Dynamic tuning of enhanced intrinsic circular dichroism in plasmonic stereo-metamolecule array with surface lattice resonance

2.1 CD of single stereo-SRR dimers

Figure 1a illustrates the configuration and geometric parameters of a gold stereo-SRR dimer with the upper SRR rotated clockwise by an angle θ with respect to the y-axis. Here, the horizontal displacement d between the two SRRs is intentionally introduced to enhance near-field coupling at the gap area [88], [89], [90], [91], [92], and the vertical displacement s can be used to manipulate the coupling and the phase retardation. Depending on the relative position and twist angle, the SRR dimer can be left-handed (L-Enantiomer) or right-handed (D-Enantiomer). The spacer layer (e. g., solidfiable photopolymer, PC403) is supposed to have the same refractive index as the silica substrate (n_silica = n_spacer = 1.50), while the superstrate material is set to be air (n_sup = 1.00). When circularly polarized light is incident normally onto the structure from the air side, plasmonic coupling between the electric dipole mode of the upper SRR and the quadrupole mode of the lower one results in the formation of hybridized bonding dipole-quadrupole (BDQ) and antibonding dipole-quadrupole (ABDQ) resonance modes (Figure 1b) [84], [85]. Plasmon hybridization between two electric dipole modes of the dimer is neglected here due to their significant phase mismatch. More detailed information can be found in Figure S1. Such hybridization modes can be selectively excited by RCP and LCP incidences, depending on the phase retardation between the two SRRs. As a result, the difference in excitation efficiency of the two circular polarized incidences is expected to generate CD signals around the resonance frequency of the SRR dimer.

Figure 1:

Geometric configuration and plasmon hybridization of a modified gold stereo-SRR dimer. (a) Schematic views of the modified stereo-SRR dimer, showing geometric parameters such as ring radius r = 90 nm, width w = 40 nm, gap width g = 30 nm, thickness h = 40 nm, vertical separation s = 60 nm, horizontal separation d = 90 nm and twisted angle θ = 60°. The refractive index of the substrate n_sub = n_silica = n_spacer = 1.50, and the superstrate n_sup = 1.00. (b) Plasmon hybridization between the electric dipole and quadrupole modes in a D-Enantiomer, forming an antibonding dipole-quadrupole (ABDQ) and a bonding dipole-quadrupole (BDQ) resonance.

The absorption cross-section (Abs) spectra of the single modified stereo-SRR dimer (D-Enantiomer) under RCP and LCP incidences are shown in the upper panel of Figure 2a. As expected from our qualitative reasoning, the RCP mode is located at a lower energy (990 nm), which corresponds to the bonding mode (BDQ), whereas the LCP mode lies at a higher energy (880 nm), corresponding to the antibonding mode (ABDQ). In addition, the resonance shoulder around 1100 nm under the LCP incidence is attributed to the excitation of a hybridized dipole mode (Figure S1). As a result, a positive differential absorption (ΔAbs = Abs_LCP – Abs_RCP) peak occurs at 880 nm and a negative one at 987 nm as shown in the lower panel of Figure 2a, leading to the CD response of the stereo-SRR dimer. The corresponding near-field and surface charge distribution profiles at the two CD peaks are rendered in Figure 2b,c, respectively. Clearly, the surface charge profiles confirm the electric dipole mode of the upper ring and the quadrupole mode of the lower ring at their resonance wavelengths. However, there is a π phase difference for the quadrupole mode of the lower ring at the two resonances, confirming our analysis of hybridized ABDQ and BDQ modes.

Figure 2:

CD response of a single modified gold stereo-SRR dimer. (a) Absorption cross-section spectra of a single D-Enantiomer under LCP and RCP incidences (upper panel) and corresponding differential absorption (ΔAbs) spectrum, i. e., CD spectrum (lower panel). (b, c) Near-field enhancement (|E/E₀|, left panels) and surface charge (right panels) distribution profiles at the ABDQ (b) and (c) BDQ resonance wavelengths.

