1. Introduction

Metasurfaces are two-dimensional metamaterials composed of dense arrays of metallic or dielectric nanostructures placed on planar substrates [1,2]. By configuring each element to operate as an efficient optical nano-antenna or resonator, the intensity and/or phase of incident light can be manipulated at a subwavelength scale [3–5]. With the recent development of nano-fabrication technologies, a variety of passive or devices, such as lenses, polarizers, absorbers, and filters, have been demonstrated [6–10]. Due to the inherent merits of ultrathin flat structure, flexibility in design, and ease of fabrication using planar lithographic tools, these metasurface-based devices are becoming promising to replace bulky optical components.

As the next logical step, there has been a growing interest to realize active metasurfaces that can be tuned electrically [11–21]. Several groups have demonstrated electro-optic tuning by embedding graphene [15,16], transparent conducting oxide (TCO) [17–20], and electro-optic (EO) polymer [21] as active materials inside metallic metasurfaces. In these demonstrations, metallic structures were preferred over dielectric counterparts, as they could also serve as highly conductive electrodes to potentially realize high-speed modulation. On the other hand, inherent plasmonic losses in metals have been the major obstacle in achieving high-quality (high-Q) resonance at near-infrared or shorter wavelengths. As a result, previous demonstrations were often limited to operation in mid-infrared wavelengths [15–18,20] or with insufficient efficiency [21].

In this work, we propose a novel EO-polymer-based metallic metasurface modulator operating at 1.55-μm wavelength, that utilizes bimodal resonance. Among various active materials, we select EO polymer for several reasons; it exhibits large EO coefficient over 200 pm/V [22–25], ultrahigh-speed modulation capability beyond 40 GHz [25,26], simple and low-cost spin-coating-based fabrication that enables flexible device design [25–28], and high material reliability proved in commercial products [26]. Unlike previous demonstrations based on similar schemes [17–21], we judiciously design the structure, so that two metal-insulator-metal (MIM) resonant modes are excited inside the EO polymer. By utilizing the strong coupling between these two modes, we demonstrate that a sharp dip emerges in the reflected spectrum, having significantly higher Q factor than that obtained when a single-mode Fabry-Perot (FP) resonance is employed. As a result, we numerically demonstrate a thin (<1 μm) surface-normal intensity modulator with 15-dB extinction ratio under a refractive index change of 8.5 × 10⁻³, corresponding to the modulation voltage of less than 10 V. Due to the highly conductive metallic electrodes and low parasitic capacitance, we estimate that the RC bandwidth should easily exceed 100 GHz.

2. Proposed structure and principle

The schematic of the proposed metasurface modulator is depicted in Fig. 1. The EO polymer with thickness of d is sandwiched between the bottom Au layer and the top thin Au grating layer. The grating period Λ is designed to be shorter than the wavelength of light, so that the diffraction is prohibited. The thickness (200 nm in this work) of the top Au layer is designed to be larger than the skin depth to eliminate direct coupling from the incident light into EO polymer. The bottom Au layer is also set to the same thickness, so that it operates as an almost perfect reflective mirror.

 

Fig. 1 Schematic (a), cross-section (b), and (c) modulation principle of the proposed surface-normal metasurface modulator.

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As a plane-wave light with the electric field polarized perpendicularly to the grating (along x in Fig. 1) is normally incident to the device, it excites MIM waveguide modes propagating in ± x direction inside the Au/EO-polymer/Au layers [see Fig. 1(b)]. When these MIM waveguide modes satisfy the FP condition, the light is confined strongly inside the EO polymer and eventually absorbed by the metal. As a result, we obtain a resonant dip in the reflected spectrum as shown schematically in Fig. 1(c). It has been demonstrated that such resonance generally has relatively low Q factor due to the metallic losses of MIM modes [17–21]. We will, however, demonstrate in the next section that the Q factor can be increased significantly by judiciously designing the structure, so that two MIM FP modes are excited simultaneously and couple strongly.

