Substrate-Induced Chirality in an Individual Nanostructure

TL;DR

This paper reports the first experimental observation of substrate-induced chirality in a single nanostructure, revealing how substrate placement can induce chiral optical responses in heterogenous nanoparticle arrangements.

Contribution

It demonstrates that placing a nanostructure on a substrate can induce chirality and enable chiral optical effects that are otherwise forbidden, advancing understanding of substrate-nanostructure interactions.

Findings

Substrate placement induces chirality in nanostructures.

Chirality leads to differential extinction, circular dichroism, and optical rotation.

First experimental evidence of substrate-induced symmetry breaking in nanostructures.

Abstract

We experimentally investigate the chiral optical response of an individual nanostructure consisting of three equally sized spherical nanoparticles made of different materials and arranged in \ang{90} bent geometry. Placing the nanostructure on a substrate converts its morphology from achiral to chiral. Chirality leads to pronounced differential extinction, i.e., circular dichroism and optical rotation, or equivalently, circular birefringence, which would be strictly forbidden in the absence of a substrate or heterogeneity. This first experimental observation of the substrate-induced break of symmetry in an individual heterogeneous nanostructure sheds new light on chiral light-matter interactions at substrate-nanostructure interfaces.

Equations

$${\mathbf{S}}_o=\mathbf{M}{\mathbf{S}}_i\text{,}$$

$$\begin{array}{rl}\text{CB}& =0.5[m_{12}-m_{21}]\text{,}\\ \text{CD}& =0.5[m_{03}+m_{30}]\text{.}\end{array}$$

Full text

chirality, circular dichroism, circular birefringence, heterogeneity, substrate-induced

I Introduction

Lord Kelvin defines chirality as the property of a geometrical figure who’s “image in a plane mirror, ideally realized, cannot be brought to coincide with itself” Kelvin (1904). Chiral molecules and nanostructures exhibit circular anisotropies Snatzke (1968); Tang and Cohen (2010) — left- and right-hand circular polarizations (LCP and RCP) experience different real and imaginary parts of the refractive index. The former is the origin of circular birefringence (CB), while the latter results in circular dichroism (CD) Lindell et al. (1994); Barron (2009). Importantly, circular anisotropies are invariant with respect to reversal of the propagation direction of circularly polarized light (CPL) Barron (1986); Arteaga (2010); Kuwata-Gonokami et al. (2005); Maslovski et al. (2009); Arteaga et al. (2014, 2016) and their proper measurement requires some caution.

For instance, CD is usually defined as a measure of differential extinction of CPL and therefore necessitates polarization analysis of the transmitted light Arteaga (2010), unless it is observed as an average value of monodisperse solutions Barron (2009). In the presence of linear anisotropies, which are typical for chiral structures Fan and Govorov (2012), the difference in intensity of the transmitted light ($\Delta T$) for LCP and RCP illumination along a certain direction does not necessarily represent CD as defined above, but rather a combination of circular and linear anisotropies Schellman and Jensen (1987); Arteaga (2010); Arteaga et al. (2014, 2016). Contrary to CD and CB, linear anisotropies invert their sign upon wavevector reversal Arteaga (2010); Arteaga et al. (2014, 2016) and the average value of $\left\langle\Delta T\right\rangle$ for backward and forward illumination represents CD Arteaga (2010); Arteaga et al. (2014, 2016); Hentschel et al. (2012).

The direction of illumination itself plays an important role for the optical response of anisotropic objects Schellman and Jensen (1987); Fan and Govorov (2012); Korger et al. (2013). Even achiral planar structures may show pronounced tunable CD and CB under oblique illumination, which is typically referred to as extrinsic or pseudo-chirality Verbiest et al. (1996, 1998); Plum et al. (2009a); Singh et al. (2010); Sersic et al. (2012); Yokoyama et al. (2014); Lu et al. (2014); Leon et al. (2015); Nechayev et al. (2018). Consequently, a measurement of CD and CB along a fixed direction of illumination does not necessarily indicate structural chirality.

