Tunable optical chirality in a metamaterial platform with off-resonantly coupled metal&#x2013;dielectric components

Pavlos Pachidis; Vivian E. Ferry

doi:10.1364/OE.26.017289

1. Introduction

Chiral metamaterials are artificial materials consisting of subwavelength units that lack mirror symmetry and an inversion center. Characteristically, chiral media have different extinction spectra under left-handed (LCP) and right-handed (RCP) circularly polarized light. The figure of merit for optical chirality, defined as the ratio of the difference in extinction under each incident polarization to the extinction under unpolarized illumination, is orders of magnitude stronger for chiral metamaterials than for chiral molecules [1–3]. The selectivity to incident polarization has made chiral metamaterials viable candidates for a variety of applications, including all-optical nanophotonic circuits and sensors [4–8].

Despite the extensive literature on 2D and 3D chiral metamaterials in the visible [9–12], infrared [13–15], and terahertz regimes [16–18], there are few demonstrations of switchable chiral metamaterials. Most strategies explored to date tune the electromagnetic interactions in systems where all components of the chiral assembly are resonantly coupled to each other [14]. One of the initial demonstrations involved reconfiguring solution-based DNA-assembled gold nanoparticles [19,20], but in the solid state these reconfiguration processes can be slow [21]. To alter the chirality without necessitating reconfiguration, systems that change the coupling between elements via photoconductivity or phase change materials have also been used to switch the sign of the circular dichroism (CD) signal [21–24]. To expand the possibilities for chiral metamaterials, including dynamically switchable systems, systems that incorporate different materials are needed.

In this paper, we investigate a metamaterial platform with off resonantly coupled metal – dielectric components where small changes in the refractive index of the dielectric nanostructure influence the sign of the CD signal. Using finite-difference time-domain (FDTD) simulations, we show that changes in the refractive index of the dielectric component in the order of 10⁻² result in inversion of the sign of CD signal. Instead of altering the hybridized mode of the resonantly coupled plasmonic components of the system, the system inverts its weak but clear CD signal in response to changes in the scattering interactions between the plasmonic and non-plasmonic nanostructures of the assembly. We then explore the mechanism that leads to changes in the sign and magnitude of the CD response of the system upon changing the refractive index of the dielectric nanostructure. This response is present regardless of the shape of the dielectric structure, and the overall magnitude of the CD is strengthened as the scattering cross section of the dielectric structure increases. Finally, we show some related assemblies that could expand the range of materials integrated into this platform.

This study of the interaction between plasmonic and dielectric components influences the design of chiral metamaterials that integrate multiple materials systems, and shows how interactions between the components affects the chiral optical properties. Phase change materials (PCMs) that change their refractive index upon exposure to external stimuli such as heat or light could potentially be used to realize these effects dynamically [25,26].

2. Chiral metamaterial with tunable CD signal

2.1 Structure of the chiral platform and simulation methods

The platform we present is shown in Fig. 1(a), and consists of two gold nanorods in a lower plane and a dielectric disk placed over the center of one of the rods and displaced in the vertical direction by 30 nm. This is a modified version of the system used by Ferry and Hentschel et al. [27], but it differs in that one component is a dielectric material, which changes the properties of the system. The two gold nanorods form achiral hybridized eigenmodes, with two dips in the transmission spectrum at 1876 nm and 2249 nm [Fig. 1(b)]. The dips correspond to an antibonding and bonding dipolar mode respectively. When the dielectric disk is added, the system becomes chiral, giving rise to an asymmetric transmission spectrum under LCP and RCP illumination. Considering the analysis in reference 27, we placed the disk over the center of the nanorods where the electromagnetic field is at a minimum, so that the disk does not significantly shift the resonances of the nanorods. The system was embedded in a cladding medium with refractive index equal to 1.55, and has 4-fold symmetry to avoid any polarization conversion effects.

Fig. 1 (a) Schematic of the assembly. The assembly is composed of two gold nanorods with a dielectric disk on top. The individual rods have length = 380 nm, width = 70 nm, and height = 40 nm and are positioned 70 nm above the glass substrate. The dielectric disk has a diameter of 180 nm and thickness of 60 nm, and is placed over the center of the rods at a 30 nm vertical distance. The disk is 70 nm below the surface of the cladding medium that has a total thickness of 270 nm. The assemblies are arranged with a C4 rotation symmetry, and the lattice constant is 2000 nm. (b) Simulated transmission spectra of the device under LCP and RCP illumination with n_disk = 3.5 and n_medium = 1.55.

