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Birefringence-Induced Modulation of Optical Activity in Chiral Plasmonic Helical Arrays Arum Jung, Changho Kim, and Bongjun Yeom J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00521 • Publication Date (Web): 10 Apr 2017 Downloaded from http://pubs.acs.org on April 10, 2017

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The Journal of Physical Chemistry Letters

Birefringence-Induced Modulation of Optical Activity in Chiral Plasmonic Helical Arrays Arum Jung, Changho Kim and Bongjun Yeom* Department of Chemical Engineering, Myongji University, Yongin, 17058, Korea * e-mail: [email protected]

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ABSTRACT Chiral nanomaterials are characterized by handedness morphology on the nanoscale, manifested as preferential interaction with circularly polarized light. However, the origin of this light-matter interaction remains elusive. Here, we simulated a model of chiral helical arrays of plasmonic nanoparticles with central anisotropic nanopillars, to examine the effect of birefringence on the collective chiroptical response. Contrary to typical assumptions in previous works, we varied the biaxial refractive indices of the central nanopillars and observed a significant modulation of optical activity by calculating and characterizing circular dichroism (CD) spectra. The chiroptical response exhibited a sign change compared with that of the isotropic condition in a specific parametric range of negative birefringence. In addition, the CD peak increased by 3 to 16 as the ordinary refractive index increased from 1.5 to 3.0. These results are likely to be useful for designing chiral nanomaterials for applications in metamaterials, biosensors, and optoelectrical devices.

TOC

KEYWORDS Chiral nanomaterials; surface plasmon; optical activity; birefringence; circular dichroism; anisotropy

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Three-dimensional (3D) nanomaterials can exhibit chirality that reflects broken translational and rotational symmetry1,2. Recently, such chiral nanomaterials received significant attention owing to their optical characteristics in the near infrared (NIR) to ultraviolet (UV) range of frequencies and their potential applications in advanced devices such as biosensors3, chiral catalysis systems4,5, and metamaterials for perfect lenses and cloaking devices6,7. However, synthesis and design of chiral nanomaterials remain challenging, owing to technical difficulties associated with their preparation and characterization8. In addition, some fundamental issues related to the light-matter interaction between chiral nanomaterials and circularly polarized light (CPL) remain elusive, because the chiroptical response of these materials is highly sensitive to their nanoscale organization9. The chiroptical response characteristics of chiral nanomaterials are related to their asymmetric 3D nanostructures1,2,8. Therefore, sculpting these nanostructures is important for controlling the materials’ chiroptical response characteristics. Among various materials used for synthesizing chiral nanostructures, plasmonic nanomaterials have been extensively studied10–14. These materials are advantageous owing to their strong coupling of localized surface plasmons to incident electromagnetic waves. Various synthesis methods have been suggested and used for fabricating chiral plasmonic nanomaterials, including self-assembly methods10,11,15, e-beam lithography12,16, and modified vapor deposition methods17–20. Among the reported geometries of chiral materials, helical geometry with chirality has been the most studied one10,11,19–23. DNA-based self-assembled nanohelices decorated with plasmonic nanoparticles fall into this category10,24,25. To analyze the chiroptical response characteristics of such complicated structures, optical properties of constituent materials should be characterized first. However, birefringence of anisotropic dielectric materials has been typically ignored. For example, the

