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Shape-dependent light scattering properties of subwavelength silicon nanoblocks Ho-Seok Ee, Ju-Hyung Kang, Mark Brongersma, and Min-Kyo Seo Nano Lett., Just Accepted Manuscript • Publication Date (Web): 10 Feb 2015 Downloaded from http://pubs.acs.org on February 10, 2015

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Nano Letters

Shape-dependent light scattering properties of subwavelength silicon nanoblocks Ho-Seok Ee,†, § Ju-Hyung Kang,‡, § Mark L. Brongersma,‡,* and Min-Kyo Seo†,* †

Department of Physics and Institute for the NanoCentury, KAIST, Daejeon 305-701, Republic of Korea

‡

Geballe Laboratory for Advanced Materials, 476 Lomita Mall, Stanford, California 94305-4045, United States

§

These authors contributed equally to this work.

Abstract: We explore the shape-dependent light scattering properties of silicon (Si) nanoblocks and their physical origin. These high-refractive-index nanostructures are easily fabricated using planar fabrication technologies and support strong, leaky-mode resonances that enable light manipulation beyond the optical diffraction limit. Dark-field microscopy and a numerical modal analysis show that the nanoblocks can be viewed as truncated Si waveguides, and the waveguide dispersion strongly controls the resonant properties. This explains why the lowest-order transverse magnetic (TM01) mode resonance can be widely tuned over the entire visible wavelength range depending on the nanoblock length, whereas the wavelength-scale TM11 mode resonance does not change greatly. For sufficiently short lengths, the TM01 and TM11 modes can be made to spectrally overlap, and a substantial scattering efficiency, which is defined as the ratio of the scattering cross section to the physical cross section of the nanoblock, of ~9.95, approaching the theoretical lowest-order singlechannel scattering limit, is achievable. Control over the subwavelength-scale leaky-mode resonance allows Si nanoblocks to generate vivid structural color, manipulate forward and backward scattering, and act as excellent photonic artificial atoms for metasurfaces.

Keywords: silicon nanoblock / leaky-mode resonance / resonant scattering / scattering cross section / structural color

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Subwavelength nanostructures support optical resonances that facilitate highly efficient interconversion between propagating electromagnetic waves and strongly localized electromagnetic near-fields. Their outstanding ability to receive and concentrate optical radiation has been used to improve spectroscopy1–3 and imaging techniques,4,5 sensing,6 heat transfer,7,8 nonlinear signal conversion,9–12 photodetection,13–15 and solar energy harvesting.16–19 Resonant subwavelength nanostructures are also essential as photonic artificial atoms to form metasurfaces which are ultrathin planar optical components that provide arbitrary control of the phase, amplitude, polarization, and/or wavefront of a light beam.20–24 In recent decades, metallic nanostructures have been investigated intensively and used to concentrate light into deep subwavelength volumes via collective electron excitations known as surface plasmons. However, their application has been limited in extent because of the lossy nature of metals. Recently, high-refractive-index dielectric nanostructures, e.g., semiconductor nanospheres and nanowires, have been proposed as a good alternative to their metallic counterparts in many applications,25–28 owing to not only their low material losses but also their ability to support both electric and magnetic resonant modes in simple geometries.29,30 The excitation of strong optical resonances, termed Mie or leaky-mode resonances, breaks down the stereotype that useful sizes of dielectric nanostructures have to be limited to the wavelength-scale or larger dimensions. In particular, the fundamental TM01 mode, which is easily excited in semiconductor nanowires by plane wave excitation, affords a truly subwavelength-scale mode area beyond the free-space optical diffraction limit and thus allows the demonstration of vibrant structural color generation, high-performance photovoltaics, and a variety of nanoscale opto-electronic devices.14,31–35 However, in contrast to those of semiconductor nanowires, the detailed properties of the optical resonances in subwavelength-scale Si nanoblocks have not been thoroughly investigated yet. For example, most theoretical analyses of the leaky-mode resonances of threedimensional nanoparticles are based on the Mie scattering theory assuming spherical or ellipsoidal shapes,25,29 although there are a few theoretical investigations on optical properties of less symmetric objects.36 To provide guidelines for engineering semiconductor nanoblocks for a desired application, rigorous and systematic research on the leaky-mode resonances in subwavelength-scale nanoblocks is required. Given the ease of fabrication of such structures using planar device fabrication technologies, this is a very worthwhile endeavor.