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To simulate the response of our platform we used FDTD simulations. The complex refractive index data for gold was modeled using a Lorentz-Drude-Debye fit from Rakic et al. [28]. The refractive index of the glass substrate was n = 1.45. The CD response is first quantified by the dissymmetry in transmission under RCP and LCP illumination $(T_{R C P} - T_{L C P})$ . The far-field CD response was measured in two different ways to ensure the accuracy of the results. Due to the C4 symmetry of the simulated lattice, we initially calculated the CD response by using linearly polarized light. Using the magnetic and electric field distributions of the simulation with linearly polarized light, we calculated the field distribution for circularly polarized light by adding the appropriate phase to the fields [29]. For comparison, we also ran two simulations on each structure with different circular polarizations of incident light, and calculated the difference in the resulting transmission spectra. The results were identical. To stabilize the simulations and ensure convergence, we used 64 layers of PML boundary conditions along the z-direction of the simulation and Bloch boundary conditions in the x and y-directions.

2.2 Tunable CD signal

In this system, the refractive index of the dielectric disk tunes the sign and magnitude of the CD response. Figure 2(a) shows the simulated CD response for the assembly, where each data series corresponds to an assembly containing a disk of a different refractive index. Two effects are observed. First, changing the refractive index of the disk between $n_{d i s k} > n_{m e d i u m}$ and $n_{d i s k} < n_{m e d i u m}$ reverses the sign of the CD spectrum. Second, as the refractive index contrast of the disk compared to the cladding $(| n_{d i s k} - n_{m e d i u m} |)$ increases, the magnitude of the CD signal increases. This behavior can be understood by considering the dielectric disk – gold nanorod interactions. In the assembly, the disk interacts with the nanorods solely through scattering interactions since the disk is non-absorbing. Figure 2(b) shows the calculated scattering cross section of the disk alone: as the refractive index contrast between the disk and the cladding medium increases, the scattering cross section of the disk increases. The increased power scattered from the disk enhances the chiral scattering interactions among the components of the assembly, and leads to a stronger CD response.

Fig. 2 (a) CD response ( $T_{R C P} - T_{L C P}$ ) of the system as a function of the refractive index of the dielectric disk. The medium has a refractive index of 1.55, and the color scale denotes the difference between the refractive index of the disk and the medium. The magnitude and sign of $n_{d i s k} - n_{m e d i u m}$ determines the magnitude and sign of the CD response. (b) Calculated scattering cross section of the disk at the high energy CD peak ( $λ = 1815 n m$ ), where the refractive index of the disk is increased from $n_{d i s k} = 1$ to $n_{d i s k} = 2.1$ . These values represent the lower and upper limit of the refractive index of the disk in our CD calculations.

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2.3 Mechanism for CD signal reversal

To understand the mechanism of the reversal of the chiral response, we examined the effect of the dissymmetry in absorption on the sign and magnitude of the CD signal. In Fig. 3(a), we compared the dissymmetry in transmission and absorption under circularly polarized illumination for systems with n_disk = 1 and n_disk = 2.1. Although refractive index changes of this magnitude are not necessary to observe a change in the sign of the CD spectrum, these extreme cases are shown for clarity. We calculated the absorption spectrum of the system’s unit cell using the formula:

A = 1 - T - R

and measuring the power transmitted (T) and reflected (R) from the system.

Fig. 3 (a) The dissymmetry in absorption (continuous line) and transmittance (dotted line) of the unit cell of the platform have similar magnitude and sign for systems with $n_{d i s k} = 2.1$ (red) and $n_{d i s k} = 1$ (blue). (b) Absorption spectra of the individual nanorods for the case without a disk on top. The dotted line is the absorption of the nanorod that contains the disk in the chiral geometry, while the dashed line is the absorption of the nanorod that does not contain the disk in the chiral geometry, as shown in the schematic inset. For the achiral system, the difference in absorption by the individual nanorods have the same magnitude but opposite sign and thus the composite system is not optically active, signified by the solid black line. (c) Absorption spectrum of individual gold nanorods in systems where $n_{d i s k} = 2.1$ (red) and $n_{d i s k} = 1$ (blue). The dotted lines denote the differential absorption by the nanorod with the disk on top, while the segmented lines indicate the dissymmetry in absorption by the nanorod without the disk.

