Giant circular dichroism and its reversal in solid and inverse plasmonic gammadion-shaped structures

Shan Wu; Pingping Qu; Jianqiang Liu; Dandan Lei; Kaiyin Zhang; Shutao Zhao; Yongyuan Zhu

doi:10.1364/OE.24.027763

1. Introduction

Linearly polarized light can be shown to consist of right and left handed circularly polarized components with equal intensity. For the right (left) handed circularly polarized light (CPL), an observer looking toward the light source will see the electric vector rotating in a clockwise (counterclockwise) sense. Circularly polarized light is chiral, that is, cannot be superimposed onto its mirror image. A chiral molecule has different absorption when illuminated with the left or right CPL, this effect called circular dichroism (CD) [1, 2]. CD spectrum reveals chiral properties of molecules and biomolecules, which is a useful tool in spectroscopy techniques for the detection and characterization of biomolecules [3]. In general, the CD response is weak. For example, for most small molecules, the dissymmetry factor g<10⁻³ at visible wavelengths [4], where the dissymmetry factor is defined as g≡|2(A_ll-A_rr)/(A_ll + A_rr)|, A_rr and A_ll are the absorption rate in right and left CPL [1]. In recent years, some plasmonic structures are employed to enhance the CD responses, ranging from single chiral particle [5,6] to two-dimensional chiral structures [7–9], and solid metallic nanospirals [10,11], to complex chiral arrangements of metallic nanoparticles [12,13]. The conventional chiral structures are built up by the metallic nanoparticles, such as rod particle [14], L-shaped particle [15], gammadion-shaped particle [16–18], and the others [19, 20], on which the localized plasmonic resonance can be excited. The interaction of the plasmonic resonances in individual nanoparticle or its component via the strongly localized electric fields enhances the CD response [21, 22]. On the other hand, based on Babinet's principle, an inverse metallic structure, i.e. a nanoaperture array in a continuous metallic film also exhibits cavity plasmonic resonance with the strongly localized electric field. In complex plasmonic nanostructures consisted of solid and inverse metallic nanostructure, elemental plasmon modes can also couple and exhibit novel properties, such as electromagnetically induced transparency (EIT) [23], dispersionless optical activity [24, 25], asymmetric transmission and optical rotation [26]. In this work, we investigate the CD response of solid and inverse gammadion-shaped metallic structure. A giant dissymmetry factor g = 1.58 can be obtained at wavelength 922 nm, which is three orders of magnitude higher than those found in common biomolecules. Furthermore, we also show that the sign of the CD spectrum may be controlled by tuning the relative distance between the solid and inverse gammadion-shaped structures. Further analysis reveals that the Fabry-Perot (F-P) resonance of cross-polarization conversion of electric field governs this change.

2. Material design and calculation

The three-dimensional schematic view of the solid and inverse gammadion-shaped metallic structure is shown in Fig. 1(a), with the geometrical parameters illustrated in Fig. 1(b). The whole system consists of two metallic structures separated by the silica with thickness d: one being a right-twisted gammadion metallic nanoparticle array embedded in silica substrate and the other being a left-twisted gammadion nanoaperture array in metallic film covering the sample surface. A circularly polarized light propagates in a positive z direction. The CD spectra are calculated by the finite-difference time-domain (FDTD) method [27]. The Drude-model dielectric function is used for metal (silver) with a plasma frequency of 1.374 × 10¹⁶ rad/s and a collision frequency of 2.02 × 10¹⁴ rad/s [28]. The permittivity of silica substrate is set as 2.25, and background environment is assumed to be air with a permittivity of unity.

Fig. 1 (a) Three-dimensional schematic view of the solid and inverse gammadion-shaped metallic structure. (b) Geometrical parameters of the unitcell: period P = 700 nm, l = 300 nm, w = 100 nm and the thickness of gammadion-shaped metallic particle and aperture t = 50 nm with the distance between the upper and lower layers d = 160 nm.

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3. Results and discussion

In our calculation, the CD is defined as

CD = A_{r r} - A_{l l} = T_{l l} - T_{r r}

where A and T is the absorbance and transmittance for the right (rr) and left (ll) CPL incident waves (the first and the second subscript means out and in, respectively.), which are given by A = 1-R-T, where R is reflectance. The equality in (1) follows from R_rr = R_ll, R_rl = R_lr = 0, and T_rl = T_lr = 0, which can be guaranteed from the reciprocity theorem and the C₄ rotational symmetry of the structure, respectively [16, 17, 29]. Figure 2(a) shows the transmittances of right (T_rr) and left (T_ll) CPL and the CD spectrum. There are two CD peaks at wavelengths about 778 nm and 922 nm. For these two peaks, their amplitudes reaches 0.32 and 0.51, and the dissymmetry factors g are 1.17 and 1.58, respectively, which are larger than those of single layer and bilayer solid gammadion structures [18].

