Giant circular dichroism induced by tunable resonance in twisted Z-shaped nanostructure

Circular dichroism (CD) is useful in molecular chemistry, pharmaceuticals, and bio-sensing. In this paper, twisted Z-shaped nanostructure (TZN) is proposed to achieve giant CD. The TZN is composed of three vertical and twisted nanorods. Given that the resonance of vertical nanorod is only observable for left circularly polarized light excitation but is subdued for right circularly polarized light excitation, which leads to the giant CD effect approaching 88%. The subdued resonance of vertical nanorod can be excited by rotating the bottom nanorod. The CD properties can be tuned by the length of nanorods and the gap between them. These results would guide the design of plasmonic chiral nanostructures for achieving giant CD effect. © 2017 Optical Society of America OCIS codes: (260.2110) Electromagnetic optics; (240.6680) Surface plasmons; (160.1585) Chiral media; (250.5403) Plasmonics; (260.5740) Resonance. References and links 1. S. M. Kelly, T. J. Jess, and N. C. 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CD may arise from many different modes.3D helix and helix-like ACPNs typically produce CD owing to the significant interactions between electric and magnetic resonance [12][13][14][15][16][17].2D planar ACPNs, such as gammadions, present relatively small CD resulted from the existence of only electric dipole mode [18,19].Some previous studies have considered oblique excitation for enhancing CD [20][21][22][23].Under LCP and RCP excitations, large CD is generated because of the existence of electric and magnetic modes.Bi-layer twisted ACPNs, such as twisted-arc, bi-layer cross, and coupled-oscillator, exhibit larger chirality than singlelayer ones, where bonding and anti-bonding modes exist [24][25][26][27][28][29].Researchers in recent works have shown that plasmonic Fano resonance can enlarge the optical chirality by 30% in 2D planar metallic nanostructure.In these studies, CD signals appear at the same resonant modes for LCP and RCP excitations [30][31][32][33].If CD signals are designed at different modes for LCP and RCP excitations, giant CD effect would occur.
In this paper, the twisted Z-shaped nanostructure (TZN) arrays are proposed and its optical properties are theoretically investigated by finite element method (FEM) simulations.The absorption spectra exhibit that an off-resonance dip for LCP and an anti-bonding resonance peak for RCP clearly occur at the same wavelength.As a result, a pronounced CD is generated with a maximum of 88%.The current density distributions demonstrate that the resonance of vertical nanorod is only excited for LCP but is subdued for RCP light.The effects of geometric parameters on CD are also studied.These findings can guide the design with strong optical chirality for practical application in bio-sensing.

Structure and computational method
The TZN in this study is composed of three mutually vertically displaced and twisted nanorods, as shown in Fig. 1(a).The front and top views with the definition of the associated parameters are displayed in Figs.1(b) and 1(c).The top and bottom nanorods are in the same geometry parameters with fixed width of 30 nm and height of 30 nm, and varied lengths L. The vertical nanorod has fixed length of 30 nm and widths of 30 nm, and varied height H. G denotes the gap between the vertical nanorod and the top or bottom nanorods; θ expresses the rotary angle of the bottom nanorod with respect to x axis, θ = 90° in the TZN [Fig.1(c)].The TZN can be left-or right-handed depending on the rotary angle of the bottom nanorod.In this study, the periods of the TZN arrays are fixed with P x = 300 nm and P y = 300 nm in the x and y directions, respectively.Three-dimensional finite element method software COMSOL Multiphysics is used to calculate the transmittance of the TZN arrays.The minimum mesh size (3 nm) is 10 times less than the minimum width (30 nm) of the TZN, which satisfies the COMSOL stability criteria (convergence).The refractive index of sliver is taken from Ref [34].and the refractive index of air is fixed as 1.The excitation sources are RCP and LCP light along the -z direction and the magnitude of the incident electric field is set at 1 V/m.The infinite array is simulated using unit cell with periodic boundary conditions along the x and y directions.The Perfectly Matched Layers are applied at the top and bottom of the computational domain for absorbing light which pass through the Ports.The transmittance is defined as T = P out / P in , which is the ratio of output power to incident power.The absorption is defined as A = 1-T-R, where R is reflectivity.The optical chirality is defined as CD = A LCP − A RCP , where A LCP and A RCP is the absorption under LCP and RCP illumination.