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The CD response $(T_{R C P} - T_{L C P})$ is a result of the contributions from differences in absorption and reflection under illumination by RCP and LCP light, and is given by:

T_{R C P} - T_{L C P} = (A_{L C P} - A_{R C P}) + (R_{L C P} - R_{R C P})

where

R_{L C P} - R_{R C P}

represents the difference in reflection for RCP and LCP light. Figure 3(a) suggests that only the absorption term of Eq. (2) is significant, since the sign and magnitude of the dissymmetry in transmission of systems with n_disk = 1 and n_disk = 2.1 is similar to the sign and magnitude of the dissymmetry in absorption. This indicates that the change in the absorption of the system induced by the changes in the refractive index of the disk determines the sign and magnitude of the CD response of the system.

We then calculated the absorption in each nanorod individually, using the electromagnetic fields inside the plasmonic nanostructures. Figure 3(b) shows the dissymmetry of absorption of RCP and LCP light for each nanorod in the achiral case. Without a disk in the assembly, the nanorods absorb the two polarizations differently. The rod that contains the disk in the chiral case (denoted by a dotted line) absorbs more LCP than RCP light, while the other rod absorbs more RCP than LCP light. The total dissymmetry in absorption of the composite chiral assembly is found by adding the dissymmetry in absorption of RCP and LCP light by each nanorod. In the achiral case, the dissymmetry in absorption for the two rods have the same magnitude but opposite sign, and thus the composite system exhibits no dissymmetry in absorption (solid line in Fig. 3(b)). However, when $n_{d i s k} \neq n_{m e d i u m}$ , the magnitude of the difference in absorption of circularly polarized light by the individual nanorods of the assembly is not equal, leading to dissymmetry in absorption by the chiral assembly [Fig. 3(c)].

Regardless of the refractive index of the disk, the nanorod with the disk on top absorbs more light under LCP illumination than RCP illumination. Conversely, the nanorod without the disk absorbs more RCP than LCP. When $n_{d i s k} = 1$ , the nanorod without the disk on top has a greater magnitude of absorption dissymmetry near the high energy CD peak (1815 nm) than the nanorod with the disk. Since the nanorod without the disk absorbs more RCP light than LCP light, the net effect on the assembly is that RCP light is preferentially absorbed. At the lower energy CD peak (2217 nm), the nanorod with the disk exhibits greater dissymmetry than the nanorod without the disk, producing the opposite sign response. In contrast, in the system with $n_{d i s k} = 2.1$ , the dissymmetry in absorption by the nanorod with the disk on top is larger near the high energy CD peak, and at the lower energy peak the dissymmetry is larger in the nanorod without the disk. The sign of the dissymmetry in absorption of the chiral assembly with $n_{d i s k} = 2.1$ is thus opposite from the sign of the dissymmetry in absorption of a chiral assembly with $n_{d i s k} = 1$ . This behavior indicates that the refractive index of the disk reverses the sign of the CD signal of the system by changing the magnitude of the dissymmetry in absorption by the individual nanorods in the chiral assembly.

2.4 Chiral near-fields

The analysis above describes the absorption within the individual nanorods, but many of the applications of chiral metamaterials rely upon the chiral electromagnetic fields surrounding the nanostructures [30,31]. We therefore investigated the chiral nature of the electromagnetic fields excited by the system. Figures 4(a) and (b) show xy cross sections of the calculated optical chirality enhancement for a system with $n_{d i s k} = 1$ , calculated 10 nm above the top interface of the disk. The pseudoscalar optical chirality enhancement, $\hat{C} (r)$ , quantifies the chirality of the near fields, and is given by

\hat{C} (r) = \frac{C (r)}{C_{C P L}} = - \frac{ε_{0} \cdot ω}{2 | C_{C P L} |} Im (E^{*} (r) \cdot B (r))

where

C (r)

is the optical chirality of the electromagnetic field, normalized by the optical chirality of circularly polarized light denoted by

| C_{C P L} |

[32,33]. In these figures, only areas with

\hat{C} (r) > 1

are shown, denoting superchiral fields.

Fig. 4 Calculations of the optical chirality enhancement for a system with $n_{d i s k} = 1$ at $λ = 1815$ nm (high energy CD resonance peak). A cross section is shown at 10 nm above the top side of the disks under (a) RCP and (b) LCP illumination.