Fig. 2 (a) The calculated right (black solid line) and left (red dash line) circular polarized transmission spectra and the CD spectrum (blue short dash dot line) of the system. (b) The calculated electric field E_xy (black solid line), E_yy (red dash line) components and the phase difference (blue short dash dot line) of the transmitted light with the y-polarization incident light.

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To investigate the physical mechanism of the above results, we convert the circular polarized transmission into linear polarized transmission. Based on the Jones matrices [30] we have

(\begin{matrix} t_{r r} & t_{r l} \\ t_{l r} & t_{l l} \end{matrix}) = \frac{1}{2} (\begin{matrix} (t_{x x} + t_{y y}) + i (t_{x y} - t_{y x}) & (t_{x x} - t_{y y}) - i (t_{x y} + t_{y x}) \\ (t_{x x} - t_{y y}) + i (t_{x y} + t_{y x}) & (t_{x x} + t_{y y}) - i (t_{x y} - t_{y x}) \end{matrix})

where t_ij is the transmitted coefficient, and the subscript ij stands for incident polarization j and transmitted polarization i. For a Lorentz-reciprocal structure, the scattering matrix must be symmetric, requiring t_xy = -t_yx [21, 29–31]. Furthermore, our structure has the C₄ rotational symmetry with t_xx = t_yy [29]. And thus, t_rl = t_lr = 0 in the Eq. (2). The CD can be calculated as

CD = {| t_{l l} |}^{2} - {| t_{r r} |}^{2} = - 2 Im [t_{x y}^{*} (t_{x x} + t_{y y})] = - 4 E_{y y} E_{x y} \sin Δ φ

where E_yy and E_xy are the normalized electric field amplitudes in the linear polarization transmission, and $Δ φ = φ_{y y} - φ_{x y}$ is the phase difference. From Eq. (3), it is obvious that the prerequisite for CD is non-zero E_yy, E_xy and Δφ. Generally, for the conventional single-layer metallic perforated structures, the excited surface plasmon polaritons (SPPs) cannot produce the linear polarization transmission conversion, i.e. E_xy = 0. It is because the incident linear-polarized light cannot excite the SPPs modes along the direction perpendicular to the incident electric field. However, for the special structure, the excited localized surface plasmons (LSPs) can drive the induced charges into another direction, forming linear polarization conversion, i.e. E_xy≠0 [28]. Here, in our proposed structure, utilizing the scattering of the LSPs excited in lower gammadion-shaped metallic particles, the excited SPPs modes in upper metallic film is not only along the direction of the incident electric field but also along the direction perpendicular to the incident electric field. Figure 2(b) shows the normalized E_xy, E_yy and Δφ spectra in far field. It can be seen from Fig. 2(b) that the spectral line shape is similar to that of the enhanced optical transmission (EOT) in metallic perforated structures [32]. There are three peaks A (776 nm), B (943 nm) and C (1083 nm) in E_xy spectrum corresponding to the SPPs [A(1,0), G(1,1) and G(1,0), where A stands for air-metal surface and G for silica-metal surface, (m,n) is the reciprocal vector.]. For the E_yy spectra, the peaks A and B exist, however, peak C disappears. The phase difference $Δ φ \in (0 °, - 180 °)$ in the wavelength range from 750 nm to 1058 nm. Thus, based on Eq. (3) we can get a large positive CD effect. However, for the peak C there is a near-complete cross-polarization conversion, i.e. E_yy≈0, resulting in a near-zero CD. It is due to the destructive interference of electromagnetic wave emitted from the different zone on the upper surface. Figure 3 represents the electric field E_xy and E_yy components of the peaks A, B and C on the air-metal surface. Unlike the electric field for peaks A and B, the E_yy component of peak C have an opposite phase in the zone (1) and zone (2) [Fig. 3(f)]. These act as two anti-parallel dipoles whose emitted electromagnetic waves interfere destructively in far field, leading to a near-zero E_yy component.

Fig. 3 The electric field E_xy (a-c) and E_yy (d-f) components of peaks A, B and C on the air-metal surface, respectively.

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In addition, we discover that the sign of the CD spectrum may be controlled by tuning the distance between the two metallic layers. Figure 4(b) depicts the two-dimensional grayscale image of the CD with distance d. There is an inversion of the CD sign when the distance d increases. In order to survey this change of the CD, we plot the CD spectrum at wavelength 923 nm [Fig. 4(c)]. As the distance d increases, the CD value firstly increases to 0.52 at d = 160 nm, and then decreases, even vanishes completely at d = 260 nm. When d is larger than 260 nm, the CD sign is inversed. From Eq. (3), one can conclude that the sign of the CD is determined by the phase difference Δφ. Thus, we show the CD spectra and the phase difference Δφ for the thickness d = 160 nm and 340 nm in Fig. 4(a). Different from the sample of d = 160 nm, the phase difference $Δ φ \in (0 °, 180 °)$ in the wavelength range from 750 nm to 1058 nm as d = 340 nm. It causes the inversion of the CD sign.