A practically interesting case are quasi-planar nanostructures (QPNs) with broken in-plane reflection symmetry (or asymmetric QPNs), such as a flat spiral of finite thickness or an asymmetric planar arrangement of arbitrarily sized spheres. Since the sense of twist of a flat spiral inverts with the reversal of the direction of observation and circular anisotropies are invariant under wavevector reversal Barron (1986); Arteaga (2010); Kuwata-Gonokami et al. (2005); Maslovski et al. (2009); Arteaga et al. (2014, 2016), QPNs can not show any CD or CB when illuminated normally to their inherent plane of mirror symmetry. However, QPNs may show a strong chiroptical response in differential transmission ($\Delta T$), differential absorption ($\Delta A$), differential scattering and asymmetric polarization conversion of CPL Papakostas et al. (2003); Reichelt et al. (2006); Fedotov et al. (2006, 2007); Husu et al. (2008); Valev et al. (2009); Plum et al. (2009b, 2010); Zhukovsky et al. (2011); Eftekhari and Davis (2012); Arteaga et al. (2014, 2016); Banzer et al. (2016); Vinegrad et al. (2018). All aforementioned differential measures must invert their sign with the reversal of the illumination direction, if the QPNs are embedded in a homogeneous background. This fundamental difference between the illumination direction-dependent $\Delta T\backslash\Delta A$ and strictly forbidden circular anisotropies attracted significant attention and was discussed in the context of optical reciprocity Kuwata-Gonokami et al. (2005); Fedotov et al. (2006, 2007); Plum et al. (2009b, 2010); Arteaga et al. (2014); Barron (1986); Bai et al. (2007); Maslovski et al. (2009); Arteaga et al. (2016); Hopkins et al. (2016).

However, for experimental investigation, QPNs are commonly positioned on a substrate, which breaks the forward-backward symmetry for normally incident CPL. Furthermore, a substrate converts the morphology of the system from achiral to chiral. Substrate-induced emergence of CD and CB that are invariant under wavevector reversal has been experimentally confirmed in arrays of asymmetric QPNs Kuwata-Gonokami et al. (2005); Arteaga et al. (2016) and in asymmetric arrays of nanoholes Arteaga et al. (2014). At the same time, non-zero $\Delta A$ has been demonstrated for individual nanohelices Woźniak et al. (2018) and single asymmetric QPNs under normally incident CPL Banzer et al. (2016); Vinegrad et al. (2018). Differential scattering of CPL was shown for symmetric QPNs under oblique illumination Lu et al. (2014) and a variety of individual nanostructures under normal incidence Lin et al. (2019). However, to the best of our knowledge, substrate-induced emergence of differential extinction (CD) and CB in an individual QPN under normal incidence and, hence, its conversion into chiral morphology, have not been experimentally investigated to date.

Here, we apply back-focal plane (BFP) or $\mathbf{k}$-space Mueller matrix spectropolarimetry Arteaga (2010); Osorio et al. (2015); Arteaga et al. (2014); Mohtashami et al. (2015); Arteaga et al. (2016) to investigate the emergence of substrate-induced chirality in an individual asymmetric QPN. The QPN consists of three nanospheres of radii $r=90\,\mathrm{nm}$ arranged in [math] bent geometry Banzer et al. (2016) with estimated gaps of $2\,\mathrm{nm}$ between neighboring particles (Fig. 1$\boldsymbol{a}$ and 1$\boldsymbol{b}$), which are positioned on a glass substrate using a pick-and-place procedure Bartenwerfer et al. (2011); Mick et al. (2014). The in-plane reflection symmetry of the nanotrimer is broken by its heterogeneous material composition Banzer et al. (2016) — the two upper nanoparticles in Fig. 1$\boldsymbol{b}$ are made of silicon (Si) Palik (1985), while the third one is made of gold (Au) Johnson and Christy (1972). The glass substrate breaks the forward-backward symmetry under normal incidence and renders the whole system structurally chiral. We experimentally reconstruct the emerging CD and CB spectra, which would be strictly forbidden in the absence of a substrate or heterogeneity.

