1. Introduction

Few-layer metasurfaces have recently attracted tremendous interests to achieve emergent functionality to control and manipulate light including perfect absorption [1–3], antireflection [4–6], polarization conversion and amplitude-phase control of light [7]. These few-layer metasurfaces are usually composed of two or more layers of metallic structures with different geometric designs. To understand the electromagnetic property of the few-layer metasurface, the entire structure can be considered as a single-layer homogenous thin film with certain effective permittivity (ε) and permeability (μ) that are responsible for the functionality (e.g. perfect absorption [2]). Recent studies show that each layer in the few-layer metasurface acts as a homogenous thin film (meta-film) that allows light to propagate through or to be reflected at the interfaces between meta-films [3,4,7]. Light reflected at each layer results in constructive or destructive interferences at certain interface of the structure and thereby bring forth the desired functionalities. It has been shown that the transmission and reflection of light from the entire few-layer metasurface can be very well derived by assembling all layers of meta-films using their effective permittivity and permeability [3,4,8]. In the multilayer metafilm model, the inter-layer resonance coupling is usually neglected because the operating frequency is usually far-away from the resonance (if any) of each layer. However, the resonance in the metafilm can still affect the behavior of neighboring-layers through capacitive or inductive coupling, especially when the separation between layers are very small.

We choose a metallic disk array (MDA) metasurface that acts as an anti-reflection coating layer atop a metallic hole array (MHA). It has been shown that such MDA layer can significantly increase the extraordinary optical transmission (EOT) of the MHA [4] by eliminating the undesired reflection. EOT is well kwon as a phenomenon that the transmission of light though subwavelength apertures (e.g. MHA) is greatly enhanced by the surface plasmon polariton (SPP) resonance at the interface between metallic structure and dielectric [9–13]. The enhanced interaction between light and active layer of optoelectronic devices due to the EOT has been widely used to achieve improved performance or extended functionality, for instance, color and polarization sensitivity, dynamic-range enhancement, and so on [14–21]. Our recent work has shown that the EOT can be greatly increased by suppression of the reflection using conventional thin-film antireflection coating (ARC) method [22] or metamaterial-based antireflection coating (meta-ARC) [4]. In this work, we focus on the impact of inter-layer coupling effect on the performance of meta-ARC that arises due to alignment-shift between the gold disk array (GDA) and MHA, and the shape variation of gold disks (GDs). Such alignment-shift and shape variation are inevitable due to the imperfections of samples during the nano-fabrication process.

2. Geometry and dimensions of meta-ARC

Our meta-ARC consists of a planar gold disk array (GDA) atop the benzocyclobutene (BCB) layer, which is placed on top of a gold film with an array of circular apertures (MHA) as illustrated in Fig. 1. All structures were fabricated with the standard semiconductor process (spin coater & photolithography). The geometrical parameters of GDA and MHA are as follows: pitch ($p$) = 1.8 μm, aperture diameter in MHA ($d_{MHA}$) = 0.9 μm, disk diameter in GDA ($d_{GDA}$) = 1.26 μm, thickness of MHA ($t_{MHA}$) and GDA ($t_{GDA}$) = 0.05 μm, BCB thickness ($t_{BCB}$) = 0.35 μm. The fabrication process has been described in detail elsewhere [4].

 

Fig. 1 Scanning electron microscope (SEM) images and illustration of meta-ARC (GDA on BCB layer) on MHA structure with fabrication induced alignment-shift and shape-variation. (a) Developed photoresist pattern, followed by e-beam deposition of gold. (b) Nonzero sidewall angled GDs (using a lift-off process with acetone to remove the photoresist layer shown in (a). (c) Cross-sectional view of alignment-shifted GDA to MHA. (d) Schematic view and geometrical parameters of meta-ARC on MHA.

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3. Fabrication-induced imperfections

As shown in Figs. 1(a)-(c), the shape-variation of GDs (i.e., additional gold thickness $t_{ring}$ and nonzero sidewall angle $\theta$) is attributed to the gold deposition on the circular holes of the developed photoresist sample (not vertical sidewall) that defines GD structure or e-beam deposition geometry (distance from the gold source and collimation), followed by a lift-off process. Such fabrication process inevitably results in a sidewall-angled GD shown in Fig. 1(b). Another imperfection, the spatial deviation of GDs is associated with the alignment-shift between GDA and MHA as shown in Fig. 1(c), which results from the alignment errors to be about 0.5 μm (Karl SUSS MA/BA6 Mask Aligner was used to expose the photoresist). We performed numerical simulations to investigate the effect of shape-variation and alignment-shift using CST Microwave Studio, which utilizes a finite integration technique. Figure 1(d) shows the configuration of meta-ARC:MHA used in simulations, where the shape-variation and alignment-shift are described by parameters ($t_{ring}$,$\theta$) and ($a,b$), respectively.