By applying the poling voltage between the top and bottom Au layers, the EO polymer is poled vertically along z direction to induce electro-optic coefficient r₁₃, r₂₃ and r₃₃ in x, y, and z directions, respectively [23]. Under a realistic poling voltage, r₃₁ and r₃₂ is approximately 1/3 of r₃₃ [29–31]. When modulation voltage is applied using the same electrodes, we can, through Pockels effect, change the refractive index of the EO polymer and shift the resonant wavelength λ₀, so that the intensity of reflected light is modulated at λ₀, as shown in Fig. 1(c). The change in refractive index can be expressed as [29,30]

The amount of wavelength shift ∆λ required to obtain desired extinction is inversely proportional to the Q factor of the resonant dip. Since ∆λ is proportional to the amount of refractive index change, we see from Eq. (1) that the required ∆λ is proportional to V_mod/d. Therefore, the required V_mod to achieve a given extinction ratio is proportional to d/Q. We thus define the figure-of-merit (FOM) of our modulator as Q/d; in order to reduce the modulation voltage, we need to optimize the structure to maximize Q/d.

3. Numerical results and discussion

We first simulate the reflectance of the proposed structure by the finite-difference time-domain (FDTD) method. For simplicity, we assume the width of the grating in y direction to be infinity, so that two-dimensional (2D) simulation is performed. A periodic boundary condition is employed in x direction while absorptive condition with perfect matched layers (PMLs) is applied at z boundaries. The dielectric permittivity of EO polymer is represented as a tensor, where the refractive indices (n_x, n_y and n_z) are set to be 1.65 in the absence of modulation. The complex permittivity of Au is modeled by fitting Drude-Lorentzian poles to the experimental data [32].

3.1 Reflectance property

Figure 2 shows the calculated reflectance of the device with d = 500 nm, plotted as a function of grating period Λ and wavelength λ. For convenience, the grating gap g ( = Λ - a) is fixed to 400 nm. From Fig. 2, we see that a number of resonance valleys emerge along well-defined curves. From the electric field profiles shown in Fig. 2 insets, we presume that these curves correspond to the FP resonance conditions for the TM₀ and TM₁ MIM modes, respectively. To confirm this speculation, we plot in Fig. 3(a) the dispersion curves for the TM modes of Au/EO-polymer/Au MIM waveguide with d = 500 nm. Indeed, we can see that in the wavelength range from 0.9 to 1.8 µm, two propagating modes (TM₀ and TM₁) co-exist inside the MIM waveguide. By using the propagation constant of each mode, we can then derive the FP resonance conditions for respective modes as

 

Fig. 2 Reflectance as a function of grating period Λ and wavelength. Inset shows Re(E_y) distribution at two curves.

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Fig. 3 (a) Dispersion relationship of Au/EO-polymer/Au MIM waveguide (b) Calculated Fabry-Perot resonance of MIM modes overlaid on the reflectance plot. d = 500 nm in two plots.

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The calculated FP resonance conditions are overlaid by white solid curves in Fig. 3(b). Here, TM_n,m denotes the FP resonance condition for the TM_n waveguide modes (n = 0, 1, 2,…) with index m ( = 2, 4, …) in x direction as defined in Eq. (2). We approximate $\phi$ to be a wavelength-independent constant, and fit to 1.53 rad (TM_0,m) and 4.14 rad (TM_1,m) to have best agreement with the FDTD results. While slight mismatch arises due to the fact that $\phi$ actually depends on wavelength, reasonable agreement is observed between the FDTD results and analytically derived FP resonance conditions.

More importantly, we notice from Fig. 3(b) that a sharp resonant dip emerges at Λ ∼1 μm and wavelength of around 1.5 μm, where TM_0,2 and TM_1,2 FP curves approach. Such feature is present at the anti-crossing point of a strongly coupled bimodal resonant system in general [33], and has been demonstrated in various other systems, such as high-contrast gratings (HCG) [8, 34, 35] and coupled ring resonators [36]. In our case, two MIM modes satisfy the resonant condition simultaneously and couple strongly at this anti-crossing point. Due to the destructive interference between these two modes, external coupling to the outgoing plane wave is suppressed, leading to increase in Q factor [33]. We can therefore realize high-Q resonance at the wavelength of our interest, by deliberately changing the EO polymer thickness d and the period Λ.

