1. Introduction

Periodic arrays of opaque metal nanostructures have attracted enormous interest because of their tunable and scalable spectral electromagnetic properties, such as optical activity [1, 2], circular dichroism [3, 4], and asymmetric transmission (AT) [5]. AT refers to the differences in transmission intensity of different handedness propagating in the same direction. In other words, AT is the difference between transmitted intensities for opposite propagation directions of the same light [6, 7]. This intriguing phenomenon has attracted significant interest because of its wide application in designing polarization transformers, detectors, polarization rotators, circulator, and optical isolator devices [8–16].

Over the past decades, many complex three-dimensional (3D) nanostructures have been explored to generate the AT effect in circularly or linearly polarized light [17, 18]. AT effect of helical plasmonic nanostructures originates from introduction of spatial asymmetry [19, 20]. Bilayer structures have also been introduced to generate the AT effect, which is a consequence of the interplay of electric and magnetic responses between two layers [21–25]. However, 3D devices hold disadvantages in wide practical applications because of their complicated fabricating process, especially at the micro- and nanoscales [19–21]. Recently, AT effects of 2D nanostructures have been studied owing to their easy fabrication and potential wide applications. In planar chiral nanostructures, AT effect can be attributed to excitation of enantiomerically sensitive plasmons [26–32] and excited electric and magnetic dipole responses in lossy low-symmetry metamaterials [33, 34]. In planar achiral nanostructures, AT effects can be achieved by introducing oblique incidence onto any lossy periodical array of nanostructures [15, 35, 36]. In the above-mentioned planar structures, further improving AT effects via a new mechanism remains a research hotspot.

In this study, tilted rectangular nanohole (TRNH) arrays in a square lattice are proposed to realize the AT effect. The resultant AT effects are then investigated by finite element method. Numerical results show two visible AT modes in the transmission spectra. Physical mechanisms of two modes are studied by introducing charge distributions. One mode is due to localized surface plasmon (LSP) resonance around the two ends of TRNH, and the other is due to surface plasmon polaritons (SPPs) on a gold film. The mechanism of SPPs provides a novel way to generate AT effect. Effects of structural parameters of TRNH on AT properties are also studied. These results provide a novel mechanism for realizing the AT effect and will aid the design of plasmonic devices to achieve an increased and tunable AT effect.

2. Structure and Computational Method

The proposed schematic planar TRNH arrays are shown in Fig. 1(a), where circular light is incident along the −z direction and structure parameters of unit cell of TRNH arrays depicted in Fig. 1(b). The thickness of the film is t. The square periods are P in both x- and y- directions. The rectangular nanohole has a length of l and a width of w. the tilted angle α represents the orientation angle between direction along length of rectangle and x-axis direction. The dielectric functions of gold are taken from the experimental data of Johnson and Christy [37]. Numerical simulations have been conducted to characterize TRNHs by using the FEM software COMSOL Multiphysics. 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.

 

Fig. 1 (a) Schematic of TRNH arrays with perforated gold film and (b) Its unit cell with the the associated geometric features.

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For the right-handed circular polarization (RCP) light illuminating along −z direction, $T_{-+}^{-z}$and$T_{++}^{-z}$represent transmission coefficients of (left-handed circular polarization) LCP and RCP light, respectively. The same principle is applicable to incident LCP light propagating along + z direction. For a planar chiral medium, it has been verified that$T_{++}^{+z}=T_{++}^{\text{-}z}$, and $T_{-+}^{+z}\text{=}{T}_{+-}^{-z}$ [29].

In this paper, light is always incident from −z direction. Therefore, AT can defined as the following equation for a clear and concise expression,

3. Results and Discussion

Figure 2(a) shows the transmittance spectra of TRNH arrays under LCP and RCP light illumination with the following parameters: l = 520 nm, w = 200 nm, t = 80 nm, α = 22.5°, and P = 620 nm which are used as a controlled group in this study. Two significant resonance modes at λ_I = 670 nm (Mode I) and λ_II = 651 nm (Mode II) are observed in the transmittance spectra for both RCP and LCP light illuminations. Figure 2(b) reveals the appearance of notable AT effects at the two modes. The difference in T₊₋ and T₋₊ leads to the AT effect.

 

Fig. 2 Transmission (a) and AT (b) spectrum spectra of TRNH arrays under RCP and LCP light illuminations with structural parameters.

