Influence of Geometrical Parameters on the Optical Activity of Chiral Gold Nanorods

Chiral metal nanoparticles (NPs) offer a powerful means of inducing and harnessing optical activity. However, due to the incomplete knowledge of the underlying growth mechanisms, there is still limited control over the achievable morphological detail and, consequently, over the resulting optical activity. Therefore, theoretical modeling is needed to guide experimental development toward optimizing the plasmonic chiroptical response. Toward filling this gap, herein an extensive parametric analysis is presented, via computer‐aided‐design (CAD) models and full‐wave electrodynamic simulations, which aims at systematically analyzing the influence of structural changes on the plasmonic circular dichroism (CD) spectra of rod‐shaped gold NPs comprising helical indentations on achiral nanorod cores. From this analysis, interesting patterns in the plasmon‐mediated resonant behavior are identified and cause–effect relationships are drawn that may serve as a go‐to recipe for the understanding and fabrication of these NPs and their applications, such as spectroscopic (bio)detection including CD spectral shifts and surface‐enhanced Raman optical activity.


Introduction
A wide variety of nanoparticles (NPs) have been reported during the past decades, which offer a broad range of research and development opportunities in areas of photonics, electronics, difference between the imaginary part of the index of refraction for two circularly polarized states (left-handed LHCP and righthanded RHCP polarized light) with respect to the opposite one, exhibiting an optical circular dichroism (CD) effect and causing optical activity. [11]he interactions of light with noble metal NPs are stronger than those with chiral molecules, as a result of collective electron oscillations that are reflected in so-called localized surface plasmon resonances (LSPR). [12,13]As a consequence, artificial chiral plasmonic nanostructures also display more intense CD. [14] The interest in understanding the mechanisms involved in plasmonic CD arises from the potential applications in biomedical imaging, nanosensing, metamaterials, etc.Indeed, plasmonic optical activity has been shown to be relevant toward studies of microorganisms, remote biological sensing, analytical chemistry, negative refractive materials, and circularly polarized devices. [11,14,15,16]he fabrication of chiral metal NPs has been reported using both top-down (lithography) and bottom-up (chemical synthesis) methods. [17,18]Although lithography has been shown to produce well-defined NPs with a superior degree of monodispersity, colloid chemistry methods offer production at a larger scale and modification of the obtained NP morphologies through simple variation of experimental parameters.Additionally, the high volume of synthetic research during the past decades offers a wide range of NP compositions, morphologies, and sizes that can be used to tailor in turn the morphological detail of chiral NPs.The main concept behind chiral growth in solution involves the use of chiral molecular additives, which influence the growth mechanisms of metal nanocrystals.From amino acids and peptides [3,19,20] to chiral co-surfactants, [21,22] the library of chiral inducers keeps growing and so does the collection of available chiral NP morphologies.However, due to the insufficient knowledge of the growth mechanisms related to different chiral inducers, there is still limited control over the morphological detail and, consequently, over the resulting optical activity.Therefore, theoretical modeling is needed to guide the experimental development toward optimizing the plasmonic optical activity of chiral metal NPs.
In previous work, [21,22] we applied 3D computer-aided design (CAD) models to confirm the presence of chiral plasmon modes and optical activity in anisotropic gold nanocrystals with quasihelical morphology.Following the experimental determination of the chiral morphologies, a model was created by introducing helical grooves and wrinkles with different tilt angles, all around the surface of rod-shaped Au NPs.Our results revealed a correlation between the chiral morphology of nanocrystals and the resulting optical activity, additionally demonstrating that the chiral plasmonic response can be modulated through variation of the geometrical features.We present herein a theoretical parametric analysis, using CAD models and full-wave simulations, to analyze in detail the influence of structural changes on the plasmonic CD spectra (defined as (CS L -CS R )/(CS L +CS R ), where CS denotes the corresponding absorption, scattering or extinction cross section), of rod-shaped gold NPs with superimposed helical wrinkles.Understanding how plasmonic chirality can be maximized should help improve experimental design toward optimized chiroptical response, as well as applications derived therefrom, such as spectroscopic (bio)detection, including CD spectral shifts and SEROA (surface-enhanced Raman optical activity). [23,24]

Results and Discussion
We performed an extensive parametric variation of geometrical features on quasi-helical Au nanorods.The model was inspired by recently reported experimental results [21] and involved a central Au NR surrounded by thin grooves with varying inclination angles.We used a central NR with quasi-square cross-section, following a recent experimental study of the morphological evolution during chiral growth. [22]By running full-wave numerical simulations, we aimed at correlating the variation in morphological details with the variation of the absorption, scattering, and extinction cross sections, as well as the corresponding CD spectra for such chiral Au NRs.
