Imaging Chirality of Optical Fields near Achiral Metal Nanostructures

The local circularly polarized fields were visualized by near-field polarimetry imaging, and the spatial features of the observed circularly polarized...
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Article Cite This: ACS Photonics 2018, 5, 1486−1492

Imaging Chirality of Optical Fields near Achiral Metal Nanostructures Excited with Linearly Polarized Light Shun Hashiyada,† Tetsuya Narushima,†,‡ and Hiromi Okamoto*,† †

Institute for Molecular Science (IMS) and The Graduate University for Advanced Studies (SOKENDAI), 38 Nishigonaka, Myodaiji, Okazaki, Aichi 444-8585, Japan ‡ PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan S Supporting Information *

ABSTRACT: Chiral systems (consisting of materials and incident radiation) respond differently to left- and right-handed circularly polarized light macroscopically. As a consequence, only chiral materials show intrinsic macroscopic optical activity, and only chiral systems generate circularly polarized light from linearly polarized incident light. In the nanoscopic regime, in contrast to this general rule for macroscopic cases, it is theoretically expected that achiral (nonchiral) systems can locally generate circularly polarized fields. Here, we report experimental evidence for that situation in achiral systems consisting of gold nanostructures and linearly polarized incident light. The local circularly polarized fields were visualized by near-field polarimetry imaging, and the spatial features of the observed circularly polarized fields were qualitatively reproduced by a simple dipole model. The present results may provide a novel technique to produce controllable circularly polarized optical fields in nanospaces. KEYWORDS: chirality, optical activity, nanomaterial, plasmonics, polarimetry, scanning near-field microscope

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optical field has not been experimentally confirmed, it may provide novel technique to produce controllable CP optical fields in nanospaces if it is actually observed. In this article, we report experimental observation of local CP optical fields in the peripheries of achiral two-dimensional gold nanostructures excited with LP light. The polarization measurements of local optical fields are achieved by near-field polarimetry based on an aperture-type scanning near-field optical microscope (a-SNOM). To confirm the universality of local CP optical field generation in achiral nanostructures, we investigate two nanostructured samples with different structural symmetries. One is achiral and anisotropic nanorectangles and the other one is two-dimensionally isotropic nanodisks. Our experimental results show that the nanorectangle and the nanodisk locally generates both left- and right-handed elliptically polarized optical field, whose spatial distribution is point-symmetric with respect to the center of the nanostructure. We also show that the experimentally obtained spatial features of local CP optical fields can be explained by a qualitative model calculation where the excited plasmon on the nanostructure is represented as an oscillating point dipole. These results suggest that the symmetry of the photoexcited states of the nanostructure, rather than the geometrical symmetry of the nanostructure, is essential to generate local CP optical fields. These findings could serve as a basis for the

INTRODUCTION Structural symmetry of the material determines the selection rules of optical transitions.1 A chiral material that lacks mirror symmetry shows macroscopic optical activity, and it has different responses to left- and right-handed circularly polarized (CP) light.2 The selection rule of macroscopic optical activity states clearly that a chiral material shows optical activity, whereas an achiral (nonchiral) one does not. This simple and clear selection rule has been utilized for detecting and characterizing chirality of unknown materials. Circular dichroism (CD) is a representative method to provide a measure of optical activity, which is defined as the differential absorption between left- and right-handed CP light and is widely used in materials and biological sciences. However, recent nanoscopic studies have revealed that the simple correlation between macroscopic chirality and optical activity mentioned above is invalid in the regime of nanospace. Experimental nano-optical imaging studies have demonstrated that even achiral metal nanostructures show CD signals locally.3−5 Because of the local CD activity, it is expected that achiral nanostructures generate chiral light, as typified by CP light, in the near field regime at the local CD active site, where responses to left- and righthanded CP light are different. Theoretical studies have predicted that CP optical field can be generated locally even by linearly polarized (LP) light irradiation of achiral nanostructures when illumination of LP light on the nanostructure resonantly excites oscillating polarization (e.g., a surface plasmon).6,7 Although such a behavior of local CP © 2018 American Chemical Society

