Optical chirality from dark-field illumination of planar plasmonic nanostructures

TL;DR

This paper demonstrates that dark-field illumination can induce optical chirality in planar plasmonic nanostructures, enabling circular dichroism effects similar to true chiral scatterers, with potential for planar device engineering.

Contribution

The study reveals that dark-field illumination induces optical chirality in planar nanostructures through geometric projection effects, providing a new method to engineer optical chirality in planar devices.

Findings

Circular dichroism observed in single oligomers under dark-field illumination.

The peak chiral response wavelength shifts with nanoparticle separation.

Amplification of circular dichroism in closely packed planar arrays.

Abstract

Dark-field illumination is shown to make planar chiral nanoparticle arrangements exhibit circular dichroism in extinction analogous to true chiral scatterers. Circular dichrosim is experimentally observed at the maximum scattering of single oligomers consisting rotationally symmetric arrangements of gold nanorods, with strong agreement to numerical simulation. A dipole model is developed to show that this effect is caused by a difference in the geometric projection of a nanorod onto the handed orientation of electric fields created by a circularly polarized dark-field that is normally incident on a glass substrate. Owing to this geometric origin, the wavelength of the peak chiral response is also experimentally shown to shift depending on the separation between nanoparticles. All presented oligomers have physical dimensions less than the operating wavelength, and the applicable extension to closely packed planar arrays of oligomers is demonstrated to amplify the magnitude of circular dichroism. The realization of strong chirality in these oligomers demonstrates a new path to engineer optical chirality from planar devices using dark-field illumination.

Equations

$$\text{allowdisplaybreaks}[1]{\mathrm{E}}_{\mathrm{TE}}^{(\pm )}$$

$${\mathrm{E}}_{\mathrm{TM}}^{(\pm )}$$

Full text

SZU] Nanophotonics Research Centre, Shenzhen University & Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China \alsoaffiliation[RMIT] School of Engineering, RMIT University, Melbourne, VIC 3001, Australia

ANU] Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia \alsoaffiliation[AEP] School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA

SZU] Nanophotonics Research Centre, Shenzhen University & Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

RMIT] School of Engineering, RMIT University, Melbourne, VIC 3001, Australia

Melb] School of Physics, University of Melbourne, VIC 3052, Australia

SZU] Nanophotonics Research Centre, Shenzhen University & Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China \alsoaffiliation[RMIT] School of Engineering, RMIT University, Melbourne, VIC 3001, Australia

SZU] Nanophotonics Research Centre, Shenzhen University & Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

Dark-field (DF) imaging is one of the more straightforward avenues to directly observe resonances of single plasmonic nanoparticles, and has thereby found function in nanoparticle-assisted monitoring of few or single molecules1, 2, 3 and spatially resolved monitoring of reactions 4. Yet DF is less common than bright-field in the related pursuit of discriminating enantiomers of chiral molecules using more complex nanoparticle systems. The operation itself is portable to DF settings: existing investigations have sought to introduce a bias in the signed magnitude of local helicity density $h\!=\!\mathrm{Im}\{\mathbf{E}^{*}\!\cdot\mathbf{H}\}$, to promote a net difference in coupling strength between a nanoparticle antenna and oppositely handed chiral molecules5, 6. The nanoparticle geometry is therefore a design freedom used to bias the helicity distribution generated under LCP (positive $h$) or RCP (negative $h$) illumination, for instance: it was shown that a nanoparticle antenna could foreseeably be designed to scatter only a single helicity of light7. However, the majority of experimental investigations have pursued an intermediary goal using true chiral geometries to produce circular dichroism (CD), a variation in the extinction (total power dissipated) from LCP and RCP illuminations, and then relying on some degree of helicity conservation in scattering8 to create a helicity bias. Here we reveal that DF illumination is beneficial for this task because it: (i) enables simple planar chiral nanoparticle arrangements to exhibit CD in a manner comparable to true chiral scatterers, and (ii) allows employment of desireable geometric symmetries that would otherwise be expected to suppress CD.

