. However, the impact of such an approach on the treatment of macular edema secondary to CRVO is yet to be explored. Additionally, possibly more so than in nAMD, the treatment burden in CRVO significantly lessens over time as the disease appears to stablize more effectively, potentially enabling further extension of treatment intervals as the disease stabilizes.

Further data, including those from the LEAVO study, suggest that a lower treatment intensity may have a detrimental impact on functional outcomes. It is possible that the lower number of injections through 52 weeks in LEAVO compared with CENTERA (approximately 7.0 vs 9.2 injections, respectively) allowed for persistent fluid and more recurrences. Initial monthly dosing for CRVO may need to be more protracted than the typical treatment schedule of three initial monthly doses in nAMD.

Published studies, including LEAVO, [START_REF] Hykin | Clinical Effectiveness of Intravitreal Therapy With Ranibizumab vs Aflibercept vs Bevacizumab for Macular Edema Secondary to Central Retinal Vein Occlusion: A Randomized Clinical Trial[END_REF] have also demonstrated the superior durability of IVT-AFL compared with ranibizumab, as evidenced by the lower mean number of injections over 100 weeks with IVT-AFL (10.0 vs 11.8 injections, respectively). However, the vision gains in LEAVO at 100 weeks (+15 letters for IVT-AFL) were not as high as those reported in CENTERA at 76 weeks (+20 letters), possibly supporting the requirement for proactive treatment (such as T&E) in patients with CRVO.

This study had a number of strengths, including a high statistical power of ≥90%, inclusion of a broad range of baseline visual function (73-24 ETDRS letters; 20/40 to 20/320 Snellen equivalent) and early initiation of treatment. Limitations of this study are that it was a single-arm study with no active comparator, thus potentially limiting the interpretation of the results. However, the single-arm design was chosen to evaluate the utility of the T&E regimen in patients with CRVO, as this regimen has not previously been analysed in large clinical studies within this patient population. Furthermore, the analysis of the last and next planned treatment intervals was post hoc in nature, which limited the interpretation of the data.

Overall, clinically meaningful and significant improvements in functional and anatomic outcomes were achieved with IVT-AFL administered using a T&E regimen in patients with macular edema secondary to CRVO. Treatment intervals were also extended, and the majority of patients achieved a last and next planned treatment interval of ≥8 weeks.

the authors, was provided by ApotheCom, UK, and was funded by Bayer Consumer Care AG, Switzerland.

d) Author Contributions

All authors contributed to the conceptualization of the study design, data curation, investigation, visualization, and provided critical review of the manuscript.

Access to data and data analysis

Availability of the data underlying this publication will be determined according to Bayer's commitment to the EFPIA/PhRMA, "Principles for responsible clinical trial data sharing." This pertains to scope, time point, and process of data access. Data access will be granted to anonymized patient-level data, protocols and clinical study reports after approval by an independent scientific review panel. Bayer is not involved in the decisions made by the independent review panel. Bayer will take all necessary measures to ensure that patient privacy is safeguarded.

Table of Contents Statement

CENTERA evaluates the efficacy and safety of intravitreal aflibercept treat-and-extend dosing in patients with macular edema secondary to central retinal vein occlusion. Overall, clinically meaningful improvements in functional and anatomic outcomes were achieved. Treatment intervals were extended, and the majority of patients achieved last and next planned treatment intervals of ≥8-weeks. These results support the use of intravitreal aflibercept treat-and-extend dosing in patients with macular edema in central retinal vein occlusion within clinical practice.

  letters at baseline and 72.3 (18.5) letters at Week 76 (mean change: +20.3 [19.5] letters) (Figure 2). Overall, 70.0 % (n=112) of patients gained ≥15 letters and 95.6% (n=153) of patients maintained vision (<15 letters loss) from baseline to Week 76 in the FAS (last observation carried forward [LOCF]). Categorical BCVA gains and losses from baseline to Week 76 are shown in Supplemental Figure 1.

  As such, Bayer commits to sharing, upon request from qualified scientific and medical researchers, patient-level clinical trial data, study-level clinical trial data, and protocols from clinical trials in patients for medicines and indications approved in the United States (US) and European Union (EU) as necessary for conducting legitimate research. This applies to data on new medicines and indications that have been approved by the EU and US regulatory agencies on or after January 1, 2014.Interested researchers can use www.clinicalstudydatarequest.com to request access to anonymized patient-level data and supporting documents from clinical studies to conduct further research that can help advance medical science or improve patient care. Information on the Bayer criteria for listing studies and other relevant information is provided in the Study sponsors section of the portal.

Figure captions FIGURE 1 .

 captions1 Figure captions

FIGURE 2 .

 2 FIGURE 2. Mean change in BCVA from baseline to Week 76. Full analysis set; last

FIGURE 3 .

 3 FIGURE 3. Mean change in CRT from baseline to Week 76. Full analysis set; last

a

  Both cases were related to study drug and IVT injection procedure. Safety analysis set. AE = adverse event; APTC = Anti-Platelet Trialists' Collaboration; IVT = intravitreal; IVT-AFL = intravitreal aflibercept; SAE = serious adverse event; TEAE = treatment-emergent adverse event.

TABLE 1 .

 1 Patient Baseline Demographics and Disease Characteristics

	Characteristic

TABLE 2 .

 2 Safety Overview at Week 76

	Number of patients (%)

Acknowledgments a) Funding/Support

This study was sponsored by Bayer AG, Leverkusen, Germany. Medical writing and editorial support for the preparation of this manuscript was funded by Bayer Consumer Care AG, Switzerland. Bayer AG participated in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

b) Financial

Disclosures J-FK: Consultant for Alcon, Allergan, Bayer, Kanghong, Krys, NanoRetina, Novartis, Novo Nordisk, Roche, Théa, and Zeiss Dr. Monica Asencio Duran Dr. Catalina Esmerado Appiani Dr. Laurent Lalonde Dr. John Gonder Dr. Michel Giunta Dr. Varun Chaudhary Dr. Michael Fielden Dr. Serge Bourgault Dr. Karim Hammamji Prof. Michael Larsen Prof. Henrik Vorum Dr. Jennifer Arnold Dr. Andrew Chang Dr. Alan Luckie Prior presentation EURETINA 2020 Virtual Congress, 2-4 October

Methods

The authors thank all the patients and investigators who participated in the study. Medical writing and editorial support for the preparation of this manuscript, under the guidance of