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ABSTRACT: Narrow high refractive index nanowires sustain weakly guided modes ... numerical electromagnetic simulations how the lifting of the degenera...
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Generating Optical Birefringence and Chirality in Silicon Nanowire Dimers Xin Zhao, Mohammad Hossein Alizadeh, and Bjoern M. Reinhard ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b00501 • Publication Date (Web): 25 Aug 2017 Downloaded from http://pubs.acs.org on August 26, 2017

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ACS Photonics

Generating Optical Birefringence and Chirality in Silicon Nanowire Dimers

Xin Zhao,† M.H. Alizadeh,‡ and Björn M. Reinhard*,† †Departments

of Chemistry and ‡Electrical and Computer Engineering and The Photonics Center, Boston University, Boston, MA 02215, United States *Email: [email protected]

ABSTRACT: Narrow high refractive index nanowires sustain weakly guided modes with significant mode volume outside of the nanowire. This modal spill-over makes them interesting photonic materials for a multitude of applications. In this manuscript we fabricate dimers of nanowires with lengths up to 1.4 µm, radii down to 55nm, and edge-to-edge separation down to 60nm through anisotropic etching from crystalline silicon (Si). We investigate how the properties of the weakly confined fundamental HE1,1 mode in Si nanowires are modified by their integration into dimers. In particular, we characterize through combination of experimental spectroscopy and numerical electromagnetic simulations how the lifting of the degeneracy of HE1,1x and HE1,1y modes in dimers of Si nanowires generates linear birefringence, spin angular momentum and superchirality. Achiral Si nanowire dimers are found to create locations of strongly enhanced near-field chirality in the gap between the nanowires, where the field can interact with the ambient medium. Keywords: Silicon nanowire, guided modes, optical birefringence, optical chirality

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INTRODUCTION Semiconductor nanowires are emerging as a versatile class of electromagnetic materials for controlling and enhancing light-matter interactions. Semiconductor nanowires have been used as color pixels with morphologically tunable spectral responses, 1–4 polarization-sensitive photodetectors,5 solar absorbers,6–10 and tunable antennas to enhance radiative rates and emission directionalities of quantum emitters11–13 much as their plamsonic counterparts14,15 but with low ohmic losses. In addition, nanowires have shown potential to create unusual transverse spin angular momentum16 and to generate chiral forces that dominate over optical gradient forces17. Silicon (Si) nanowires, in particular,

are of interest as Si is an abundant element, Si nanofabrication technologies are well advanced,18–20 and the combination of Si nanophotonics with Si electronics has high practical relevance for the generation of optoelectronic devices.21 The potential of Si nanowires in nanoscale optics, photonics and optomechanics22 is well recognized, but previous studies focused predominantly on individual Si nanowires.1,23,24 The optical properties of discrete structures containing multiple interacting nanowires are even more complex25 and less well understood. In this work we combine experimental spectroscopy and electromagnetic simulations to characterize some unique optical properties that emerge from nanowires after their integration into dimers. The optical properties of individual high refractive index Si nanowires are defined by electromagnetic modes1,2 that are solutions to a – in the case of infinitely long wires – well known dispersion relation.7 Finite nanowires sustain in addition to waveguide modes also Mie-resonances, and the relationship between Mie resonances and guided and leaky waveguide modes has recently attracted significant interest.25–28 It was shown before that for light incident normal to the long nanowire axis the optical spectra are determined by Mie resonances, but that for grazing angles the incident light couples to guided modes.27,29 For the latter, the momentum mismatch between free space photons and guided modes is compensated by scattering mechanisms at the

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ends of the nanowires. Since in our experimental work the incident k-vector is parallel to the nanowire axis, the spectral response is dominated by the waveguide modes. Due to symmetry considerations, the mode spectra of Si nanowires are dominated by hybrid HE modes, which contain both magnetic (H-) and electric (E-) field components along the direction of propagation. HEl,m modes have 2l intensity maxima around the circumference of the nanowire and m maxima along the radial direction. For very thin nanowires only the fundamental HE1,1 mode with no cut-off frequency is excited. Intriguingly, HE modes can become weakly confined in thin nanowires.30–32 Different from guided modes that are confined to the interior of the nanowire,33 these weakly confined modes sustain an evanescent field outside of the nanowire due to their subwavelength diameter.1,11,34,35 Due to their mode volume outside of the nanowire, these modes provide unique opportunities for generating new functionalities in assemblies of interacting nanowires that have no counterpart in individual Si nanowires. The conceptually simplest geometry for studying these electromagnetic interactions is a dimer containing two nanowires with overlapping mode volumes. A dimer of Si nanowires has a lower symmetry than an individual nanowire and the resulting spatial patterning of the refractive index can break the symmetry of the modes in the individual nanowires. In the case of the fundamental HE1,1 mode, which in individual nanowires is two-fold degenerate and exists with two orthogonal E-field polarizations in x- and y-directions (HE1,1x and HE1,1y), the presence of the second nanowire facilitates an orientation-dependent refractive index that lifts the degeneracy of HE1,1x and HE1,1y. In this manuscript we combine experimental spectroscopy and electromagnetic simulations to demonstrate that discrete dimers of Si nanowires

