Giant local circular dichroism within an asymmetric plasmonic nanoparticle trimer

We investigated the near-field response in silver nanoparticle aggregates to the excitation of circular polarized light. In a right-angle trimer system, the local field intensity excited by right-hand circularly polarized light is almost one thousand times larger than the left-hand case. By analyzing the polarization and phase of the local field in plasmonic hotspots, we found this local circular dichroism is originated from the near-field interference excited by orthogonal polarized incident lights. The local circular dichroism can be tuned by the rotation of the third particle, the interparticle distance, and the dielectric environment. This phenomenon could also widely exist in more complicated nanoaggregates. These findings would benefit for resolving light handedness, and enhancing circular dichroism and optical activity.

We investigated the near-field response in silver nanoparticle aggregates to the excitation of circular polarized light. In a right-angle trimer system, the local field intensity excited by right-hand circularly polarized light is almost one thousand times larger than the left-hand case. By analyzing the polarization and phase of the local field in plasmonic hotspots, we found this local circular dichroism is originated from the near-field interference excited by orthogonal polarized incident lights. The local circular dichroism can be tuned by the rotation of the third particle, the interparticle distance, and the dielectric environment. This phenomenon could also widely exist in more complicated nanoaggregates. These findings would benefit for resolving light handedness, and enhancing circular dichroism and optical activity. C hiroptical effects are typically characterized by small differences of extinction coefficients or refractive indexes in the interaction of left-hand circularly polarized light (LCP) and right-hand circularly polarized light (RCP) with chiral molecules, leading to circular dichroism (CD) or optical activity (OA) 1 . The CD spectroscopy is widely used to investigate the subtle structural information of organic and biological molecules 2 . High concentration and large quantity of chiral specimens are usually demanded for reliable signal-to-noise. Concepts borrowed from molecular science, giant CD or OA response have been observed in metallic nanostructures such as spirals 3 , crosses 4-6 , nanorods 7 , helixs 8,9 , oligomers 10,11 , pyramidals 12 , etc 13 . The mechanism of either exciton-plasmon interaction between chiral molecules and metal nanostructures 14,15 , or near-field interactions in plasmonic nanostructures with chiral geometry [16][17][18] , makes the CD or OA response much stronger than the one from merely chiral molecules. The surface enhanced Raman optical activity (SEROA) of chiral molecule is contributed to the plasmonic hotspots in metal nanoparticles 19,20 . The change of symmetry in nanoaggregates would alter the polarization response of Raman scattered light 21 . Also, new chiral center might generate for different sorption sites in aggregates, which makes it challenging to obtain the stability and repeatability of SEROA. Recently, it was found even for an achiral molecule in a planar nanoparticle trimer, Raman scattering of the molecule can carry a considerable degree of circular polarization, that is, scattered circular polarization Raman optical activity (SCP ROA) 22,23 . The origin of this plasmonic ROA in the molecule-aggregates system is also the nanoantenna effect of asymmetric particles excited by the Raman emission of the molecule 24 . The single-molecule ROA may open a new perspective on the characterization for structural biology and pharmaceutical industry 25 . Actually, local field in the nanogap of aggregates could also have CD characteristic, which might result in incident circular polarization ROA 26,27 and local scattering OA 28 . For example, the large scattering OA has been locally observed in random fractal aggregates of silver nanoparticles by photon scanning tunneling microscopy. OA properties of aggregates have been simulated to reproduce the experiment observations [28][29][30][31] . However, in the complicated coupled nanoparticles system [32][33][34][35] , a fundamental insight into the relation between the near field and geometry under the excitation of circularly polarized light (CPL), is still needed for deeply understanding the origination of these OA phenomena, which will also be beneficial for the design of plasmonic CD or ROA nanostructures.