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Examination of the optical chirality enhancement shown in Fig. 4(a) and (b) reveals that the metal-dielectric platform can support strong chiral fields that are localized around different nanorods depending on the chiral illumination. For systems with n_disk = 1 under RCP illumination, the nanorod without the disk is surrounded by stronger superchiral fields, while the opposite nanorod supports weaker chiral fields. In contrast, under LCP illumination the nanorod with the disk on top excites stronger superchiral fields, while the nanorod without the disk on top supports weaker chiral fields. This behavior is in accordance with the absorption and transmission presented in Fig. 3(c); the nanorod that preferentially absorbs more RCP or LCP light is the one that supports the strongest chiral fields under RCP or LCP illumination, respectively. The strong optical chirality enhancement above the disks underlies the potential use of this platform in a wide range of applications [34,35]. For example, the tunable sign and location of the chiral electromagnetic fields surrounding the system based on the polarization of illumination could be used to dynamically influence the absorption and emission properties of light emitting materials [36,37].

3. Modifications to the original system

3.1 Modifying the shape and size of the dielectric component

Since the magnitude of the system’s CD signal is influenced by the scattering interactions of the dielectric disk with the nanorods, tuning the shape of the dielectric structure should affect the magnitude of the CD response but not the sign of the response. We verified this by comparing different shapes and sizes of dielectric scatterers to determine which structures give rise to the most pronounced chiroptical response. Figure 5 shows the CD response for assemblies where the dielectric scatterer is either a disk or a square with different dimensions. Representative spectra are shown for three disks (diameters of d = 180 nm, 300 nm, and 380 nm) and three squares (edge lengths of d = 200 nm, 290 nm, and 380 nm). The largest diameter/edge length matches the length of the nanorod. Similarly to the case of changing the refractive index contrast [Fig. 2], increasing the size of the dielectric component enhances its scattering cross section, thereby enhancing the scattering interactions between the dielectric component and the gold nanorods. Importantly, changing the shape of the dielectric component from a disk to a square does not hinder the ability of the system to change the sign of the CD spectrum. Increasing the distance between the dielectric disk and the gold bars decreases the magnitude of the CD spectrum slightly, similarly to results previously shown with metallic structures in reference 27.

Fig. 5 CD response ( $T_{R C P} - T_{L C P}$ ) of systems with disks and squares of varying diameters and diagonals (denoted by d) with n = 1 (blue) and n = 2.1 (red). The reversal of the CD response when $n_{d i s k} - n_{m e d i u m}$ switches sign is not affected when the shape of the scatterer changes from a disk to a square.

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Additional simulations on systems where the dielectric component is a rectangle or an ellipsoid [Fig. 6] indicate that the sign of the CD spectrum reverses whenever $n_{d i s k} - n_{m e d i u m}$ changes sign, regardless of the shape or orientation of the dielectric scatterer to the nanorods. This is advantageous for fabrication of the platform, as variations in the shape of the dielectric structure do not inhibit the reversible CD response of the system.

Fig. 6 (a) CD response for systems where the dielectric components are rectangles with the same dimensions (200 nm x 380 nm x 70 nm), but one of them is along (continuous line) and the other one is perpendicular (dashed line) relative to the long axis of the nanorod underneath. (b) CD response for systems where the dielectric components are ellipsoids with the same dimensions (long axis = 400 nm, short axes = 100 nm), but different orientation relative to the long axis of the nanorod underneath.

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The relationship between scattering cross section of the dielectric component and the magnitude of the CD response is shown in Fig. 7, which plots the magnitude of the high [Fig. 7(a)] and low energy [Fig. 7(b)] CD peaks $({| T_{R C P} - T_{L C P} |}_{\max})$ against the scattering cross section for a range of different dielectric nanostructures. We examined the optical response of assemblies where the dielectric component of the chiral assembly is an ellipsoid (dark and light blue), a rectangle (orange, purple and red) or a disk (green) with n = 1. The markers in the graph represent the shape of the scatterer and its orientation relative to the long axis of the nanorod underneath, while the color and size of the marker denote the dimension that was elongated and the relative size of the scatterer, respectively. Regardless of the shape of the scatterer, similar dependence of the magnitude of the high and low energy CD peak on the scattering cross section is observed. This is consistent with the idea that dielectric scatterers with larger dimensions, and therefore larger scattering cross sections, should interact more strongly with the nanorods underneath, and thus enhance the optical chirality of the system.