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sustaining weakly confined modes represent a versatile materials platform for manipulating light polarization, generating spin angular momentum, and enhancing near-field chirality. METHODS Nanofabrication. A Piranha treated Si substrate (1 cm x 1cm) was first spin-coated with A3 poly (methyl methacrylate) (PMMA) for electron beam lithography (EBL). Designed periodic nanohole dimers were then pattern through EBL by Zeiss SUPRA 40VP SEM equipped with a Deben electron beam blanker. After development in a methyl isobutyle ketone (MIBK) / isopropanol (IPA) =1:3 solution, the EBLpatterned Si substrate was evaporated with Al through electron beam evaporation (CHA Industries, Fermon, CA, U.S.A.) to reach a final thickness of 60nm. The Al served as the protective layer for the final reactive ion etching (RIE) process. Inductively coupled plasma reactive ion etching (ICP-RIE, STS company) was used with a gas mixture of SF6/C4F8 (60 / 160 sccm) with an upper electrode powered at 1100 W for 5-8 min to generate Si nanowire arrays with a final height of approximately 1.4 µm. The Al mask was finally removed by Al etchant –Type A. Optical Microscopy and Spectroscopy; Determination of ρ. All optical characterizations were performed with an upright microscope (Olympus BX51W1). For reflection measurements, unpolarized white light from a 100 W Tungsten lamp was focused on the sample using a 20x air objective (N.A.= 0.4). The light was polarized with a linear polarizer (LPVIS100, Thorlabs, Inc.), whose orientation defined the direction, θ, of the incident light polarization. Reflected light from the sample was collected with the same objective and focused either on the entrance port of a 300 mm focal length

Figure 1: Fabrication scheme and SEM characterization of silicon dimers. a) Geometry of Si nanowire dimers (side view) as defined by the parameters nanowire radius (R), length (L), and edge-to-edge separation (G). ϕ defines the angle of incidence for the excitation light. Top views are provided as insets. The polarization angle (θ) is the angle that the E-field of the incident light forms with the dimer x-axis. b) Flow chart of the Si nanowire dimer fabrication. c-e) 30° tilted SEM images of silicon dimers: c) Dimer array with rotating dimer axis from 0 (bottom) to π/2 (top) with a step of π/12 (scale bar =1 µm); d) Dimer array with increasing radii from 55 nm (bottom) to 90 nm (top) with a step of 5 nm (scale bar = 1 µm); e) Zoomed in SEM images of individual dimers marked in d) (scale bar =200 nm).

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ACS Photonics noted, the simulations assumed an infinite layer of Si as substrate. The effective refractive indices of fundamental modes were extracted from a mode expansion monitor with a broadband mode source. The silicon nanowire dimers were assumed to have infinite length and to be suspended in air. Stokes parameters were calculated using the standard far-field projection, which returns the linear vector field components Eθ and Eφ. The linear vector field components were then converted to circular components EL and ER with 1 the following relations: 𝐸𝐿 = (𝐸𝜃 − 𝑖𝐸𝜑 ) and 𝐸𝑅 = 1 √2

Figure 2: Far-field simulation results. a) Set-up of simulation of backscattering spectrum. b) Simulated backscattering spectra for D1.4μm,70nm,G with G = 50 nm – 250 nm. c) Backscattering spectra of the HE mode obtained with three different incident polarization directions θ = 0 (HE1,1x only), π/4 (HE1,1x and HE1,1y), π/2 (HE1,1y only) for D1.4μm,70nm,50nm. d) Spectral peak positions of HE1,1x and HE1,1y in D1.4μm,70nm,G as function of G.