Received: December 11, 2017 Published: January 25, 2018 1486

DOI: 10.1021/acsphotonics.7b01511 ACS Photonics 2018, 5, 1486−1492

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ACS Photonics

0°, and the azimuth angle θ ranges from +90° to −90°. To analyze polarization changes induced by the sample, we constructed near-field images with the η and θ values obtained by subtracting the incident polarization (ηin, θin) from the measured (η(r), θ(r)) at position r. The incident polarization was evaluated on the glass substrate without the nanostructures (details in Supporting Information). From a perspective of conservation law of optical chirality,12−14 the change of optical chirality flux induced by the material corresponds to dissipation of the optical chirality density in the material. The images with η and θ thus provide information on local optical chirality density near the sample. Near-Field Polarimetry Imaging of a Single Gold Nanorectangle. We first observed the spatial feature of the plasmon mode of the gold nanorectangle to identify its characteristics by near-field extinction imaging. In our previous study with near-field CD imaging, we experimentally found that the gold nanorectangle showed locally strong CD activity around its corners.4,5 This result indicates that rectangle has chiral interaction with light because of the local chirality. Thus, the generation of local CP optical field in the gold nanorectangles is expected. The gold nanorectangle used in the present study showed plasmon resonance with a peak at ∼780 nm (Figure 2a). The near-field extinction spectrum was acquired near the center of the rectangle, i.e., the observed extinction band is caused by a plasmon mode of a (macroscopically) allowed optical transition. In the near-field imaging of the nanorectangle, we used LP light parallel to the long axis of the rectangle at a wavelength of 800 nm. In this case, the plasmon of the rectangle is excited under the preresonance condition because the excitation wavelength (800 nm) is slightly longer than the plasmon resonance wavelength (780 nm). The near-field extinction image showed strong extinction near the long sides of the rectangle (Figure 2b). This strong extinction corresponds to the antinode of the excited plasmon mode. The spatial structure of the extinction for the rectangle is similar to that seen on the gold nanodisk.15 The extinction band is thus identified as an allowed dipole-like plasmon mode oscillating in the same phase on the left and the right sides of the rectangle. Figure 2c,d shows simultaneously obtained near-field images of ellipticity angle η and azimuth angle θ for the single gold nanorectangle, respectively. Although the nanostructure and incident optical field do not have any chirality, CP optical fields were locally generated in the periphery of the rectangle. The extremal values of η and θ signals found near the corner of the rectangle were as high as ∼±15°, which were 1 order of magnitude larger than those obtained with the macroscopic measurements for the chiral gold gammadion nanostructures (∼±1°).16 The local η and θ signals showed a point-symmetric (or 2-fold rotationally symmetric) distribution with respect to the center of the rectangle that correctly reflected the geometrical symmetry of the nanostructure. Such antisymmetric distributions of η and θ signals in the individual nanorectangle lead to approximately null signals on average over the entire rectangle. These results suggest, as described below, that the observed signals are attributable to the local chirality and/or the local anisotropy rather than the macroscopic anisotropy of the nanorectangle that may yield linear birefringence (LB) and linear dichroism (LD). Because of the different lengths of the short and long sides of the rectangle, the macroscopic refractive index and absorbance for LP light along the long axis must be different from those for LP light along the

design and control of (circularly) polarized optical fields at nanospaces.