We vary the shape of GDs with additional gold thickness $t_{ring}$ and sidewall-angle $\theta$, and numerically simulated the transmission of the meta-ARC:MHA sample (it can be seen by SEM images that $t_{ring}$ ~0.02 μm and $\theta \ll 45°$). Figure 2 shows the obtained transmission spectra for ($t_{ring}, \theta$) = ($0$ μm, $0°$), ($0.02$ μm, $0°$) and ($0.02$ μm, $45°$) in addition to the difference in transmission between ideal-shaped GDs and imperfect-shaped GDs given by ${\Delta }_i=\left[\left(T_i-T_{(0,0)}\right)/T_{(0,0)}\right]\times 100,$ where $i=$ ($0.02$ μm, $0°$) and ($0.02$ μm, $45°$). At two peaks corresponding to the first (second) order SPP resonance, 6.32 μm (4.38 μm), the transmission difference is found to be −0.1% (−0.26%) and 1.0% (−3.2%) for ${\Delta }_{(0.02,0)}$ and ${\Delta }_{(0.02,45)}$, which is owing to very small ratio of fabrication-induced shape-variation to resonance wavelength (for instance, 0.02 μm / 6.3 μm $\approx$ 0.003).

 

Fig. 2 Simulated transmission spectra due to shape-variation of GDs. ${\Delta }_i$ (symbols) represents the difference in transmission between meta-ARC:MHA with ideal-shaped and imperfectly-shaped GDs. Shape-variation is described with ($t_{ring}, \theta$), where $t_{ring}$ is additional gold thickness (0 and 0.02 μm) and $\theta$ is the sidewall-angle (0° and 45°) of GDs as displayed in Fig. 1(d). The color convention is as follows: black for (0 μm, 0°), red for (0.02 μm, 0°) and blue for (0.02 μm, 45°).

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In order to estimate the influence of alignment-shift of GDs on the performance of meta-ARC, we observe the difference of transmission enhancement factors ($\text{TEF}$) between experiment and simulation with various $(a, b)$ as shown in Fig. 3. $\text{TEF}$ is defined as $T_{meta-ARC:MHA}/T_{MHA}$ with $T_{meta-ARC:MHA}$ ($T_{MHA}$) being the transmission of meta-ARC:MHA (MHA). ($a, b$) is varied from perfectly aligned ($a=0\cdot p$ and $b=0\cdot p$) to completely alignment-shifted GDs ($a=0.5\cdot p$ and $b=0.5\cdot p$), where $p$ is the periodicity of GDA. Detailed experimental results have been reported in Ref [4]. In Fig. 3, black (blue) symbols represent the alignment-shifted GDs with $a\le 0.5$ μm and $0\le b\le 0.9$ μm with y-axis on the left side ($a\ge 0.7$ μm and $0\le b\le 0.9$ μm with y-axis on the right side), respectively. In addition, $\text{TEF}$ difference at transmission peak wavelength of 6.32 μm (the first-order SPP) and 4.38 μm (the second-order SPP) related to the first-order (second-order) SPP resonance is presented in the Fig. 3(a) and 3(b), respectively. As ($a, b$) increases from (0, 0) to (0.9 μm, 0.9 μm), three smallest difference of $\text{TEF}$ at the first (second) SPP resonance can be found to be 0.1 (0.05), 0.08 (−0.15) and 0.07 (−0.08) at ($a, b$) = (0.3 μm, 0.7 μm), (0.3 μm, 0.9 μm) and (0.5 μm, 0.5 μm), respectively. Normally incident $x$-polarized light was used for simulation as indicated in Fig. 1(d). However, in the experiment, an unpolarized incident light was used to measure the transmission of meta-ARC:MHA (i.e., average of transmission intensity for $x$- and $y$-polarizations). Therefore, it is of great importance to consider the averaged difference of $\text{TEF}$ with ($a, b$) and ($b,a$), i.e., averaged difference of [(0.3, 0.7), (0.7, 0.3)], [(0.3, 0.9), (0.9, 0.3)] and [(0.5, 0.5), (0.5, 0.5)]. Simulated $\text{TEF}$ with alignment-shifted GDs by 0.5 μm in $x$- and $y$-direction is found to be closest to the measured $\text{TEF}$. This analysis indicates a good quantitative agreement with alignment-shifted GD measured by SEM image in Fig. 1(c).