In this paper, the local field response to the CPL excitation in nanoparticle dimer and trimer was investigated. We found the near-field enhancement in an asymmetric trimer is highly dependent on the polarization rotation. The local field at a hotspot excited by RCP is much larger than the LCP case. The dependence originates from the near-field interference in the strong coupled nanoantenna system and can be tuned by the rotation of the third particle, the interparticle distance, and the dielectric environment. Similar to far-field CD, we introduce a parameter r in order to evaluate the local CD. Both positive and negative r are found in the asymmetric nanoantenna system. Besides, r is very sensitive to the environment. This study could provide a more flexible way to design plasmonic nanostructures with strong CD or ROA response for various applications such as polarization sensitive devices 3,8 and plasmonic sensors 36,37 .

Results
To understand the near-field response of nanoparticle aggregates to the CPL, analytic electromagnetic solutions to multi-sphere system simulations based on the generalized Mie theory (GMT) is performed 38 . The incident and scattered fields are expressed as a sum of vector spherical harmonics (VSH). The scattered fields from particles are calculated by the method of order-of-scattering 39 . The local field at any point is the sum of the incident field and coupling fields scattered from all of the particles (see Methods). We first consider a silver nanoparticle dimer (R 1 5 R 2 5 40 nm, with the gap distance d 5 1 nm, Fig. 1a) excited at l 5 532 nm with linear polarization. The highest near-field enhancement is obtained when the excitation is polarized parallel to the dimer axis (y-axis) which induces the coupled dipole in the dimer. For the perpendicular polarized excitation, there is nearly no field enhancement for this uncoupled dimer. Generally, the relation between the near field in the dimer gap and incident field can be expressed as: where E N I and E N H are the near field components parallel and perpendicular to the dimer axis, respectively, and E i I and E i H are the corresponding components of the incident field. The enhancement tensor G dimer can be written as: Then, we have to analyze each element in this tensor. As shown in Fig. 1b, the field in the gap is highly dependent on the incident polarization, hence, we have g 11 ? 0 and g 12 5 0 in this dimer case. Furthermore, at the surface of the metal, the enhanced near field in the junction is almost perpendicular to the surface irrespective of the incident polarization (white arrows in Fig. 1b). Then, both g 21 and g 22 are set to be zero. Hence, only the factor g 11 5 jg 11 je iD1 is non-zero, where D 1 is the phase difference between the near field E N I and incident field E i I , induced by the light scattering. The near-field enhancement M dimer 5 jE N j 2 /jE i j 2 5 jg 11 j 2 .
When the incident light is circularly polarized, the near field in the dimer gap can be obtained by introducing the expression of the incident CPL into the formula (1), where ''2'' and ''1'' correspond to LCP and RCP incidences, respectively. Then we have the magnitude of the near field jE N j 5 jg 11 j E 0 , which is irrelevant to the optical rotation. The case will be quite different if we introduce another particle into the dimer system. As shown in Fig. 1c, the right-angle trimer is formed by positioning a particle (R 5 40 nm) on the right side of the 2 nd one with the distance d 5 1 nm. Here we still consider the local field in the gap between the 1 st and 2 nd particles. As shown in Fig. 1d, the near-field enhancement for the perpendicular (x-axis) polarized excitation is comparable with the parallel (y-axis) polarized case at l 5 532 nm. The near-field enhancements for the two orthogonal polarizations as a function of polarization and wavelength are shown in Fig. 1e and 1f, respectively. Obviously, due to the strong coupling of the 3 rd particle with the dimer, the local field in the gap is insensitive to the incident polarization, especially in the wavelength range of 500 , 600 nm.