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RESULTS AND DISCUSSION Near-Field Polarimetry. Figure 1a schematically illustrates our approach to the near-field polarization measurement; LP

Figure 1. Experimental scheme. (a) Schematic of near-field polarimetry for measuring the polarization of optical fields. (b) The polarization state of the in-plane electric field, showing the ellipticity angle η and the azimuth angle θ.

optical near-fields illuminate the nanostructured sample with the a-SNOM operating in the illumination (I)-mode, and the polarization states of the scattered light are analyzed in the far field regime by a polarimeter consisting of a photoelastic modulator (PEM) and a linear polarizer (see Methods). The aSNOM operating both under the I-mode8 and under the collection (C)-mode9 has been proven to be a powerful tool for measuring the polarization distribution close to the nanostructures. In the C-mode, optical near-fields generated by the sample are directly collected by a probe, where the optical arrangement of the C-mode is reciprocal to that of the I-mode. We note that optical images taken by the I- and C-mode arrangements were found to be equivalent to each other for near-field experimental configurations,10 in a similar manner as in far-field optics where the reciprocity theorem is established.11 Here, we assume that the reciprocity is also valid in the nearfield polarization measurements, and thus the polarization map taken under the I-mode is presumably equivalent to that taken under the C-mode. Under the C-mode, however, the polarization of the light before analyzed by a polarimeter could be considerably disturbed at the probe due to a bent part of the fiber probe or an irregularity in the aperture shape. Under the I-mode, although a lens used for collecting the scattered light may slightly disturb the polarization of the light, the effect is much less than that of the probe. Thus, usage of the I-mode SNOM is preferred to measure the polarization of local optical fields with higher accuracy. We therefore adopted the Imode arrangement for the near-field polarimetry. To elucidate the polarization states of the light near the nanostructure, we determine the ellipticity angle η (in degrees) = 90 sin−1{sin(2ψ)sin δ}/π and the azimuth angle θ (in degrees) = 90 tan−1{tan(2ψ)cos δ}/π of the polarization ellipse (as illustrated in Figure 1b), where the angles ψ = tan−1(Ey0/ Ex0) and δ = φy − φx characterize the amplitude ratio and the phase difference between the y- and x-components of electric field (E = E0eiφ, where E0 and φ represent the amplitude and phase of the electric field, respectively), respectively.11 The ellipticity angle η ranges from +45° (left-handed CP light) to −45° (right-handed CP light) and represents LP light when η = 1487

DOI: 10.1021/acsphotonics.7b01511 ACS Photonics 2018, 5, 1486−1492

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Figure 2. SNOM measurements of a single gold nanorectangle. (a) Near-field extinction spectrum obtained at the center of the gold nanorectangle (190 nml × 65 nmw × 55 nmt). The wavelength used for near-field imaging (800 nm) is indicated by the vertical line. Inset: Scanning electron micrograph of the gold nanorectangle. (b−d) Simultaneously obtained near-field extinction (b), ellipticity angle η (c), and azimuth angle θ (d) images for the single gold nanorectangle irradiated with linearly polarized optical field (the polarization direction is indicated by arrows). The dashed lines indicate the approximate position of the rectangle. (e, f) The line profiles of ellipticity angle (e) and azimuth angle (f) along the horizontal lines in (c) and (d), respectively. Scale bars: 100 nm.

is considered to be weak enough. Considering that this effect arises from a multiple scattering process, the possible optical activity signals from this Born-Kuhn system should be thus negligible. Based on these considerations, the experimentally observed η and θ signals are caused by local CP optical fields generated by the gold nanorectangle that is locally irradiated with LP optical field parallel to the long axis of the rectangle, and not by the possible artifacts mentioned above. In addition, as long as the optical reciprocity is valid, the achiral gold nanorectangle irradiated with LP light along the long axis generates local CP optical fields in the periphery of the rectangle. Model Calculation of Local Circularly Polarized Optical Field Generation. To discuss the mechanism of the CP optical field generation near the gold nanorectangle, we simulated the spatial distributions of η and θ based on a simple model where the plasmon excited on the rectangle is approximated as an oscillating point dipole.6,7 Suppose that the point dipole is induced by the linearly polarized plane-wave electric field propagating in +z direction, Ein = E0J ei(kz−ωt), where ω and k represent the angular frequency and the wavenumber, respectively. The polarization state is determined by the Jones vector J. In the present case, J = Jx = t(1,0) to reproduce the x-polarized incident field of the experiment (Figure 3a). The induced dipole fields close to the dipole (kr ≪ 1) can be described approximately by18