2.2 Enhanced CD with surface lattice resonances

In order to highlight the importance of SLR in enhancing plasmonic chiroptical effects, we arrange chiral stereo-SRR dimers in a C₄-symmetric supercell to avoid circular birefringence (Figure 3a). The supercell has a period p = 890 nm and the center-to-center distance between two adjacent dimers is 450 nm. The simulated transmission and absorption spectra of the array under RCP and LCP incidences as well as the corresponding transmission CD spectrum are plotted in Figure 3b. An ensemble CD spectrum by assuming no coupling between adjacent dimers is also overlaid as a dotted line for comparison. One can immediately see two pronounced positive and negative CD peaks at 831 and 949 nm for the array, both blue-shifted compared to the reference spectrum. This can be attributed to the effective mode volume overlapping between SRR dimers in the array (Figure S2 in Supporting Information). The positive CD peak increases slightly compared with that of the single dimer (red circle), while the negative CD peak at 949 nm (blue solid circle) is enhanced to 0.70, which is 6 times larger than the ensemble CD spectrum. This is a clear evidence that electromagnetic coupling between adjacent dimers plays an important role in the chiroptical signal enhancement. In fact, it has recently been demonstrated that the coupling between a localized plasmon resonance and the Bragg resonance of a periodic lattice be used to improve the resonance quality factor and light absorption [110]. It should be noted from Figure 3b that there is another resonance peak located at 1078 nm, which is the bonding dipole-dipole (BDD) mode of the chiral stereo-SRR, whose near-field and surface charge distribution profiles can be found in Figure S3.

Figure 3:

CD responses of a stereo-SRR dimer array organized in C₄ symmetry. (a) Schematic views of the stereo-SRR dimer array. (b) The transmission (upper panel) and absorption (middle panel) spectra with RCP (blue lines) and LCP (red lines) incidences, and the corresponding CD in transmission of the array (solid line, lower panel). The dotted line in lower panel is calculated from equation ΔT = 4 × ΔAbs/p², which is the ensemble average of CD response calculated by neglecting the coupling between dimers. The vertical dashed lines denote the spectral positions of corresponding RAs, and the tick labels on the right side represent the converted cross section values by multiplying the area of the unit cell (p²).

The above observation of enhanced CD in the array of C₄-arranged chiral stereo-SRR dimers can be attributed to the emergence of SLR modes due to collective oscillation of LSPRs in each unit cell. In short, for a periodic plasmonic nanoparticle array, Rayleigh anomalies that are associated with light diffracted parallel to the array surface, occur at [96], [97], [98], [99],

where n_med is either the refractive index of the superstrate (n_sup) or the substrate (n_sub), and (i, j)_med denotes the diffraction order. When the incident angle is just across RAs at a plasmon resonance band, the unit cells diffractively couple to each other, creating a propagating SLR mode. The spectral positions of relevant RAs are denoted by the gray dashed lines in Figure 3b. As a result, plasmonic non-radiative absorption is increased by the enhanced interaction between incident field and lossy metal but plasmonic radiative scattering is suppressed due to diffraction coupling, leading to an overall sharp resonance peak with high Q-factor [104]. Therefore, the absorption of a chiral plasmonic nanostructure array is expected to be greatly enhanced under an appropriate circularly polarized incidence but negligible for the opposite one, leading to a pronounced CD peak. It is worth to emphasize that, although the refractive indexes of the superstrate and substrate are not equal (n_sub = 1.50, n_sup = 1.00), the index-matching condition here is not a necessary requirement to realize strongly enhanced CD response.