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properties of DNA fibers on which plasmonic nanoparticles are located have not been accounted for in the characterization of chiral helical assembly of plasmonic nanoparticles10,24. As another example, the work on helical assemblies of nanorods did not account for the anisotropy of elongated twisted fibrils22. Chiral plasmonic nanoshells17 and chiral cross-fingered nanorods26 utilized the structures of plasmonic nanomaterials without other comprising materials for interpretation of optical responses. There is one article describing the existence of circular extinction induced by the anisotropy of dielectric materials coupled with chiral plasmonic materials11. Likewise, most previous studies only considered plasmonic materials for chiroptical response characterization. To the best of our knowledge, the possible impact of other constituent materials with birefringence on the overall chiroptical response has not been systematically addressed. In this work, we investigated chiroptical responses of helical arrays of plasmonic nanoparticles with centrally located birefringent dielectric nanopillars. The geometry of the model is chosen based on the previous work10, and selected as a representative model since it is one of the most studied cases among various types of chiral nanomaterials10,24,25. We varied the ordinary and extraordinary refractive indices of the centrally located dielectric nanopillars based on the range of experimental conditions for several types of strained polymers and inorganic materials (Table S1 in Supporting Information)11,17,22. We utilized the finite element method (FEM) for solving Maxwell’s equations using a wave optics module for describing 3D models of chiral nanostructures11,23. Chiroptical responses were analyzed by calculating the circular dichroism (CD) for wavelengths in the visible range, corresponding to the range of plasmonic resonance. Interestingly, in the case of negative birefringence with refractive index values above 2.5, the CD spectra exhibited a sign change compared with the isotropic scenario. This sign inversion of the CD spectra by anisotropy is reported here for the first time. In addition, the peak magnitude increased by as much as 16 times when the ordinary 4


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index of refraction increased from 1.5 to 3.0. We assumed that a change in the birefringence of centrally located nanopillars can deflect the direction of the electric field flux from plasmonic nanoparticles, resulting in the modulation of the overall summation of absorption, as shown in a 3D visualization of electric field lines. Additionally we investigated effects of other geometrical parameters, such as number and diameter of nanoparticles, and width of nanopillars, to the overall chiroptical responses. Our results are likely to be useful for designing chiral nanomaterial systems for potential applications in broadband circular polarizers7, negative refractive index materials6,27, chiral catalysis devices4,5, and biosensors3. We simulated a chiral helical assembly system with plasmonic Au nanoparticles with the dielectric nanopillar located in the center. The geometrical model was built based on the experimental and simulation results done by Kuzyk et al10. Geometrical parameters for helical array of nanoparticles, such as number of nanoparticles, pitch and number of turns, are identical with literature. However, different to the previous study, we added the dielectric nanopillar at the center of chiral arrays with variation of refractive indices as isotropic, positive and negative birefringences. The system consisted of nine spherical Au nanoparticles with diameters of 10 nm, helically arrayed around a birefringent dielectric nanopillar with the width of 22 nm and length of 96 nm (Figure 1a and Figure S1 in Supporting Information). The width and length of central nanopillars were arbitrary chosen to be similar size to other chiral nanomaterials10,17,18,19. The distance between the Au nanoparticles and the nanopillar was 1 nm. For the nanopillar’s birefringence, the direction of the extraordinary refractive index (ne) was set to be parallel to the z axis and that of the ordinary refractive index (no) was set to be perpendicular to the z axis. We investigated the chiroptical response characteristics of this helical array by calculating its CD spectrum using the FEM, for wavelengths in the visible range (450–700 nm). The CD spectrum was obtained by subtracting the absorption of the right-handed CPL from that of the left-handed CPL, and three directional CDs from x, y, 5



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and z propagations were averaged to represent random orientation of chiral nanomaterials dispersed in aqueous media (see Computational Methods for details)11,23. First, we calculated the chiroptical response of the model with an isotropic nanopillar (Figure 1b). The refractive indices (no and ne) were set to 1.5. The CD spectrum exhibits the Cotton effect28, with a negative peak at the shorter wavelength of 520 nm and a positive peak at the longer wavelength of 550 nm; these results are consistent with previous reports10,25.

Figure 1. Simulation of chiral helical arrays of Au plasmonic nanoparticles around a central nanopillar. (a) The geometrical model used in the FEM simulations. The direction of the extraordinary refractive index is parallel to the z axis and that of the ordinary refractive index is perpendicular to the z axis. (b) The CD spectrum for the scenario of an isotropic central nanopillar. The ordinary (no) and extraordinary (ne) refractive indices were both 1.5.