II Results

We start by theoretically investigating the scattering properties of the nanosphere assembly. The sample exhibits a rich spectral behavior with several resonances, residing in the excitation and interaction of various electric and magnetic multipoles in the nanospheres constituting the nanotrimer Nechayev et al. (2018); Banzer et al. (2016). We employ a coupled-dipole model (CDM) to calculate the scattering ($\sigma_{s}$), absorption ($\sigma_{a}$) and extinction ($\sigma_{e}$) cross-sections for normally incident plane-wave CPL illumination Mulholland et al. (1994); Albella et al. (2013). In the CDM, each of the nanoparticles is modeled as a point-dipole, whose electric- and magnetic-dipole polarizability is obtained from Mie theory in free-space Craig F. Bohren, Donald R. Huffman (1983). Each of these dipoles reacts to the incident field, to the field of the other dipoles and its own reflected field Knight et al. (2009); Miroshnichenko et al. (2015); Mulholland et al. (1994); Albella et al. (2013). In Fig. 1$\boldsymbol{c}$, we plot the differential cross-sections normalized to the geometric cross-section ($\Delta Q_{j}\equiv\left[\sigma_{j}^{\text{LCP}}-\sigma_{j}^{\text{RCP}}\right]/\left[3\pi r^{2}\right]$) for the nanotrimer in free-space, illuminated with LCP and RCP along the positive direction of the $z$-axis ($+\hat{\mathbf{z}}$). Fig. 1$\boldsymbol{c}$ shows that the differential scattering $\Delta Q_{s}$ has the same magnitude and opposite sign as the differential absorption $\Delta Q_{a}$, resulting in zero differential extinction $\Delta Q_{e}=\Delta Q_{s}+\Delta Q_{a}=0$. With the reversal of the direction of illumination ($-\hat{\mathbf{z}}$), as shown in Fig. 1$\boldsymbol{d}$, $\Delta Q_{s}$ and $\Delta Q_{a}$ just interchange their amplitudes, preserving $\Delta Q_{e}=0$. Fig. 1$\boldsymbol{e}$ shows the differential cross-sections in the presence of a glass substrate ($n=1.52$) for incidence from the air side ($+\hat{\mathbf{z}}$). $\Delta Q_{s}$ and $\Delta Q_{a}$ no longer balance each other, resulting in a non-zero $\Delta Q_{e}$. Here, reversal of the direction of illumination ($-\hat{\mathbf{z}}$), as shown in Fig. 1$\boldsymbol{f}$, strongly affects the spectra of $\Delta Q_{s}$ and $\Delta Q_{a}$. Nevertheless, the same $\Delta Q_{e}\neq 0$ is retained. The CDM Mulholland et al. (1994); Albella et al. (2013) allows us to understand the origin of non-zero differential extinction of normally incident CPL in the presence of a substrate. Only when the field radiated by each of the nanospheres reflects from the substrate Sipe (1987); Miroshnichenko et al. (2015); Knight et al. (2009) and re-excites the nanospheres, we observe $\Delta Q_{e}\neq 0$. However, the CDM assumes only point-dipoles, located at the respective centers of the nanoparticles. Therefore, the CDM cannot account for strong near-field enhancement in the gaps between the actual nanoparticles, which significantly contributes to the scattering, absorption and extinction spectra. This field enhancement originates from nonradiative higher-order modes Albella et al. (2013) and therefore requires full-wave simulations. For this reason, from this point onwards we employ finite-difference time-domain (FDTD) simulations noa for a comparison with the experimental results.