The sharp resonance and CD peak located at 949 nm (blue solid circle) occurs on the long-wavelength side of the (1, 0)_sup RA (please note that to simplify the expression, the rest degenerate RAs in Figure 3b are not indicated here), and the resonance quality factor is larger than that of the localized resonances shown in Figure 2a, which are the signatures of coupling light into SLR mode [104]. Besides that, the near-field distributions shown in Figure S4 demonstrate that there are relatively strong field enhancements between the unit cells, and propagating waves are observed along both x- and y-directions, which further reveal the excitation of the SLR. The corresponding field pattern for a single stereo-SRR in the unit cell (Figure 4) is consistent with Figure 2c, demonstrating that, indeed, it is the BDQ mode. As expected, the excitation efficiency of BDQ mode inherits from its single structure situation. This behavior is also confirmed in Figure 4b where near-field is greatly enhanced. In this case, the BDQ mode is efficiently excited by RCP incidence, giving rise to enhanced absorption (Abs ∼ 0.84), whereas LCP illumination stands on the opposite side with negligible absorption (Abs ∼ 0.14). It should be noted that although the (1, 1)_sub RA in the substrate is around the same spectral range, it is almost overlapped with the maximum point of the sharp resonance. This behavior does not satisfy the relation between an RA and SLR mode, and it should not be the main contribution of the enhancement. This can also be verified in Figure 4b that the field enhancement around the upper rings are stronger than that of the lower ones, demonstrating that the SLR is caused by the diffraction coupling of the BDQ mode in the superstrate. Actually, the (1, 1)_sub RA mostly interacts with the BDD mode at 1078 nm (Figure S3) and is beyond the scope of this study. We therefore dismiss the (1, 1)_sub SLR hereafter throughout this paper.

Figure 4:

Near-field enhancement (left panels) and charge distribution (right panels) of one dimer in the supercell array at the positive and negative CD peaks shown in Figure 3, where the ABDQ (a) and BDQ (b) modes are excited. BDQ mode are greatly enhanced compared with single dimer situation due to the diffraction coupling.

The broad resonance peak at 831 nm is attributed to the ABDQ mode (Figure 4a), and interestingly, exhibiting weak chiroptical enhancement (Figure 3b). This is from the fact that, the ABDQ mode is located, on one hand, at the short-wavelength side of (1, 0)_sup RA, thus no (1, 0)_sup SLR resonance, and on the other hand far away from (2, 0)_sup RA, yielding weak diffraction coupling. As a result, chiral stereo-SRR dimer arrays at this band restore to uncoupled situation, where the corresponding CD signal is comparable to that of ensemble CD spectrum. This phenomenon can be confirmed in Figure 4a where the near-field enhancement is also comparable with that of the single dimer (Figure 2b). Another example sharing the same mechanism is the hybridized magnetic dipole-dipole mode centered at 2100 nm. As shown in Figure 5 and Figure S5, the CD response of the stereo-SRR dimer array appears in its magnetic dipole-dipole coupling range. When the magnetic resonance wavelength is far away from the RAs, there is no diffraction coupling between unit cells. As a result, the CD response of the array is almost identical to that for an ensemble of the same number of single SRR dimers without diffraction coupling (lower panel, Figure 5). The maximum CD in transmission is only about 0.12, and it is in accordance with the experimental results reported in previous studies [93]. Considering that the magnitude of differential absorption cross sections for the hybridized magnetic dipole resonances are comparable with that of the ABDQ and BDQ modes (Figures 2 and S4), the excitation of SLRs can be an effective approach for enhancing the intrinsic CD responses.

Figure 5:

CD responses related to the magnetic dipole resonance of the stereo-SRR dimer array shown in Figure 3. Upper panel: transmission spectra under RCP (blue lines) and LCP (red lines) incidences; Lower panel: corresponding transmission CD spectrum for the dimer array (solid line) and the CD spectrum calculated for an ensemble of uncoupled single dimers (ΔT = 4 × ΔAbs/p², dotted line).

2.3 Optimized condition for enhanced CD

SLRs and LSPRs are two resonance modes that stem from distinct physical mechanisms. In other words, SLRs is a collective resonance mode with high Q-factors and can be manipulated by tuning the period of the arrays. In contrast, LSPRs solely depends on the property of metamolecules. Therefore, one is able to tune the two resonances independently in order to get optimized chiroptical effect. We carried out the period sweep of the supercell while keeping dimer distance unchanged within unit cell. The contour plot of the corresponding transmission and absorption spectra (the upper and middle panels), as well as CD signal (the lower panel) for different periods are depicted in Figure 6. The RAs calculated from Equation (1) is superimposed as dashed lines for comparison.

Figure 6:

(a) Transmission under RCP (upper panel) and LCP (middle panel) incidences, as well as CD spectra (lower panel) for the stereo-SRR dimer arrays with different periods. (b) The corresponding RCP and LCP incidences absorption (upper and middle panels), as well as CD in absorption (lower panel) spectra. The unit has been converted into absorption cross section (μm²) by multiplying the area of the unit cell. The dashed lines indicate RAs, and the blue and red arrows in Figure 6b denote the BDQ and ABDQ resonances, respectively.