short axis. These effects are LB and LD and may change the polarization of light that pass through the rectangular nanostructure when the polarization plane of the incident light is tilted with respect to the principal axes of the rectangle. If the polarization effects induced by macroscopic LB and LD response of the material contribute to the η and θ images, then they should show nonzero η and θ values on the symmetry planes, resulting in their integrated values over the whole nanostructure being finite. Our results showed that the nanostructure did not generate CP light macroscopically, while it locally generated CP optical fields. Thus, the contributions of macroscopic LB and LD of the rectangle to the observed η and θ signals are negligibly small. Artifacts may also arise from the near-field probe, which may induce optical near-field interaction between the probe and the nanostructured sample: the plasmon excited on the nanostructure induces an optical field near the nanostructure, and this field may recurrently excite plasmons of the probe metal coating (i.e., multiple scattering) when their resonance frequencies are close to the excitation frequency. When the probe position deviates from the symmetry plane of the rectangle, the induced polarization on the probe metal coating is not parallel to the polarization on the rectangle. Thus, if the probe and the nanostructure interact strongly with each other and the recurrently excited polarization of the probe and the polarization on the nanostructure (rectangle) plasmon mode form chiral geometry, then the system can be regarded as a Born-Kuhn system17 and it may exhibit macroscopic optical activity. However, the excitation wavelength (800 nm) used in this study is away from the plasmon resonance wavelength (∼600 nm) of the probe with the aperture diameter of 100 nm; thus, the interaction between the nanostructure and the probe

Edipole(r) = 1488

3n(n ·p) − p r3

(1) DOI: 10.1021/acsphotonics.7b01511 ACS Photonics 2018, 5, 1486−1492

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Figure 3. Model calculation for the generation of chiral optical near-fields. (a) The model for the polarization analysis of the optical fields near an oscillating point dipole. (b) Plot of the vector-field induced by the point dipole. (c, d) The spectra of amplitude (c) and phase (relative to external incident field) (d) of the induced field arising from the oscillating dipole (see Method for details). Vertical solid and dotted lines indicate wavelengths for excitation of the dipole under preresonance and rigorous-resonance conditions, respectively, corresponding to images (e, f) and (g, h). (e, f) Maps of ellipticity angle η (e) and azimuth angle θ (f) of the optical fields near the dipole under rigorous-resonance excitation condition. (g, h) Maps of η (g) and θ (h) of the optical fields near the dipole under preresonance excitation condition. Scale bars: 100 nm.

⎛ αx 0 ⎞ ⎟⎟E in p = ⎜⎜ ⎝ 0 αy ⎠

We calculated the spatial distributions for η and θ of the total fields Etotal near the dipole under rigorous-resonance (Figure 3e,f) and preresonance (Figure 3g,h) conditions (see Method for details). Regardless of the resonance condition, the ellipticity angle (η) maps (Figure 3e,g) showed both positive and negative values, which indicate that left- and right-handed elliptically polarized fields are generated near the dipole. In addition, the azimuth angle (θ) maps (Figure 3f,h) showed that their spatial structures significantly depend on the resonance condition (as shown in Figure 3f,h). The η and θ maps calculated under the preresonance condition (Figure 3g,h), which is close to the present experimental condition, is qualitatively in good agreement with the experimentally obtained ones (Figures 2c,d). The results indicate that the resonant excitation of the dipole (plasmon) on the material is essential for generation of local CP optical fields in the periphery of the achiral object. Near-Field Polarimetry Imaging of a Single Gold Nanodisk. From the viewpoint of local optical activity, nanomaterials may generate CP light locally at the CD active site, where responses to left- and right-handed CP light are different. In fact, we have experimentally observed the local CP optical fields in the vicinity of the corners of the single gold nanorectangle, which are locally CD active,4,5 in the previous section. Although a rectangle is an achiral structure, it shows local CD activity arising from the local structural chirality of the anisotropic geometry. In contrast, a two-dimensional isotropic structure, for example, a circular disk, shows neither macroscopic CD activity nor local CD activity at any position, from the geometrical consideration. A naive consideration may lead us to assume that no local CP optical field can be generated on the disk irradiated with LP light because the local CD is zero at any position on the disk (i.e., the absorbance for left-handed