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The physical mechanism of AT effect is then investigated. Figure 3 shows the normalized charge distribution at the two resonant modes. In Mode I, under RCP illumination, charges mainly distribute on two ends of the rectangular nanohole. This distribution can be attributed to LSP resonance [Fig. 3(a)]. Strong LSP resonance leads to additional energy dissipation at two ends of the nanohole; such dissipation is responsible for circular polarization conversion and low transmission, as shown in Fig. 2(a). Under LCP illumination, weak LSP resonance occurs [Fig. 3(b)]. The difference in resonance intensities results in an AT effect at Mode I. in Mode II, under RCP light illumination, charges mainly focus at two longitudinal sides of the rectangular nanohole [Fig. 3(c)]. The characteristic charge distributions show that SPPs on the gold film contribute to the AT effect. Under LCP illumination, a charge distribution similar to that under RCP illumination ensues. Charge intensity of LCP illumination is stronger than that of RCP illumination; this discrepancy leads to a positive AT signal in Mode II.

 

Fig. 3 Charge distributions of TRNH arrays at resonant wavelength for (a) (c) RCP and (b) (d) LCP light illumination. The resonances are labeled mode I and II.

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The influence of period on AT effect is analyzed by varying P from 600 nm to 640 nm with the other parameters fixed as those in Fig. 2. Figure 4 shows transmission and AT spectra of TRNH arrays. As P increases, Modes I and II red shift. Maximum intensities of both T₊₋ and T₋₊ are achieved at P = 630 nm. In the AT spectrum in Fig. 4(c), two modes are observed. With increasing P from P = 600 nm to P = 640 nm, Mode I red shifts from λ_I = 662 nm to λ_I = 694 nm, whereas Mode II red shifts from λ_II = 634 nm to λ_II = 670 nm. When a gold film is illuminated by incident light, SPPs are generated on the surface. The relationship between SPP wavelength, λ_SPP, and incident wavelength is as follows:

 

Fig. 4 Transmission spectra of TRNH arrays under (a) LCP and (b) RCP light illuminations and (c) AT spectrum of with different periods.

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Figure 5 displays the effects of structural parameters on AT properties. Figure 5(a) shows the AT of TRNH arrays with length l varying from 500 nm to 540 nm in the controlled group. Resonant wavelength and intensity of Mode I strongly depend on l given that Mode I results from LSP resonance around the rectangular nanohole, and LSP resonance is strongly dependent on shape, size, and morphology of nanostructures. On the contrary, Mode II exhibits no remarkable shift as a result of the presence of SPPs on the film, and the period remains unchanged, as indicated in Fig. 5(a). Similarly, Mode I strongly depends on the width w of the rectangular nanohole, whereas Mode II show no visible shift with increasing w. Figure 5(c) illustrates the effects of film thickness on AT properties. With increasing t from t = 72 nm to t = 88 nm, Mode I blue shifts from λ_I = 676 nm to λ_I = 668 nm, and Mode II red shifts from λ_II = 648 nm to λ_II = 656 nm. With increasing t, the cross section of charge oscillation increases and results in the decreased effective aspect ratio of charge oscillations and blue shifting of Mode I. In Mode II, charges accumulate at the longitudinal sides of the rectangular nanohole and pass through the film. Total length of the charger oscillation is the sum of the period and film thickness. With increased t, total length of charge oscillation increases, leading to the red shift of Mode II.

 

Fig. 5 AT spectra of TRNH arrays with (a) different length l, (b) different width w and (c) different thickness t.

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The effects of tilted angle on AT properties of TRNH arrays are evaluated by varying $\alpha$from $\alpha =0°$to$\alpha =45°$. The other parameters are the same as those in the controlled group. AT properties are strongly dependent on $\alpha$(Fig. 6). When$\alpha =0°$,$\alpha =45°$, no AT effect can be observed in the spectra because TRNH assumes symmetry. AT effect can be observed only when the orientation angle$\alpha \ne n\times 45°,n\in Z$and leads to an intrinsic lack of mirror symmetry of the array. Charge distributions at the peak and valleys in the AT spectra show the resonant modes. The mode around λ = 620 nm for $\alpha =7.5°$ is due to multiple dipole charge oscillation. The mode around λ = 650 nm for $\alpha =37.5°$ is due to SPPs on the film and involves the same mechanism as that in Figs. 3(c) and 3(d). The mode around λ = 660 nm for$\alpha =30°$is due to LSP resonance around the two ends of the rectangular nanohole and involves the same mechanism illustrated in Fig. 3(a).

 

Fig. 6 AT spectra of TRNH arrays different orientation angle α with fixed length l = 520 nm, width w = 200 nm and t = 80 nm.

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4. Conclusion

In conclusion, TRNH arrays in a square lattice are proposed to generate AT effects. Transmission properties and charge distributions obtained by finite element method illustrate the AT properties and their mechanism. As LSP or SPP occurs at around TRNH under circular polarization light excitation, remarkable AT effects are achieved. The mechanism of SPPs provides another way to achieve AT effect, especially, when the period of arrays matches the wavelength of SPPs. AT properties also strongly depend on structural parameters, such as length, width, thickness, and tilted angle of the TRNH. Results provide a novel method for effectively producing and tuning the AT effect, thus widely broadening potential plasmonic device applications, such as asymmetric wave splitters and optical isolators.