Tridirectional Polarization Routing of Light by a Single Triangular

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Tridirectional polarization routing of light by a single triangular plasmonic nanoparticle Yoshito Y Tanaka, and Tsutomu Shimura Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b00672 • Publication Date (Web): 07 Apr 2017 Downloaded from http://pubs.acs.org on April 7, 2017

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Tridirectional polarization routing of light by a single triangular plasmonic nanoparticle Yoshito Y. Tanaka*†‡ and Tsutomu Shimura† †Institute of Industrial Science, University of Tokyo 4-6-1 Komaba, Meguro-ku, Tokyo 1538505, Japan ‡

Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 3320012, Japan

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ABSTRACT

Achieving high directionality of scattered light in combination with high flexibility of the direction using plasmonic nanoparticles is desirable for future optical nanocircuits and on-chip optical links. The plasmonic characteristics of nanoparticles strongly depend on their geometry. Here, we studied directional light scattering by a single-element triangular plasmonic nanoparticle. Our experimental and simulation results demonstrated that the triangular nanoparticle spatially sorted the incoming plane wave photons into three different scattering directions according to their polarization direction, including circular polarization, despite its compact overall volume of ~λ3/300. The broken mirror symmetry and rotational symmetry of the triangular nanoparticle enabled such passive tridirectional polarization routing through the constructive and destructive interference of different plasmon modes. Our findings should markedly broaden the versatility of triangular plasmonic nanodevices, extending their possible practical applications in photon couplers and sorters, and chemo-/biosensors.

KEYWORDS. Plasmonic nanoantenna, triangular nanoprism, directionality, Fano resonance, polarization router, tridirectional scattering


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Metal nanoparticles support localized surface plasmon resonance (LSPR), collective oscillations of free electrons that provide a way to control photons at deep-subwavelength scales. This unprecedented ability has spurred their use in a vast range of nanophotonics technologies, such as biological sensing,1 surface-enhanced spectroscopy,2 photovoltaics,3 and nanolasers.4 Many plasmonic nanodevices rely on the confinement and enhancement of photons at nanometer length scales. Recent developments have led to a number of device designs that direct the scattered photons in a particular direction.5-8 Achieving high directivity is essential to develop efficient nanoscale plasmonic transmitters, receivers, and sensors. To obtain directional scattering of a plane wave perpendicular to its propagation direction, in other words, side scattering, multiple-element array antennas with carefully designed phase differences, such as the Yagi–Uda geometry, are used.9-12 Phase optimization requires spectral tuning of the plasmon resonance and spatial tuning of the antenna geometry by precise nanofabrication. Recently, directional side scattering has been achieved even in a single-element nanoparticle with broken mirror symmetry, that is, in V- and U-shaped nanoparticles, by the interference between dipole and higher-order plasmon modes.13,14 These simple directional nanoantennas facilitate their design optimization. For nanophotonic device applications, the effectiveness of directional nanoantennas would be markedly improved by adding the ability to spatially sort the incoming photons according to their parameters, such as energy or polarization. Most studies on nanoantennas for directional photon sorting have focused on color routing with bidirectional light scattering. A pair of closely spaced bimetallic disks can be used to direct scattered photons of two different energies to the left or right of the incident propagation direction.15,16 Such bidirectional color


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routing has been also demonstrated in an asymmetric dimer of nonmetallic silicon nanoparticles and V-shaped silicon particle,17,18 as well as in a metal nanodisk with a rod-shaped aperture.19,20 In this Letter, we report a single-element triangular metal nanoparticle that exhibits tridirectional polarization routing; that is, the ability to sort incoming plane wave photons into three different side-scattering directions according to their polarization direction. This simple geometry can be fabricated by not only top-down approaches, as required for the previously reported directional nanoantennas, but also by bottom-up approaches,21-24 i.e., particle synthesis, which are more facile and less expensive than top-down approaches. While the sharp tips of triangular nanoparticles have previously been used for strong localized confinement and enhancement,25,26 here, we utilize the broken mirror symmetry and rotational symmetry of triangular particles to achieve polarization-dependent tridirectional side scattering. A scanning electron microscopy (SEM) image of the triangular nanoparticle studied in this work is shown in Figure 1a. We fabricated 30 nm-thick gold particles on a glass coverslip by electron-beam lithography combined with a lift-off process. LSPR in the nanoparticle was excited by normal illumination of linearly polarized incident light along the y-axis, as illustrated in Figure 1b. The triangular nanoparticle on a glass substrate displayed two strong resonances in the simulated extinction spectra (Figure 1c). The corresponding charge distributions revealed dipole and quadrupole modes at ∼1300 and ∼730 nm, respectively (Figure 1d).