imaging spectrometer (Andor Shamrock) with a CCD detector (AndorDU401-BR-DD) for spectroscopic analysis or for the acquisition of images. An analyzer (another linear polarizer) was mounted in front of the spectrometer. We recorded spectra with an analyzer parallel and perpendicular to the polarizer. After background subtraction, the resulting intensity spectra 𝐼∥ (𝜆) and 𝐼⊥ (𝜆) were used to calculate the birefringence coefficient as 𝜌(𝜆)= 𝐼⊥ (𝜆) / 𝐼∥ (𝜆).36,37 Darkfield images were collected using unpolarized white light without analyzer through a 50x dark-field objective. Measurement of Stokes Parameters. Measurements of Stokes parameters were performed on the same microscope. A rotatable linear polarizer was used to define the input polarization. The collected light was sent through a Stokes analyzer, comprising a quarter wave plate and linear polarizer before detection in the spectrometer. At each wavelength the total intensity (I), the difference between xand y-polarized linear components (Q), the difference between linear polarizations oriented at an angle of π/4 and 3π/4 (U), and the difference in contributions from rightand left-handed circularly polarized light (V) were measured as described elswhere.38 The normalized Stokes parameters S1-3 were then determined as function as wavelength as S1=Q/I, S2=U/I, S3=V/I. FDTD Simulations. Electromagnetic simulations were carried out using finite difference time domain (FDTD) (Lumerical Solution Inc.) software. For far-field simulations of backscattering spectrum, a total field scattered field (TFSF) source with the k vector pointing towards the substrate in the z-direction was used. The perfectly matched layer (PML) boundary condition was imposed on all planes. A 2dimensional x-y plane monitor was placed above the injection plane of the TFSF source to collect the backscattered light from the silicon nanostructures. Unless otherwise

√2

(𝐸𝜃 + 𝑖𝐸𝜑 ).

For the near-field electric intensity simulations the dimers were excited by a plane wave propagating along the zdirection. A periodic boundary condition was imposed on the x-y plane and the PML boundary condition was applied to the z direction. The near-field data was collected using a 2D monitor in the x-y plane perpendicular to the long nanowire axis. This plane was chosen to dissect the nanowires at their midpoint. The optical chirality data was collected using a 2D monitor in the x-z plane to show the phase accumulation. No substrate was involved in these simulations. For all far-field simulations, the maximum mesh size was set to be 10 nm in the domain of the simulation in all three directions. For near-field simulations, the maximum mesh size was set to be 4 nm in the domain representing the nanowires and 10 nm for the rest of the domain. Simulation needed typically less than 6 GB of memory and can be ran on a single core local computer within 20-60 min.

RESULTS AND DISCUSSION Fabrication of Dimers of Silicon Nanowires. Figure 1a shows the general geometry of the Si nanowire dimers considered in this work. Throughout this manuscript we will refer to the different dimers as DL,R,G where L is the length of the dimers, R the radius of the monomers, and G the edgeto-edge separation between the two wires. The angle θ defines the orientation of the incident E-field relative to the nanowire dimer axis, which is chosen to be oriented along the x-axis. Nanowire dimers were fabricated through anisotropic reactive ion etching as outlined in Figure 1b.12 In a first step, electron-beam lithography (EBL) was used to generate aluminum (Al) disks on a Si substrate. The Al disks create a protective mask for the subsequent Si reactive ion etching (RIE) using SF6/C4F8 plasma. After the Si etching is complete, the Al is removed in the last step through Al etchant. Due to some residual lateral etching of Si through SF6/C4F8 plasma, the edge-to-edge separation of the nanowires differed somewhat from the design, as defined by the electron-beam lithography generated mask. The geometric parameters L, R, and G of the fabricated samples were, therefore, determined after the fabrication through inspection in the SEM. Figure 1c and d shows representative SEM images of arrays of nanowire dimers. Unless otherwise noted, we kept the separation between individual nanowire dimers ≥ 2 μm to avoid diffractive coupling. Our Si etching strategy facilitated the experimental realization of dimers with R as small as 55 nm and with L as long as 1.4 µm. The minimum G used in this study was 60 nm. Under the chosen experimental