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In this work, we theoretically and experimentally reveal the light scattering properties of Si nanoblocks that feature critical dimensions on the deep subwavelength scale. Finite-difference time-domain (FDTD) simulations and dark-field scattering microscopy are used to analyze the gradual evolution of the leaky-mode resonances of a nanoblock to those of an infinitely long nanowire. A wide spectral tunability across the visible is demonstrated as the size is changed. We also find that different resonances exhibit different dependences of the resonant wavelengths on the length of the blocks. This can be used to spectrally align scattering resonances and to achieve very large scattering efficiencies.36-38

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Figure 1. (A) Schematic illustration of Si nanoblocks under planewave illumination. The Si nanoblocks have a square cross section of side d and a length of L. (B) Two-dimensional map of the calculated scattering efficiency Qsca of Si nanoblocks with a square cross section measuring 60 nm on a side as a function of the wavelength of light and the nanoblock length under normally incident TM-polarized planewave illumination. Profiles of the scattered electric field parallel to the nanoblock axis (left) and total intensity of the scattered electric field (right) for an infinitely long Si nanowire with a square cross section measuring 60 nm on a side at (C) TM11 (λ0 = 440

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nm) and (D) TM01 (λ0 = 725 nm) mode resonances. The square cross section of the nanoblock and nanowire measures 60 nm on a side. The field and intensity magnitudes are normalized to those of the incident planewave.

The resonant modes supported by one-dimensional Si nanowires can be characterized as transversemagnetic (TM) or transverse-electric (TE) modes similar to those in cylindrical nanowires. They can be labeled similarly by analyzing them in cylindrical coordinates. With that choice, the modes are written as TMml or TEml, where m and l are the azimuthal and radial order mode numbers, respectively. The azimuthal mode number is linked to the number of antinodes a in the dominant field that are encountered in a trajectory along the circumference of the structure (m = a/2). One can think of this quantity as the number of effective optical wavelengths that fit around the circumference. The radial order mode number describes the number of field maxima that are encountered along a radial direction within the structure. Under planewave illumination with the electric field parallel (or perpendicular) to the long axis of a nanoblock, only TM (or TE) modes can be excited for symmetry reasons. These resonances can be followed in their evolution from those of an infinitely long nanowire to those of a finite-length nanoblock. Figure 1A shows a schematic illustration of a series of Si nanoblocks with a square cross section on a quartz substrate under normally incident planewave illumination. The total-field/scattered-field technique39 was employed in the FDTD simulation to realize the planewave incidence and analyze the scattering properties of the Si nanoblocks rigorously. The dispersive dielectric constant of Si was handled by using the auxiliary differential equation (ADE) method40 and fitting the experimentally determined refractive index of Si (see the Methods).41 Figure 1B shows a two-dimensional map of the calculated scattering efficiency Qsca of Si nanoblocks with a square cross section measuring 60 nm on a side as a function of the length of the nanoblock and the wavelength of the incident light. The scattering efficiency is defined as the ratio of the scattering cross section to the physical cross section of the nanoblock. When the incident planewave is polarized parallel to the long axis of a nanoblock (along the y axis), only TM resonances are excited. The Si nanoblocks exhibit two strong TM resonances in the spectral range from 400 to 1000 nm. The two resonances are derived from the TM01 and TM11 modes of an infinitely long nanowire having a cross section identical to that of the nanoblock. The TM11 mode has a relatively narrow spectral width, and its resonance wavelength of λ0 = 440 nm is almost independent of the