A simplified sketch of the experimental scheme is depicted in Fig. 2$\boldsymbol{a}$. It consists of two microscope objectives (MOs) in confocal configuration for focusing and collimation of the incident light Banzer et al. (2010, 2016). A three-dimensional (3D) piezo actuator positions the mounted sample in the focal plane. The incident light only partly fills the aperture of the upper MO with numerical aperture (NA) of $\text{NA}=0.9$, such that the nanotrimer is effectively illuminated by a weakly focused Gaussian beam with $\text{NA}_{\text{eff}}=0.4$ from the air side ($+\hat{\mathbf{z}}$). The transmitted and scattered light is collected by a second oil immersion MO with $\text{NA}=1.3$. The beam then passes two liquid crystal variable retarders (LCVRs) (slow axes at [math] and [math]) and a linear polarizer (LP) for projection onto different polarization states Bueno (2000). Finally, a lens images the polarization-filtered intensity distribution in the lower objective’s BFP onto a charge-coupled device (CCD) camera.

The position of the sample relative to the excitation beam is crucial for properly performing the spectropolarimetry of an individual nanostructure. Fig. 2$\boldsymbol{b}$ shows a raster scan image of the total transmitted intensity, obtained by moving the nanotrimer sample in a $500\times 500\,\text{nm}^{2}$ region around the focus. We record and average the polarimetric properties over a $10\times 10$ grid, covering an area of $250\times 250\,\text{nm}^{2}$ around the estimated center, which is indicated by reduced transmission in Fig. 2$\boldsymbol{b}$.

To reconstruct the $4\times 4$ Mueller matrix $\mathbf{M}$, determining the polarization response of the system, we must invert the following identity Arteaga (2010):

[TABLE]

where $\mathbf{S}_{i}$ and $\mathbf{S}_{o}$ are the input and the output Stokes vectors, respectively. To this end, we illuminate our sample with an overdetermined set of six input polarization states, estimated to be $\left\{\text{RCP, LCP, X, Y, diagonal, antidiagonal}\right\}$, and analyze the transmitted light. For each position of the sample in the grid $(x,y)$, we acquire angularly resolved output Stokes vectors $\hat{\mathbf{S}}_{o}{(x,y,\mathbf{k})}$ and integrate them $\mathbf{S}_{o}(x,y)=\iint\hat{\mathbf{S}}_{o}{(x,y,\mathbf{k})}\mathrm{d}^{2}\mathbf{k}$ over the angular region of $\text{NA}_{\text{eff}}=0.4$, where we detect the far-field interference of incident and scattered light (Fig. 2$\boldsymbol{c}$). Finally, averaging $\mathbf{S}_{o}(x,y)$ over the grid provides us with the desired output Stokes vectors $\mathbf{S}_{o}=\overline{\mathbf{S}_{o}(x,y)}$. We also determine the actual experimental input Stokes vectors $\mathbf{S}_{i}$ by performing the same procedure on a plain glass substrate. Using these six input and six output polarizations, we invert Eq. 1 and obtain the experimental Mueller matrix $\mathbf{M}_{exp}$. However, experimental noise, the finite integration region of $\text{NA}_{\text{eff}}=0.4$ and averaging of the Stokes vectors over the grid may result in a matrix $\mathbf{M}_{exp}$, which is unphysical and contains depolarization, inhibiting the analysis of CB and CD. Therefore, we apply Cloude’s sum decomposition Cloude (1990), providing us with the closest physical and non-depolarizing estimate $\mathbf{M}$ of $\mathbf{M}_{exp}$. Finally, we calculate CB and CD from the elements $m_{ij}$ of $\mathbf{M}$ Arteaga (2010):

[TABLE]

In Fig. 3$\boldsymbol{a}$ and 3$\boldsymbol{c}$, we present the obtained experimental results for CB and CD, respectively, quantifying the chiroptical response. For comparison, Fig. 3$\boldsymbol{b}$ and 3$\boldsymbol{d}$ show results obtained from FDTD simulations. The nanotrimer is modeled as a system of three perfect spheres with radii $r=90\,$nm and inter-particle gaps of $2\,$nm, placed on a glass substrate ($n=1.52$) and arranged in the geometry shown in Fig. 1$\boldsymbol{a}$. The Si nanospheres are surrounded by a $\text{SiO}_{2}$ Palik (1985) shell with estimated thickness of $8\,$nm, correspondingly reducing the core diameter.