Fig. 4 (a) The CD spectra (black solid and red dash line) and the phase difference Δφ (blue dash dot and short dot line) for the distance d = 160 nm and 340 nm. (b) Two-dimensional greyscale image of the optical transmission with the distance d. (c) The CD (at wavelength 923 nm) vs. the distance d (i.e. along the black dash line pointed by the arrow).

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The change of the CD sign represents the different interaction between the right- and left circularly polarized light and metallic structures. It is one of important physical features of our mixed structures. The conventional reversals of the CD sign have three cases. Firstly, when a chiral structure changes its handedness, its CD sign can be reversed without the deep physical reasons [18]. Secondly, the reversal of the CD sign occurs in different wavelength range due to the different coupling mode between the localized electric and magnetic resonances [21]. Thirty, the sign of the CD at a given wavelength can be controlled by tuning the relative wavelength of the plasmonic hybridized mode [15] or the conductivity of dielectric in hybrid metamaterial [33]. To reveal the underlying mechanism for the change of the CD sign in our proposed structures, we plot the two-dimensional greyscale image of the electric field component E_xy with the distance d in Fig. 5. A dark line with E_xy = 0 in Fig. 5 (red circular line) is just the dividing line between the negative and positive CD in Fig. 4(b), which depends linearly on the distance d, which is a Fabry-Perot (F-P) resonance mode with the effective index n_eff = 1.68.

Fig. 5 The two-dimensional greyscale image of the electric field component E_xy with the displacement d of the middle silica layer. The red circular and green square lines represent the F-P resonance and Rayleigh diffraction modes, respectively.

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Assumed that the system is illuminated by the y-polarized plane wave propagating in the positive z direction. The electric field E_xy is reradiated by the SPPs propagating along the x direction (defined as SPP_x) in the upper metallic film excited by the scattering component E_LSPx of the LSPs resonances produced in lower gammadion-shaped metallic particles. E_LSPx in the positive z direction can be written as

E_{L S P x +} = E \cos (ω t + \frac{2 π n_{e f f}}{λ} z)

Via the reflection of the upper metallic film, it would be given by

E_{L S P x -} = E \cos (ω t - \frac{2 π n_{e f f}}{λ} z + π)

where n_eff is the effective index. Thus, total electric field would be given by

E_{L S P x} = E_{L S P x +} + E_{L S P x -} = 2 E \sin (\frac{2 π n_{e f f}}{λ} z) \cos (ω t + \frac{π}{2})

When the distance between the two metallic layers d = z₀ = λ/2n_eff, the stationary wave (i.e. Fabry-Perot resonance) is formed with E_LSPx = 0 in the upper metallic film. Note that no SPP_x is excited at this condition. Thus, the E_xy = 0, and CD = 0.

As d = z_{0} + z',

E_{L S P x} = 2 E \sin (\frac{2 π n_{e f f}}{λ} z') \cos (ω t + \frac{π}{2} + π)

Compared to d<z₀ [Eq. (6)], the phase increases a π radian. Subsequently, the phase difference Δφ decreases a π radian, resulting in an inversion of the CD sign. Figure 5 also shows a clear anticrossing behavior with the splitting energy of 40 meV, which could be attributed to a strong coupling [34, 35] between the F-P modes and the Rayleigh diffraction modes [36–38] in the metal-silica interface.

4. Conclusion

In conclusion, we have proposed a solid and inverse metallic structure composed of a right-twisted gammadion metallic nanoparticle array and a left-twisted gammadion nanoaperture array. A strong circular dichroism can be obtained. And the sign of the CD responses can be reversed through the increases of the distance between the two metallic layers. Further, we have also discussed the physical mechanism of circular dichroism, and demonstrated that the changes of the CD are heavily dependent on the polarization conversion E_xy. Our work provides a fundamental understanding of circular dichroism in the complex plasmonic structures as well as the potential applications in switchable metamaterials.

Funding

National Natural Science Foundation of China (NSFC) (Grant Nos. 11264021, 51271059, and 11604052); and Anhui Provincial Natural Science Foundation (Grant Nos. 1608085MA10); Talent Foundation of Anhui Provincial Higher Education (No. gxyqZD2016189).

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Giant circular dichroism and its reversal in solid and inverse plasmonic gammadion-shaped structures

Abstract

1. Introduction

2. Material design and calculation

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (5)

Equations (8)

Optics Express