The ABDQ and BDQ modes are excited around, respectively, 840 and 940 nm, which are denoted by the red and blue arrows in the upper and middle panels of Figure 6b. We therefore distinguish the period of supercell in three regions according to the relative position between (1, 0)_sup RAs and LSPRs band. For lattice period 800 nm < p < 950 nm, RAs intersect with LSPRs modes, resulting in strong SLR modes. In this case, BDQ mode is effectively excited under RCP incidence. The CD response therefore gets enhanced and reaches maximum when p = 890 nm. When the period of supercell is smaller than 800 nm, (1, 0)_sup RA are shifted to far short-wavelength side of LSPR modes. Therefore, their diffraction coupling is relatively weak. For large lattice period (p > 950 nm), LSPRs lies above (1, 0)_sup RA and thus cannot oscillate collectively. On the contrary, LSPRs start to interact with (1, 1)_sup and (2, 0)_sub higher order RAs. The solid lines in the upper panel of Figure 7a represent the absorption spectra of a sparse array with a large period (p = 1210 nm). Although the pronounced resonances are spectrally overlapped with higher order RAs (the vertical dashed lines), it has little effect on LSPRs except a resonant blue-shift. The resonance shift can be attributed to the effective mode volume overlapping between neighboring SRR dimers, which is similar to the result in Figure 3b. In contrast, the absorption of the two resonances for the array is comparable with that of the single dimer (lower panel, Figure 7a). In other words, chiroptical effects of these regions restores to uncoupling situation. This behavior, again, can be explained by the near-field distributions of the sparse array (Figure 7b,c) which are almost identical with that of the single dimer situation (Figure 2b,c).

Figure 7:

CD responses of a sparse stereo-SRR dimer array. (a) Absorption spectra of the sparse array with p = 1210 nm for LCP and RCP incidences (upper panel), and the corresponding CD in absorption spectrum (lower panel). The dotted lines in the upper panel are the absorption spectra of a single dimer scaled by a factor of 4, the dotted line in the lower panel is the ensemble CD single calculated based on the single dimer, the vertical dashed lines denote the spectral positions of several RAs, and the tick labels on the right side represent the converted cross section values by multiplying the area of the unit cell. (b) Near-field enhancement (left panels) and charge (right panels) distributions of the ABDQ, and (c) BDQ hybridized resonances for the sparse array.

2.4 Enhancing chiroptical effects with other metamolecules

Given the concept that SLRs and LSPRs can be tailored independently, it is possible to exploit SLRs as a universal approach to enhance the chiroptical effects of LSPRs based metamaterials. A typical example is shown in Figure S6 where gold stereo-SRR dimer arrays with spatial shift d = 0 can be strongly enhanced by adjusting the lattice spacing. In addition, here, we demonstrate the robustness of SLRs from a new chiral metamolecule, that is, the chiral quadrumer. Figure 8a illustrates the schematic of a chiral quadrumer array composed of two sets of orthogonally corner-stacked gold nanodisk dimers [46]. The quadrumer array is chosen deliberately for the following two reasons. First, it is easier to fabricate such structure with the current nanolithography method, and it is also possible to further enhance the chiral responses of more complex oligomer cluster arrays [47], [48], [49]. Second, the intrinsic CD signal for a single chiral quadrumer is extremely weak (Figure S7), especially compared with a single stereo-SRR dimer. Nevertheless, our numerical simulation result indicates that the quadrumer supercell array also exhibits strong CD responses (solid line in the lower panel, Figure 8b). A dip-to-peak profile centered around 1250 nm is observed due to the selective excitation of the hybridized longitudinal resonances, that is, the antibonding (ABDD) and bonding (BDD) dipole-dipole resonances (inset of Figure 8a). Compared with single chiral quadrumer whose ensemble CD signal is smaller than 0.1 (dotted line, magnified by 5 times for a better visualization), the positive CD peak located at 1320 nm is enhanced by 10 times. As shown in Figure S9, we also simulate the transmission spectra and calculate corresponding transmission CD of these structures under circular polarized illumination from the substrate side, which reveal slightly reduced CD values with negligible polarization conversion, thereby confirming the presence of intrinsic chirality in these structures [50]. The near-field distributions of LSPR modes shown in Figure S8 indicates that the CD peak (CD = –0.42) located at 1103 nm stems from the diffraction coupling of ABDD mode by (1, 1)_sub RA in the substrate. In addition, the sharp peak around 1320 nm is the (1, 0)_sup SLR mode by the diffraction coupling of the BDD mode in the superstrate. This coupling is even stronger than that of the ABDD mode, whose CD signal in transmission is about 0.60. The CD peak centered at around 900 nm is the transverse hybridized resonance and will not be discussed in this work.