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Figure 1. (a) Scanning electron microscopy image of a gold triangular nanoparticle. The side length and height of the nanoparticle are 350 and 30 nm, respectively. The scale bar is 100 nm. (b) Illustration of the coordinate system used. The triangular nanoparticle was irradiated with linearly polarized light. (c, d) Simulated extinction (red), scattering (green), absorption (blue) spectra (c) of the particle in (a) and z-component electric field distributions (d) of the plasmon modes with resonance peaks at ∼1300 nm (top) and ∼730 nm (bottom) in (c), which correspond to dipole and quadruple modes, respectively. The latter closely represent the charge density distributions. The incident light is polarized along the y-direction in (b). Suitable interference between spatially and spectrally overlapping dipole and quadrupole components enables unidirectional scattering.12,13,27-29 The amplitude and phase of individual components can be changed by the wavelength of incident light; in other words, the interference condition strongly depends on the incident wavelength. Because the quadrupolar resonance is much sharper and weaker than the dipolar resonance in Fig. 1(c), their spectral overlap to enhance the interference for directional scattering can be seen in the region close to the


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quadrupolar resonance, while the interference effect is negligible in the region close to the dipole resonance. Figure 2a displays the angular distributions of the scattered light intensity recorded at three different wavelengths around the quadrupolar resonance (marked A–C in the extinction spectrum). These angular distributions with azimuthal angle ϕ and polar angle θ in Figure 1b were measured using back focal plane (BFP) imaging (see Methods for optical characterization details).

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The triangular nanoparticle exhibits strong lateral directionality. The maximum

intensity direction is close to (ϕ, θ) = (0°, 45°). In general, nanoparticles emit mainly scattered light into a higher-index substrate,27 and index matching shifts the scattering direction to θ = 90° in the sample plane, as shown in Supporting Information Figure S2a. Directional side scattering was clearly observed over a broad wavelength range of around 150 nm. To quantify the directionality of this nanoantenna, directivity is defined as the ratio of the scattered light intensity in the positive x-direction to that in the negative (see Methods and Supporting Information for calculation details), which is the same definition as in other relevant works. 13,15,18 Directivity values are shown together with the extinction spectrum in Figure 2a. The maximum directivity of ~12 dB is observed at a slightly longer wavelength than the quadrupole resonance peak. This value is comparable to the directivities achieved by other directional nanoantennas.13,15 As the incident wavelength shifts away from the quadrupole resonance peak and approaches the dipole peak, the directivity decreases and the scattered angular distribution becomes symmetric; i.e., a simple dipole radiation pattern. These experimental results are in excellent agreement with the numerical calculations for the triangular nanoparticle (Figure 2b). In addition, the calculated angular distributions indicate that the light scattering in the forward direction is much weaker than the directional scattering in the lateral direction.


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Figure 2. Scattered light patterns and directivity of a triangular nanoparticle on a substrate. (a) Measured angular distributions of scattered light at different wavelengths of incident light. The angular distributions with azimuthal angle ϕ and polar angle θ in Figure 1b were obtained using back focal plane imaging. The scattered patterns were recorded at the positions A–C marked in the extinction spectrum of the nanoparticle (black line, left axis). The wavelength dependence of the directivity calculated from the experimental angular distributions is shown together with the extinction spectrum (red circles, right axis). White dashed boxes in image A are the angular areas used for the directivity calculation. (b) Corresponding theoretical angular distributions and extinction spectrum considering directivity. The color scale indicates normalized scattered light intensity. To gain further insight into the nature of the directional side scattering by the triangular nanoparticle, we measured the dependence of the scattered light patterns on the incident polarization direction. The excitation light wavelength was fixed at the peak of the directivity spectrum in Figure 2a. Figure 3 displays the BFP images recorded at different incident


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polarization angles ψ in Figure 1b. The scattered light was directed to roughly three different directions, ϕ = 0°, 120°, and 240° at θ = 45°, and their angular distributions strongly depended on ψ (also see Supporting Information Movie 1). At ψ = 0°, 60°, and 120°, we observed unidirectional side scattering to ϕ = 0°, 120°, and 240°, respectively. In contrast, the nanoparticle mainly exhibited bidirectional scattering with different intensity ratios at ψ between 0°, 60°, and 120°, with almost equal intensity at ψ = 30°, 90°, and 150°. However, rotating the polarization angle did not cause marked changes in the intensity and shape of the plasmon resonance spectra of the triangular nanoparticle (Figure 4a). The scattered light intensities in the three directions I0°, I120°, and I240° changed with cos2(ψ), cos2(ψ−60°), and cos2(ψ−120°), respectively, while their total intensity I0°+I120°+I240° was almost constant over the polarization rotation (Figure 4b and c). Furthermore, tridirectional scattering with nearly equal intensity was observed in the case of circularly polarized incident light, as shown in Figure 4d. These experimental results demonstrate that a single-

element triangular nanoparticle can function as a nanophotonic polarization router that sorts the incoming plane wave photons into three different scattering directions according to their polarization direction, which is strongly supported by the numerical calculations presented in Figure 3b and 4e (also see Supporting Information Figure S2b and Movie 2). It should be noted that the overall volume of the single router is less than λ3/300, where λ is the incident light wavelength.