The geometrical model for numerical experiments comprised a gold NR of square section (78 × 78 nm 2 ) and 137 nm in length (this initial geometry is best appreciated in Figure 1A), on which 16 helical grooves were excavated all around the surface, giving rise to 16 helical wrinkles that unfold along the lateral surfaces.To mimic similar experimental NPs, [21] wrinkles with different tilt angles were alternated, resulting in helices with two leveled and two inclined steps per pitch.The wrinkle width was initially fixed at 3.5 nm and the separation distance between wrinkles (groove width) was 2.5 nm.
We first studied the influence of groove depth on the chiroptical response.Shown in Figure 1 are the calculated absorption, scattering, and extinction cross sections (ACS, SCS, ECS) for a colloidal distribution of the above-described chiral Au NRs (typically 600 particles with random orientation and interparticle spacing greater than 500 nm) under left-and right-handed illumination, as well as the resulting absorption, scattering, and extinction CD spectra.Four different groove depths were considered in Figure 1 (1.4 nm, 14 nm, 18 nm, and 25 nm), and their corresponding spectra reveal an increasing chiroptical activity as the excavated grooves become deeper (in other words, when the NR surface becomes more wrinkled).It should be noted that, in this series, the thickness of the central NR core decreases as the groove depth is increased.This trend confirms that the origin of the experimentally observed chiral optical activity is associated with the chiral NP morphology.Figure 1B, with an almost achiral response, shows transverse and longitudinal plasmon bands at around 550 nm and 750 nm, respectively.The scattering contribution is found to be above absorption in most of the visible and near-infrared (NIR) range (except at lower wavelengths because of the absorption contribution of interband transitions in gold), as expected for this relatively large NR.
As the depth of the grooves increases (at the expense of the central NR becoming thinner) and the wrinkles become more pronounced, a redshift of the longitudinal plasmon band is observed, and to a lesser extent also of the transversal one.Importantly, two other characteristic effects are found to emerge: i) as the wrinkles become more pronounced, the absorption contribution increases, up to the point of exceeding that from scattering (see, e.g., Figure 1K and further discussion below); ii) a new plasmon mode is observed, both in scattering and in absorption, which is particularly intense under LHCP illumination, but also to a lesser degree and slightly redshifted under RHCP light.This new plasmon mode is already visible for the case of shallow wrinkles (1.4 nm deep) but is somewhat concealed because it overlaps with the more intense transversal mode (Figure 1A,B) and becomes more noticeable for deeper grooves (14 nm and greater).As the groove depth increases, this mode redshifts significantly, getting differentiated as a separate mode (Figure 1E,H,K).It thus appears that this is a chiral mode arising from the wrinkled NR surface, which would become achiral if the wrinkles were made achiral (as illustrated in Figure S1, Supporting Information, for a NR with perfectly parallel wrinkles and different groove depths; even though new superimposed modes also emerge here due to the achiral wrinkled surface, becoming more noticeable as the groves get deeper, the new modes are identical under both circular polarizations).Consequently, the CD intensities in the spectra (Figure 1C,F,I,L) increase, and the corresponding bands gradually shift to longer wavelengths as the groove depth increases.The origin of the chiroptical activity observed in Figure 1F   thus be linked to the contribution of this new achiral plasmon mode to the cross sections.Additionally, careful inspection of the spectra in Figure 1B,E,H,K reveals that the achiral superimposed mode spreads to longer wavelengths well beyond its peak resonance, including an inversion (meaning a reversal of the LHCP and RHCP contributions to the CSs) somewhere between its peak and the longitudinal plasmon.This is symptomatic of the chiral mode hybridizing differently with the longitudinal and transversal achiral modes, which correlates well with the observation of an inverted (and less intense) upper CD band, extending beyond the longitudinal plasmon band (Figure 1C,F,I,L).
