Chiral Nanostructures Studied Using Polarization-Dependent

Article pubs.acs.org/JPCA

Chiral Nanostructures Studied Using Polarization-Dependent NOLES Imaging Jeremy W. Jarrett,† Patrick J. Herbert,† Scott Dhuey,‡ Adam M. Schwartzberg,‡ and Kenneth L. Knappenberger, Jr.*,† †

Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States

‡

S Supporting Information *

ABSTRACT: The Nonlinear Optical Localization using Electromagnetic Surface fields (NOLES) imaging technique was used to generate optical images in which the position of a chiral object could be determined with nanometer precision. Asymmetric gold bowtie nanostructures were used as a model system with 2D chirality. The bowties functioned as a chiral nonlinear medium that converted the fundamental of a Ti:sapphire laser to its second harmonic frequency. The bowties consisted of two lithographically prepared equilateral triangles (base = 75 nm, height = 85 nm, thickness = 25 nm) separated by a 20 nm gap. Asymmetric bowties were formed by lateral displacement of one triangle by 10 nm, yielding C2 point group symmetry. The chirality of the bowtie nanostructures was confirmed via nonzero second-harmonic generation circular dichroism (SHG-CDR) ratios, which came from single-particle SHG measurements. The SHG-CDR ratios were validated using numerical finite difference time domain simulations that quantified the relative magnitudes of gap-localized electromagnetic fields at the harmonic frequency resulting from excitation by left and right circularly (LCP and RCP) and linearly polarized fundamental waves. The relative electric dipolar and magnetic dipolar contributions to the SHG responses were determined using single-particle continuous polarization variation (CPV) SHG measurements. The spatial localization precision obtainable for individual chiral nanostructures was determined by statistical analysis of the SHG image point spread function. Our results demonstrated that both the chiral image contrast, which resulted from LCP and RCP excitation, and the corresponding localization precision was dependent upon the relative magnetic dipole/ electric dipole ratio (G/F). A localization precision of 1.13 ± 0.13 nm and left-to-right image enhancements of 400% were obtained for bowties with the highest G/F ratios using 5 s frame exposure times. The polarization dependence and magnetic dipole amplification confirmed here demonstrate that the NOLES imaging technique is a powerful method for studying chiral specimens with high spatial precision. chiral surface fields when excited using circularly polarized light.17−19 As a result, these nanostructures can function as both electric and magnetic field transducers that amplify magnetic fields upon optical excitation.19 These advances could permit development of enhanced circular dichroism (CD) and magneto-optical spectroscopy and imaging techniques Optical microscopy has provided significant breakthroughs in materials science and biophysics through the acquisition of spatially resolved images of heterogeneous chemical environments. However, molecular-level details and nanoscale domains are not resolvable when using conventional far-field microscopes. Super-resolution techniques that utilize statistical localization analysis,20−23 structured illumination,24−26 and photoactive switching27−29 have emerged in recent years to permit nanometer precisions for determining the position of an

1. INTRODUCTION Metallic nanostructures represent a promising class of materials with size- and structure-dependent optical and electronic properties.1 In particular, the development of fabrication and assembly techniques that permit control over nanoscale structure has stimulated expectations for tailored optical devices that function over a wide range of electromagnetic frequencies including sensors,2 biological labels,3 therapeutics,4−7 hybrid photovoltaics,8,9 catalysts,10,11 and meta-materials.12 This wide range of applications for nanometals arises because their optical and electronic properties are strongly influenced by size and shape in a manner not exhibited by their bulk counterparts. For example, excitation of the localized surface plasmon resonance (LSPR) in metal nanostructures generates large electromagnetic surface fields at material-specific frequencies. As a result, amplification of optical signals using plasmonic nanoparticle transducers is possible, which allows for enhanced molecular spectroscopy and imaging capabilities.13−16 Plasmonic nanostructures also mediate nonlinear optical (NLO) processes and can function as negative-index meta-materials.12 Very recently, it was shown that plasmonic nanostructures form © 2014 American Chemical Society