Next, we varied the value of the extraordinary refractive index (ne) to investigate the effect on the CD spectrum, while the value of the ordinary refractive index (no) was 1.5 (Figure 2). The extraordinary refractive index (ne) was varied from 1.0 to 2.0, in steps of 0.1. We divided the variation range of the extraordinary refractive index into three sub-ranges: 1) 6


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the negative birefringence region (no = 1.0 to 1.4), 2) the isotropic point (no = 1.5), and 3) the positive birefringence region (no = 1.6 to 2.0). Please note that the result for the isotropic case (no = ne =1.5) is marked by the black line, and is replotted from Figure 1b. The result for the isotropic case served as a reference against which the results for the negative and positive birefringence cases were compared. In the case of negative birefringence, with ne = 1.0 (blue line), the CD spectrum exhibited one negative peak at 530 nm, with the peak intensity of 0.37. When the value of the extraordinary refractive index was increased from 1.0 to 1.4, the peak’s magnitude decreased and reached –0.06. After passing through the isotropic condition of no = ne = 1.5, a single positive peak emerged and increased as the extraordinary refractive index increased through the region of positive birefringence. At ne = 1.6, the peak’s amplitude was positive and the peak’s intensity was 0.09 at the wavelength of 540 nm. The peak’s intensity reached 0.27 for ne = 2.0. These results show that the magnitude of the preferential absorptions of CPLs can be significantly modulated by modulating the biaxial refractive indices of the central nanopillar located at the inner core of the helical array of Au nanoparticles. Also it is noted that these modulations were majorly attributed to the anisotropy of the central nanopillars, but not to the change of average refractive indices (Figure S2 in Supporting Information). The control parameter in this work differs from previously suggested ones that were related to a phase change of the entire medium surrounding chiral nanostructures16,24.

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Figure 2. CD spectra for different extraordinary refractive indices. The value of the ordinary refractive index (no) was 1.5 in all cases, and that of the extraordinary refractive index (ne) was varied in the 1.0–2.0 range, in steps of 0.1.

We investigated the effect of the magnitudes of refractive indices, for three different cases negative birefringence (N), isotropic point (I), and positive birefringence (P) (Figure 3). We set the differences (∆n) between the ordinary and extraordinary refractive indices to -0.5 and +0.5 for the N and P regions, respectively. Then, the ordinary refractive index (no) was varied to assume the values of 1.5, 2.0, 2.5, and 3.0. Figure 3a shows the cases for no = 1.5 with ∆n = -0.5 (ne = 1.0, N), 0 (ne = 1.5, I), and +0.5 (ne = 2.0, P), that were selected from Figure 2b. When no was gradually increased to 2.0, 2.5, and 3.0 in Figures 3b, 3c, and 3d, respectively, the peak intensity in the CD spectrum increased as well. In the cases of positive birefringence (red triangles in Figures 3b–d), the positive peak intensity increased by 78%, 173%, and 267% for no = 2.0, 2.5, and 3.0, respectively, compared with the case of no = 1.5. In the isotropic cases (black circles in Figures 3b–d) the positive peak intensity increased nearly 16-fold, from 0.05 for no = 1.5 to 0.78 for no = 3.0. This was accompanied by the disappearance of the Cotton effect and by the intensification of individual positive peaks. These results indicate

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that electrical dipoles of plasmonic particles becomes polarized due to scattered light around anisotropic nanopillar and experience decoupling of hybridization, as suggested by the hybridization model and coupled dipole theory29,30. In the negative birefringence cases (blue squares, Figures 3a–d) the negative peak gradually disappeared as the refractive index increased from no = 1.5 to 2.5. Finally, at no = 3.0 (Figure 3d), the CD peak became positive, with the peak intensity of 0.43 at 540 nm. This implies that for refractive indices above 2.5, the chiroptical response of a chiral helical assembly always exhibits a preferential extinction to the left-handed CPL.