We further simulated the near-field enhancement distributions (electric field enhancement) under LHCP and RHCP illumination.Figure 2 shows the distributions under excitation at the wavelengths of the transversal and longitudinal LSPR modes for the achiral NR depicted in Figure S1J, Supporting Information, as well as at those for the transversal, longitudinal, and chiral mode leading to the highest CD intensity, for the chiral NR in Figure 1G.Both NRs have equal wrinkle width and similar groove depth.Although at first glance the surface plasmons in Figure 2A,B may appear different, close inspection reveals that both are equal except for the existence of mirror symmetry with respect to the plane containing the direction of incidence and the NR axis (left/right mirror symmetry in the case of the rendering planes of the figure).The mirror symmetry is best observed in the horizontal cuts shown in Figure 2C (the full set of calculated near-field rendering planes sliding through the NRs can be seen in the Supplementary Movies).This symmetry is fully consistent with the achiral response of this particle, meaning that, despite the apparent differences in near-field distribution, the far-field cross sections are the same under LHCP and RHCP excitations.This type of symmetry does not hold in the case of the chiral particle in Figure 2C-E.The distributions of surface plasmon field enhancement show significant asymmetries in both distribution and magnitude, which cannot simply be attributed to rotation or mirroring of the plasmon mode, but rather indicate a very different response of the chiral NR to LHCP and RHCP excitations.This effect is observed at all the analyzed wavelengths and is particularly evident at the CD peak wavelength (Figure 2D).The surface plasmons at this wavelength are very different for both excitations, which in turn can be considered as the source of the observed high CD magnitude.Higher magnitudes are obtained for LHCP illumination, with respect to RHCP, which correlates well with a positive CD value.Conversely, the surface plasmon modes are (only slightly) stronger in the RHCP response at the longitudinal resonance (Figure 2E), which is also consistent with a less intense negative CD value.
Near-field distributions were also calculated for the complete set of NRs shown in Figure 1 and are provided in Figure S2.For the smallest grooves, the near-field enhancement maps under LHCP and RHCP illumination are nearly symmetric in both magnitude and shape (left-right mirror symmetry), as explained above and expected for an achiral NR, meaning that the tiny helical features hardly provide the NR with an overall chiral character.The picture is different in all other cases of NRs with deeper wrinkles.The field distributions for plasmon modes under LHCP and RHCP illumination are no longer symmetric and their magnitudes also change due to the presence of chiral  helical wrinkles.This is particularly clear in Figure S2H,K, Supporting Information, corresponding to the chiral modes in the NRs depicted in Figure 1G,J, respectively.This is a further confirmation that the origin of plasmonic chiroptical activity can be associated to the helical structure along the NR.The simulated plasmon modes under both LHCP and RHCP excitations at different slices through the NRs can be seen in Supplementary Movies S1-S12, Supporting Information.
Let us now return to the effect of the enhanced absorption for increased groove depth.Absorption and scattering have different origins and are affected differently by morphological changes.Figure 1B,E,H,K depicts the evolution of the linear spectra as the surfaces on Au NRs become more wrinkled.It can be clearly observed that the absorption contribution gradually increases as compared to scattering, especially at longer wavelengths.Since the size of the NR remains fixed in this series, this enhanced absorption is likely related to the gradually increased contribution of the (chiral) wrinkled features, in agreement with recently reported experimental results. [22]To further distinguish whether the increased absorption stems from the chiral morphology or simply from the presence of sharp and deep wrinkles, we look again at the results for an achiral wrinkled NR.It is clear from Figure S1, Supporting Information, that, even without a chiral geometry, the presence of deeper wrinkles gives rise to an increase in the relative absorption contribution.To gain a better insight on this effect, we examine the magnitudes of the near-field distributions in a transverse plane for both chiral (Figure S2, Supporting Information) and achiral NRs (Figure S3, Supporting Information).In all cases, strong local field enhancement is found to be confined within the grooves, commensurate with a quasi-continuum of coupled open cavities or even a single bent 3-wall rectangular waveguide.These strong near-field enhancement values correspond mostly to confined, nonradiative modes with poor momentum matching to free-space radiation: the radiation from opposite surfaces of the groove essentially cancels each other, resulting in large heat-induced loss and therefore higher light absorption as the grooves become deeper.