Special Issue: A. W. Castleman, Jr. Festschrift Received: February 11, 2014 Revised: March 4, 2014 Published: March 4, 2014 8393

dx.doi.org/10.1021/jp501488k | J. Phys. Chem. A 2014, 118, 8393−8401

The Journal of Physical Chemistry A

Article

Figure 1. (a) Schematic representation of the NLO microscope. Components included: M: mirror; P: polarizer; λ/2: HWP; λ/4: QWP; ASL: aspherical lens; S: sample; Obj.: high numerical aperture, compound objective lens; DM: dichroic mirror; SP: short-pass filter; BP: band-pass filter; EMCCD: electron multiplying charge coupled device. (b) Calculated electric field maps for asymmetric Au bowtie structures with linearly (left) and circularly (right) polarized excitation sources. This panel provides a representation of the geometry of the lithographically prepared nanostructures.

2. EXPERIMENTAL AND COMPUTATIONAL DETAILS Sample Preparation. The procedure for Au bowtie fabrication is described in detail by Fromm et al.30 Briefly, the Au bowties were prepared via electron beam lithography (EBL) on a glass coverslip. Before EBL writing, the coverslip was cleaned in acetone and baked in an oven to remove moisture. A 50 nm thick layer of polymethyl(methacrylate) (PMMA) (1% in chlorobenzene, 950 000 MW) was spun onto the substrate followed by 40 nm of an Aquasave charge dissipation layer for exposure on glass. The sample was then baked in an oven to harden the resist and remove residual solvent. After EBL writing, the resist was developed using a high contrast cold process at 5 C° in a 30% water in isopropyl alcohol solution for 100 s with ultrasonication. Then, the sample was plasma-etched in O2 (100 sccm, 200 mT, 85 V) to remove residual resist. A 20 nm Au layer was then deposited using an electron beam evaporator, and the patterns were transferred to the substrate via a lift-off process with acetone. NOLES Imaging. The experimental setup for the transmission microscope used for NOLES imaging is depicted in Figure 1a. The excitation source was a mode-locked Ti:sapphire laser (82 MHz, Spectra-Physics Tsunami) with a center wavelength of 800 nm. A linear polarizer was placed in the beam path to ensure a high extinction ratio of linearly polarized light. Next, the beam passed through a half-wave plate (HWP) to orient the laser polarization direction with the interparticle axis. Once the orientation was set, a quarter-wave plate (QWP) was introduced to allow, through rotation, the variation of the polarization from linear to elliptical to circular. The fundamental was then focused onto the sample with a single aspheric lens (numerical aperture, NA = 0.23). The SHG was collected in the transmission direction using a 1.25 NA, 100× oil immersion objective. The transmission geometry, which utilized a single focusing lens, was selected to avoid detrimental phase shifts induced by multielement compound objectives. Second-harmonic (SH) photons were isolated from the fundamental using a series of optical filters (short-pass, Chroma Technology, 680 nm; band-pass, Chroma technology, HQ 400/ 20m-2P, centered at 400 nm) and focused to the entrance slit of a spectrometer (Andor Technology, Shamrock 303i)

emission point source. The highest localization precisions are achieved when the optical signals that provide image contrast are maximized. The majority of localization techniques rely on fitting fluorescence images to a two-dimensional Gaussian point spread function (PSF).20 Recently, we reported a photobleachfree method called Nonlinear Optical Localization using Electromagnetic Surface fields (NOLES) imaging that provides 1 nm localization precisions with rapid throughput (images were acquired at a frame rate of 2 frames/s).21 The position of the point source was determined with high precision by correlating optical and electron microscope images. The NOLES method utilizes plasmon amplification of NLO signals to achieve high spatial precision. Here, we show that second-harmonic generation (SHG)detected CD spectroscopy of chiral bowtie nanostructures yields NLO images that could routinely provide nanometer localization precision when analyzed using the NOLES imaging technique. Moreover, the localization precision increased by 400% when the appropriate circularly polarized state of light was used to excite the chiral nanostructures. The interplay between nanoscale structure and localization precision was clearly evident. Bowties yielding the greatest CD localization precision corresponded to nanostructures with the largest ratios of relative magnetic dipole/electric dipoles (G/F); the relative magnitudes of these contributions were determined from single-particle continuous-polarization variation (CPV-SHG) measurements. These results demonstrate that the NOLES technique provides both high spatial precision and nanoscale structural information. In doing so, this technique represents a promising platform for CD imaging with high spatial precision, meaning that it could be a viable approach to developing spatially resolved magneto-optical measurements. The remainder of this article is organized as follows: experimental and computational details are provided in section 2, the optical properties of the chiral nanostructures, including the spatial profile of electromagnetic surface fields at the harmonic frequency, experimental single-particle SHG-CDR and CPV-SHG measurements, quantification of nonlinear susceptibilities of the bowties, and statistical localization analysis are given in section 3, and conclusions are provided in section 4. 8394