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conditions only wires with R > 50 nm had enough mechanical stability for high aspect ratios with lengths, L > 1 μm. Thinner wires bent and did not generate high-quality structures. Despite obvious advantages of thicker nanowires with regard to structural stability, we limited R to the range of 55 – 85 nm. We chose this range as for larger R values the HE1,1 mode shifted out of the detection range of our spectrometer, which was limited to wavelengths < 1100 nm. Dimer Formation Lifts Mode Degeneracy of Si Nanowires and Introduces Linear Birefringence. Fundamental HE1,1 modes in individual Si nanowires can be optically excited. The modes travel along the nanowire until they reach the substrate-nanowire interface where they are either reflected or transmitted. Especially for weakly confined modes that by definition have a large modal volume in the ambient medium, a notable refractive index mismatch between nanowire and Si substrate will result in significant levels of reflection into free space.1 To validate that dimer formation has a measurable effect on the far-field response of high refractive index Si nanowires, we first simulated the backscattering spectra of Si nanowire monomer and dimer as function of gap separation, G. In the simulations the samples were illuminated with a plane wave whose wave-vector was parallel to the long nanowire dimer axis (ϕ = 0) using a total-field/scattered field (TFSF) approach. Details of the simulation geometry are included in Figure 2a. Although the nanowires, as shown in Figure 1e, have slightly tapered shapes, for the sake of simplicity we treated them as vertical cylinders. We verified in simulations (Figure S1) that the observed tapering did not affect the general trends discussed for ideal vertical nanowires. Figure 2b shows the simulated spectra of D1.4μm,70nm,G with G = 50 nm – 250 nm as well as for an individual nanowire (Monomer) obtained for an incident E-field orientation of θ = π/4. In the wavelength range λ = 550-1000 nm the spectrum is dominated by the HE1,1 mode, and the polarization of the incident light ensures that both HE1,1x and HE1,1y modes are excited. For G > 250 nm the spectrum of the HE1,1 mode of the dimer has essentially the same spectral position and similar shape as the monomer (data not shown), but for G ≤ 250 nm a red-shift and asymmetric broadening on the long wavelength side indicates a splitting of HE1,1x and HE1,1y modes. We simulated HE1,1x and HE1,1y spectra for linearly x- or y-polarized excitation light for D1.4μm,70nm,50nm. The comparison of the spectra obtained for θ = 0, π/4, π/2 (Figure 2c) confirm that the shoulder that emerges for G ≤ 250 nm on the long wavelength side in the dimer spectra shown in Figure 2b stems from the red-shifted HE1,1x mode. Next, we evaluated the HE1,1x and HE1,1y peak positions for D1.4μm,70nm,G as function of G (Figure 2d). HE1,1x shows a much stronger dependence on G than HE1,1y, resulting in a splitting of the two modes as G decreases. Despite the removal of the degeneracy, the spectra of the HE1,1x and HE1,1y modes retain a significant overlap due to the natural widths of these weakly confined modes. Figure 3a shows the simulated E-field intensity maps for HE1,1x and HE1,1y for D1.4μm,70nm,50nm and D1.4μm,70nm,200nm at the respective peak wavelengths of their reflection spectra. The E-fields associated with the HE1,1x modes in the two nanowires are pointing towards each other along the wire-wire connection axis, whereas the E-fields of the HE1,1y mode have a perpendicular orientation. As G decreases, the E-field

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Figure 3. Simulation of effective index of silicon dimers. a) Near-field intensity maps of the HE1,1x and HE1,1y modes of D1.4μm,70nm,G at G = 50 nm and G = 200 nm. The evaluated xy-plane was located at a height of 700 nm. b) E-field intensity for HE1,1x (square) and HE1,1y (diamond) as a function of gap width, G. c) Top: Simulated effective refractive index for a dimer (D2μm,70nm,G) as function of G for an excitation polarization pointing either along the x- (nx) or y-axis (ny). For theses simulations, the dimer is assumed to be in the air with no substrate. Bottom: Phase shifts between Ex and Ey as function of G at a fixed wavelength of 845nm assuming a propagation length of 1 µm (dark grey diamond) and 2 µm (pink triangle). d) Polarization ellipses for DL,70nm,60nm with (left to right) L = 1.4 μm, 1.7 μm, 2.0 μm. The orientation angle, ψ, is included.