In Figure 1, we show the experimental scattering spectra of a planar, gold nanorod oligomer with 6-fold rotational symmetry, depicted in (a), under right- and left-circular polarized (RCP and LCP) illuminations from (d) DF with a 0.8​ –​ 0.95 NA condenser. The extinction spectra of the same hexamer under RCP and LCP illuminations from normal incidence plane waves is also shown in Figure 1(c) for comparison. The DF scattering $S$ is measured as the transmission collected by a 0.6 NA objective lens, and this can be seen to vary significantly between RCP and LCP under DF illumination, whereas the extinction under normal incidence plane waves which was obtained by subtracting the transmission from unity does not vary. The resonant peaks under DF are found at the wavelength of $704\,{\rm nm}$ and $713\,{\rm nm}$ in the scattering spectra of LCP and RCP of $\psi=60^{\circ}$, respectively. To characterize the chiral response, we define a chiral signal $\Delta_{S}=(S_{\scriptscriptstyle\mathrm{RCP}}-S_{\scriptscriptstyle\mathrm{LCP}})/(S_{\scriptscriptstyle\mathrm{RCP}}+S_{\scriptscriptstyle\mathrm{LCP}})$, as plotted in Figure 1e. Note that a single gold nanorod oligomers can exhibit strong chiral response over $\Delta_{S}=0.3$ while on resonance at a wavelength of 670 nm. In the Supplementary Material, further derivations show that the absence of chiral signal under normal plane wave illumination follows from having 3-fold or more rotational symmetry, encompassing substrate, once assuming each nanorod supports only a single dipole moment. The scattering presented indeed appears to show significant CD, much like that which occurs for geometrically chiral antennas9, 10, or with obliquely incident plane waves on achiral antennas that lack inversion symmetry11. However, the gold nanorod oligomer in Figure 1 is planar and has inversion symmetry in the absence of substrate, meaning CD is largely not expected. Yet other forms of chiral signal, such as circular conversion dichroism, are also not expected due the presence of rotational symmetry, discussed further in the Supplementary material. The presence of at least 3-fold rotational symmetry is notably an example of desireable symmetry: it forbids scattering of oppositely handed fields in the transmission direction along its principle axis12, thereby promoting the generation of a uniform helicity distribution under circularly polarized illumination. The origin of the chiral signal we observe therefore warrants further attention, particularly given true three-dimensional chirality is challenging in fabrication, with subsequent interest in finding new avenues for chiral optical response in two-dimensional plasmonic structures13, 14, 15, 16, 17, 18 In the coming discussion, we will show that true circular dichroism can be expected to occur under DF illumination due to a difference in the magnitude of the applied electric projected onto the nanorods, which occurs due to ellipticity in the DF polarization when confined to plane of the nanorods. A preferred orientation therefore exists when a nanobar’s long axis is aligned with the major axis of the polarization ellipse, and the substrate is shown to vary the angle of this polarization axis between LCP or RCP DF illumination. This thereby leads to circular dichroism that depends on the orientation of the nanorods and only exists under DF illumination.

Let us consider a simplified model where we assume each gold nanorod behaves as an anisotropic point dipole aligned to the long-axis of the nanorod, and denote this orientation with a unit vector $\bm{\hat{\psi}}$. We can recognize that the dipole moment amplitude of each nanorod is equal up to a phase shift with that of every other nanorod, because the propagation axis of the circularly polarized DF illumination is parallel the rotational symmetry axis of the oligomer. This means a symmetric rotation of the global coordinate system is equivalent to a phase shift of the applied field. So we only need to consider a single nanorod, which we define as lying on the $\mathbf{\hat{x}}$-axis and shifted by a distance $\delta_{x}$. The substrate is placed a distance $\delta_{z}$ along $-\mathbf{\hat{z}}$, i.e. below the dipole. To construct a DF illumination, we first consider the electric field from an annular ring of circularly polarized plane waves with incoming propagation ($\mathbf{k}$) vectors forming a circle in the tranverse $\mathbf{k}$-space, as illustrated in Figure 2(a) for a polar incident angle $\phi$. Our dipole will experience the projection of the applied electric field onto its orientation $\bm{\hat{\psi}}$, and this can be decomposed into the contributions from azimuthal, or transverse electric $\mathbf{E}_{\scriptscriptstyle\mathrm{TE}}\cdot\bm{\hat{\theta}}\cdot\bm{\hat{\psi}}\equiv\mathrm{E}_{\scriptscriptstyle\mathrm{TE}}$, polarizations and from polar, transverse magnetic $\mathbf{E}_{\scriptscriptstyle\mathrm{TM}}\cdot\bm{\hat{\phi}}\cdot\bm{\hat{\psi}}\equiv\mathrm{E}_{\scriptscriptstyle\mathrm{TM}}$, polarizations. The TM field also includes an extra $\pm\frac{\pi}{2}$ phase shift to impose a circular polarization. The resulting projection of electric field onto our dipole, will therefore given by: $\mathrm{E}^{\scriptscriptstyle(\pm)}=\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TE}}+\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TM}}$, with $\pm$ indicating LCP and RCP, respectively. We provide derivation of $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TE}}$ and $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TM}}$ in the Supplementary Material, and state the result here.