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In the asymmetric structures, one triangle was laterally shifted 10 nm in the x-direction, reducing the point group symmetry from C∞v to C2, which is chiral in 2D. Figure 1b illustrates the geometry of an asymmetric bowtie. Material dielectric constants for Au were taken from Johnson and Christy.32 The light source used in the simulations was a plane wave (350−1000 nm wavelength) either linearly or circularly polarized. Two plane wave sources were used to generate circularly polarized light. The sources had orthogonal polarization and a π/2 or −π/2 phase shift induced to one of the waves to produce right circularly polarized (RCP) and left circularly polarized (LCP), respectively. Perfectly matched layers were used at all simulation boundaries to absorb waves leaving the simulation domain. The source wave was injected in the negative zdirection from above the bowtie. For studies on the symmetric structures, the interparticle gap between apexes of the triangles was varied from 2 to 35 nm, and the scattering spectra were simulated using linearly polarized (both parallel and perpendicular to the interparticle axis) and circularly polarized light as excitation sources. The electric fields were mapped out at the fundamental and harmonic wavelengths for both symmetric and asymmetric structures with a constant 20 nm interparticle gap. The mesh size in the simulations was chosen to be 2 nm to provide high numerical accuracy with reasonable computation time.

coupled to a cooled EMCCD (Andor Technology, iXon Ultra 897). The microscope was also capable of bright-field imaging by focusing a halogen light source (SPL-2H, Photon Control Inc.) on the sample plane and collecting the image. This imaging mode was used to locate the bowtie grids for SH imaging. SH images were extracted as individual frames from recording videos of the NLO source as a function of polarization state of the fundamental wave. All data analysis was performed with Igor Pro v6.34 using home-written scripts. The experimentally measured SHG images were fit with a 2D Gaussian to construct a 3D PSF, and parameters from this fitting were used in the localization analysis. The precision of determining the centroid location (x0,y0) of the PSF was calculated using eq 1, derived by Thompson et al.20 1/2 ⎛ σ2 8πσ 4b2 ⎞ a2 + 2i 2 ⎟ Prei = ⎜ i + 12N aN ⎠ ⎝N

(1)

where Prei (i = x or y) is the x- or y-directional precision of the center position of the PSF, σi (i = x or y) is the standard deviation from the 2D Gaussian fit, N is the number of photons detected, a is the pixel size of the image (in nm), and b is the standard deviation of the background (in photons). N, the number of detected photons, is the sum of SH photons counted on all pixels falling under the 2D Gaussian fit. The signal counts from the EMCCD were converted to the number of incident photons detected at the harmonic wavelength using the following equation ⎛ cts ⎞⎛ S ⎞ E V = ⎜ ⎟⎜ ⎟(3.65) ⎝ g ⎠⎝ QE ⎠

3. RESULTS AND DISCUSSION Asymmetric Au bowties were chosen as a model system with defined 2D chirality. The building unit of the bowtie nanostructures, a rounded triangle with a base length of 75 nm, an altitude of 85 nm, and a thickness of 25 nm, was first simulated. The scattering spectrum of the isolated triangle was numerically simulated with FDTD methods for both linearly and circularly polarized excitation sources (Figure S1, Supporting Information). The simulations revealed two different modes that could be excited for the triangular nanostructure depending on the source polarization. Excitation using linear polarization aligned parallel to the base of the triangle yielded a mode with a maximum scattering intensity at 2.01 eV. When the source polarization was orthogonal to the triangle base (parallel to the triangle altitude), a scattering peak was detected at 1.94 eV. Circularly polarized light resulted in excitation of both of these modes. In order to understand the optical properties of the bowtie nanostructures, polarization-dependent scattering spectra and electric field profiles were simulated. The computed scattering spectra resulting from linearly and circularly polarized excitation of an asymmetric bowtie with a 20 nm interparticle gap is shown in Figure 2a. The optical properties were also simulated for symmetric bowties, and those results are portrayed in Figure S2 (Supporting Information). Excitation using light linearly polarized in the plane orthogonal to the bowtie interparticle axis generated a single scattering peak at 2.01 eV (Figure 2a, blue dash−dot line). This scattering peak is energetically degenerate with the mode obtained for the isolated triangle using polarization parallel to the nanostructure base. Excitation using light linearly polarized in the plane parallel to the interparticle gap generated a single scattering peak at 1.81 eV (Figure 2a, red dashed line). The scattering spectra resulting from linearly polarized excitation oriented along the interparticle gap was qualitatively similar to the response obtained for isolated triangles excited with linearly polarized light oriented along the nanostructure altitude, but