For the CPL excitation, the relation between the scattered and incident field can still be depicted by formula (1) with a response tensor G trimer for the trimer. Just as we did in the dimer case, it is still necessary to know the elements in G trimer . First, as the electromagnetic boundary relation still holds for trimer case, the polarization of near field in the gap is perpendicular to the metal surface (white arrows in Fig. 1d). Hence, we still have g 21 5 g 22 5 0 for tensor G trimer . Second, different from the dimer case, the perpendicular E i H could also result in significant enhancement E N I , therefore both g 11 and g 12 are generally nonzero. So the near field for CPL excitations can be written as: where g 11 5 jg 11 je iD1 , g 12 5 jg 12 je iD2 , and D 2 is the phase difference between the near field E N H and incident field E i H . After simple derivations, the near-field enhancement for the CPL incidence can be obtained: Obviously, M CPL depends highly on the field enhancement factors jg 11 j and jg 12 j, and especially the phase difference between D 1 and D 2 . For example, at l 5 532 nm, jg 11 j 2 < jg 12 j 2 5 0.8*10 5 , and D 1 2 D 2 < p/2. The field enhancement at the gap for LCP and RCP excitation will be M LCP 5 2.6*10 2 and M RCP 5 1.6*10 5 , respectively. The enhancement in the gap excited by the RCP light is much larger than the LCP case as shown in Fig. 2a, that is, the local CD. Actually, the local CD is the consequence of the near-field destructive/constructive interferences determined by the D 1 2 D 2 when the factor g 11 *g 12 are nonzero. Similar near-field interference mechanism had been used for controlling the surface plasmon polaritons in plasmonic waveguides 40,41 .
According to the definition of CD signals for far-field transmission or reflection 22 , we introduce a ratio r to evaluate the difference of near-field enhancement for incident LCP and RCP, which is defined as A giant local CD response r 5 0.998 is obtained for the right-angle trimer at 532 nm. For other wavelengths, the partial interference results in the local CD spectrum shown by the black curve in Fig. 2b.
If a chiral molecule is situated in a symmetric dimer, the interaction between the molecule and nanoparticles would result in a farfield plasmonic CD [29][30][31] , although the hotspot in dimer gap does not have near-field CD response as discussed above. For the asymmetric timer case, the near-field intensity in the gap could have 1000 times difference depending on the handedness of light. This will add to the complexity of molecule-induced plasmonic chirality. It can be expected that the far-field CD signal, especially the term originated from the exciton-plasmon interaction, could be enhanced or weakened, determined by the combination of the corresponding positive or negative near-field CD and the optical rotatory dispersion of the molecule at surface plasmon resonance wavelength.

Discussion
The local CD is highly dependent on the geometry of the nanoantenna. Fig. 3a shows how the near-field enhancement M and CD response r change as the rotation of the 3 rd particle around the dimer. When h 5 0u, the linear trimer corresponds to the point group D 'h 42,43 . The perpendicular (x-axis) polarized incidence will excite weak coupled p u mode. Hence, similar to the dimer, the enhancement factor g 12 < 0, and M LCP 5 M RCP , i.e., r 5 0. When the 3 rd particle is rotated around the dimer (h 5 0u , 90u), a C 2v trimer is formed. In this configuration, both A 1 and B 2 plasmon modes 42 can be excited and result in considerable field enhancement in the dimer gap irrespective to the incident polarization, i.e., both g 11 and g 12 are nonzero. Consequently, the local CD response r grows with the increase of h and reaches its maximum around 90u. After passing 90u, the 3 rd particle gets closer to the 1 st one and finally forms an equilateral trimer (D 3h group) at h 5 120u. Both degenerate E9 modes in the D 3h trimer can be excited by two orthogonal polarizations 43 . When the incident polarization is parallel to the 1 st -2 nd dimer axis, three particles coupled each other strongly and result in the nearfield enhancement in the particle gaps, i.e. a large factor g 11 . While for the perpendicular polarized incidence, the E9 mode is contributed by the dipolar coupling of 3 rd with 1 st and 2 nd particles, while the interaction between 1 st and 2 nd particles is rather weak. Hence, there is almost no near-field enhancement in the 1 st -2 nd dimer gap, i.e., jg 12 j = jg 11 j. Then, local CD response r drops rapidly to zero again when h 5 120u. www.nature.com/scientificreports Apart from the structural asymmetry, r is also related to the magnitude of the coupling between 2 nd and 3 rd particles. As shown in Fig. 3b, when d is only several nanometers, both g 11 and g 12 are nonzero. According to the formula (5), r (black curve) is close to one, indicating a strong local CD response. The near-field enhancement for RCP excitation is much larger than the LCP case (green and red curves for LCP and RCP, respectively). As d increases, the 2 nd -3 rd interparticle coupling becomes weaker, which causes g 12 dropping rapidly to zero. Correspondingly, r turns to be zero just as the dimer case.
