Electrically tunable two-dimensional metasurfaces at near-infrared wavelengths

Jinyoung Hwang; Jong Wook Roh

doi:10.1364/OE.25.025071

1. Introduction

Metasurfaces built with planar arrays of rationally designed subwavelength antennas allow for unusual manipulations of light that cannot be attained using traditional optical materials [1]. The extraordinary optical responses in the planar structure facilitate the development of various applications, including ultrathin flat lenses with diffraction-limited performance [2], holograms that generate high-resolution and low-noise 3-D images [3], and optical vortex plates [4]. In addition, the surface-confined character of the metasurface and its compatibility with the conventional semiconductor fabrication process offer the potential to achieve nanoscale on-chip photonic devices [1].

To extend the metasurfaces’ application areas even further, it is important to introduce an actively tunable metasurface for which the optical response of the constitutive antennas can be individually modulated using postfabrication control [5]. For example, spatial light modulators, dynamic beam steering, reconfigurable imaging, and advance pulse shaping can be achieved by externally controlling the phase and/or amplitude of the light that the individual antennas on the metasurfaces emit, resulting in a dynamic wavefront transformation of light [1].

The active modulation of the building blocks can be accomplished by incorporating the following into the metasurface system: active materials such as transparent conducting oxides [6], graphene [7], phase-change materials (e.g. GeSbTe) [8], and liquid crystals [9]; the optical properties of these materials can be switched using external stimuli. Transparent conducting oxides, particularly indium tin oxide (ITO), allow for remarkable changes in the complex refractive index in the near-infrared region [10]. These changes are induced by modifying the carrier concentration. Recently, switchable metasurfaces based on a gold-striped antenna array have been demonstrated using ITO’s carrier-induced refractive index change, thereby providing a promising way to realize electrically tunable beam-steering metasurfaces [11].

In this work, an electrically tunable 2-D metasurface made of an array of cylindrical dielectric resonators is introduced. ITO is integrated in the metasurfaces’ individual building blocks as an electrically controllable active material; the refractive index of ITO can be modulated using carrier concentration. To change the carrier concentration of the ITO, a control system is embedded in each antenna; this system is based on the configurations of conventional metal-oxide-semiconductor (MOS) capacitors, and it can send precise electrical signals to the active materials with a fast modulation speed and low power consumption. The feasibility of the proposed structures is proven through numerical calculations, including the finite-difference time-domain (FDTD) method (FDTD Solutions, Lumerical Solutions) for optical simulations and technology computer-aided design (TCAD) modeling (Sentaurus Device, Synopsys) for device simulation.

2. Device structure

The actively tunable metasurface proposed in this work is based on a 2-D planar array of silicon (Si) nanodisks on a gold plate, as shown in Fig. 1(a), which has a resonance in the near-infrared region [12, 13]. In particular, the periodic array of the dielectric antennas has a diameter and height of 300 nm and 100 nm, respectively, and it is arranged with a periodicity of 800 nm. The array exhibits a resonance at the wavelength of 1240 nm (see Fig. 1(b)) when excited by a normally incident plane wave. At the resonance wavelength, a magnetic dipole mode is created inside the resonator [14–16], as depicted in the instantaneous electric and magnetic field distributions provided in Fig. 1(c) and 1(d), respectively. In this instance, the concentrated electric field appears in the middle of the Si nanodisk.

Fig. 1 (a) Schematic showing a single Si nanodisk antenna on a gold plate. The diameter and height of the nanodisk are 300 nm and 100 nm, respectively, and the periodic spacing of the antenna array is 800 nm. (b) Simulated reflectance (black solid line) and phase shift (red solid line) for the periodic array of the Si nanodisk antenna shown in (a). (c) Calculated electric field intensity in the x-z plane across the center of the nanodisk (upper panel) and in the x-y plane positioned 50 nm above from the bottom of the nanodisk (lower panel), and (d) magnetic field intensity in the y-z plane across the center of the nanodisk (upper panel) and in the x-y plane 50 nm above from the bottom of the nanodisk (lower panel) for an x-polarized normal plane wave incidence at the resonance wavelength of 1240 nm. The arrows on the color map indicate the directions of the fields.