Figure 3. CD spectra for negative (N), isotropic (I), and positive (P) birefringence cases. The value of the ordinary refractive index (no) was (a) 1.5, (b) 2.0, (c) 2.5, and (d) 3.0. In the isotropic case (I), no and ne were identical, and the difference between ne and no was -0.5 (N) and +0.5 (P). 9



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We visualized normalized electric fields and relative electric fields applied to the chiral helical assemblies to better understand the modulation of CD spectra. We chose positive and negative birefringence cases of Figure 3a as representative cases. And the electric fields under the directional incidence of LCP along y-direction were chosen due to consistency in the preferential interactions to CPL for y-directional and averaged CD spectra (Figure S3 in Supporting Information). In Figure 4, the intensity of the relative electric field is proportional to the lengths of the arrows, and normalized electric fields are also displayed onto the surfaces of the models, with the color scale ranging from 0 (blue) to 5 (red). As shown in Figures 4a and 4c, the normalized electric fields are similarly distributed, for both the positive and negative birefringence cases. Plasmonic nanoparticles are typically associated with stronger electric fields than central nanopillars, and the electric field is localized to the interface between nanoparticles and nanopillars where the color is slightly brighter. On the other hand, relative electric fields exhibit major directional differences. As shown in the boxed area in Figure 4b, in the case of positive birefringence the electrical flux is deflected in the outward direction, away from the nanopillar (the same area is also contoured by the dotted lines in Figure 4a). On the other hand, in the case of negative birefringence (Figure 4d), the electrical flux is oriented toward the nanopillar. The results of this visual inspection can be utilized for qualitatively explaining the differences between the CD spectra in the N and P regimes. The larger refraction index (ne = 2.0) in the positive birefringence case increases the degree of scattering of left-handed CPL at the surface of the central nanopillar31, therefore yielding a positive CD peak, as shown by the red triangles (P) in Figure 3a. On the other hand, reducing the refraction index to 1.0 (N) has the opposite effect. Relatively weak scattering around the nanopillar reduces the CD spectrum, which can be correlated with the appearance of a negative CD peak, as shown by the blue squares (N) in Figure 3a. 10


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Figure 4. 3D visualization of relative electric fields, using arrow plots. (a–b) Positive (ne = 2.0) and (c–d) negative (ne = 1.0) birefringence cases, with the ordinary refractive index (no) at 1.5 in all cases. The applied electric fields are left-handed CPLs at 540 nm and 520 nm for (a–b) and (c–d), respectively, propagating in the y direction. Normalized electric fields are additionally shown on the surfaces of the models, using the color scale ranging from 0 to 5.

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Then we investigated the effects of other geometrical parameters to chiroptical responses. Firstly we varied the number of plasmonic nanoparticles, while keeping pitch and turns of helices. As shown in insets of Figure 5a-c, increase of the number of nanoparticles (n = 9, 11 and 13) simultaneously reduces the distance between nanoparticles as 9.5 nm, 5.1 nm and 2.0 nm, respectively. For n = 11, we can observe intensification of CD spectra with increase of maximum peak intensities for all spectra without change of peak signs. However, when n is further increased to 13 (Figure 5c), CD spectra from 3 different cases becomes similar showing dip-peak pattern of positive cotton effects with positive maximum peaks located at higher wavelengths. Also it is noted that the intensities of maximum peaks are increased by 2-3 orders comparing with original geometries with n = 9. We also varied the diameters of NPs (d) and the widths of the central nanopillar (w) to observe their effects on the chiroptical properties. As d is decreased as 10, 8 and 6 nm, we can observe that intensities of CD peaks are gradually decreased (Figure 5a, d, e). However the effects of anisotropy are still active as we observe the sign of CD peaks stayed same to the original cases (Insets of Figure 5d and e). In similar fashion, reduction of the width of the central nanopillars (w) to 22, 18, 12 nm results in gradual decrease of CD peak intensities while keeping their signs (Figure 5a, f, g).

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Figure 5. Chiroptical properties of chiral plasmonic arrays with variations of geometrical parameters. (a) Original CD spectra of isotropic case (I), positive (P) and negative (N) birefringence cases with number of nanoparticles (n) = 9, diameter of nanoparticles (d) = 10 nm, width of the central nanopillar (w) = 22 nm. These are identical to Figure 3a and placed for easier comparison to other spectra. CD spectra of (b-g) calculated based on following variations. (b and c) n = 11 and 13, respectively. (d and e) d = 8 and 6 nm, respectively. (f and g) w = 18 and 12 nm, respectively. Geometrical model used in each simulation is placed in the inset.