components of the HE1,1x modes overlap, facilitating a coupling of the modes and resulting in a redistribution of the Efield. The E-field intensity map for D1.4μm,70nm,50nm reveals that the E-field becomes strongly focused in the gap between the wires for short separations. The interaction between the E-field components of the HE1,1y modes is much weaker. Plots of the peak E-field intensity of the dimer as function of G for HE1,1x and HE1,1y are included in Figure 3b and confirm stronger interactions along the x- than y-axis. Our computational analysis verifies that the nanowire dimer structure, due to its intrinsic anisotropy, under simultaneous excitation of HE1,1x and HE1,1y lifts the degeneracy of these modes and introduces strongly orientation dependent interactions between the nanowires. Based on the orientation of the E-field relative to the nanowire dimers we anticipate different refractive indices along x- and y-direction. To verify this hypothesis, we simulated the refractive indices nx and ny for infinitely long nanowire dimer with radius of R = 70 nm as function of G in the range between 20 – 300 nm using FDTD simulations (Figure 3c, top panel). The plots confirm a growing divergence between nx and ny as G decreases. Due to this birefringence, the x- and y-components of the E-fields associated with the HE modes accumu2𝜋 late a phase difference, 𝛾 = Δ𝑛 𝐿 ,39 as they propagate 𝜆

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along the nanowires (Figure 3c, bottom panel). In this expression Δn = nx - ny is the difference in refractive index along x- and y- direction at wavelength λ. As a result, the phase difference of the x- and y-components of the HE1,1 Efield generates elliptically polarized reflected light for γ = [0 – π/2] and [π/2 – π], circularly polarized light for γ = π/2, and linearly polarized light for γ = π. To better illustrate polarization status as a function of L, we describe the polarization of light by its electric field vector in a plane perpendicular to the direction of propagation with two orthogonal components Ex and Ey. Figure 3d plots the FDTD-simulated polarization ellipses of the reflected light obtained for DL,70nm,60nm, L = 1.4 μm, 1.7 μm, 2.0 μm, and θ = π/4 with the orientation angle 𝛹 which is the ‘orientation’ of electromagnetic wave. The shape of the ellipse is defined by the magnitudes of the Ex and Ey components and the relative phase between them. For linearly polarized light a straight line is obtained while completely circularly polarized light results in a circle.40 The simulated polarization ellipses and the orientation angles together confirm that with increasing length of the nanowire dimer the polarization state of the reflected light transforms from elliptical to circular. The numerical simulations predict that the Si nanowire dimer D2μm,70nm,60nm achieves a phase shift of γ = π/2. This dimer configuration effectively functions as quarter wave plate (QWP). Validation of Optical Birefringence and Polarization Rotation in Fabricated Nanowire Dimers. To experimentally validate the induction of an optical birefringence by nanowire dimerization in our fabricated samples, we quantified the intensities of the reflected light with parallel (𝐼∥ ) and perpendicular (𝐼⊥ ) polarization relative to the incident polarization vector as a measure for a potential polarization rotation. Figure 4a shows a plot of the birefringence coeffi𝐼 cient 𝜌 = ⊥ as function of wavelength, λ, for D1.4μm,80nm,65nm 𝐼∥

with different incident light polarizations, ranging from θ = π/4 to θ = π/2 . All data were recorded from nanowire arrays with lateral dimensions of approximately 25 x 25 μm2 containing 100 dimers. The dashed line shows the 𝜌(𝜆) plot for the corresponding monomer as control. Importantly, only the dimers show a significant peak in 𝜌, and – as predicted – the effect is strongly dependent on the orientation of the incident polarization relative to the dimer axis. An incident light polarization of θ = π/4, which has an equivalent E-field component along both x- and y-direction, generates much higher 𝜌 values than the π/2 polarization (E-field aligned along y-axis). For the latter, the phase shift γ is approximately zero. Next, we set out to test the dependence of 𝜌 on the width of the gap separating the nanowires. To that end, we measured the 𝜌 values for D1.4μm,70nm,G as function of G. The 𝜌(𝜆) spectrum red-shifts and broadens with decreasing gap separation for an incident light polarization of θ = π/4 (Figure 4b). Importantly, the magnitude of 𝜌(𝜆) increases with decreasing G We also measured 𝜌(𝜆) as function of R for dimers with constant length (L = 1.4 μm) and separation (G = 65 nm) (Figure 4c). Similar as observed for individual silicon nanowires,1 the HE1,1 mode, red-shifts with increasing R. Importantly, the width of the spectra decreases with increasing R. This effect is consistent with a gradually increasing confinement of the modes to the interior of the nanowire with increasing R diminishing the splitting of HE1,1x and HE1,1y modes. To compare the experimental 𝜌(𝜆) data with theoretical predictions, we included the simulated 𝜌(𝜆) spectra corresponding to Figure 4a-c in Figure 4e-g. To account for the numerical aperture (N.A.) of the optical system (N.A. = 0.4) used in the experiments, we assumed an incident angle of ϕ = 10° in the simulations. Although the simulated 𝜌(𝜆) spectra are systematically red-shifted, they have similar shapes