[TABLE]

Here ${r}_{\scriptscriptstyle\mathrm{TE}}$ and ${r}_{\scriptscriptstyle\mathrm{TM}}$ are Fresnel reflection coefficients for the air-substrate interface and $J_{n}$ is the $n^{\mathrm{th}}$ order Bessel function of the first kind. A chiral signal can now be defined for the magnitude of the applied electric field projected onto $\bm{\hat{\psi}}$, being: $\Delta_{\mathrm{E}}=(|\mathrm{E}^{\scriptscriptstyle(-)}|^{2}\!-|\mathrm{E}^{\scriptscriptstyle(+)}|^{2})/(|\mathrm{E}^{\scriptscriptstyle(-)}|^{2}+|\mathrm{E}^{\scriptscriptstyle(+)}|^{2})$. When using our dipole model, $\Delta_{\mathrm{E}}$ is equal to the chiral signal for the extinction $\sigma$ of the whole oligomer $\Delta_{ext}=(\sigma_{\scriptscriptstyle\mathrm{RCP}}-\sigma_{\scriptscriptstyle\mathrm{LCP}})/(\sigma_{\scriptscriptstyle\mathrm{RCP}}+\sigma_{\scriptscriptstyle\mathrm{LCP}})$, see Supplementary Material. Circular dichroism therefore exists only due to a difference in the magnitude of the electric field projected onto $\bm{\hat{\psi}}$. However, when there is no substrate $\mathrm{E}^{\scriptscriptstyle(\pm)}=-(\mathrm{E}^{\scriptscriptstyle(\mp)})^{*}$, hence $|\mathrm{E}^{\scriptscriptstyle(+)}|^{2}=|\mathrm{E}^{\scriptscriptstyle(-)}|^{2}$, and $\Delta_{\mathrm{E}}$ is precisely zero. It is only when we account for the substrate that $\Delta_{\mathrm{E}}$ becomes nonzero for this DF illumination, recognizing that $\Delta_{\mathrm{E}}$ remains zero for normal plane waves. In Figure 2(b) we integrate $\mathrm{E}^{\scriptscriptstyle(\pm)}$ over $\phi$ assuming a uniform amplitude plane wave distributed on an annular solid angle section in $\mathbf{k}$-space ($\mathrm{d}\Omega\!=\!\sin\!\phi\mathrm{\;}d\theta\mathrm{d}\phi$) truncated to the DF condenser’s 0.8​ –​ 0.95 NA range. To deconstruct what is happening, we first note that the electric field lying in the plane of the nanorods is not necessarily circularly polarized when displaced from the propagation axis. The electric field incident on the dipole will therefore have an elliptical polarization, leading to increased extinction when its major axis aligns with $\psi$. Said another way, we cannot separate $\psi$ dependence as a common unitary factor from the sum of $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TE}}$ and $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TM}}$. We can also see that interchanging the sign of $\psi$ in Eq. 1 and 2 is equivalent to interchanging $|\mathrm{E}^{\scriptscriptstyle(+)}|^{2}\leftrightarrow|\mathrm{E}^{\scriptscriptstyle(-)}|^{2}$. As such, circular dichroism implies the magnitude of electric field projected onto $\psi$ is not equal to that projected onto $-\psi$. Given $\psi$ dependence cannot be separated as a common unitary factor from the sum of $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TE}}$ and $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TM}}$, circular dichroism can be expected whenever the applied electric field’s major polarization axis is aligned with any $\psi\neq 0,$ 90°, being angles for which $e^{\pm i\psi}=-e^{\mp i\psi}$. Explicitly, the Bessel functions in (1) and (2) are real valued, and without a substrate ($r_{\mathrm{TE}}=r_{\mathrm{TM}}=0$): $|\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TE}}|$ is maximized at $\psi=0$ , and $|\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TM}}|$ is maximized at $\psi=\frac{\pi}{2}$. Note also that these two maxima are $\frac{\pi}{2}$ out of phase. The major polarization axis, without a substrate, is therefore aligned to either $\psi=0$ or 90°, hence no circular dichroism. However, when introducing a substrate, the phase acquired in reflection due to $\delta_{z}$ makes the phase of $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TE}}$ and $\mathrm{E}^{\scriptscriptstyle(\pm)}_{\scriptscriptstyle\mathrm{TM}}$ depend on $\phi$. The in-phase components when integrating over $\phi$ are therefore no longer going to uniformly be at $\psi=0$ or 90°, indicating the major polarization axis will be rotated, hence leading to circular dichroism. It is worth recognizing that this ellipticity in the periphery of a beam resembles that from the optical spin-Hall effect19, such from the reflection of a Gaussian beam at an interface. Moreover, a linear-polarized Gaussian incident on an interface will generate a symmetric cross-polarization in the portion of the beam periphery perpendicular to the original polarization axis.20 For a circular-polarized Gaussian, as the sum of two linear-polarized Gaussians, this effect can be expected to rotate the major axis of the transverse elliptical polarization out of alignment with $\psi=0,90\degree$. In the Supplementary Material, we also recalculate $\Delta_{E}$ from a DF modeled as a superposition of two Gaussians with NA 0.95 and NA 0.8, and show it predicts a circular dichroism magnitude closer to that seen in experiment. We, therefore, conclude that the transverse orientation of applied electric fields, from a circularly polarized DF incident on a substrate, provides preferential coupling of LCP and RCP into the considered oligomers, associated with an angular dependence on the nanorod orientation $\psi$.