Results and discussion
The absorption and CD spectra of structures with different parameters are calculated among the wavelengths from 0.5 µm to 1.0 µm.Figure 2 absorption spectra of A LCP and A RCP leads to a significantly large CD of 88% (the red line in Fig. 2(a)).For simplicity, the resonance modes are divided into modes I, II, and III (labeled as Mode I, Mode II, and Mode III) in the CD spectrum.The CD spectra for right-and lefthanded enantiomer are exactly mirror symmetric to each other.In order to investigate the associated physical dependencies of absorption spectra, the absorption of the TZN arrays under x and y polarization excitations are also studied [Fig.2(b)].Three peaks of λ = 0.65 µm, λ = 0.71 µm, and λ = 0.78 µm appear in the absorption spectrum.The absorption of the TZN arrays under x and y polarization excitation are overlap, which is resulted from the same parameters of top and bottom nanorods along x and y directions.Thus, the linear birefringence is negligible [26][27][28].Given that a linearly polarized light consists of equivalent LCP and RCP light, the wavelength position of the absorption peaks for circular polarized light are coincident with that of linearly polarized light.
The modes of different peaks are emulated to understand the absorption mechanism of TZN arrays under linear polarization excitation.Figure 3(a) plots the proportional current densities at absorption peaks of the TZN for x polarization excitation.The red arrows denote the direction of current densities.The purple arrows in Fig. 3(b) represent the equivalent electric dipole moments of nanorods.At λ = 0.65 µm, the excited currents occur in the top and vertical nanorods, while the current in the bottom nanorod is relatively weak.As a result, effective electric dipole moments occur in the top and vertical nanorods.The courterpropagating electric dipoles of the top and vertical nanorods create bright anti-bonding mode [35,36].Correspondingly, at λ = 0.71 µm, the major current densities are distributed in the top and bottom nanorods and associated electric dipole moments form anti-bonding mode.Electric dipole mode occurs at λ = 0.70 µm for one horizontal nanorod structure (not shown in this paper).At λ = 0.78 µm, the intense currents in the top and vertical nanorods form an effective electric dipole, which is regarded as the dark bonding mode.
Using this argument, the proportional current densities and the equivalent electric dipole moments at the absorption peaks of the TZN for LCP and RCP excitations are also performed, as depicted in Figs.3(c)-3(f).For LCP, the current densities of three nanorods reveal bright anti-bonding mode at λ = 0.65 µm and dark bonding mode at λ = 0.79 µm.The pronounced off-resonance dip at λ = 0.71 µm is due to the destructive interference between the narrow bright mode and the broad dark mode.For RCP, at λ = 0.71 µm, the strong effective current densities are concentrated in the top and bottom nanorods.Accordingly, antibonding mode is induced.In the vertical nanorod the currents are negligible and the resonance is subdued; this phenomenon differs in LCP and RCP excitations.In other words, the effective charge oscillations in the vertical nanorod are polarization-controlled for circular polarized light, thereby resulting in the different dipoles coupled modes.The giant chirality in the absorption spectra emerges at the distinct resonance modes for LCP and RCP excitations.The chiral system of the TZN can be viewed as a right-handed enantiomer in which resonance is easier to be excited under LCP than under RCP illumination.
To explore the CD effects of TZN arrays for LCP and RCP excitations, rotary angle θ is changed from 0° to 90° with fixed H = L = 140 nm, and G = 20 nm.Under RCP excitation, the subdued resonance in vertical nanorod is excited gradually as θ decreases [Fig.4(a)].Figure 4(b) illustrates that the amplitude of the three CD modes weaken distinctly, and the modes exhibit smooth spectrum shift with the decrease in θ.As θ = 0°, the TZN is achiral and the three modes disappear.The shift of Modes I and II is due to the change of the asymmetric resonance line shape.Therefore, rotating the bottom nanorod enables a way to switch on and off the resonance of TZN.The spectra of varied parameters of TZN arrays are sequentially investigated to probe the mechanism of resonance in enhancing the CD effect.Gap G is first changed from 20 nm to 40 nm with fixed H = L = 140 nm, and θ = 90° [Fig.5(a)].Modes I and II blue shifts, Mode III red shifts, and the magnitudes of CD signals decrease with the increase in G. Mode I is ascribed to the dark bonding mode for LCP, which presents the attraction between electric dipoles.As G increases, the attraction decreases, thereby leading to a decrease in the length of equivalent electric dipole oscillations and blue-shift of Mode I. On the contrary, Mode III is attributed to the bright anti-bonding mode showing repulsion between electric dipoles.An increase in G can decrease the repulsion, thus rendering the increased effective electric dipole moments and red-shift of Mode III.Mode II exhibits blue-shift because of the asymmetric narrowed resonance line shape with the increase in G.The increase in G causes the near-field coupling between the top or bottom nanorods and the vertical nanorod weakened.Accordingly, the resonance strength intensely weakens, thereby leading to the diminishing of CD signals.The value of H and L is relevant to the effective electron oscillation length in three nanorods.When H = L = 140 nm, the wavelength of off-resonance dip for LCP matches that of antiboding mode peak for RCP, then CD spectrum presents the highest value.In this paper, the period is fixed at P x = 300 nm and P y = 300 nm.With the further increase of the period, the resonant wavelengths exhibit red-shift (not shown in this paper).Experimentally, the TZN arrays can be fabricated through three runs of aligned electron beam lithography.The TZN is composed of three separated nanorods, so the displacement between nanorods layers along the x and y directions are inevitable during experimentation.To demonstrate the effect of the displacement, the CD spectra of different relative displacements are discussed, as shown in Fig. 6. Figure 6(a) reveals the displacement Δx between the vertical and bottom nanorod along the x direction (the top and vertical nanorod layers is well-aligned).Figure 6(b) illustrates the displacement Δy of top nanorod and vertical nanorod along the y direction (the bottom and vertical nanorod are well-aligned).Figure 6 show that the tiny displacement does not affect the CD properties obviously.