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Figure 3. Directional polarization routing of light. Measured (a) and calculated (b) angular distributions of the scattered light intensity at different incident polarization directions. Arrows indicate the incident polarization direction at the angle ψ in Figure 1b. The incident wavelength is fixed at the peak of the directivity spectrum in Figure 2.


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Figure 4. (a) Measured (left) and calculated (right) extinction spectra at different polarization angles ψ of 0° (black), 45° (blue), and 90° (red). (b) Polarization dependence of the scattered intensities in three different directions ϕ of 0° (red), 120° (blue), and 240° (green) at θ = 45°. The scattered light intensities in the three directions I0°, I120°, and I240° are fitted by cos2(ψ), cos2(ψ−60°), and cos2(ψ−120°), respectively. (c) The total intensity I0°+I120°+I240°, which is almost constant as the polarization rotation changes. (d, e) Measured (d) and calculated (e) angular distributions of the scattered light intensity with circularly polarized incident light. The scattering behavior of the triangular nanoparticle is determined by its LSPR modes based on its triangular geometry. The unidirectional side scattering originates from the


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interference between a dipolar mode and a quadrupolar mode supported by the entire geometry with the broken mirror symmetry. The scattered far-field intensity at a certain azimuthal angle ϕ in Figure 1b is given by |D(ϕ)exp[iη(ϕ)] + Q(ϕ)exp[iξ(ϕ)]|2= D(ϕ)2 + Q(ϕ)2 + 2D(ϕ)Q(ϕ)cos(η(ϕ) - ξ (ϕ)), where D(ϕ) (or Q(ϕ)) and η(ϕ) (or ξ (ϕ)) are the amplitude and phase, respectively, of the fields radiated by dipole component (or quadrupole component), and it is a sum of the individual mode contributions and an interference term.31 The interference effect can be remarkable for D(ϕ) ~ Q(ϕ). The radiated fields from dipole and quadrupole components in Figure 1d have distinct field symmetries (see Supporting Information Figure S3). Their interference is constructive in one direction and destructive in the opposite when the phase differences are 0 and π, respectively. At the much longer wavelength of the excitation light than resonance peaks, the dipole fields in the both directions oscillate in-phase with the excitation light, while the quadrupole field oscillations in the positive and negative x-directions exhibit the phase differences of -π/2 and +π/2, respectively, from the excitation light. As shown in Supporting Information Figure S4, the relative phases of the radiated fields as well as the plasmon modes are shifted by π with changing the excitation wavelength around their resonance spectral positions. Thus, the phase differences between the dipole and quadrupole fields in the positive and negative x-directions, η(0°) - ξ (0°) and η(180°) - ξ (180°), approach to 0 and π, respectively, at the wavelength between the dipole and quadrupole resonance peaks because the dipole resonance is located at the longer wavelength than the quadrupole one, resulting in directional scattering in the positive x-direction. On the other hand, it is difficult to achieve directional scattering in the negative x-direction because η(0°) - ξ (0°) and η(180°) - ξ (180°) in the shorter wavelength region than the quadrupole resonance peak go toward +π/2 and -π/2, respectively, which prevents the interference between the dipole and quadrupole fields. These


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discussions explain the dependence of the scattered light patterns and the directivity on the excitation wavelength in Figure 2. Furthermore, the triangular rotational symmetry enables the excitation of the three quadrupole modes Q0°, Q60°, and Q120° at different axes along the triangular sides of the nanoparticle. The excitation ratio of these quadrupole modes is modulated by the polarization direction of the incident light. Suitable interference with the dipole components D0°, D60°, and D120° produces the directional main beam and two side-lobe radiations in the directions perpendicular and parallel, respectively, to each axis along the triangular sides of the nanoparticle (see Supporting Information Figure S5). The directional main radiations into ϕ = 0°, 120°, and 240° are out of phase with each other, leading to their separation, as illustrated in Figure 3 and Supporting Information Figure S2b. In addition, the constructive interference of the directional beams with the side-lobe radiations slightly shifts the maximum scattering directions, which is most clearly seen in the scattered angular distributions at ψ = 30°, 90°, and 150°. In the case of a triangle in which all three sides are equal, the plasmon modes on different axes exhibit the same resonance properties, i.e., Q0° = Q60° = Q120° and D0° = D60° = D120°, resulting in the polarization-independent scattering efficiency and the equal distribution of the scattered light in three directions by the polarization rotation of the incident light (Figure 4 and Supporting Information Movie 2). This scattering behavior by the polarization rotation is significantly different from that at the dipole resonance wavelength (Supporting Information Movie 3). In addition, altering the side lengths of the triangular nanoparticle allows the directional polarization routing to be easily scalable with regard to the operation wavelength (Supporting Information Figure S6).