 

Fig. 3 Difference of transmission enhancement factors (TEFs) between experiment and simulation at (a) first-order and (b) second-order SPP resonance as a function of ($a, b$) resulting from the alignment-shifted GDA and MHA.

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4. E-field distribution and discussion

To better understand the influence of the spatial deviation of GDA, we investigate how the transmission, $x$- and $z$-components of electric field intensity change for selected four types of samples, namely the MHA on GaAs substrate (indicated as Sample A in Fig. 4, black), a BCB layer coated MHA (Sample B, green), alignment-shifted meta-ARC on MHA (Sample C, red; Sample D, blue), and a perfectly aligned meta-ARC on MHA (Sample E, light blue), where a 0.35 μm thick BCB layer is applied to the Samples B-E. Here, two extreme cases for the alignment-shifted GDs are (i) ($a, b$) = ($0.5\cdot p$, $0.5\cdot p$) (i.e., GDs of Sample C are relatively off from the center of apertures in MHA layer by a half periodicity in both $x$- and $y$-directions) and (ii) ($a, b$) = ($0.5\cdot p$,$0\cdot p$) (i.e., GDs of Sample D are at a distance of $0.5\cdot p$ apart in only $x$-direction from the center of holes in MHA layer). The simulated transmission spectra of the above-mentioned Samples A-E are plotted in Fig. 4(a). The transmission enhancement ratio (defined as $T_j/T_A$, where j = B, C, D, E) at the first-order SPP resonance is found to be ~1.12, ~1.44, ~1.61 and ~1.83, respectively, in addition that the transmission peak of sample A is only slightly shifted by less than 0.09 μm ($\Delta \lambda /\lambda =$0.09 μm / 6.27 μm ≈1.4%) even with BCB layer and meta-ARC layer. The advantage drawn from these results is that our meta-ARC can be readily utilized with MHA integrated optoelectronic device to improve the device-performance because the peak wavelength of MHA resulting from SPP resonance is not shifted and the fabrication tolerance (spatial variation of GDs) can be allowed in some degree (transmission of Sample C, the maximally alignment-shifted GDs atop the BCB layer on MHA, is obtained with ~44% increase, as compared with Sample A).

 

Fig. 4 (a) Simulated normal incidence transmission spectra of MHA on GaAs substrate (Sample A, black), a BCB coated MHA (Sample B, green), the maximally alignment-shifted meta-ARC on MHA (Sample C, red: ($a, b$) = (0.9 μm, 0.9 μm)), the alignment-shifted meta-ARC on MHA (Sample D, blue: ($a, b$) = (0.9 μm, 0 μm)), and a perfectly aligned meta-ARC on MHA (Sample E, light blue: ($a, b$) = (0 μm, 0 μm)). Here, a 0.35 μm BCB layer was used for sample B-E. Inset shows that the schematic views of sample A-E. The dash and solid black lines denote the MHA and GDA position, respectively. (b) Diagram of sample structure to calculate the electric field intensity (${\left|E_i^j(z)\right|}^2\equiv I_i^j(z)$, where $i=x, z$ and $j=$ Sample A-E). (c) Calculated $\left|E_z\right|$ at the half thickness of BCB layer ($z=20.2$ μm), $y/p=0, 0.25, 0.35, 0.5$ along $x$-direction and the simulated $E_z$ distributions of sample C-E at each of the first-order SPP resonance wavelength in the plane $y=0$. (d) Enhancement ratio of $x$-component of electric field intensity at the first-order SPP resonance, at the position of $x$ = 0 μm and $y$ = 0 μm in $z$ -direction, as compared with $I_x(z)$ of Sample A ($\equiv I_x^j(z)/I_x^A(z)$, where $j$ = B, C, D and E samples) (e) $z$-component of electric field intensity at $x$ = 0.54 μm and $y$ = 0 μm in $z$-direction for all samples ($I_z^j(z)$, where $j$ = Samples A-E), mainly displayed with a range of penetration depth ($~1/e^2$). Inset shows that the enhancement ratio of transmission (vs. Sample A, MHA) is well matched with one calculated using $I_x (z=0 \text{μm})$.