For chiral NRs, the above discussion also translates into chiroptical behavior.Increasing the depth of grooves results in an increase of both scattering and absorption contributions to the CD intensity (with a slight redshift).However, as can be seen in Figure 1, for depths greater than ≈14 nm the scattering contribution to CD saturates and remains constant in intensity, whereas the absorption contribution continues to grow above that of scattering, becoming the main contribution to the CD (Figure 1L).Since it is well known that absorption and scattering play different roles in various applications of plasmonics, for those applications where scattering chiroptical activity is of primary interest, e.g.imaging and color display, it would be preferable to restrict wrinkle growth below ≈5 nm.On the contrary, deeper wrinkles would be more efficient for absorptionbased applications such as light absorbers and heaters.
The previous discussion illustrates the impact of groove depth on linear UV-Vis-NIR and circular dichroism spectra.][22] Therefore, we carried out an additional series of simulations to calculate the ACS, SCS, ECS, and CD for colloidal (randomly oriented) distributions of chiral Au NRs under left-and right-handed excitation (Figure 3).In this series, the NRs are designed to contain identical central NR cores (with square cross-section) but increasingly thicker chiral wrinkles, thereby mimicking the actual synthesis procedure.Different wrinkle depths of 1.5 nm, 5 nm, 10 nm, and 15 nm were considered (Figure 3A,D,G,J).The respective spectra are shown in Figure 3B,E,H,K.Interestingly, a similar trend was observed to that reported in Figure 1.A new plasmon mode -associated with chiral wrinkled helices -is observed, with a higher contribution to the response under LHCP illumination.This mode grows in intensity and redshifts as the wrinkles become deeper, in turn resulting in a more intense chiral response (CD), as shown in Figure 3F,I,L.The ratio between absorption and scattering is also observed to increase in this case for the longitudinal mode as the wrinkles become more pronounced.It is however noteworthy that the longitudinal mode displays a moderate redshift for increased wrinkle depth (Figure 3B,E,H,K), which indicates that it is mainly determined by the aspect ratio of the achiral seed core (constant in this case but gradually increasing in Figure 1) and the increasing dielectric constant of the surrounding effective medium made of Au wrinkles and solvent.Consequently, the effect of the quasi-helical wrinkles on the NR surface is mainly reflected in the formation of the chiral mode.Representation of the electric field enhancement in a centered transversal plane under LHCP and RHCP illumination (Figure S4, Supporting Information) shows again that asymmetry arises as the chiral plasmonic mode decouples from the transversal one (Figure S4G,J, Supporting Information).
Although experimental control over geometrical parameters is still limited, modeling is proposed here as a guide for further manipulation of the chiral plasmonic signal.Therefore, we analyzed the effect of wrinkle width on the optical behavior of chiral NRs. Figure 4B,E,H,K depicts the calculated SCS, ACS, and ECS, while the corresponding CD spectra are plotted in Figure 4C,F,I,L.The simulations were carried out for different values of wrinkle widths of 1 nm, 2 nm, 3 nm, and 4 nm, respectively, while keeping the other geometric parameters unchanged as much as possible.(Note that the separation between wrinkles can be kept approximately unchanged for the different wrinkle widths, by varying the number of helicoidal wrinkles around the NR surface.)The simulated results reveal that, an increase in wrinkle width does not alter the main transversal and longitudinal plasmon resonances (≈600 nm and 1000 nm, respectively, see Figure 4B,E,H,K).This is again due to the constant dimensions of the central achiral NR, in this case with a negligible variation of the effective medium in the chiral shell.However, the changes in wrinkle width do have an impact on the chiral plasmon mode, which slightly shifts toward longer wavelengths for increasing wrinkle width.Still, the intensity of the scattering and absorption CD and its position only moderately increase for the thicker wrinkles, while the CD intensity is significantly lower for the thinnest ones (Figure 4C).The spectra in Figure 4B reveal that the thinnest wrinkles have a higher absorption-to-scattering ratio, which is likely related to a more wrinkled surface, so the field inside the grooves is mainly non-radiative, contributing to higher thermal losses.This is supported by the calculated near-field intensity maps (Figure S5A,B, Supporting Information), where the highest field enhancement seems to be concentrated inside the grooves, leading to increased energy dissipation.Interestingly, we also observed an increased absorption contribution to the CD for the chiral NRs with thicker grooves (Figure 4L), which may be related to a slightly smaller inter-wrinkle spacing for this case (note that this space cannot take arbitrary values but is fixed by the wrinkle width and the tilt angle in the two inclined steps of the pitch).