(2)

where EV is the total energy of photons per pixel, cts is number of counts (per pixel) detected, g is the amount of electron multiplying (EM) gain applied, S is the CCD sensitivity, QE is the quantum efficiency of the camera at the harmonic frequency, and 3.65 is a physical constant for electron creation in silicon.31 The number of photons per pixel was then calculated by dividing EV by the energy of a single photon at the harmonic frequency. The image pixel size (a) was calibrated by imaging a TEM grid via bright-field with 400 nm light. The bar width was measured in pixels (244.89 ± 3.49 pixels) and then compared to the physical bar width determined by SEM (35.36 ± 0.46 μm). The value for a was found to be 144.37 ± 2.77 nm. The standard deviation of the background, b, was determined by collecting a background image. Then, using the same pixel locations as those for determining N, the standard deviation of the background signal (in photons) was calculated. The localization precision values were determined for all successive frames as the experimental parameters were systematically changed. Average and standard deviations were determined by analyzing multiple frames from the videos at each condition. Computational Method. Lumerical FDTD Solutions, commercial electromagnetic software based on the FDTD method, was used to perform simulations on Au bowtie nanostructures. Au bowties were modeled as two triangular prisms with rounded corners. The prisms had a thickness of 25 nm along the z-axis, an altitude of 85 nm along the y-axis, and a base length of 75 nm along the x-axis to match the fabricated structures. Symmetric structures were made such that a YZplane of symmetry ran through the altitudes of both triangles. 8395



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followed the same trends with interparticle gap size as excitation with linear polarized light. The high-energy peak remained at a constant energy as the interparticle gap increased, and the lower-energy peak shifted to higher energies. These results are summarized in Figure 2b, where the peak positions are plotted as a function of interparticle gap size. Taken together, the polarization and distance dependence of the simulated spectra indicated that the low-energy mode resulted from electromagnetically induced dipole−dipole coupling of plasmon modes oriented along the altitude of the triangular building blocks that formed the bowties, and the high-energy mode resulted from excitation of resonances oriented along the base of the isolated triangles. On the basis of these simulations, the fundamental and harmonic energies used in our experiments were not resonant with the plasmon modes of bowties formed with 20 nm interparticle gaps. Insight into the NLO-CD response was first obtained by simulating the spatial electric field at the fundamental and harmonic wavelengths using LCP, RCP, and linearly polarized light. The simulated electric field maps showed significant differences depending on the polarization state of the source, especially in the nanoscale volumes confined to the interparticle gap. Specifically, in the simulations of asymmetric structures, a stronger electric field was generated in the interparticle gap when LCP excitation was used over RCP excitation (Figure S3, Supporting Information). Because the intensity of second-order NLO signals increases as the fourth power of local field strength,37 these results suggested that asymmetric bowtie nanostructures could be used as a model system to analyze structure-dependent chiral surface fields and their effect on CD imaging with high spatial precision. Electric field maps generated at the harmonic and fundamental frequency are presented in the Figures S3 and S4 (Supporting Information), respectively. Before quantifying the polarization dependence of NLO images generated using chiral nanostructures, the energy and power dependence of the measured signals were analyzed to verify that the image contrast resulted from SHG. The log of the experimentally measured SH signal from a single bowtie is plotted versus the log of the power of the incident fundamental wave in Figure 3a. The data were fit via nonlinear least-squares regression to a power law, and the resultant exponent was 2.08 ± 0.05. This observed quadratic power dependence confirmed that the signal resulted from a second-order NLO process. An energy-resolved spectrum of the NLO signal, revealing a discrete peak at the SH energy (3.10 eV, corresponding to a 1.55 eV fundamental), is shown in Figure 3b. Taken together, these data confirm that the NLO signal recorded from the Au bowtie nanoscale structures originated from SHG. In order to verify that the chiral nanostructures would yield nonzero NLO CD signals, we quantified differential CD in the SHG signal from the asymmetric bowtie nanostructures. Differential CD was obtained from the sample upon excitation with LCP and RCP polarization states of the fundamental light and was computed by a normalized quantity designated as the SHG circular difference ratio (SHG-CDR), given by