Actually, the local CD response widely exists in asymmetric nanoparticle antennas. In Fig. 4a, we consider a non-identical trimer with the radii 30 nm, 40 nm, and 50 nm for the 1 st to 3 rd particles, respectively, and a fixed surface-to-surface distance d 5 1 nm. The electric field enhancement at the hotspot for LCP and RCP excitations are shown by green and red curves, respectively. Due to the asymmetric coupling between particles, the wavelength dependences of the nearfield enhancement g 11 and g 12 become quite complex. Hence, the difference in the spectrum of the near-field enhancement for LCP and RCP will result in the negative CD response r 5 20.89 at 535 nm, and positive r 5 0.74 at 605 nm (black curve). At l 5 535 nm, the near field for LCP excitation will be much larger than the RCP case as shown in the Fig. 4b.
As discussed above, the geometry and size determine the plasmonic modes excited in the nanoantenna, and consequently the local CD. Another important parameter influencing the surface plasmon coupling is the environment. Fig. 5 shows the spectrum of r for the right-angle trimer in air, water, and oil, with the refractive indexes n s 5 1, 1.33, and 1.5, respectively. The peak of wavelength-dependent r has an obvious red-shift with the increasing of n s . Similar to the resonance shift in surface plasmon resonance sensors, the CD response in the gap in asymmetric structures is quite sensitive to the environment. The sensitivity factor, i.e., the shift in peak position per unit change in the refractive index of the surrounding medium, is 450 nm per refractive index unit, which is generally larger than usual sensitivity factor of localized surface plasmon peak 44 .
In conclusion, we have investigated the near-field response in silver nanoparticle aggregates under the excitation of circular polarized light. We found that, the near-field enhancement of the hotspot in a right-angle trimer is highly dependent on the polarization rotation, that is, local CD originated from the near-field interference in the strong coupled particle system. The local CD can be evaluated by the parameter r. It is obtained a nearly unity r in the right-angle trimer excited at l 5 532 nm, where the near-field excited by RCP is much larger than the LCP case. This phenomenon widely exists in non-identical trimers, and can be tuned by the rotation of the 3 rd particle and the interparticle distance. Furthermore, we found the CD response is quite sensitive to the environment and could be detected by the Raman signals of molecules, or fluorescence of quantum dots in one of the particle gaps. The manipulation of optical response through polarization and geometrical parameters opens possibilities for a wide range of applications, such as SERS [45][46][47] or ROA substrates 22,48 , polarization sensitive devices 8 , sensors 36 and bioapplications 18 , etc. (a) Local field intensity and CD response at the hotspot as a function of the rotation of the 3 rd particle around the 2 nd particle. (b) Local field intensity and CD response at the hotspot as a function of the distance d between the 3 rd and 2 nd particle. The green and red curves are for LCP and RCP excitations, respectively. The CD response r is shown by the black curve to the right axis. The excitation wavelength is 532 nm. Methods Based on the generalized Mie theory 39 , the incident and scattered electromagnetic fields are expanded into vector spherical harmonics (VSH). The expansion coefficients for incident field are well known as Mie coefficients. The scattered electric fields for N-spheres system are: where l W E is the matrix of VSH, N T n is the scattering matrix for the N-spheres system: G N is the incident coefficient for N th sphere, y (N) is called response matrix of the system (for details see Ref. 39