3.2 Intensity modulation property

As discussed in Section 2, it is essential to maximize the FOM, defined as Q/d, to reduce the modulation voltage. In order to find the optimal EO polymer thickness d, we plot in Fig. 4 the Q factor of TM_0,2 FP resonance in the 1550-nm wavelength range as well as Q/d as a function of d. For different EO polymer thickness, we fine-tune the grating period Λ within the range from 1.00 to 1.04 μm, so that the TM_0,2 FP mode exits inside the wavelength range between 1530 and 1570 nm. From Fig. 4, we see that Q factor increases periodically as TM_0,2 resonance intersects with TM_n,2 (n = 1, 2, …). For example, the Q factor increases to 87 to exhibits a strong peak at d = 500 nm, corresponds to the anti-crossing point of the TM_0,2 and TM_1,2, that we have discussed in Fig. 3(b). Additional peaks emerge as we increase d to 1030 and 1600 nm, which correspond to the anti-crossing of TM_2,2 and TM_3,2 modes, respectively. Due to the smaller loss of the MIM modes with increasing d, these peaks have higher Q factor. However, if we compare Q/d to evaluate the overall modulation efficiency, we see that a maximum Q/d of 0.174 nm⁻¹ is obtained at d = 500 nm. We assess this Q/d value to be more than 5 times improvement from the simulated result presented in [21].

 

Fig. 4 Calculated Q factor and figure of merit (Q/d) with different EO polymer thickness.

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From Fig. 4, we can conclude that the optimal EO polymer thickness to obtain largest Q/d is 500 nm. In this case, other parameters of the modulator are determined as Λ = 1 µm and a = 600 nm. Using this optimized structure, we calculate the change in reflection spectrum under modulation. Figure 5(a) shows the reflectance spectrum for various values of ∆n_z. Note that ∆n_z represents the refractive index change for the E_z component under modulation, and we assume ∆n_x = ∆n_y = ∆n_z/3 as explained in Eq. (1). From Fig. 5(a), we see that the resonant wavelength shifts continuously from 1536 nm to 1546 nm as we change ∆n_z from −8 × 10⁻³ to 8 × 10⁻³. As a result, at a signal wavelength of 1541 nm, the intensity of reflected light can be modulated as a function of ∆n_z as shown in Fig. 5(b). For example, we can achieve 15-dB intensity modulation with 5-dB insertion loss by ∆n_z of 8.5 × 10⁻³. Assuming the r₃₃ coefficient of 200 pm/V [22–25], the required driving voltage in this case is calculated from Eq. (1) as V_mod = ± 4.7 V.

 

Fig. 5 (a) Reflectance spectrum with ∆n_z varied from −8 × 10⁻³ to 8 × 10⁻³, (b) Modulation characteristic of reflected light at wavelength of 1541 nm.

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Since the change of refractive index of EO polymer originates from electronic polarization, having an inherent response in the order of picoseconds [25,26], the bandwidth of the modulator should be limited by the RC delay of the electrodes. Unlike the previous active metasurfaces based on metal-oxide-semiconductor (MOS) capacitor [17–20], relatively thick EO polymer (d = 500 nm) with small radio-frequency (RF) permittivity (ε = 2.7) of our device results in ultra-small capacitance of 48 aF/µm². Combined with the high conductivity (4.2 × 10⁷ S⋅m⁻¹) of the Au grating used as the electrode, the RC bandwidth is estimated to be easily over 100 GHz for a realistic case with the grating length l of 500 µm.

4. Conclusion

We have proposed and numerically demonstrated a novel ultrathin (< 1 μm) surface-normal EO-polymer-based metallic metasurface modulator operating at 1.55-µm wavelength. Significant increase in modulation efficiency was achieved by exploiting the strong coupling between two MIM modes inside the grating, which generated a sharp resonance at the anti-crossing point of their dispersion curves. An optimized structure with 500-nm-thick EO polymer and 1-μm-pitch Au grating demonstrated 15-dB intensity modulation under a refractive index change of 8.5 × 10⁻³, corresponding to the modulation voltage of ± 4.7 V. Owing to inherently high-speed response of EO polymer as well as small RC constant due to high conductivity of Au and small capacitance of EO polymer, this modulator can potentially operate at bandwidth exceeding 100 GHz. With relatively easy fabrication and scalability to two-dimensional arrays, the proposed device should be attractive for wide ranges of applications, such as high-density optical interconnects, free-space optical communication, and high-speed imaging.