Figure 2. (a) Simulated scattering spectra for an asymmetric bowtie nanostructure with a 20 nm interparticle gap. The spectra were generated with LCP and RCP light (solid black line) and linearly polarized light parallel (red dashed line) and perpendicular (blue dotted−dashed line) to the interparticle axis. (b) Plot of the simulated peak position versus interparticle gap size for asymmetric Au bowties. Black circles represent data obtained from simulations using a linearly polarized source parallel (open circles) and perpendicular (closed circles) to the interparticle axis, respectively. The position of the scattering peaks observed with circularly polarized excitation is marked with green triangles (RCP excitation) and blue squares (LCP excitation). The red lines mark the position of the simulated scattering peak for an isolated triangle when the excitation source was polarized parallel (solid) and perpendicular (dashed) to the base of the triangle.

the resonance was shifted to lower energies for the bowtie. The spectrum generated with circularly polarized excitation (Figure 2a, solid black line) produced both the 2.01 and 1.81 eV modes. In order to understand the origin of the different scattering energies obtained for the isolated triangular and bowtie nanostructures, we investigated the effect that changing the interparticle gap size had on the simulated spectra. The gap was changed from 2 to 38 nm, and the scattering spectra were simulated with linearly and circularly polarized excitation sources. The spectrum generated with light polarized parallel to the interparticle axis contained a single peak with a central energy of 1.59 eV for bowties with a 2 nm interparticle gap, and the energy of this peak shifted toward higher energy as the gap size was increased. This response was similar to the plasmon ruler behavior known for colloidal nanoparticles.33−36 Therefore, this mode was attributed to electromagnetic dipole− dipole coupling. Excitation with light polarized perpendicular to the interparticle axis excited the higher-energy mode (2.01 eV), which did not change as the gap size was increased. Over the interparticle gap sizes simulated, the observed trends in the scattering peak positions were consistent with those previously reported.30 Both modes were excited when circularly polarized sources were used. The peak positions in the scattering spectra

|SHG‐CDR| =

RCP 2(I2LCP ω − I 2ω ) RCP I2LCP ω + I 2ω

(3)

where I2ω was the experimentally measured SHG signal for LCP or RCP excitation. A visual representation of SHG-CDR is depicted in Figure 4. In this figure, SH images (left) and the 8396



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the (top) panel were generated with LCP light, and data in the (bottom) panel were generated with RCP light. Parameters from the 2D Gaussian fitting were used in the NOLES imaging analysis, which is described in more detail in sections 2 and 3. A large and unmistakable difference in the intensity of the SH spot was observed for the two different polarization states of the fundamental wave, demonstrating the chirality of the bowtie nanostructure. The corresponding SHG-CDR was measured to be 0.90 ± 0.05. The differential response from 12 different asymmetric bowties is summarized in Figure 5. These data show large CDR

Figure 3. Confirmation of SHG. (top) Quadratic dependence of the measured SH intensity on the incident laser power. This confirmed that the signal resulted from a second-order NLO process. Error bars represent 1-σ standard deviations. (bottom) An energy-resolved scattering spectrum acquired for one Au bowtie. The fundamental excitation wave was 1.55 eV, and a discrete peak was observed at the SH energy (3.10 eV).