Figure 8:

Enhanced CD spectra from chiral gold quadrumer arrays. (a) Schematics of the quadrumer array organized in C₄ symmetry. The supercell parameters are: period p = 850 nm, center distance between two adjacent quadrumer in a unit cell d = 430 nm, radius of the disk r = 80 nm, disk thickness t = 30 nm, gap size between the two disks on the same layer h = 10 nm, separation between the upper and lower layer s = 50 nm, and refractive index of the substrate n_sub = 1.80 and the superstrate n_sup = 1.50. Inset: the plasmon hybridization scheme between the longitudinal resonances of the two dimers on the upper and bottom layers. (b) The transmission (upper panel) spectra under RCP (blue lines) and LCP (red lines) incidences, and the corresponding CD in transmission of the array (solid line, lower panel). Inset: the charge distributions of the two CD peaks. The dotted line is the ensemble CD in transmission calculated based on the single quadrumer by neglecting the coupling between unit cells (magnified by 5 times for a better visualization), and the vertical dashed lines denote the spectral positions of RAs.

2.5 Dynamic tuning of transmission CD

One important nature of SLR, in general, is that its excitation efficiency depends dominantly on the spectral overlapping between RAs and LSPRs. Considering the fact that the excitation of SLRs don't relying on index-matching conditions, it is therefore envisioned that the chiroptical properties of a given structure can be dynamically controlled by manipulate the frequency detuning of LSPRs, an approach that one can easily play with by modifying the superstrate's index such as flowing in different liquid materials [111], or integrated with a phase-change material layer [70], [71]. This is of particularly advantageous for practical applications such as polarization engineering approaches, polarization sensitive imaging, and stereo display technologies, where the geometry of functional materials cannot be changed [69], [70], [71], [73], [74], [75], [76], [77], [78], [79]. For a qualitative assessment, we simulated the CD response of chiral quadrumer array embedded in different superstrates, as shown in Figure 9. The corresponding transmission spectra of chiral quadrumer array under LCP and RCP incidences are represented in Figure S10. As expected, the spectral positions and intensities for both ABDD and BDD modes are strongly modified under different superstrate indexes. When the refractive index is small (n_sup = 1.00), CD signals are relatively weak, given by –0.18 and 0.26 for the ABDD and BDD modes, respectively (black line, Figure 9a). The intensities of both CD peaks increase with the increasing refractive index, reaching a maximum value when n_sup = 1.50, where the CD in transmission are more than one times stronger than that of n_sup = 1.00 situation (red line, Figure 9a). By further increasing n_sup (>1.50), the intensities of the CD peaks start to decrease, where the CD in transmission with n_sup = 2.00 are comparable with that of n_sup = 1.00 (cyan line, Figure 9a).

Figure 9:

Dynamic tuning of CD responses. (a) The CD spectra in transmission under different superstrate indexes for the same chiral quadrumer array, where the sign of CD signal is switched around the spectral positions marked with yellow bars. (b) Transmission spectra under RCP (upper panel) and LCP (middle panel) incidences, as well as the CD responses (lower panel) for the quadrumer array under different superstrate indexes. The dashed lines show the spectral position of RAs, and the dotted lines in the lower panel denote the evolution of ABDD and BDD modes.