On the basis of the above discussion, we also analyzed the dependence on the groove width (inter-wrinkle distance), while maintaining other geometrical parameters unchanged, including wrinkle width, as summarized in Figure 5. Groove widths of 1.5 nm, 2.5 nm, 4.5 nm, and 7.5 nm were considered.In this case, both the transversal and longitudinal plasmon modes were found to red-shift for increasing inter-wrinkle distance, with a slightly more pronounced shift of the transversal plasmon, as observed from Figure 5B,E,H,K.Additionally, the SCS decreases, especially in the longitudinal plasmon, while the ACS increases in the transversal band.Regarding the achiral plasmon, it is observed that this superimposed mode blueshifts as the distance between wrinkles increases.Remarkably, at the same time the CD bands (Figure 5C,F,I,L) slightly redshift and decrease in intensity.This can be explained by the fact that, as previously mentioned, the achiral plasmon has a broadband spreading beyond the peak resonance.On the other hand, the absorption-to-scattering ratio in the CD contribution stays almost constant also in this case (Figure 5F,I,L), except for the case of the smaller inter-wrinkle separation (Figure 5C), where a significative increase of the absorption CD is observed.
We consider for completeness the effect of the helical direction of rotation on the spectra and optical activity of the chiral NRs, to confirm that the responses to LHCP and RHCP incident polarizations are exchanged with each other, giving rise to an inversion of the CD.Plotted in Figure S7, Supporting Information, are the SCS, ACS, ECS, and CD spectra for a chiral NR as that shown in Figure 1G, but with the opposite direction of rotation of the helical wrinkles.Indeed, the results clearly show that the spectra calculated under LHCP and RHCP illumination are exchanged with respect to those shown in Figure 1H, whereas the CD is equal in magnitude to that of Figure 1I, but with an inverted sign.This further confirms that the differences between the achiral plasmon modes arising under LHCP and RHCP excitations (the one being stronger and the other weaker and redshifted) are due to the direction of rotation of the superimposed helix.If the rotation is reversed, the achiral plasmon modes are exchanged with each other.

Conclusions
On the basis of Maxwellian electrodynamic simulations, this theoretical work pinpoints, by means of an extensive parametric study of the geometrical features of quasi-helical chiral Au nanorods, the dependence between the absorption, scattering, and extinction cross sections (and associated CD spectra) of such chiral plasmonic scatterers and their defining morphological details.Remarkably, these numerical results reveal a plethora of interesting phenomena that may offer a range of potential opportunities in the design/synthesis and use of these biosensing platforms, viz.: i) the growth of aggregated chiral wrinkles on an otherwise achiral core seed gives rise to a new chiral mode, superimposed to the (usual) fundamental transverse and longitudinal modes; ii) the fact that these longitudinal/transverse LSPRs essentially depend on the core seed reinforces the fact that the chiral mode stems from the chiral wrinkles grown on the core surface; iii) as grooves and wrinkles get deeper, a redshift of the chiral mode occurs, which in turn increases the dichroism signal; iv) dissipation loss -and therefore the absorption/scattering ratio-increases with the depth of the grooves but is independent of other morphological details; the strong field-intensity localization within these dents can be qualitatively substantiated through the eigenmodes of the corresponding "open cavities": although these modes do not couple efficiently to free-space radiation, electron and electron-phonon relaxation processes do offer alternative routes of energy decay through photon-to-heat conversion, rendering these eigenfrequencies complex; v) the loci of the above-mentioned chiral modes shift with both the wrinkles' width and inter-spacing.In fact, the chiroptical response increases (decreases) with the former (latter).Also, albeit to a much lesser extent, the absorption/scattering ratio grows as the width becomes very small (more field confinement).We propose that these observations draw a rich artillery of morphology-to-chiroptics cause-effect correlations, which not only reveal the richness of these helicoidal shapes as platforms that induce angular momentum on incident light, but can also help establish a systematic and comprehensive roadmap to pre-designing and building up these chiral systems in a judicious fashion.