Figure 5. Absolute values of the SHG-CDR calculated from the SH intensity measured from 12 different Au bowties. The horizontal axis applies a number index to each of the 12 bowties. The error bars are 1σ standard deviations.

raw SH data overlaid with the corresponding 2D Gaussian fit (right) from an asymmetric bowtie structure are shown. Data in

values, indicative of chiral SH scattering point sources. The CDR values reported in Figure 5 ranged from 0.39 to 1.83. These measurements indicated that sample heterogeneities

Figure 4. Sample SH image obtained with (top) left and (bottom) right circularly polarized excitation. The left panels are single frames of the recorded SHG from a Au bowtie. The scale bars correspond to 500 nm. The right panels are the raw 3D SHG data with an overlay of the 2D Gaussian fit used in NOLES imaging. 8397



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Figure 6. SHG line shapes obtained from SHG continuous polarization variation experiments on four different asymmetric Au bowtie nanostructures. Solid points represent experimental data, and the solid lines are a fit to the data using eq 7. The vertical dashed lines indicate the QWP angles when LCP and RCP excitation was generated. Error bars represent 1-σ standard deviations.

were present in the lithographically prepared bowtie structures. Indeed, structural heterogeneity of the bowties was observed in SEM images (see Figure S5 (Supporting Information) for representative SEM images). These SEM images revealed that the bowtie nanostructures were not identical, leading to structurally specific interfacial electromagnetic field distributions and unique SHG-CD responses for each bowtie. These structural variations would not have been detectable using ensemble measurements. In the remainder of this paper, we describe the use of single-particle optical measurements to quantify structure-specific contributions to the NLO signal, which are then correlated with the resultant localization precisions and CD image contrast. The contribution of magnetic dipoles to the NLO responses of asymmetric bowties was implicit in the nonzero CD values reported in Figure 5. To gain further insight into the NLO properties of the Au bowties, CPV measurements were performed. For the CPV experiments, the SH intensity was recorded as the polarization state of the fundamental wave was continuously changed using a rotating QWP. Analysis of the resultant SHG-CPV line shape allowed for quantification of the relative electric and magnetic dipolar contributions to the nonlinear response. In general, SHG originates from P, an induced nonlinear polarization at the fundamental frequency, and M, a magnetization component at the harmonic frequency, expressed as17,18,38 Pi(2ω) =

Mi(2ω) =

j,k

I(2ω) = |FE P2(ω) + GES2(ω) + HE P(ω)ES(ω)|2

(5)

where F, G, and H represent linear combinations of the nonlinear susceptibility tensors χeee, χeem, and χmee and are generally complex valued. EP(ω) and ES(ω) denote the P- and S-polarization components of the electric field vector of the fundamental wave. The P-laboratory frame was defined to be parallel to the bowtie interparticle axis. This axis was determined experimentally by changing the orientation of linearly polarized fundamental light using a HWP in the absence of the QWP; the plane yielding maximum SH intensity corresponded to the bowtie interparticle axis. Equation 5 can be modified to include the experimentally controllable parameter, φ, by expressing EP(ω) and ES(ω) in terms of φ

j,k

∑ χijkeem (2ω , ω , ω)Ej(ω)Bk (ω) j,k

(4b)

where i, j, and k represent the Cartesian coordinates for the laboratory frame, ω is the carrier frequency of the fundamental wave, E is the electric field, and B is the magnetic induction of the incident light. χ represents the nonlinear susceptibility tensor where the first superscript refers to the harmonic wave and the second two terms represent the fundamental waves. The indices in the superscript, e and m, represent electric and magnetic dipolar transitions, respectively. The intensity of the SH field can be expressed by including P and M as nonlinear sources as follows

∑ χijkeee (2ω , ω , ω)Ej(ω)Ek(ω) +

∑ χijkmee (2ω , ω , ω)Ej(ω)Ek(ω)

(4a)

Ep(ω) = E0(cos2 φ + i sin 2 φ) = P(φ)

(6a)

Es(ω) = E0(1 − i)sin φ cos φ = S(φ)

(6b)

These substitutions transform eq 5 into 8398



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Figure 7. The localization precision plotted versus the QWP angle for the bowtie nanostructures presented in Figure 6. These plots demonstrate how the localization precision determined by the NOLES imaging method can be amplified by selective excitation of magnetic dipoles with circularly polarized light. Error bars represent 1-σ standard deviations.