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Next, we investigate $x$- and $z$-components of electric field at the first-order SPP resonance along $z$-direction of GaAs substrate ($E_x(z)$) and along x-direction in the middle of BCB layer ($E_z(x)$) when the direction of polarized incoming light is parallel to $x$-axis. First, we observe $E_z(x)$ for spatial deviation of GDA (Samples C-E) at $z=20.2$ μm (at the half thickness of BCB layer, as indicated in Fig. 4(b)) and $y/p=0, 0.25, 0.35, 0.5$ (at the center, edge of hole in MHA, at the edge of the disk in GDA, the half pitch, respectively). The simulated $E_z(x)$ of Samples D, E (C) tends to decrease (increase) as $y/p$ increases. This tendency can be qualitatively interpreted by the accumulated charges and electric field strength at various $y$-position: the maximum accumulated charges and electric field intensity are around the hole / disk edges, and they are decreased as the distance from $x$-axis increases (location-dependent due to spatial variation of GDA). Moreover, $E_z$ can be considered as the coupling ($\eta$) between GDA layer and MHA layer, which is clearly seen in $E_z$ distribution (in the plane $y=0$) of Sample C-E as displayed in the right panel of Fig. 4(c). For $y/p=0$, as the spatial deviation gradually decreases (i.e., $x, y=p/2$ for Sample C; $x=p/2$ for Sample D; $x, y=0$ for Sample E), the interaction between MHA and GDA is stronger (${\eta }_E>{\eta }_D>{\eta }_C$), which results in enhancing / suppressing the transmission / reflection. The channel-waveguide properties of the hole are known to influence the transmission properties, i.e., changing the coupling strength between localized SP (GDA) and propagating SP (MHA) layers is attributed to enhanced transmission. In addition, the amplitude and phase for Sample E can be calculated using the multiple-layer model (based on a transfer matrix method) developed in our previous publications, satisfying the perfect antireflection condition. Second, Figs. 4(d) and 4(e) show the calculated $x$- and $z$-component electric field intensity (${\left|E_i^j(z)\right|}^2\equiv I_i^j(z)$, where $i=x, z$ and $j$ = Samples A-E), respectively. The $I_x^A(z)$ at the center of MHA’s aperture ($x$ = 0 μm and y = 0 μm) from $z$ = 20 μm to $z$ = 0 μm as displayed in Fig. 4(d) (the interface between MHA and GaAs substrate is set to 20 μm in $z$-axis) and ~13.69 V²/μm² was obtained at $z=0$ μm. Also, the enhancement ratio is defined as $I_x^j/I_x^A$, where $j$ = Samples B-E and it is found to be ~1.11 (B), ~1.43 (C), ~1.60 (D), ~1.81 (E) at $z=0$ μm. The $I_z^j\left(z\right)$ at $x=$ 0.54 μm and $y=$0 μm ($j$ = Samples A-E) and $~1/e^2$ decay are apparent from Fig. 4(e). The inset of Fig. 4(e) shows that the ratio of the transmitted light intensity of Samples B-E to that of Sample A ($=T_j/T_A$, black circle) is in excellent agreement with the enhancement ratio calculated using $E_x$ ($=I_x^j/I_x^A$, red cross).

5. Conclusion

We have numerically investigated the impacts of resonance coupling between GDA and MHA layers on the performance of meta-ARC at the SPP resonance wavelengths through alignment-shifts and shape-variations. As compared to the ideal-shaped GDs, the change in transmission intensity due to fabrication-induced shape-variation of GDs (with a slightly angled sidewall and additionally deposited thin gold) was found to be ~0.1% and ~0.26% at the first and second order SPP resonance wavelengths, respectively. Also, the first order SPP-transmitted light can be increased by more than 44% even with the maximum change of resonance coupling between GDA and MHA. Our results drawn from this work can be used to as a basis to realize the practical, easy-to-fabricate, structurally tunable antireflection coating layer for next generation of optoelectronic devices associated with a variety of plasmonic architectures.