We investigated the effects of anisotropy on the chiroptical response characteristics of chiral helical arrays of Au plasmonic nanoparticles. Contrast to the other previous studies ignored the anisotropy of the constituent materials10,17,22,24, we observed that the birefringence properties of the centrally located dielectric nanopillar can strongly determine the optical properties of the overall chiral nanostructure. This involves differentiating the magnitudes of scattering at the surfaces of nanopillars along with a change in refractive indices. The CD spectra calculated based on the extinction of CPLs were found to fluctuate significantly, 13



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affecting the CD peak magnitude. In addition, we observed an inversion of the CD peak magnitude owing to the negative birefringence of the central nanopillar. We believe that the results and conclusions of this study are likely to contribute to the design and development of chiral materials, with applications to advanced optical devices and biosensors.

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COMPUTATIONAL METHODS Model of chiral plasmonic helical arrays

The model geometry of chiral nanostructure is

composed of plasmonic helical array with central nanopillar as shown in Figure 1a and Figure S1 in Supporting Information referring to same geometry used in Ref 10. Nine plasmonic gold nanoparticles (n = 9) with diameter (d) of 10 nm is arrayed in right-handed direction around the central nanopillar. The nanopillar has width (w) of 22 nm and length of 96 nm. Distance between each Au nanoparticle and the nanopillar is set to be 1 nm. The center of Au nanoparticles located at both ends of helical array is positioned 10 nm apart from the ends of the nanopillar in z direction. For birefringent optical properties of central nanopillar, the direction of the extraordinary refractive index is parallel to the z axis and that of the ordinary refractive index is perpendicular to the z axis. The refractive index of gold nanoparticle is taken from Ref 32. CD spectra were calculated by solving

Calculation of circular dichroism (CD) spectra

Maxwell’s equations in wave optics module embedded in commercial software, COMSOL Multiphysics via the finite element method (FEM) (Eq. 1). Left-handed circularly polarized light (LCP) and right-handed circularly polarized light (RCP) are expressed by combination of two orthogonal plane waves with addition or subtraction of

phase differences

between waves to generate circularly polarized lights. For examples, LCP and RCP propagating +z direction are shown in Eq. 2 and Eq. 3, respectively. ( : relative permittivity,

: relative permeability, : permittivity of a vacuum, σ: conductivity, : free-space wave number, κ: angular frequency, E0 : the amplitude of the electric field of incident light, wave number)

∇ × ( ∇ × ) − − = 0

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(Eq. 1)

k: the


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() = .() =

[" # $%&' + ) #

[" # $%&' + ) #

√

√

+ ,

$%&'*

+ ,

]

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(Eq. 2)

]

(Eq. 3)

CD spectra were obtained by subtracting the absorption cross-section (abs) of RCP from that of LCP for each simulated condition (Eq. 4). Scattering cross-section was not considered in this study due to insignificant contribution to overall extinction (Supporting Information Fig S4)10,25. Absorption cross-sections were calculated by integration of resistivity loss (Qloss) over total volume of chiral helical array with the central nanopillar and divided by incident power flux (P0) (Eq. 5)11. CD spectra were obtained by average of 3 directional CDs with incident lights along x, y, and z axis10 (Supporting Information S3). Environments were set as water (nwater = 1.33).

CD = 123 () − 123(.) 123 = ∭< 56788 9:/

(Eq. 4) (Eq. 5)

CD spectra were then normalized by the peak intensity of positive case (no = 3.0 and ne=3.5), the highest value with original chiral geometries (n = 9, d = 10 nm, w = 22 nm). Relative electric field was plotted for 3D visualization of Figure 4. The relative electric field (Erel) is the difference between the calculated electric field (E) and the background field (Eback). Relative electric field in Figure 4 is plotted with arrows in 3D plots with proportional size to the normalized intensity of electric field and specified numbers of 250 arrows were uniformly distributed over the entire surfaces of the calculated geometries.

Supporting Information. Additional pictures of simulated geometry are included. CD spectra with isotropic cases with n no = ne = 1.3, 1.5, and 1.7. Directional CDs for ordinary

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refractive index = 1.5. Comparison of absorption cross-sections to scattering and extinction cross-sections.

ACKNOWLEDGEMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Education) (No. NRF-2015R1D1A1A01058029).

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