I(2ω) = I(φ) = |F P2(φ) + GS2 (φ) + H P(φ)S(φ)|2

to RCP, and a 75% decrease in intensity was found from LCP to linearly polarized light. In contrast, Figure 6b portrays the NLO response from of a bowtie nanostructure that exhibited right-handed chirality. In this case, the RCP intensity was larger than the LCP intensity by 40%. The G/F ratio of 2.08 ± 0.03 obtained for this structure also indicated relatively large magnetic dipolar contributions to the NLO signal. The SHGCPV line shape in Figure 6c was also asymmetric. The G/F ratio calculated from this nanostructure was 1.79 ± 0.04, which indicated that although magnetic dipole contributions were prominent in this nanostructure, the electric dipole contributions also had a significant influence on the NLO response. Thus, the sensitivity to RCP versus LCP excitation was not as pronounced in Figure 6c as it was in Figure 6a. Finally, the nanostructure used for the data in Figure 6d yielded a symmetric line shape. The G/F ratio of this data was 0.73 ± 0.03, the lowest value reported here. This value for G/F suggested that in this case, the electric dipolar component of the NLO signal was more significant than the magnetic dipolar component, although a nonzero value of G was obtained. The NLO response from this bowtie was not selective to one circularly polarized state of light over the other and had the greatest intensity when excited with linearly polarized light. Similar to the SHG-CDR values, the CPV data yielded structure specific results. In this section, we compare the relative electric and magnetic dipolar contributions to the SHG signals, which were quantified using SHG-CPV, with the localization precisions achievable using polarization-dependent NOLES imaging. Specifically, the effectiveness of using circularly polarized light to excite magnetic dipoles and amplify NLO signalsresulting in improved localization precision. At each polarization state of

(7)

Using eq 7, the single-particle coefficients F, G, and H were quantified by analyzing the experimentally measured SHG intensity with respect to φ. Of these coefficients, G is the only component that solely depends on magnetic dipolar contributions and vanishes when the nonlinear response can be described purely by electric dipolar contributions. The F coefficient depends solely on electric dipolar contributions. Thus, taking the ratio of the magnitudes of the magnetic dipolar to electric dipolar contributions (G/F) provided a metric for determining the relative contribution of magnetic to electric dipolar character in the nonlinear signal. A higher G/F value translated to more dominant magnetic dipolar contributions in the NLO signal. SHG-CPV data collected from four different asymmetric Au bowtie structures are depicted in Figure 6. These data represent four general cases that were observed experimentally. The SHG-CPV line shapes were fit to eq 7 to determine the F, G, and H coefficient magnitudes, and the fitting results are presented in the legend of each panel. The vertical dashed lines in the plots represent QWP angles where LCP and RCP light was generated. Figure 6a shows a highly asymmetric line shape. In this case, the SHG intensity recorded was much greater with LCP excitation than that with RCP excitation. The G/F ratio was 3.0 ± 0.1, which indicated that the NLO signal consisted of larger relative contributions from magnetic dipoles as compared to electric dipoles. This nanostructure was very sensitive to the incident polarization state, yielding the largest signal when one circularly polarized state of light was used. A 95% decrease in intensity was observed by changing the fundamental from LCP 8399



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Table 1. G/F Values, Precision Values, and Percent Change in Precision Values for Structures from Figures 6 and 7 panel in Figures 6 and 7 a b c d

|F|/|G| 3.0 2.08 1.79 0.73

± ± ± ±

0.1 0.03 0.04 0.03

linear precision (nm) 2.86 1.71 2.19 1.12

± ± ± ±

0.27 0.12 0.09 0.11

LCP precision (nm) 1.13 1.81 2.21 1.74

± ± ± ±

0.13 0.06 0.09 0.25

RCP precision (nm)

% change from LCP to RCP

% change from LCP to linear

± ± ± ±

393.8 −37.57 63.18 51.72

153.1 −5.52 −0.90 −35.63

5.58 1.13 3.59 2.64

1.1 0.04 0.05 0.36

could be improved by selective excitation of magnetic dipoles using the appropriate circularly polarized state of light.

