1. Introduction

Chirality, which cannot be superimposed onto its mirror image, plays an important role in the biology, chemistry, physics and medicine [1–3]. Chiral metamaterials, a manmade engineering material, possess many peculiar optical properties such as circular dichroism [4,5], negative refractive index [6–9], extraordinary transmission [10], and asymmetric transmission (AT) [11–14]. Because AT is exceedingly useful in polarization transformers and polarization-controlled devices, the AT effect become a research hotspot in recent years [15,16]. AT refers to the transmission difference of circular polarization light illuminating from the front and back of chiral metamaterials [17,18].

Recently, researchers have proposed many complex three-dimensional (3D) and bilayer nanostructures to generate AT effect under circularly or linearly polarized light illumining [19,20]. However, the wide practical applications of 3D devices are limited because of their complicated fabrication process. Therefore, planar structures generating the mechanism of AT effect have become research hotspots owing to their easy fabrication and widely broadening potential polarization sensitive devices [21–23]. In a planar chiral nanostructure, AT effect can be achieved by utilizing novel mechanisms, such as the AT effect caused by trapped mode in gammadion-like nanostructure [21], AT effect caused by the mechanism of SPPs in tilted rectangular nanohole [22], and excited surface plasmons in the monolayer graphene film [23]. In an achiral nanostructure, the AT effect can be achieved by introducing the obliquely light, that is, extrinsic chiral [24,25].

In the above studies on 2D nanostructure, AT effects occur in either electric dipole modes or magnetic dipole modes. Electric dipole modes produce a peak in the transformation spectra, whereas magnetic dipole modes produce a valley in the transformation spectra [21,26]. This result provides a hint that a transmission peak of electric dipole mode can be split by inducing magnetic dipole mode.

In this work, the AT effects of rectangular nanohole/semicircular nanohole (RNSN) arrays are studied and compared with those of rectangular nanohole (RN) arrays. A semicircular nanohole is introduced to generate magnetic-dipole oscillation around RN, and this oscillation splits the original AT peak of the RN arrays. The effects of the structural parameters of RNSN on AT are also studied. The results not only confirm our initial hypothesis that magnetic-dipole oscillation can be used to split plasmon resonant peaks of an electric dipole oscillation but also offer a novel way to tune plasmon resonance.

2. Structure and computational method

Figure 1 depicts the schematic illustration and geometric parameters of the RNSN arrays, wherein a circular polarization light is incident along the -z direction. The film is 80 nm-thick. The rectangular nanohole is 520 nm long and 200 nm wide and tilted at 22.5° with respect to the horizontal direction (x axis). The straight side of the semicircular nanohole is parallel to the long side of the rectangular nanohole. The distance between the center of the semicircular and short sides of the rectangular nanohole is Δ, and the diameter of the semicircular side is d. The gap between the rectangular nanohole and semicircular nanohole is g. In this study, the periods of RNSN arrays are fixed at P_x = P_y = 630 nm in the x and y directions. The refractive index of gold derives from the experimental data of Johnson and Christy [27].

 

Fig. 1 (a) Schematic model of nanostructure arrays and (b) its unit cell with the associated parameters definition.

Download Full Size | PDF

The transmission spectrum and charge distribution of RNSN arrays are numerical simulated by the 3D finite element method software COMSOL Multiphysics. The periodic boundary conditions of the unit cell are set in the x and y directions, and the absorbing boundary conditions were set in the z direction. The perfectly matched layers locate at both ends of the whole model for absorbing the scattering light. The transmission is the ratio of output power to incident power, that is, T = P_out / P_in. When the right-handed circular polarization (RCP, + ) or left-handed circular polarization (LCP, + ) light is illuminated in the -z direction, the transmission light will possess both LCP and RCP light. So, the total transmission of RCP and LCP light along the -z direction are $T_{+}^{-z}=T_{++}^{-z}+T_{-+}^{-z}$and$T_{-}^{-z}=T_{--}^{-z}+T_{+-}^{-z}$, respectively. Similarly, the light along the + z direction are $T_{+}^{+z}=T_{++}^{+z}+T_{-+}^{+z}$and$T_{-}^{+z}=T_{--}^{+z}+T_{+-}^{+z}$, respectively. Thus, the conversion of transmission wave can be represented as $AT=T_{+}^{-z}-T_{+}^{+z}$or$AT=T_{-}^{-z}-T_{-}^{+z}$. According to the Lorentz Reciprocity Theorem, we can get $T_{++}^{+z}=T_{++}^{-z}$and$T_{-+}^{+z}=T_{+-}^{-z}$ [28]. Thus, the AT in the opposite direction satisfies$A{T}^{-z}=-A{T}_{}^{+z}$, that means AT value is opposite when the circularly polarized light illumine along the –z and + z direction. For the clearness and conciseness, in this study, we only consider circular polarized light along the –z direction, and define$AT=T_{-+}-T_{+-}$.