We now show this angular dependence experimentally. Gold nanorod oligomers were fabricated for the full $180^{\circ}$ range of possible $\psi$ in $15^{\circ}$ steps, as shown in Figure 3a. The dimensions of the fabricated nanorods were measured to be $43\times 94$ nm. The measured chiral signal $\Delta_{S}$ from experiment and from simulation using CST Microwave Studio, produce the maps presented in Figure 3b and c, respectively. Both show the $\psi$-dependent circular dichroism that we expected from the dipole model, with no chiral response is observed at $\psi=0,90\degree$, and opposite sign of chiral signal observed for oppositely handed chiral oligomers. The peak chiral signal here is also occurring in the vicinity of the oligomer’s resonant frequency, which is expected because this is necessary to impose large anisotropy of the nanobars. The measured chiral signal is thereby associated with significant differential scattering signal, rather than suppressing the denominator of $\Delta_{S}$, which has allowed measuring strong chiral signal from even a single oligomer. The difference in scattering magnitude of several oligomers is shown later in Figure 4a, and in simulation we also see a qualitative change in the local scattered electric field intensity depicted in Figure 4c.

There is now a second degree of freedom we have over the chiral signal: the transverse displacement of nanorods $\delta_{x}$. Moreover, referring to our model for Figure 2, specfically Eq. 1 and 2, we assume that the nanorods are optically thin $\delta_{z}\approx 0$, and then the wavelength dependence of the applied field projection is entirely due to the size of $\delta_{x}$ relative to the wavelength ($k\delta_{x}$). We should therefore expect the transverse displacement of nanorods to shift the peak chiral signal, without having to change the nanorod dimensions. In Figure 4, we present experimental investigation of nanorod oligomers when varying the center-to-center distance between opposing nanorods $D=2\delta_{x}$ from $260\,{\rm nm}$ to $420\,{\rm nm}$ in increments of $40\,{\rm nm}$. The corresponding scattering and chirality spectra are provided in Figure 4a and b, respectively. We do indeed observe a red-shift with increasing $D$ in the peak chiral signal from $\lambda=610\,{\rm nm}$ to $700\,{\rm nm}$, while the resonance wavelength of scattering signal remains largely stationary. This thereby provides an effective way to engineer the wavelength of chiral DF scattering from a subwavelength planar plasmonic structure, without changing the physical dimension of the consisting metal nanorods, such as if constrained by fabrication or assembly procedure.

As mentioned, the resonant frequency of scattering in Figure 4 is also relatively constant, despite the changes to the oligomer dimensions, which suggests that we are observing a resonance that is dominantly determined by that of a single nanorod. Additionally, the presented oligomers have a subwavelength physical footprint, owing to existence of quasistatic surface plasmon resonances when confined in highly subwavelength photonic devices21, 22, 23, 24. These both suggest that we should be able to directly translate the chiral operation of a single oligomer into a homogenized metasurface platform. So let us explore arrays of oligomers, as to show relevance of these concepts also toward pursuit of plasmonic metasurfaces for polarization control, and other applications for flat optics25, 26, 27, 28 that capitalize on 2-dimensional fabrication.

In Figure 5, we present experimental measurements of arrays of nanorod oligomers with lattice periods ranging from 510 nm to 1020 nm. The strongest chiral response is observed for the array with $p=680\,{\rm nm}$ whose maximum chiral signal $\Delta_{S}$ is over 0.5, which is approximately three times greater than the equivalent single oligomer in Figure 3. Yet, simultaneously, no substantial wavelength shift is observed in the chiral signal peak, suggesting that the circular dichroism remains as the same field projection mechansim that occurs for the single oligomer. As such, the lattice period is a parameter with which we can optimize the chiral signal magnitude without impacting wavelength shifts, and the nanoparticle spacing within a constituent oligomer is a parameter than governs wavelength shifts of the chiral signal.