(2)

Here, p is the dipole vector in xy-plane and α is the complex electric polarizability of the material (single nanorectangle). The total electric fields near the dipole is then expressed as ⎡ ⎛(3x 2 − r 2)/r 5 ⎞⎤ ⎛1 ⎞ ⎟⎥ E total(r) = E in + Edipole(r) = E0ei(kz − ωt )⎢⎜ ⎟ + αx⎜⎜ ⎟⎥ ⎢⎝ 0 ⎠ 5 3 xy / r ⎝ ⎠⎦ ⎣

(3)

Figure 3c,d shows the calculated spectra of amplitude and phase (relative to the incident external field) of the induced oscillating dipole, respectively (see Method for details). We note that the phase of the dipole-induced field shifts from that of the incident external field when the induced oscillating dipole is resonant with the incident field (Figure 3d). As shown in Figure 3b, the induced dipole generates not only the x-component parallel (or antiparallel) to the incident field but also the y-component perpendicular to the incident field in the region where xy ≠ 0. As a result, the phase difference between x- and y-components of the total field arises. This means that the electric field vector rotates in the region of xy ≠ 0; in other words, elliptically polarized field is generated. The direction of rotation of the electric field vector is determined by the sign of y-component of the induced dipole field. The field rotates counterclockwise and clockwise in the region where xy > 0 (the first and third quadrants in the xy-plane) and xy < 0 (the second and fourth quadrants in the xy-plane), respectively. Consequently, the leftand right-handed CP fields have a spatial structure of four lobes (d-orbital like structure) in the xy-plane at arbitrary z, as predicted from eq 3. 1489

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Figure 4. SNOM measurements of a single gold nanodisk. (a) Near-field extinction spectrum obtained at around the center of the gold nanodisk. The excitation wavelength (700 nm) used for near-field imaging is indicated by the vertical line. Inset: Scanning electron micrograph of the gold nanodisk (130 nmD × 20 nmt). (b−g) Simultaneously obtained near-field extinction (b, d, f) and ellipticity angle η (c, e, g) images for a single gold nanodisk observed with linearly polarized optical field (polarization direction indicated by arrows). Scale bars: 100 nm.

polarization state and the spatial structure of light localized in a nanospace.

CP light and that for right-handed one are the same). However, the model calculation using an oscillating point dipole predicts that, regardless of the geometry of the nanostructure, CP optical fields can be generated locally near the nanostructure if the dipolar plasmon of the nanostructure is resonantly excited by LP light. If the CP optical field is experimentally observed near the disk, then the symmetry of the photoexcited states (dipolar excitation) of the nanostructure, rather than the geometrical symmetry of the nanostructure, is essential for generation of local CP optical fields. We thus conducted mapping of near-field extinction and ellipticity signals of the local optical fields generated by gold nanodisks. The peak of the near-field extinction spectrum acquired near the center of the gold nanodisk was found at ∼730 nm (Figure 4a). In the near-field imaging of the nanodisk, we used LP light with a wavelength of 700 nm. The near-field extinction image showed a strong extinction spot near the center of the disk (Figure 4b,d,f). We found that the extinction spot had a simple single extremum structure and was slightly elongated along the direction of the incident polarization. From this feature, the extinction band was identified as a dipolar plasmon mode.19 As shown in Figure 4c, the near-field image of the ellipticity angle η of the nanodisk is similar to that of the nanorectangle (Figure 2c) when the disk was locally excited with LP optical field of azimuth angle θin ≈ 0°. When the incident polarization was rotated in the clockwise direction (θin ≈ −23°) and anticlockwise direction (θin ≈ +57°), the spatial structure of the local η signals also rotated in the clockwise (Figure 4e) and anticlockwise (Figure 4g) directions, respectively. This observation can be explained by the model using a point dipole with two-dimensional isotropic polarizability (αx = αy in eq 2). These results strongly support the idea that the generation of local CP optical fields in the vicinity of the achiral object is caused by resonant excitation of an oscillating dipole (plasmon). The results also suggest that this phenomenon can be potentially used to realize the design and control of the