The transmission spectra under RCP and LCP incidences as well as CD spectra are depicted in Figure 9b. The dashed lines denote the spectral positions of the RAs, and the dotted lines in the lower panel of Figure 9b schematically show the evolution of ABDD and BDD modes. The RAs from the substrate stay unchanged with increasing n_sup, whereas the LSPRs band and RAs from the superstrate shift to lower energies. Nevertheless, the RAs in the superstrate red shift more rapidly compared with that of the LSPRs. Therefore, when n_sup is small enough (e. g., n_sup = 1.00), resonance band of the quadrumer locates far away from the RAs. The corresponding SLRs cannot be effectively excited, thereby leading to weak CD responses. When n_sup increases, the ABDD and BDD modes start to intersect with (1, 1)_sub and (1, 0)_sup RAs, respectively. In this case, strong diffraction coupling takes place between nearby unit cells, yielding enhanced CD responses. A further increase in refractive index (n_sup > 1.50) separate the LSPRs band and RAs again, which is the reason of decreasing CD responses. Interestingly, the sign of CD signals can be switched progressively around the spectral position marked with yellow bars in Figure 9a, which means that the quadrumer array has flipped into “opposite enantiomer” simply by changing its cover materials.

2.6 Modified Born–Kuhn model

The modified plasmonic Born–Kuhn model can be used to describe the underlying physics for the SLR-enhanced chiroptical response. The plasmonic Born–Kuhn model has found tremendous success in explaining the plasmonic chiroptical effects [11], [46], where the optical activity of plasmonic chiral materials can be interpreted as the coupling between two oscillators resonating perpendicularly to each other. The schematic is shown in the inset of Figure 10, where a yellow oscillator (u₁ = A₁e^–iωt) is placed at the upper layer and a blue oscillator (u₂ = A₂e^–iωt) is located at the bottom layer. In the modified Born–Kuhn model, each oscillator represents the collective SLR modes of top (bottom) resonance layer only. This treatment is a natural way of modeling longitudinal propagating resonances as the upper (lower) nanostructure layer plays, respectively, the dominate role when the RAs of the superstrate (substrate) are involved in the formation of SLRs. The coupling between the superstrate (substrate) RAs with the opposite side of layer is neglected. As a result, these oscillators inherit from the basic properties of RAs such as non-resonant features and independent spectral position determined only by surrounding materials themselves. In this way, the two collective resonances are independent. The damping of the collective resonances would be weaker than that of the localized resonances.

Figure 10:

Comparison between the calculated CD in transmission (circular points) and the fitted spectra from the Born–Kuhn model (solid line) for the chiral quadrumer array shown in Figure 8. Inset: the plasmonic Bohn–Kuhn model with only the longitudinal resonances of the upper and bottom layers are considered. The fitting parameters are ω₀₁ = 242.84 THz, ω₀₂ = 258.20 THz, γ₁ = 3.65 × 10¹² s^–1, γ₂ = 2.28 × 10¹³ s^–1, and κ₁₂ = 1.08 × 10²⁸ s^–2.

As a result, the dynamic equation of the SLR-enhanced chiral metamaterial responding to circularly polarized waves is given by the following Lorentzian equations of two coupled oscillators [46],

where ω₁₍₂₎ denotes the resonance frequency, γ₁₍₂₎ is the damping of the corresponding oscillator, κ₁₂ is the coupling strength of the two oscillators, s is the vertical distance between the two dimers, and g₁₍₂₎ denotes the coupling strength of the oscillator with the incident field. The CD responses are related to the nonlocality tensor Г(ω) [112], and one can get an analytical expression of the CD in transmission with a detailed derivation shown in the method section [46],

where N₀ is the charge carrier density. Equation (3) forms the central result of the modified Born–Kuhn model and agrees well with the simulation spectra from the quadrumer array, as shown in Figure 10. In addition, it has been shown that the diffraction coupling in the superstrate is stronger than that of the substrate, and the fitted result, indeed, reveals that the damping of the upper oscillator that embedded in the superstrate is weaker than that of the lower one in the substrate (γ₁ < γ₂), indicating a more effectively coupling with the RA in the superstrate, and the intensity of the positive CD peak is stronger than that of the negative one. Note that, in addition to the longitudinally hybridized resonance considered in the Born–Kuhn model, the transversely hybridized resonance for the upper and lower nanodisk dimers leads to the chiral resonance at around 900 nm, which explains the difference between the FDTD calculation and the Born–Kuhn model results in this spectral range.