3. Results and discussion

Figure 2(a) shows the transmission and AT spectra of the RN arrays under LCP and RCP illuminating. The structural parameters of the rectangular nanohole are presented above. The step for the wavelength is 0.1 nm. For both T_+- and T_-+, a peak appears in the transmission spectra. AT effect also appears around this peak. Figure 2(b) shows the transmission and AT spectra of the RNSN arrays under LCP and RCP illuminating with g = 30 nm, d = 200 nm, and x = −100 nm. Two obvious peaks and one valley between them occur in the transmission spectra. We denoted them as Modes I, II, and III in Fig. 2(b). The introduction of semicircular nanohole leads to the splitting of the original AT peak. The Q-factor of Mode II approximately reaches 658.5.

 

Fig. 2 Transmission and asymmetric transmission spectra of (a) RN arrays and (b) RNSN arrays under circular polarized excitation.

Download Full Size | PDF

To gain deeper understanding on the nature of the above phenomena, surface charge distributions at the resonant wavelength of the top surface of the RN and RNSN arrays are calculated in the Fig. 3. Red and blue parts represent the positive and negative charges, respectively. As shown in Fig. 3(a, b), charges mainly distribute along the two longitudinal sides of the rectangular nanohole at λ = 657.9 nm and form the electric dipole oscillations P_R and P_L under right circularly polarized (RCP) and left circularly polarized (LCP) light illumination, respectively. In Mode I [Figs. 3(c), (d)] of RNSN, under RCP light illumination, positive charges mainly distribute on the right side of the semicircular nanohole, whereas negative charges mainly distribute on the other side of the rectangular nanohole. This charge distribution show that the electric dipole oscillation P_R-I along the rectangular nanonole contributes to the resonant wavelength. The charge distribution under LCP light illumination is similar to that under RCP light illuminating ensues, and the electric dipole oscillation P_L-I forms. The charge intensity of RCP illumination is stronger than that of LCP illumination, and this discrepancy leads to a positive AT signal in Mode I. In Mode II [Figs. 3(e), (f)] of RNSN, charges mainly flow along the metal film around the semicircular nanohole and form the magnetic dipole oscillations M_R-II and M_L-II under RCP and LCP illumination, respectively. The magnetic dipole oscillations are parallel to the incident and scattered fields, and cannot interact with each other. Therefore, the coupling between the formation of surface charge distribution and the free space is very weak [29,30]. This high-Q oscillation mode knows as the trapped mode, and resulting in the lower transmission conversion [21,26,31]. Thus, transmission valleys form around the resonant wavelengths. The direction of M_R-II is opposite to that of the incident light, reducing the oscillation of incident light on the metal film. So, the charge distribution has the lighter color in the Fig. 3(e) comparing with the Fig. 3(f). In Mode III [Figs. 3(g), (h)], under RCP light illumination, negative charges mainly distribute around the semicircular nanohole, whereas positive charges mainly distribute on the other side of the rectangular nanohole. These charge distributions form the electric dipole oscillation P_R-III along the rectangular and semicircular nanonoles. Similarly, these charge distributions form the electric dipole oscillation P_L-III under LCP light illumination. Moreover, the charge intensity of RCP illumination is stronger than that of LCP illumination, and this discrepancy leads to a positive AT signal in Mode III.

 

Fig. 3 The surface charge distributions of the RN (a)-(b) and RNSN (c)-(h) at resonance modes.