Figure 4: Characterization of birefringence of silicon dimers. a-c) Experimental optical birefringence spectra, ρ(λ), for a) D1.4μm,80nm,65nm for different polarization angles, θ, of the incident light. b) for D1.4μm,70nm, G for different G values as specified (θ = π/4). c) for D1.4μm, R ,65nm for specified R values (θ = π/4). d) Measured Stokes parameter for D1.4μm,75nm,65nm with incident polarization of θ = π/4 (solid line) and θ = π/2 (dash-dotted line). e-h) Corresponding simulation results for (a-d). Inset of f): Peak wavelength of the measured (black) and simulated (pink) ρ(λ) spectra as function of G.

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as the measured 𝜌(𝜆) spectra and reproduce the wavelength-dependent trends of the experimental spectra. The inset in Figure 4f compares the peak wavelength as a function of G for the experimental (black squares) and simulated (pink dots) 𝜌(𝜆) spectra. Potential reasons for the systematic shift of the peak wavelength between experiment and simulation include – among others – imprecisions in the determination of the nanowire diameter due to their 3D geometry which complicates precise SEM measurements and differences in the refractive index as the etching process might lead to a deposition of a thin film containing S and F and might disorder the surface of the Si. Furthermore, a systematic error in the SEM-determined nanowire radius of only 4 nm leads to a spectral shift of 50 nm as illustrated in Figure S2.

Figure 5: Si nanowire dimers are color and polarizationsensitive nanopixels. a) Top: Dark-field images of D1.4μm,R,60nm dimer arrays with from left to right: R = 75 nm, 65 nm and 55 nm . Images were recorded with a Nikon d5200 DSLR camera through the eyepiece of a microscope. Bottom: Schematic drawing of the dimer geometry b) Reflection image of an array of nanowire dimers with different orientations of the dimer axis. (from top to bottom: 0 to 𝜋/2 with a step of 𝜋/12; two subsequent rows have identical orientations). The sample is illuminated with x-polarized white-light through a 20x objective with an N.A. of 0.4. Images were acquired with a cross-polarized analyzer positioned in front of the CCD detector. c) Left: SEM micrograph (top view) of a dimer array as used in (b) in which the dimer axis is systematically rotated from the top to the bottom. Right: Schematics of the nanowire orientation for clarification.

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To experimentally test the predicted polarization rotation in nanowire dimers we measured the Stokes parameters for one selected dimer configuration, D1.4μm,75nm,65nm (Figure 4d). These measurements were performed in the wavelength range of 680-1000 nm for an incident light polarization angle of θ = π/4 and θ = π/2 as control. The four Stokes parameters, S0-3, describe the total intensity d(S0), and the polarization of the light (S1-3). S1 is a measure of linear polarization pointing along the x- or y-axis. S2 is a measure of linear polarization oriented with an angle of +π/4 / - π/4 relative to the x-axis and S3 measures the amount of right or left circularly polarized light. The comparison of the Stokes parameter plots obtained for θ = π/4 and θ = π/2 in Figure 4d illustrates vividly that irradiation of the nanowire dimer with an incident E-field that has both x- and y-components changes the incident polarization state. Whereas S1 is nearly constant and S2, S3 are almost zero across the monitored wavelength range for incident light with θ = π/2, the substantial contribution from S3 in a broad spectral range for θ = π/4 confirms elliptically polarized light. The maxima/minima in S1, S2 at around 780 nm where S3 is close to zero indicates a rotation of the incident linear light polarization at that wavelength. We also simulated the Stokes parameters as function of wavelength for D1.4μm,75nm,65nm for θ = π/4 and ϕ = 10° (Figure 4h). As observed before in case of the 𝜌(𝜆) , the simulations show a systematic red-shift when compared to the experimental data but otherwise reproduce the relative trends and shapes of the experimental plots very well. Overall, the systematic dependence of 𝜌(𝜆) on the geometric parameters of the dimers, R and G, as well as the measured and simulated Stokes parameters validate that the fabricated Si nanowire dimers generate polarization-dependent optical birefringence and create spin angular momentum. Although the nanowires fabricated in this study with a maximum length of L = 1.4 μm do not meet the requirements for generating circularly polarized light, we anticipate that an improvement of the current or development of new fabrication strategies, potentially combined with changes of the operational wavelength, will make it possible to realize phase shifts between Ex and Ey components of up to γ = π/2. Polarization- and Wavelength-Sensitive Silicon Nanowire Pixels. Individual Si nanowire dimers with the dimensions investigated in this work provide sufficient optical cross-section to be independently detectable. The nanowire dimers represent nanopixels with tunable spectral properties whose response depends on the incident light polarization. This is demonstrated in Figure 5. Figure 5a shows dark-field images of nanowire dimers with different radii. The “color” of the nanowire dimers is tuned from red (R = 75 nm), over green (R = 65 nm to) to yellow (R= 55 nm). If the sample is illuminated with linearly polarized light, and a cross-polarized analyzer is placed in front of the detector, the reflected intensity depends on the orientation of the nanowire dimers with regard to the incident light polarization. This is demonstrated in Figure 5b. The figure contains the image of an array of D1.4μm,70nm,60nm dimers, whose dimer axis is systematically rotated in steps of π/12 from the top to the bottom. Two subsequent lines in the array have identical orientation. In the two top rows the dimer axis is parallel to the x-axis, whereas for the two bottom rows the dimer axis lies along the y-axis. A SEM image of a similar array