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length of the nanoblock. Considering that the half-wavelength in the Si medium, λ0/2nSi, is ~50 nm and thus similar to the width of the nanoblock, it is understandable that the wavelength-scale TM11 mode is shifted very little by changes in the length of the nanoblock. On the other hand, the resonance wavelength for the fundamental TM01 mode is larger (λ0 = 725 nm) and the cross-sectional area is significantly smaller than the square of the half-wavelength of light in the medium, (λ0/2nSi)2. Note that the subwavelength-scale TM01 mode resonance can be widely tuned across the entire visible wavelength range from 440 to 725 nm by changing the length of the nanoblock from 150 to 650 nm. The tuning range can be extended to the near-infrared range by using wider nanoblocks. As the length of the nanoblock increases, its resonant modes are gradually converted into the leaky resonant modes of an infinitely long nanowire.31 When the length of the nanoblocks exceeds 650 nm, the resonant wavelengths and spectral widths of the TM01 and TM11 modes converge to those of an infinitely long nanowire and the scattering cross section divided by the nanoblock length approaches the one-dimensional scattering cross-sectional length of the infinitely long nanowire. Figures 1C and 1D show the scattered electric field profiles of the TM11 (λ0 = 440 nm) and TM01 (λ0 = 725 nm) modes supported by the infinitely long nanowire, respectively. The TM11 mode, with a higher azimuthal mode number (m = 1), features a nodal plane in the core of the nanowire, and the electric field intensity maximum occurs near the bottom of the nanowire (Figure 1C). The asymmetry of the field profiles is due to the presence of the substrate and retardation effects. The electric field profile of the TM01 mode shows a single maximum near the center of the nanowire (Figure 1D). As the length of the nanoblock becomes smaller than 650 nm, the subwavelength-scale TM01 mode resonance rapidly blue-shifts, and it eventually spectrally overlaps the TM11 mode resonance when the length of the nanoblock is reduced to 150 nm. The favorable overlap of the TM01 and TM11 mode resonances enables a notably large scattering efficiency of ~9.95, and the scattering cross section approaches the theoretical lowestorder single-channel scattering limit for a subwavelength-scale nanostructure.37,38 This strong scattering phenomenon based on the spectral alignment of two resonances will be discussed in detail later, together with the near- and far-field profiles of the TM01 and TM11 modes of the nanoblocks. The undulation in the magnitude of the scattering efficiency of the TM11 mode with changing nanoblock length in Figure 1B is due to the

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presence of higher-order longitudinal Fabry–Perot (FP) resonances supported by the two reflecting end facets of the nanoblocks. Under TE-polarized illumination, only wavelength-scale TE01 resonances are supported at 440 nm almost independently of the length of the nanoblock (see Supplementary Figure S1).

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Figure 2. (A) Dispersion curves of the TM01 (solid) and TM11 (dashed) modes supported by square Si nanowires with cross-sectional widths of 60 nm (red), 80 nm (green), and 100 nm (blue) placed on a quartz substrate as a function of the wavenumber along the nanowire axis, kmode. The solid gray lines represent the light lines in the air (upper) and quartz (lower), respectively. (B) Effective length of nanoblock (Leff = π/kmode) for the TM01 (solid) and TM11 (dashed) modes of the Si nanowires as a function of the resonance wavelength from the dispersion curves. The plots are overlaid on top of the scattering efficiency map of the Si nanoblock with a cross-sectional width of 60 nm from Figure 1B.

To understand the length dependence of the TM11 and TM01 resonances of the nanoblocks systematically, we calculated the dispersion curves of the leaky TM modes supported by the Si nanowires as a function of the wavenumber along the nanowire axis, kmode, using FDTD simulations employing a broadband point electric dipole source polarized parallel to the nanowire axis (Figure 2A). The dispersion curve of the TM11 mode is almost flat over a large wavenumber range near the zone center until it approaches the light line, and the resonant frequency of the TM11 mode is almost fixed at 680 THz, corresponding to a free space wavelength of ~440 nm (red dotted line in Figure 2A), which is the TM11 mode resonant wavelength of the Si