Download Full Size | PDF

In order to explore the influences of structural parameters of RNSN arrays on AT effect, the main parameters are simulated as follow. Figure 4 depicts the calculated transmission at different d values ranging from 180 nm to 220 nm while the other parameters are fixed as in the control group. The spectra show that Modes I and II do not shift obviously, whereas Mode III blue shift as d is considerably increased. Given that Mode I is mainly caused by electron oscillation in parts without semicircular nanohole, the increase in size of semicircular nanohole does not affect the electron oscillation. Thus, Mode I does not shift obviously. In Mode II, the resonance is caused by the magnetic-dipole oscillation crossing the gap between semicircular nanohole and rectangular nanohole, and the increase in size of semicircular nanohole does not considerably affect the magnetic-dipole oscillation. Compared with Mode I, Mode III is mainly due to electron oscillation in parts with semicircular nanohole, and the increase in size of semicircular nanohole reduces the effective refractive of index of the film, leading to a blue shift in Mode III.

 

Fig. 4 AT spectra of RNSN arrays varied diameter d of the semicircular nanohole.

Download Full Size | PDF

To investigate the effect of the position of the semicircular nanohole on the AT effect of RNSN arrays, we varied the position of the semicircular nanohole in the direction parallel and perpendicular to the side of the rectangular nanohole. Figure 5 depicts the AT spectra at different g values ranging from 20 nm to 40 nm. The spectra show that Modes I, II, and III all blue shift as g increases. In Modes I and II, the range of charge distribution increasingly becomes concentrated along the length of the rectangular nanohole as g increases. Thus, the effective electric dipole oscillation length decreases with the increase in g, causing the blue shift in Modes I and II. In Mode III, the effective electric dipole oscillation is not parallel to the direction of the semicircular movement, and the increase in gap reduces the effective refractive index of the film, causing the blue shift in Mode III.

 

Fig. 5 AT spectra of RNSN arrays varied the gap g between the semicircular and rectangular nanohole.

Download Full Size | PDF

Figure 6 shows the color map of AT value as Δ varies from −120 nm (move left) to 120 nm (move right) with other parameters fixed. The map shows that Mode I blue shifts whereas Modes II and III red shift when Δ approaches −60 nm. In Mode I, the charge distribution is increasingly becoming concentrated along the length of the rectangular nanohole as Δ approaches −60 nm. Thus, the effective electric dipole oscillation length decreases, causing Mode I to blue shift. In Mode II, when the position of the semicircular nanohole approaches −60 nm, the length of gap between the semicircular nanohole and the rectangular nanohole increases. The increase in magnetic-dipole oscillation length increases the effective refractive index, causing the red shift in Mode II. In Mode III, when the position of the semicircular nanohole approaches −60 nm, the increase in size of the semicircular nanohole reduces the effective refractive of index of the film, leading to a blue shift.

 

Fig. 6 Color map of AT values of RNSN arrays varied position of the semicircular.

Download Full Size | PDF

Additionally, the added nanoholes with other shapes were explored to verify the way of splitting AT peaks. As shown in Fig. 7, we simulate the transmission and AT spectra when the semicircular nanohole was replaced by circular and rectangular nanoholes, respectively. The charge distributions in Mode II under RCP illumination are shown, and also form the trapped mode. From the transmission conversion and AT spectra, the added circular or rectangular nanohole also splits the resonance peak. The splitting of the resonance peaks is caused by the magnetic by the magnetic dipole oscillation around the added nanohole. It demonstrates that we proposed splitting the AT signal by the trapped is a general way.

 

Fig. 7 Transmission and AT spectra about nanostructures added the circular and rectangular nanohole, respectively.

Download Full Size | PDF

4. Conclusion

In this study, the RNSN arrays are proposed to provide a method to split resonance peak. Transmission properties and charge distributions obtained by finite-element method illustrate the mechanism of AT signal splitting. We numerically present that AT signal splitting can be achieved by embedding a semicircular nanohole in RNSN arrays. Moreover, the mechanism of AT signal splitting was induced by the oscillation of magnetic dipoles. This study provides a novel method to effectively produce and tune AT effect, thus improving its detection sensitivity in the design of polarization transformers and optical devices.