Conclusion
The TZN with three nanorods is proposed to produce giant CD of 88% at the distinct resonance modes.The TZN can be viewed as a right-handed enantiomer in which resonance is easier to be excited under LCP than under RCP illumination as a result of the polarizationcontrolled feature.The simulations reveal that the chirality in the absorption spectra is attributable to the different dipoles coupled modes of three nanorods for LCP and RCP due to the polarization-controlled characteristic in vertical nanorod.The subdued resonance of vertical nanorod under RCP can be excited by rotating the bottom nanorod, thereby resulting in the on and off switch of the resonance.Moreover, CD properties are intensely dependent on the length and gap of nanorods.These results can be helpful in understanding optical chirality induced by tunable resonance and can also guide the design of artificial chiral plasmonic nanostructures with large chirality.

Fig. 1 .
Fig. 1.Configuration of TZN arrays and parameters definition (a), where the unit cell with the associated geometric features are designated in (b) x-z plane and (c) x-y plane.

Fig. 2 .
Fig. 2. The absorption and CD spectra of TZN arrays (a) under LCP and RCP illuminations; (b) under x and y polarization excitations.

Fig. 3 .
Fig. 3.The proportional current densities and the equivalent electric dipole moments at the absorption peaks for TZN under x polarizations excitation (a) and (b); under LCP excitation (c) and (d), and RCP excitation (e) and (f).The red arrows denote the direction of current densities; the black arrows reveal the direction of small current densities distributions; the purple arrows represent the equivalent electric dipole moments of nanorods.

Fig. 4 .
Fig. 4. The absorption and CD spectra of TZN arrays with varied θ values.

Figure 5 (
b) displays the CD spectra of H and L varying synchronously from 120 nm to 160 nm with fixed geometric parameters G = 20 nm and θ = 90°.Modes I, II, and III exhibit linearly red-shift with H and L increasing.This phenomenon is resulted from the extension of the effective electron oscillation length in three nanorods for LCP and RCP.Then the effect of the height of the vertical nanorod H on CD with fixed L = 140 nm, G = 20 nm, and θ = 90° is presented in Fig.5(c).The obvious red-shifts of Modes I and III are due to the extended electric dipolar moment in resonance for LCP with the increase in H. Mode II originates from the anti-bonding mode of the top and bottom nanorods.The variation in H slightly affects the shift of Mode II compared with the shifts of Modes I and III.Figure5(d) reveals the influence of the variation in L on CD with fixed H = 140 nm, G = 20 nm, and θ = 90°.As L increases, the three modes all present obvious red shift by reason of the extended electric dipolar moments.In Figs.5(c) and 5(d), the CD signals are maximal at the offresonance dip as H = L = 140 nm on account of matching resonant wavelength of nanorods.

Fig. 5 .Fig. 6 .
Fig. 5.The CD spectra of TZN arrays with (a) varied G values, (b) varied H and L values, (c) varied H values, and (d) varied L values.