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nanoblocks in Figure 1B. On the other hand, the TM01 mode is dispersive, and its dispersion curve crosses the light line (red solid line in Figure 2A). As the wavenumber increases, the resonant frequency of the TM01 mode increases rapidly, and the slope of the dispersion curve becomes even steeper near the light line of air. The frequency at kmode = 0 is ~410 THz, corresponding to a free space wavelength of ~725 nm, which is the resonant wavelength of the TM01 mode in the infinitely long nanowire. It is notable that, for a sufficiently large wavenumber, the frequency of the TM01 mode becomes as high as that of the TM11 mode. This explains the spectral overlap of the TM01 and TM11 mode resonances in a short nanoblock supporting a large wavenumber. For quantitative analysis, we overlaid the dispersion curves of the TM01 and TM11 modes of the Si nanowires on top of the scattering efficiency map of the Si nanoblock with a cross section of 60 nm, using an FP resonance condition, 2kmodeLeff = 2π (Figure 2B). Here, Leff is the effective length of the nanoblock supporting the first FP resonance along the length of the wire. In infinitely long nanowires, the planewave incident in the normal direction can only couple to the mode at kmode = 0. But, the finite nanoblocks, due to their 3D shape that features abrupt edges, enable the normally incident light to excite the leaky-modes with any possible k value. Indeed, it clearly shows that the scattering properties and spectral behavior of the Si nanoblock can be fully understood in terms of the dispersions of the leaky TM11 and TM01 modes in the nanowire with an identical width and height. The FP resonance can be made even more accurate by taking into account a reflection phase pickup at the end of the nanoblocks, as was done for plasmonic resonators42,43 and nanowires.44 The dependence of the phase pickup on the resonance wavelength causes the difference between the effective length and the actual length of the nanoblock. However, as shown in Figure 2B, the contribution of the phase pickup is not substantial for nanoblocks longer than ~200 nm.

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Figure 3. (A) Top-view scanning electron microscopy image of a fabricated Si nanoblock with a cross section of 60 nm on a side and a length of ~600 nm (scale bar: 200 nm). (B) Schematic illustration of the light scattering measurement setup based on a dark-field microscope. BS: beam splitter, LP: linear polarizer. (C) Measured scattering spectra of Si nanoblocks with different lengths. (D) Calculated scattering efficiency of Si nanoblocks with lengths corresponding to those used in the experiments. For clarity, the spectra have been displaced vertically by 5 for each additional layer.

Si nanoblocks with lengths ranging from 200 to 1000 nm were fabricated on a quartz substrate using standard semiconductor fabrication processes (see Figure 3A and the Methods). Both the width and height of the fabricated nanoblocks were fixed at 60 nm. The light scattering properties of single Si nanoblocks were measured using a dark-field optical microscope coupled to either a charge-coupled device (CCD) camera or a fiber-coupled spectrometer, as illustrated in Figure 3B. A 50× (N.A. 0.8) dark-field microscope objective was used to illuminate a single nanoblock with white light and collect the scattered signals from the nanoblock. Linear polarizers were used to control and analyze the polarization state of the incident and scattered light to

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characterize the TM mode resonances of the nanoblocks. As shown in Figure 3C, the measured TM11 resonance remains practically fixed at ~450 nm irrespective of the nanoblock length. On the other hand, the TM01 mode resonance shifts from ~600 nm to ~450 nm as the length of the nanoblock decreases from 1000 to 200 nm. Figure 3D shows the simulated total scattering efficiency for different nanoblock lengths, which agrees well with the measured scattering spectra of the leaky-mode resonances. The differences in the resonance position and scattering power between the simulated and measured spectra are due to the limited collection solid angle in the experiments and fabrication imperfection of the nanoblocks. In the experiments, only the light scattered into the objective lens with a numerical aperture of 0.8 was collected and measured under the reflected dark-field illumination condition. For example, the TM11 resonance features lower backward scattering and thus shows a smaller scattering power in reflected dark-field scattering measurement than the TM01 resonance (see Supplementary Figure S2).