The actual optical handedness of the heterogeneous trimer on substrate in Fig. 3 depends on the wavelength and changes sign in the investigated spectral range of $500\,\text{nm}\leq\lambda\leq 700\,$nm. Moreover, for an isolated nanostructure, the chiroptical response is exceptionally strong. The experimentally measured CB corresponds to a maximum optical rotation of about [math]. Assuming a thickness of $180\,$nm for the sample, this corresponds to a refractive index difference for LCP and RCP of $|\Delta n|\approx 0.015$, which is an extremely high value as compared to natural optically active media (typically $|\Delta n|\sim 10^{-5}$). Remarkably, the spectra show a characteristic fingerprint of the Born-Kuhn model dispersion Yin et al. (2013), manifested by the prominent dip in CB, accompanied by a zero-crossing for the bisignate CD, which appear around $\lambda\approx 580\,$nm in Fig. 3$\boldsymbol{a}$, 3$\boldsymbol{c}$ and $\lambda\approx 600\,$nm in Fig. 3$\boldsymbol{b}$, 3$\boldsymbol{d}$.

Qualitatively, we achieve a good overlap between the numerically and experimentally retrieved spectra. The blue-shift of the CB and CD spectra with respect to FDTD simulations may be attributed to underestimation of the SiO2 shell thickness. Additionally, the deviations of the actual sample from the ideally assumed geometry, clearly visible under the scanning electron microscope in Fig. 1$\boldsymbol{b}$, are not accounted for in simulations. As discussed earlier, any asymmetry affects the circular anisotropies, reasoning the observation of substantially higher CB and CD in experiment. Most importantly, our nanosphere assembly is extremely sensitive to the inter-particle gaps, which cannot be determined exactly and which considerably influence the optical response Albella et al. (2013). Lastly, the individual heterogeneous nanotrimer is strongly anisotropic and exhibits linear birefringence (LB) and linear dichroism (LD), which are orders of magnitude larger than CB and CD. Strong LB and LD are known to induce artifacts in measurements of CB and CD Schellman and Jensen (1987); Arteaga (2010). In the supplemental material sup , we compare the experimentally reconstructed and the simulated spectra of LB and LD. Additionally, we numerically investigate forward and backward illumination of the sample, a nanotrimer in a homogeneous environment and a nanotrimer of opposite handedness sup .

III Discussion and Conclusion

Owing to the relatively high chiral response of an individual nanostructure, such heterogeneous systems hold promise for constructing flat chiral and on-chip optical elements. First, the chiral response may be significantly enhanced by utilizing a higher refractive index substrate, by introducing structural chirality, by tailoring individual resonances of the constituents and by arranging the nanostructures in arrays which support lattice resonances. Secondly, owing to the heterogeneous environment, each of the nanoparticles in the nanotrimer assembly responds differently to the incident field Banzer et al. (2016). The latter suggests that such systems can potentially “sense” the gradient of the excitation field and distinguish the topological charge of orbital angular momentum of incident beams Nechayev et al. (2019); Woźniak et al. (2019), paving the way towards novel nanoscopic sensors and sorters.

In conclusion, we have experimentally investigated a geometrically symmetric heterogeneous nanotrimer on a glass substrate. The in-plane reflection symmetry of the system is broken by its heterogeneous material composition, while the glass substrate breaks the mirror symmetry of the whole system, transitioning its morphology from achiral to chiral. We have experimentally reconstructed the circular birefringence and circular dichroism spectra. The study of an individual nanostructure allowed us to preclude any contributions of delocalized lattice effects, collective resonances and near-field coupling effects, otherwise present in arrays of nanostructures. Additionally, our study provides a clear-cut distinction between the material- and geometry-induced chiroptical responses in a system exhibiting a heterogeneity- and substrate-induced break of symmetry, shedding light on chiral light-matter interactions at substrate-nanostructure interfaces.

Acknowledgements.

The authors gratefully acknowledge fruitful discussions with Israel De Leon, Gerd Leuchs and Paweł Woźniak.