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but with only one row for each dimer axis orientation - is included in Figure 5c. Due to the orientation-dependent birefringence of the nanowire dimers, structures whose dimer axis forms an angle of +/- π/4 with the incident light polarization most effectively rotate the incident polarization and generate a bright signal on the cross-polarized detection channel, whereas all other dimer orientations have lower intensities. Figure 5 proves that individual nanowire dimers provide sufficient signal intensity to visualize the generated optical birefringence. Furthermore, it demonstrates that nanowire dimers with a footprint below 200 nm represent photonic building blocks or pixels for more complex photonic structures whose intensity can be addressed and actively modulated through choice of the incident light polarization. Near-field Chirality of High Refractive Index Silicon Nanowire Dimers. Our analysis, so far, has focused on the far-field response associated with the weakly confined modes of Si nanowire dimers and the linear birefringence of these materials that generates elipticity and rotates the incident polarization. One unique feature that sets the generation of optical birefringence through weakly confined modes in Si nanowire dimers apart from alternative approaches based on anisotropic high refractive index waveguides or resonators39,41 is that these modes penetrate the ambient medium and do not show a strong confinement to the interior of the high refractive index material. In fact, the E-field localization observed in the gap between the nanowires in Figure 3a shows distinct resemblances with the hot-spot formation in plasmonic dimer antennas.42,43 The strong near-field enhancement in plasmonic systems has been highly instrumental in enhancing the chirality of optical fields.44–47 In general, the chirality of electromagnetic fields is described by the optical chirality density, 𝐶 = 𝜔𝜀 − 0 𝐼𝑚(𝑬∗ ∙ 𝑩) where ε0 is vacuum permittivity and B is 2 the magnetic flux.48–50 The value of C defines the ability of an electromagnetic field to enhance chiral light-matter interactions.48,51 Together with the mixed electric-magnetic dipole polarizability of a chiral molecule, C determines the difference in absorption rate for two enantiomers.47,48 Important for our current discussion is that C depends on the magnitude and orientation of the electric and magnetic fields in space and frequency domain. A parallel alignment of enhanced E and B fields that oscillate π/2 out of phase boosts C, so that it becomes possible to generate chiral fields with significantly higher C values than circularly polarized light, an effect referred as superchirality.48,54,55,56 As is evident from Figure 3a nanowire dimers with short edge-to-edge separation enhance the incident field. Importantly, the presence of orthogonal HE1,1x and HE1,1y modes from two adjacent nanowires whose electric and magnetic components accumulate a relative phase shift as they propagate along the nanowire provides opportunities for enhancing net optical chirality. The above expression for C is amenable to a numeric anal𝜔𝜀 ysis with FDTD simulations as C= 0 { |Ex||Bx|sin(Δx)+ 2 |Ey||By|sin(Δy)+{|Ez||Bz|sin(Δz)} where Δx , Δy and Δz are phase difference between Ex and Bx ,Ey and By and Ez and Bz respectively, at a particular point in space. We applied this analysis to map C around Si nanowire dimer D2μm,70nm,G with G = 40 nm at λ = 868 nm where we achieved the maximum C enhancement (Figure 6a). The dimers were irradiated by

a linearly polarized plane wave that was incident parallel to the long wire axis with θ=π/4. The map shows the value of C/C0 in the x-z plane, where we used C0, the optical chirality of circularly polarized light in free space, as reference. The simulations reveal the generation of C “hot-spots” in the gap between the nanowires where they are available for interactions with molecules from the ambient environment. The