Experimental Section
Numerical Solution of Maxwell's Equations: The M3 solver [25][26][27][28] is intended for the simulation of complex 3D realistic electromagnetic problems, from radiofrequency to optical frequencies, and was used to perform full-wave electromagnetic simulations.The fullwave solutions are based on surface-integral equations (SIEs) discretized by the method of moments (MoM). [27,29,30]In SIEMoM, the parametrization and subsequent numerical analysis are both restricted to the two-dimensional boundary surfaces of the particles, rather than a 3D space embedding of the material structure.This results in a drastic reduction in the number of unknowns compared with other approaches, thus rendering the simulation feasible despite the size of the system under consideration.SIE-MoM offers unbeaten accuracy for modeling unbounded electromagnetic scattering problems with no need for absorbing boundary conditions or surrounding empty space.Additionally, the method is robust against instabilities produced by rapid spatial variations of the permittivity, as is usually the case in plasmonic structures.SIE-MoM method is also used to explore near-field properties.Gold is described through its frequency-dependent complex permittivity, taken from optical measurements. [31,32]anoparticle Model: The initial nanorod geometry is depicted in Figure 1A, with square section (78 × 78 nm 2 ) and 137 nm in length, on which 16 helical grooves were excavated all around, giving rise to 16 helical wrinkles that unfold along the lateral surfaces.The parametric study was performed taking into account changes in height, width, helix depth, helix width, helix distance, and helix direction of rotation.The modeling and meshing of the models were performed with Solidworks and Hypermesh respectively.Having a high-quality, clean mesh, with a consistent aspect ratio across all elements is crucial for the results of the simulation.Mesh quality is key in obtaining accurate results and for the problem to be solved efficiently in terms of time and resources, and with fidelity to the underlying physics.

Figure 1 .
Figure 1.Effect of groove depth on chiral plasmonic activity.A,D,G,J) Models of chiral gold nanorods were used to simulate the chiral plasmonic properties, with groove depths of 1.4 nm, 14 nm, 18 nm, and 25 nm, respectively.B,E,H,K) Simulated absorption, scattering, and extinction cross sections of colloidal distributions of the chiral Au NRs depicted in (A), (D), (G) and (J), respectively, under left-and right-handed CPL excitation.C,F,I,L) Simulated CD spectra for the same models.

Figure 2 .
Figure 2. Simulated electric field enhancement profiles under left-and right-handed circularly polarized excitation.A-C) Profiles for the achiral Au NR model shown in Figure S1J, Supporting Information; (A,B) represented in a vertical centered plane of the NR, calculated at the transversal resonance and the longitudinal resonance (650 and 1075 nm, respectively); (C) represented in a horizontal plane (top view) near the top of the NR, calculated at the longitudinal resonance (1075 nm).D-F) Profiles for the chiral Au NR model shown in Figure 1G, represented at a centered plane of the NRs, calculated at the transversal resonance, maximum CD, and longitudinal resonance (650, 725, and 1050 nm, respectively).Illumination is from below, with a 10° inclination with respect to the Au NR axis.Animated movies for each panel are provided as Supplementary Movies S19 and S20 for (A) and (B,C), respectively, and M7-M9 for (D-F), respectively.

Figure 3 .
Figure 3.Effect of wrinkle depth on the chiral plasmonic activity for wrinkles grown from the same central gold nanorod seed.A,D,G,J) Models of chiral gold nanorods with groove depths of 1.5 nm, 5 nm, 10 nm, and 15 nm, respectively.B,E,H,K) Simulated absorption, scattering, and extinction cross sections for colloidal distributions of the chiral Au NR models in A, D, G, and J, respectively, under left-and right-handed illumination.C,F,I,L) Simulated CD spectra for the same models.

Figure 4 .
Figure 4. Effect of wrinkle width on chiral plasmonic activity.A,D,G,J) Models of chiral gold nanorods with wrinkle widths of 1 nm, 2 nm, 3 nm, and 4 nm, respectively.B,E,H,K) Simulated absorption, scattering, and extinction cross sections for colloidal distributions of chiral Au NRs depicted in (A), (D), (G), and (J), respectively, under left-and right-handed illumination.C,F,I,L) Simulated CD spectra for the same models.

Figure 5 .
Figure 5.Effect of the groove width (inter-wrinkle distance) on chiral plasmonic activity.A,D,G,J) Models of chiral gold nanorods with groove widths of 1.5 nm, 2.5 nm, 4.5 nm, and 7.5 nm, respectively.B,E,H,K) Simulated absorption, scattering, and extinction cross sections of colloidal distributions of the chiral Au NRs depicted in (A), (D), (G), and (J), respectively, under left-and right-handed illumination.C,F,I and L) Simulated CD spectra for the same models.