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CONCLUSIONS

In this study, we experimentally demonstrated that CP optical field is generated locally in the periphery of the gold nanorectangle and the gold nanodisk by resonantly exciting the dipolar plasmon mode of the nanostructure with LP light. We showed that the obtained spatial features of the local CP optical fields are qualitatively reproducible by the simple model calculation where the plasmon excited in the nanostructure is represented as an oscillating point dipole. The present results indicated the universality of local CP optical field generation near a resonantly excited oscillating dipole on any nanomaterial, and suggested that the local CP optical field can also be generated in a microscopic object such as a single atom or a molecule with LP light. Usage of chiral light as a typical example of CP light extends from various fundamental sciences to applied technologies.20,21 The metal nanostructures with chiral shapes are major source of nanoscale CP optical field, and they have been utilized for ultrasensitive characterization of biomolecules,22,23 for example. The CP light localized in the achiral nanomaterial could also function as a nanosized source of CP optical field, which may contribute to miniaturization and integration of CP light based nano-optical devices. To exploit nanoscale CP optical field in such applications, methods to design and analyze CP optical field on nanomaterials are essential. However, the local CP optical field structures are in general complicated,24−27 and development of an appropriate model for analysis is desired. The present result suggests that complex local CP optical field structure on nanomaterials can be reduced approximately into assembly of dipole-induced CP fields and might be useful for design and analysis of CP optical field structures on nanostructures. 1490

DOI: 10.1021/acsphotonics.7b01511 ACS Photonics 2018, 5, 1486−1492

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frequency (at which α takes a maximum value), eq 4 can be approximated as7

METHODS Nanostructured Sample Fabrication. Gold nanostructures used in this study were fabricated on a glass substrate using the electron-beam lithography and lift-off technique. The gold films that formed the rectangle and disk were vapor deposited on an underlying 2 nm thick Cr adhesion layer. The dimensions of the fabricated rectangle and disk were evaluated using scanning electron microscope and atomic force microscope. Near-Field Extinction Measurements. Near-field extinction spectra (here, extinction includes contributions from absorption and scattering) were measured using a home-built SNOM. Randomly polarized white laser light (Fianium) was introduced into a gold-coated aperture near-field optical fiber probe (JASCO) to generate optical near field with broad spectral range. The aperture diameter of the probe was typically 50−100 nm, which gives the approximate spatial resolution of the near-field image. The sample nanostructure was locally excited with optical near-field generated at the tip of the probe, and the scattered light was collected using an objective lens (NA = 0.45, Nikon) and detected using a spectrometer (Andor) to acquire the extinction spectra (A = log10(I0/I), where I and I0 denote transmission intensities at the sample and at the bare substrate, respectively). Near-Field Polarimetry Measurements. The experimental scheme of the near-field polarimetry measurement is explained in the main text (see Results and Discussion, NearField Polarimetry). To generate a linearly polarized optical near-field at the tip apex of the probe, we precompensated the polarization characteristics of the fiber probe with a linear polarizer (Thorlabs), a half-wave plate (Thorlabs) and a quarter-wave plate (Thorlabs). The scattered light from the sample to be analyzed was traveling through a PEM (HINDS) and a linear polarizer (Edmund Optics), and then detected by a photomultiplier tube (Hamamatsu). The PEM modulated the phase of the y-component of the electric field at the mechanical resonance frequency (Ω = 42 kHz), and thus the detected signal contains a frequency component of nΩ (where n is an integer). By demodulating the detected signal of nΩcomponents with the lock-in detection technique, the information on the amplitude E0 and the phase φ of the electric field are simultaneously obtained.28 We note that the absolute values of the x- and y-components of the electric field cannot be measured because of the intrinsic limitation of this method, and therefore, the range of possible values of azimuth angle θ is limited from +45° to −45° (for example, θ = 0° and 90° cannot be distinguished from each other). Modeling of a Dipolar Plasmon Resonance of a Gold Nanorectangle. We approximated the polarizability along the long axis of the gold nanorectangle with that of an ellipsoid. Under the electrostatic approximation, which is valid if the ellipsoid is sufficiently smaller than the wavelength of excitation light, the polarizability of the particle can be written as7,29 α(ω) =