To conclude, we have realized a subwavelength scale planar device that exhibits strong optical chirality using arrangements of plasmonic nanoparticles illuminated by dark-field. Theoretical analysis using a dipole model has explained the origin of the chiral response is a difference in the geometric projection of a nanorod onto the handed orientation of electric fields created by a circularly polarized dark-field incident on a glass substrate. The dependence of the orientation angle of the nanorods has been systematically demonstrated with experiments and numerical simulations. It was also found that the wavelength range of the chiral response can be tuned by changing the distance between nanorods, and the magnitude can be amplified through the extension to closely packed, planar arrays of oligomers. Planar plasmonic chiral devices based on the demonstrated structures can therefore be employed in the place of true chiral geometries while also benefiting from simultaneous access to desireable geometric symmetries, including rotational symmetry considered here. These results foreseeably benefit pursuits that require preferential generation of left- and right-handed helicity fields, such as nanoparticle-assisted discrimination of enantiomers.

1 Methods

Nanofabrication.  The plasmonic chiral oligomers were fabricated using 100 nm thick poly(methyl methacrylate) (PMMA) and 100 nm thick copolymer spin coated on a 500 $\mu$m thick glass substrate, then baked at 180 °C for 90 seconds. The designed patterns were written on the electron beam resist using 100kV electron beam (Vistec EBPG5000plusES) and developed in methyl isobutyl ketone (MIBK):isopropyl alcohol (IPA) solution with the ratio of 1:3. Thereafter, electron beam evaporation was performed to deposit 2 nm thick germanium adhesion layer and 30 nm gold layer followed by a lift-off process using acetone. The nanorods were designed to be 90 nm long, 40 nm wide and 30 nm thick.

Optical measurement.   Scattering spectra were measured under dark-field illumination on the plasmonic structures to examine their chirality. Broadband light from a halogen lamp was right- or left-circularly polarized (RCP or LCP) by a linear polarizer and an aligned quarter wave plate. The RCP and LCP light were focused by a dark-field condenser with the range of the numerical aperture of 0.80-0.95 which means the light in the corresponding solid angle was exclusively illuminated on the plasmonic oligomers as shown in Figure 1a. The forward scattered light from the oligomers was collected by an object with the numerical aperture of 0.60 in order to avoid the direct transmission. The collected light was resolved for the wavelength by a monochromator and then imaged on a cooled CCD (Princeton Instrument PIXIS).

Numerical simulation.  Simulations were performed using (Figures 4 and 5) CST Microwave Studio for Finite Difference Time Domain (FDTD), and (Supporting Information) Comsol Multiphysics for Frequency Domain Finite Element Method; all methods were found to provide comparable results. The dark-field illumination was modeled as a superposition of two paraxial Gaussian beams with NA 0.8 and 0.95; the respective electric field amplitudes were balanced to remove the electric field from the propagation axis in the far-field. The signal collected by a 0.6 NA objective lens in transmission was modeled as a solid angle integral of the radially outward component of the Poynting vector for the scattered field, evaluated in glass substrate at distance from the oligomer origin equal to the largest free-space wavelength. Scattered field in CST was defined as the field radiated when imposing a volumetric box of dark field illumination enclosing only the oligomer. Scattered field in Comsol was defined by first simulating the resulting field distribution from the dark field incident on the substrate interface without nanoparticles, then imposing the resulting field internal to the previously absent nanoparticles as an external field in a second simulation to calculate the scattered field. Permittivity of the glass substrate was taken to be 2.3, the permittivity of gold was taken from Johnson and Christy29, and the size of the nanorod was set at $90\times 40\times 30$ nm.

2 Acknowledgements

The work is supported by the leading talents of Guangdong province program No. 00201505 and the Natural Science Foundation of Guangdong Province under No. 2016A030312010. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). BH acknowledges the discussions on theory and simulation with A.E. Miroshnichenko, Z. Fan, S. Trendafilov and M.R. Shcherbakov, the advice of F. Demming and C. Kremers (CST) on simulations using CST Microwave Studio, and the support from A.E. Miroshnichenko, Y.S. Kivshar and G. Shvets.

{suppinfo}

Further experimental results are presented showing the dependence of the nanorod oligomers on the number of constituent nanorods. For the considered class of nanorod oligomers, we provide analysis on the consequences of their symmetry, analysis of the collective eigenmodes in a dipole model, and derivation of Eq. 1 and 2.