Figure 6. Simulated near-field optical chirality. a) Simulated near-field optical chirality (normalized) for D2μm,70nm,40nm with incident polarization of θ = π/4. b) Simulated near-field optical chirality for D2μm,70nm, G as a function of gap width. The inset shows the near-filed chirality map for D2μm,70nm,40nm with incident polarization of θ = 0. c) Simulated C and |Ex| in the center of the dimer gap along the z axis for D2μm,70nm,40nm. d) upper panel: phase difference between Ex and Bx in the gap center of D2μm,70nm,40nm along the z axis based on numerical simulations (black) and refractive index analytical model (grey); lower panel: corresponding sine values. All simulations were carried out at λ = 868 nm.

control case with same dimer and incident polarization of θ = 0 is shown in the inset of Figure 6b in which the intensity is very low (~10-6) with a net gain of 0. The generation of optically chirality in the dimers requires a simultaneous excitation of HE1,1x and HE1,1y. Only θ = π/4 yields a significant enhancement of C but not the θ = π/2 control. As anticipated, the peak C-enhancement is higher for the shorter G value (Figure 6) due to increased E-field enhancement in this configuration. A maximum local enhancement, C/C0, of ≈78 is predicted for D2μm,70nm,40nm which is especially impressive considering that the chiral field is generated with linearly polarized excitation light. Since the magnitude of the Ey and Ez components are relatively small compared to that of Ex (Figure 3b) the 2nd and 3rd terms in the above equation for C are negligible, and we will focus on the 1st term in the following analysis. We plotted the absolute value of Ex and C (leaving out the scaling factor) in the center of the gap along the z axis (black and grey line respectively) in Figure 6c. The plot shows that the periodic intensity modulations of C follow the modulation in Ex along the z axis. This finding

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alone does not explain why the intensity of C increases as the light travels through the silicon nanowire dimer from top to bottom. But the increase in C is consistent with an accumulation of phase difference between the Ex and Bx components of HE1,1x and HE1,1y, respectively, along the z axis. We plotted Δx, evaluated as the phase shift between the Ex and Bx components in the center of the nanowire dimer obtained from FDTD simulations, as function of propagation length in Figure 6d (upper panel). The phase difference between Ex and Bx overall increases with increasing propagation length. In the lower panel we plotted the sine function of Δx, which is proportional to the near field optical chirality. Figure 6c and d also contain plots of the phase shift γ between the Ex and Bx components of HE1,1x and HE1,1y that results from the differences in effective refractive index of the two modes. This “analytical” model nicely captures the increase in phase shift observed in the numerical simulations. Both simulations and our simple analytical model confirm that the sine of the phase shift increases along the z-axis, accounting for the increase in C along z in Figure 6a.

Conclusion We investigated the weakly confined fundamental HE1,1 mode in dimers of high refractive index Si nanowires and demonstrate that the degeneracy of HE1,1x and HE1,1y is lifted at short gap separations and that the modes experience different refractive indices along x- and y-axis. The optical birefringence in the dimers results in an accumulation of phase shift that can cause a rotation of the linear polarization and/or generation of spin angular momentum. The optical birefringence was detectable on the single nanowire dimer level, and discrete nanowire dimers were shown to represent polarization sensitive color pixels with tunable spectral responses. We also found that the achiral Si nanowire dimers give rise to superchiral near-field “hot-spots” under illumination with linearly polarized light. Incident light that excites both HE1,1x and HE1,1y modes creates locations of enhanced optical chirality in the gap between the nanowires. Electromagnetic simulations predict that the optical chirality of the fabricated Si nanowire dimers exceeds that of circularly polarized light by a factor of up to ≈78 in these locations of superchirality. Importantly, these chiral hot-spots are located in the gap between the two nanowires where they are available to interact with molecules from the ambient medium. The ability to enhance chiroptical effect with non-metallic nano-optical structures that are by themselves achiral makes Si nanowire dimers interesting materials for enhancing chiroptical effects in molecules.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by the National Science Foundation (NSF) (CHE- 1609778).

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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Numerical simulations of birefringence for tapered silicon nanowire dimers and simulations of backscattering spectra for silicon nanowire dimers with different radii.

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