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mode resonances are spectrally separated at wavelengths of 450 nm and 625 nm, respectively. (B) Near-field intensity distribution of electric field scattered by a 150-nm-long Si nanoblock at a wavelength of 450 nm where the TM01 and TM11 mode resonances are spectrally overlapped. (C) Far-field scattering profiles from a 400-nmlong Si nanoblock at wavelengths of 450 nm (top) and 625 nm (bottom). (D) Far-field scattering profiles from a 150-nm-long Si nanoblock at a wavelength of 450 nm. All the far-field distributions are represented by the polar (θ) and azimuthal (ϕ) angles of the spherical coordinate system (Figure 1A). The backward and forward far-field distributions are measured over the northern (0 ≤ θ < π/2) and southern (π/2 < θ ≤ π) hemispheres respectively. The center and border of the plot correspond to the vertical and horizontal directions with respect to the plane of the substrate, respectively. The backward and forward directions are defined as the directions to the air and the quartz substrate, respectively.

When a nanostructure is deep subwavelength-scale in size and supports leaky-mode resonances with a total angular momentum of l = 1, its total scattering cross section is limited to 3λ2/2π.37 Although the concept of the single channel limit is applied better to a spherical particle, it can be applied to a subwavelength nonspherical particle if the particle supports mostly the lowest-order mode. The field of the lowest-order mode spreads widely and extends far beyond the physical dimension of the structure and the fine geometry of the particle does not induce much difference in the optical response.36 In addition, a similar limit can be still worked out for a less symmetric nano-structure without requiring any geometrical limitation or resorting to the dipole channels.45 At a wavelength of 450 nm, the maximum scattering cross section of a deep subwavelength-scale nanoblock is 0.097 µm2. The scattering efficiency was estimated to be 9.95 for the nanoblock with a width and length of 60 and 150 nm, respectively, under 450 nm illumination (Figure 1B). Considering the physical cross section of the nanoblock, the calculated scattering cross section is ~0.090 µm2, which is 93% of the theoretical limit. Such a large scattering cross section is achieved by the favorable spectral overlap of the TM01 and TM11 mode resonances despite strong light absorption in Si at visible wavelength. Figures 4A and 4B show the scattered electric field intensity distributions when the TM11 and TM01 resonances are spectrally separated (400nm-long nanoblock) and when the two resonances are fully overlapped (150-nm-long nanoblock), respectively. The near-field intensity distributions of the resonant modes in the 400-nm-long nanoblock, spectrally separated

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at wavelengths of 450 and 625 nm, are almost identical to those in the infinitely long nanowire. The spectrally overlapped TM01 and TM11 resonances in the 150-nm-long nanoblock result in the superposition of their field distributions, as shown in the cross-sectional views of the near-field intensity distribution of the 150-nm-long nanoblock (Figure 4B). In addition, the fundamental FP resonance in the longitudinal direction is clearly observed and validates the effective wavelength analysis employed in Figure 2B. The spatial superposition of the two resonances with different mode numbers can also be observed in the far-field scattering profiles. We calculate the far-field distribution of the scattered field using the near-to-farfield transformation based on the reciprocity theorem.46,47 Figure 4C shows the far-field scattering profiles of the TM01 and TM11 resonances when the two resonances are spectrally separated (400-nm-long nanoblock). The farfield profile of the fundamental TM01 mode is almost identical to that of a single electric dipole located 30 nm above the quartz substrate (see Supplementary Figure S3). Because of its higher azimuthal mode number, the TM11 mode has a different far-field profile; in particular, its backward scattering is suppressed and become negligible as the length of the nanoblock increases (Figure 4C). The 400-nm-long nanoblock funnels more than 78% of the total scattering radiation (>80% of the forward scattering radiation) within a divergence angle of ±53°, corresponding to a numerical aperture of 0.8. This ability to control the far-field scattering distribution and the forward/backward scattering ratio by engineering the leaky-mode resonances in the nanoblocks is suitable for applications requiring directional light scattering and zero backscattering.29,30 The ring pattern commonly observed in the forward scattering profiles corresponds to the critical angle for a glass/air interface. As shown in Figure 4D, when the two resonances are fully overlapped (150-nm-long nanoblock), the far-field scattering distribution possesses the characteristics of both the TM01 and TM11 leaky-mode resonances. Additionally, the dependence of the far-field scattering distribution on the nanoblock length is also calculated (see Supplementary Figure S2). It is noteworthy that such unaffected spatial superposition in the near- and far-field distributions enables the large scattering power of the subwavelength Si nanoblock to approach the theoretical lowest-order single-channel scattering limit. We further note that, if the width, height, and length of the nanoblock are tuned more precisely or core-shell structures are employed, the scattering cross section can be further increased and exceed the single-channel limit.37,38