⎞ ε(ω) − εb V ⎛ ⎟ ⎜ 4π ⎝ εb + (ε(ω) − εb)L ⎠

α(ω) ≈

⎞ V ⎛ −A ⎟ ⎜ 4π ⎝ ω − ωr + i Γ/2 ⎠

(5)

where ωr is the resonance frequency and Γ is the loss term in the Drude model that gives full width at half-maximum (fwhm) of the resonance. The factor A = (ωr/2L2)(ωr/ωp)2 is a constant that depends on the plasma frequency ωp of the metal. We used eq 5 as an approximate polarizability related to the dipole-like plasmon mode of the gold nanorectangle. To calculate the spectra of the amplitude (Figure 3c) and the phase (Figure 3d) of the polarizability of the gold nanorectangle, the following parameter were used: the geometrical factor L = 0.1,30 the plasma frequency of gold ωp = 4.0π × 1015 rad s−1, the resonance frequency ωr = 1.2π × 1015 rad s−1 (≈ 780 nm), the volume of rectangle V = 190 × 65 × 55 nm3, and ωr/Γ = 5. The polarization of the local optical field was evaluated at a plane 50 nm away from the oscillating point dipole (Figure 3a) to simulate the near-field probe located approximately 20 nm above the top surface of the gold nanorectangle (the distance from the center of the rectangle to the probe is ∼50 nm). The two-dimensional data sets of calculated polarizations were smoothed in the region of 100 nm × 100 nm using a binomial smoothing algorithm to mimic the images obtained with the near-field probe with an aperture diameter of 100 nm.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b01511. Supporting note, figures and tables (PDF).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Shun Hashiyada: 0000-0002-3229-538X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Ms. A. Ishikawa (IMS) for the nanostructured sample fabrication and Dr. S. Nakao (IMS) for his help in the operation of the scanning electron microscope. This work was supported by Grants-in-Aid for Scientific Research (KAKENHI; No. JP16H06505 in Scientific Research on Innovative Areas “Nano-Material Optical-Manipulation”, Nos. JP22225002, JP15H02161, JP15K13683 to H.O. and JP17H07330, JP15J01261 to S.H.) from the Japan Society for the Promotion of Science (JSPS) and by JSPS Core-to-Core Program (A. Advanced Research Networks), and the Photon Frontier Network Program of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan. S.H. also thanks IMS and SOKENDAI for the award of scholarship.

(4)

where ε(ω) and εb are the permittivities of the metal and the environmental medium, respectively, V is the volume of the ellipsoidal particle, and L is the geometrical factor which depends on the aspect ratio of the ellipsoid. By applying the Drude model to the metal dielectric at a near resonant

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REFERENCES

(1) Atkins, P. W.; de Paula, J. Physical Chemistry, 10th ed.; Oxford Univ. Press: Oxford, U.K., 2014. 1491

DOI: 10.1021/acsphotonics.7b01511 ACS Photonics 2018, 5, 1486−1492

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DOI: 10.1021/acsphotonics.7b01511 ACS Photonics 2018, 5, 1486−1492