Fig. 7 The shape of the dielectric component is varied between a disk, ellipsoid, square, or rectangle with n = 1. The magnitude of the CD peak ( ${| T_{R C P} - T_{L C P} |}_{\max}$ ) at 1815 nm (a) and at 2217 nm (b) for each of these assemblies are plotted against the scattering cross section of the isolated dielectric scatterer. The square scatterers were either elongated along all their sides simultaneously (red), or one side was kept constant while the opposite side was elongated (purple and orange). The simulated edge lengths ranged from 200 nm to 380 nm with a step size of 30 nm. We also simulated systems with disks with varying diameters (green), where the diameters ranged from 100 nm to 380 nm with a step size of 40 nm. Lastly, we calculated the response in systems where the scatterer is a sphere with 100 nm diameter that is elongated along the direction parallel to the rod (dark blue), and perpendicular to the rod (light blue). The elongated diameter of the resulting ellipsoid varied from 100 nm (sphere) to 400 nm with a step size of 60 nm.

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3.2 Modifying the top layer of the cladding medium

The change in the sign of the CD signal also holds when the geometry of the structure is modified. In Fig. 8(a), we show calculations for a similar design, but in this case the nanorods and disk are covered with a 200 nm cladding medium, leaving the top of the disks exposed to a thin film with n = 1.65. These calculations show that changes in the refractive index of the disk induce a change in the CD signal of the proposed device, despite the modification in the configuration of the original system. Therefore, other materials with optical responses that are sensitive to the chiral near fields of the assembly [Fig. 4] could potentially be integrated into this system without disturbing the switching behavior.

Fig. 8 CD response ( $T_{R C P} - T_{L C P}$ ) for modified versions of the original chiral system. In (a), the height of the cladding medium is changed to 200nm and the top side of the disk is covered in a film with n = 1.65. The CD response is reversed upon changing the refractive index of the disk In (b), the system is perforated with holes. Changing the refractive index of a 70 nm film added on top of the modified system from 1.01 to 2.1 reverses the CD signal.

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A different modification is shown in Fig. 8(b), where the height of the cladding medium is restricted to 200 nm and the medium is perforated with holes at the same location and with the same dimensions as the disk in the original system. When a 70 nm thin film with n_film = 1.01 or n_film = 2.1 is added on top of the platform, then the composite system maintains its ability to change the sign of its CD response as the whole disk changes. Therefore, it is not necessary for the dielectric material to be localized only in the disk above the nanorods. The perforated surface of the modified design could be covered with dielectric solid, or possibly even a liquid film with tunable refractive index to control the optical chirality of the system.

4. Summary

In conclusion, we present a metal – dielectric chiral metamaterial platform where the CD response of the system is modulated by the refractive index of the dielectric component of the chiral assembly. Even though the system exhibits small chiral response, the magnitude of the CD signal can be significantly increased by enhancing the scattering cross section of the dielectric component by changing its size and shape. The difference in transmission for RCP and LCP light is due to dissymmetry in absorption by the individual nanorods, which dictates the sign of the CD response of the system. This far-field behavior is also mirrored in the chirality of the electromagnetic fields surrounding the nanostructures. Such phenomena could be experimentally realized with the use of PCMs. For instance, dichalcogenides such as Ge₃Sb₂Te₆, have been shown to change their real refractive index dramatically in the spectral range of interest with relatively low losses. Moreover, the ability to optically and electrically induce the phase transition of such materials could dynamically tune the proposed chiral system. Lastly, we suggested modifications to the original design that could expand the range of materials integrated with the platform.

Funding

Air Force Office of Scientific Research (AFOSR) (FA9550-16-1-0282).

Acknowledgments

The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper.

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Tunable optical chirality in a metamaterial platform with off-resonantly coupled metal–dielectric components

Abstract

1. Introduction

2. Chiral metamaterial with tunable CD signal

2.1 Structure of the chiral platform and simulation methods

2.2 Tunable CD signal

2.3 Mechanism for CD signal reversal

2.4 Chiral near-fields

3. Modifications to the original system

3.1 Modifying the shape and size of the dielectric component

3.2 Modifying the top layer of the cladding medium

4. Summary

Funding

Acknowledgments

References and links

Cited By

Figures (8)

Equations (3)

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