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Figure 5. (A) Dark-field optical microscope images taken from Si nanoblocks with a square cross section ~100 nm on a side. The structural color of the scattered radiation from the Si nanoblocks is tuned over the entire visible wavelength range by changing the length of the blocks. TM-polarized incidence was employed in the dark-field microscope measurement. (B) Normalized scattering resonance spectra of Si nanoblocks with lengths of 130 nm (black), 170 nm (red), and 200 nm (blue). (C) Two-dimensional map of the calculated scattering efficiency Qsca of Si nanoblocks as a function of wavelength and nanoblock length. The cross section of the Si nanoblocks is 100 nm on a side, and TM-polarized planewave illumination was taken to be normally incident in the FDTD simulations.

The wide spectral tunability of the TM01 resonant wavelength by simply changing the length of the Si nanoblocks facilitates easy control of the color of the scattered light. The spectral tuning range is determined by the width and thickness of the Si nanoblocks. For instance, when the Si nanoblocks have a width and thickness of 100 nm, the color of the scattered light can be tuned over the entire visible spectrum (see Figure 2B). Figure 5A shows dark-field optical microscopy images of 100-nm-wide and 100-nm-thick Si nanoblocks with different lengths under TM-polarized illumination taken with a 100× (N.A. 0.9) objective lens. As the length of the nanoblock changes from ~110 to ~200 nm in 10 nm steps, the color of the scattered light continuously changes from blue to green, yellow, and red (Figure 5A). This color shift is quantitatively represented by the scattering

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spectra taken from the Si nanoblocks (Figure 5B). The FDTD simulations exhibited a progressive color change over the entire visible spectrum, in good agreement with the experimentally measured scattering spectra. A twodimensional map of the calculated Qsca of Si nanoblocks with a square cross section 100 nm on a side shows that the scattering resonance shifts from ~450 nm to ~600 nm as the length of the nanoblock increases from 50 to 200 nm (Figure 5C). The resonant modes of the Si nanoblocks with a square cross section that measures 100 nm on a side show similar spectral scattering properties to those of the nanoblocks with a square cross section measuring 60 nm on a side except that the resonance modes are redshifted and higher-order modes appear in the blue spectral range. The resonance wavelength for the TM11 mode is located at ~600 nm, and the TM01 and TM11 modes overlap when the length of the nanoblock is reduced to 200 nm. Therefore, the spectrum in Figure 5C shows only a single peak, and the vivid colors in Figure 5A can be observed. Notably, the maximum scattering cross section, ~0.174 µm2, was calculated for the nanoblock with a width and length of 100 and 160 nm, respectively, at a wavelength of 590 nm, and it exceeds the lowest-order single-channel limit (~0.166 µm2). In summary, we have investigated the scattering properties of high-refractive-index Si nanoblocks with a subwavelength cross section. A gradual evolution of the leaky-mode resonances of the nanoblocks from those of an infinitely long nanowire was demonstrated both experimentally and theoretically. An analytical model based on the modal dispersion of a Si nanowire enabled a deeper understanding of the scattering properties of the TM01 and TM11 mode resonances in subwavelength Si nanoblocks and their different dependence on the nanoblock length. In the Si nanoblocks with a square cross section 60 nm on a side, the subwavelength-scale TM01 mode resonance is widely tunable across the entire visible wavelength range by varying the length of the nanoblocks, whereas the wavelength-scale TM11 mode resonance does not change greatly. As a result, the TM01 and TM11 resonances can be spectrally overlapped, and large scattering cross sections approaching the theoretical lowest-order single-channel scattering limit can be achieved. Near- and far-field distribution analysis also confirms that the superposition of the two leaky-mode resonances with different mode numbers contributes to this large scattering cross section. In addition, Si nanoblocks with a cross section of ~100 nm exhibit vivid structural color that is tunable across the visible and near-infrared range. Understanding and engineering of the leaky-mode resonances in Si nanoblocks will be highly useful for realizing various nano-optical applications that require a very large scattering efficiency and control over the forward and backward scattering.29,30