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In summary, we demonstrated the tridirectional polarization-dependent routing of light by a single triangular gold nanoparticle with an overall volume of only λ3/300. The broken mirror symmetry and rotational symmetry of the triangular nanoparticle sorted the incoming plane wave photons into three different directions that were 120° apart in the scattering process according to their polarization direction, including circular polarization. This is the first report of directional polarization routing with a single-element nanoparticle. Recently, it was shown that a silicon

nanostructure

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broken

mirror

symmetry exhibited wavelength-dependent

bidirectional side scattering into diametrically opposite directions because of its stronger magnetic scattering than that of a similar gold nanostructure.18 Therefore, a triangular silicon nanoparticle is expected to enable photon sorting into six different directions that are 60° apart according to not only the polarization direction but also the color of incoming plane wave photons. Such passive directional routers consisting of a single nanoparticle are a promising platform for on-chip signal processing in ultracompact integrated photonic devices.20 Meanwhile, triangular plasmonic nanoparticles have been paid much attention because of their strong localfield enhancement associated with their particle tips. Our findings broaden the versatility of triangular plasmonic nanodevices for possible practical applications in photon couplers and sorters, and chemo-/biosensors.

Methods To experimentally characterize the directional light scattering by a triangular nanoparticle, we recorded the angular distributions of the scattered light intensity by using the BFP imaging setup depicted in Supporting Information Fig. S1. The nanoparticles were periodically arranged


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with a pitch of 5 µm. A continuous-wave Ti:Sapphire laser with a broad wavelength tuning range (700 to 1000 nm) was weakly focused on the sample by a 10× objective lens with a numerical aperture (NA) of 0.25 (illumination spot size < 20 µm in diameter). The linear polarization of the laser beam could be changed to the desired direction and to the circular polarization by a halfwave plate and a quarter-wave plate, respectively. The scattered and directly transmitted light into the glass substrate was collected using a 60× oil immersion objective lens (NA = 1.49). To block the transmitted light, an opaque stop with a diameter that corresponded to NA < 0.3 was installed in a secondary BFP of the microscope system. This filtered BFP image was projected on a CCD camera and processed by the same procedure as in a previous paper.13 Extinction spectra were measured using white light with the same illumination system as the laser beam. The extinction spectra of the nanostructures were obtained by calculating (Ib(λ)−Im(λ))/Ib(λ), where Im(λ) and Ib(λ) are the spectra of the transmitted white light through substrates with and without nanostructures, respectively. An absorptive sheet polarizer was placed in front of the illumination objective to analyze the polarization dependence of the extinction spectra. Extinction spectra, near-field distributions, and far-field scattering distributions of the plasmonic nanostructures were numerically simulated using a full three-dimensional Maxwell calculation based on a finite element method solver (Comsol). A single triangular gold particle with a thickness of 30 nm and side length of 350 nm was placed on a substrate with a refractive index n of 1.52. The nanoparticle had radii of curvature at its corners of 10 nm. The far-field scattering distributions were calculated from the pointing vector on a 3-µm sphere surrounding the nanoparticle. Directivity was calculated for the angular areas between 45° < θ < 65° in −10° < ϕ < 10° and 170° < ϕ < 190°. The wavelength dispersion of the complex permittivity of gold measured by Johnson and Christy32 was used.


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ASSOCIATED CONTENT Supporting Information. Directivity calculations. Experimental apparatus. Simulated scattered light patterns for a triangular nanoparticle in a homogeneous medium. Radiated field patterns from dipole and quadrupole modes. Amplitude and phase of an oscillator. Interferences between multiple plasmon modes at different incident polarization angles. Simulated particle-size dependence of wavelength at maximum directivity. Videos showing measured and calculated scattered light patterns by rotating the incident polarization direction.

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

ACKNOWLEDGMENT This work was supported by JST PRESTO Grant Number JPMJPR15PA, Japan, and NIMS microstructural characterization platform as a program of "Nanotechnology Platform" of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.


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Tridirectional Polarization Routing of Light by a Single Triangular

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