the fundamental wave, we employed the NOLES technique to perform localization analysis for the measured SHG images. These data are presented in Figure 7 for the same four nanostructures studied in Figure 6. In Figure 7a, the localization precisions for the bowtie with the highest G/F ratio, and therefore largest relative magnetic dipole contributions, are depicted as a function of the polarization state of the incident fundamental wave. These data demonstrated that the ability to precisely localize the point source depended strongly on the polarization state of the fundamental. The amplification has been quantified as a percent change from the localization precision generated by one polarization state to another. Excitation with LCP light resulted in a localization precision of 1.13 ± 0.13 nm, while excitation with RCP light resulted in a localization precision of 5.58 ± 1.1 nm. This difference represented a ∼400% change in the obtainable localization precision when the excitation was changed from LCP to RCP light. Excitation using linearly polarized light resulted in a localization precision of 2.86 ± 0.27 nm, representing a ∼150% change from excitation with LCP light. The polarization-dependent localization precisions obtained for the other three bowties are portrayed in Figure 7b−d. In these cases, the effect of exciting the magnetic dipoles was less pronounced but still important. For the bowtie represented by the data in Figure 7b, the G/F ratio was 2.08 ± 0.03, and we were able to localize this particle to 1.81 ± 0.06 nm with LCP excitation and 1.13 ± 0.04 nm with RCP excitation. This represents a −35.57% change in localization precision from LCP to RCP. In this case, excitation with RCP light resulted in greater amplification of the NLO signal than did LCP excitation, opposite from what was seen in Figure 7a. The G/ F ratio obtained for the bowtie giving rise to data in Figure 7c was 1.79 ± 0.04. The localization precisions obtained for this particle were 2.21 ± 0.09 nm with LCP excitation and 3.59 ± 0.05 nm with RCP excitation, representing a 62.4% change from LCP to RCP. In Figure 7d, the case where the electric dipoles contributed more than the magnetic dipoles to the NLO signal, a localization precision change of 51.7% was observed between LCP and RCP excitation (1.74 ± 0.25 nm for LCP to 2.64 ± 0.36 for RCP). However, due to the dominance of electric dipoles in this structure, excitation with linearly polarized light produced much better localization precision (1.12 ± 0.11 nm) than excitation using both circularly polarized light sources. This represented a −35% change from LCP to linear and a −58% change from RCP to linear. The localization precisions and G/F ratios for all four nanostructures are summarized in Table 1. These experiments clearly revealed the role of magnetic dipole contributions for chiral nanostructures and, in turn, the ability to generate NLO images with large CD contrast and high spatial localization precision of the asymmetric nonlinear signal point source. In particular, the localization precisions

4. CONCLUSIONS The polarization-dependent NOLES imaging technique was used in combination with single-particle SHG-CDR and CPVSHG measurements in order to correlate the interplay between nanoscale structure and the ability to generate CD images of chiral specimens with high spatial precision. Asymmetric Au bowties of C2 point group symmetry served as a model system for determining the influence of selective magnetic dipolar excitation on resultant NLO image localization precision. Single-particle SHG-CDR experiments confirmed that the asymmetric bowties exhibited 2D chirality. The experimental measurements were consistent with electric field maps obtained using FDTD simulations that showed that the magnitude of the electromagnetic fields at the SH was dependent upon the polarization state of the fundamental wave. The relative magnetic dipolar contributions to the total SHG signals were quantified by analyzing the SHG-CPV line shapes and extracting the ratio of the magnetic and electric dipoles. Finally, NOLES imaging was used to study the effect of the magnetic dipolar contributions on the amplification of the NLO signal by selective excitation using circularly polarized light, which in turn increased the spatial precision of the optical images. These data suggest that the NOLES imaging technique is a viable platform for developing super-resolution CD imaging techniques, which may include magneto-optical measurements.

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ASSOCIATED CONTENT

S Supporting Information *

Additional FDTD simulation results and representative SEM images. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a National Science Foundation (NSF) award to K.L.K., Grant Number CHE-1150249. Financial support by American Chemical Society − Petroleum Research Foundation (51233-DNI6) is also gratefully acknowledged. Nanofabrication work at the Molecular Foundry was supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Scientific User Facilities Division, under 8400



Article

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Contract No. DE-AC02-05CH11231. We would like to thank A. Polyakov for obtaining SEM images of the samples.

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