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Furthermore, the tunable subwavelength-scale resonance makes high-refractive-index Si nanoblocks suitable as photonic artificial atoms for metasurfaces.

METHODS To fabricate Si nanoblocks, a 60-nm- or 100-nm-thick intrinsic poly-Si film was deposited onto a quartz substrate in a low-pressure chemical vapor deposition instrument at 620 °C. Then, electron beam lithography and standard reactive-ion etching (HBr/Cl2) were employed to define the nanoblocks on the substrate. The scattering spectra of individual nanoblocks were measured by a confocal microscope (Nikon Eclipse C1) coupled to a monochromator (SpectraPro, Princeton Instruments) with a spectral resolution of ~1 nm. A CCD camera (Pixis, Princeton Instruments) was connected to the monochromator. In reflected dark-field illumination using a 50× or 100× objective lens, the incident angle was ~60°, and the numerical aperture for collecting scattered radiation was 0.8 (50× lens) or 0.9 (100× lens). A linear polarizer was located in front of the light source to illuminate the nanoblock with polarization parallel to the longest axis of the nanoblock, and another polarizer was located in front of the monochromator or CCD camera to collect scattered light with the same polarization. A white light source (a halogen lamp) was employed to illuminate samples, and the scattered light from the samples was collected using a dark-field objective. The scattering spectra were normalized by the reflection spectra of the white light source from the quartz substrate. The dark-field microscope images were taken using a color CCD camera (Nikon DS-Fi1) installed on the microscope. In the FDTD simulations, the dispersive permittivity of Si was handled by the ADE method using a model with a single critical pole pair40 and the fitting parameters were obtained by fitting measured n, k data41 of single-crystalline Si over wavelength range of 400-1000 nm (see Supplementary Figure S4). The refractive index of the quartz substrate was set to 1.45. To calculate the scattering efficiency Qsca, the total-field/scatteredfield technique was employed. The spatial grid size and temporal step were set to 5 nm and 2.5 c-1 nm, respectively, where c is the speed of light. In each simulation, a normalized monochromatic planewave propagating in the negative z direction was illuminated. Time-averaged outgoing pointing vectors were obtained in the scattered-field area and divided by the physical cross section of the nanowire to obtain the scattering

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efficiency. In the simulation of the modal dispersion of the Si nanowire, the Bloch boundary condition was applied along the direction of the nanowire axis to determine the wavenumber. The spatial grid size and temporal step were set to 2.5 nm and 1.25 c-1 nm, respectively. A broadband point electric dipole source polarized parallel to the axis of the nanowire was located in the nanowire to excite the TM leaky-mode resonances.

ASSOCIATED CONTENT Supporting Information Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] and [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS M.-K.S. acknowledges support for this work from the National Research Foundation of Korea (NRF) (2013R1A2A2A01014224, 2014M3A6B3063709, and 2014M3C1A3052537). J.-H. K. acknowledges support from the National Research Foundation of Korea (NRF) (357-2011-1-C00041). H.-S. E. acknowledges support from the National Research Foundation of Korea (NRF) (2012R1A6A3A01039034). M. L. B acknowledges support from the Air Force Office of Sponsored Research under grant number FA9550-14-1-0117.

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