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To achieve an actively tunable metasurface, modulation functionality for the optical response is implemented in the Si dielectric antenna by changing the material parameters in the region where the strong electric field is generated at the resonance wavelength. According to the perturbation theory [17],

\frac{Δ ω_{r}}{ω_{r 0}} \approx \frac{\underset{V}{∭} {(Δ \vec{ε} \cdot \vec{E}) \cdot {\vec{E}}_{0}^{*} + (Δ \vec{μ} \cdot \vec{H}) \cdot {\vec{H}}_{0}^{*}} d V}{\underset{V}{∭} (ε {| {\vec{E}}_{0} |}^{2} + μ {| {\vec{H}}_{0} |}^{2}) d V}

Where

Δ \vec{ε}

and

Δ \vec{μ}

are the permittivity and permeability change of the material. respectively;

{\vec{E}}_{0}

and

{\vec{H}}_{0}

are the unperturbed electric and magnetic fields, respectively; and

\vec{E}

and

\vec{H}

are the electric and magnetic fields under the perturbation, respectively. The change of the resonance frequency,

Δ ω_{r}

, for the resonator is proportional to the overlap of the permittivity change and the electric field,

Δ \vec{ε} \cdot \vec{E}

. Therefore, to obtain efficient modulation of the resonance characteristics, we employ the active material in the middle of the dielectric resonator, thus introducing the material’s permittivity change in the presence of the strong electric field.

Details of the actively tunable resonator’s structure are illustrated in Fig. 2. As can be seen in magnified 3-D schematic of the constituent resonator in Fig. 2(a), the ITO layer, which has a thickness of 5 nm and a carrier concentration of 5 × 10²⁰ cm⁻³, is incorporated as the active material in the middle of the Si nanodisk; the permittivity of the active material can be substantially changed at the Si nanodisk array’s resonance wavelength (in the near-infrared region) by varying the carrier concentration. To actively manipulate the carrier concentration of the ITO layer, a gold circular post with diameter and height of 50 nm and 100 nm, respectively, is covered with an HfO₂ layer with a thickness of 10 nm and placed inside the ITO layer. This leads to the formation of the conventional MOS capacitor configuration, in which the metal, oxide, and semiconductor are gold, HfO₂, and ITO, respectively. In this configuration, the applied bias generates an electric field in the HfO₂ layer, and this field can induce carrier accumulation or depletion in the ITO layer near the interface between ITO and HfO₂ with fast modulation speed and low energy consumption. The material properties of undoped Si are adopted for the Si nanodisk surrounding the central ITO post, and the background carrier density is set at 10¹⁵ cm⁻³. The diameter of the nanodisk, d_Si, and the periodic distance of the resonator array in the x and y directions, labeled as Λ_x and Λ_y, respectively, are the variables used to adjust the operating resonance frequency of the metasurfaces. The height of the nanodisk is fixed at 100 nm.

Fig. 2 (a) 3-D schematic of the actively tunable metasurface. A constituent resonator is drawn at a magnified scale. (b) View of the cross-section in the x-z and x-y planes across the center of the resonator.

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3. Results and discussion

Figure 3 shows the electron-density profile in the resonator, as obtained from the TCAD simulation. Various external biases are applied to the electrical contact under the gold plate (gold contact, V_Gold), and 0V is applied to the contact on the bare ITO surface (ITO contact, V_ITO). The voltage range of the applied bias on the gold contact is limited to ± 4 V to ensure that the magnitude of the electric field in the HfO₂ layer is below the breakdown limit [18]. Fig. 3(a) presents the spatial distribution of electron density when a bias of 4 V is applied to the gold contact and 0V is applied to the ITO contact. Under the bias condition, the electron density of ITO near the interface of HfO₂ and ITO increases to over 10²¹ cm⁻³, which corresponds to the accumulation mode of the MOS capacitor. The electron-density distributions of ITO along the normal direction of the interface between the HfO₂ and ITO layers (named the x direction and indicated by the white dashed arrow in the right panel of Fig. 3(a)), under the various biases applied on the gold contact, are given in Fig. 3(b). The results show the electron accumulation and depletion at the HfO₂/ITO interface when positive and negative biases are applied to the gold contact, respectively; in addition, the modulation of the electron density at the interface ranges from about 10¹⁹ cm⁻³ to about 10²¹ cm⁻³. Note that the electron-density change in the Si region (n ~10¹⁵ cm⁻³) is negligible compared to that in the ITO region for all the bias conditions, so these data are excluded in Fig. 3(b). The complex permittivity variation for ITO at the HfO₂/ITO interface (induced by the electron-density modulation in the wavelength range of 800 ~1500 nm) is provided in Fig. 3(c), which is calculated based on the Drude model:

ε = ε_{\infty} - \frac{ω_{p}^{2}}{ω^{2} + i Γ ω}

where

ε

is the complex permittivity;

ε_{\infty}

is the permittivity at infinite frequency;

ω

is the angular frequency;

Γ

is the plasma collision frequency; and

ω_{p}

is the plasma frequency given by

ω_{p}^{2} = n_{e} e^{2} / m_{e}^{*} ε_{0}

, expressed in terms of the electron density,

n_{e}

, and the electron effective mass,

m_{e}^{*}

.

Fig. 3 (a) Electron density in the ITO and Si regions under a voltage of 4 V applied on the gold contact and with 0V applied on the ITO contact. Data on the HfO₂ and gold regions are ignored because the values are negligibly small. The enlarged plot in the right panel is of the area marked by the black dashed rectangle. (b) Electron density in the ITO and Si regions plotted along the x direction, as depicted by the white dashed arrow displayed in the magnified plot in the right panel of (a). (c) Wavelength versus complex permittivity variation for ITO at the interface of HfO₂ and ITO under the various applied biases on the gold contact; 0V is applied on the ITO contact.

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The complex refractive index profiles of the resonator under the various applied-voltage conditions are based on the electron-density profiles of ITO and Si (which are acquired from the TCAD simulation). The real and imaginary components of the refractive index at the wavelength of 1127 nm are derived from the electron-density profile shown in Fig. 3(a), with V_Gold = 4 V and V_ITO = 0 V, as presented in Fig. 4(a) and 4(b), respectively. In these figures, ITO’s modulated refractive index in the vicinity of the HfO₂/ITO interface can be observed. These results are applied to a 3-D FDTD simulation to estimate the optical response of the 2-D periodic array of the actively tunable resonator with d_Si of 280 nm and with Λ_x and Λ_y of 970 nm under a normal incidence of linearly x-polarized light. The reflectance and phase shift values are calculated as a function of wavelength for V_Gold in the range of −4 ~4 V, with a step of 1 V, and these values are given in Fig. 4(c) and 4(d), respectively. The results clearly demonstrate the change in the resonance frequency that occurs with the change in the externally applied bias. This causes the amplitude and phase modulation of reflected light at a fixed wavelength. For instance, at the wavelength of 1111 nm, the amplitude of the reflected light can be gradually reduced from 61% to 8% of the incident light by increasing V_Gold from −4 V to 3 V, and at the wavelength of 1127 nm, a phase shift modulation of 272.9° can be obtained by changing V_Gold from −4 V to 4 V. To clearly present the gradual change of the phase shift at the wavelength of 1127 nm, in Fig. 4(e), an electric field of reflected light ( $E = | E | e^{i θ}$ ) is plotted in polar coordinates along with the data calculated for V_Gold in the range of 0.1 ~0.9 V, with a step of 0.1 V. The spatial distributions of the electric field’s x component, E_x, at the wavelength of 1127 nm are given in Fig. 4(f) and 4(g) for V_Gold of 4 V and −4 V, respectively. These figures clearly depict a strong electric field generated in the region of ITO, indicating that $Δ \overset{\leftarrow}{ε} \cdot \vec{E}$ is enhanced in both cases.

Fig. 4 (a) Real and (b) imaginary parts of the complex refractive index profiles at the wavelength of 1127 nm in the area of the resonator marked by the black dashed rectangle in Fig. 3(a). The 1-D white-line plot overlaid on the 2-D contour plot is the cross-sectional data along the horizontal line across the center of the 2-D plot. (c) Calculated reflectance and (d) phase shift for the 2-D periodic array of the active tunable resonators shown in Fig. 2 under the various voltages applied on the gold contact (V_Gold) when d_Si = 280 nm, Λ_x = Λ_y = 970 nm, and when the x-polarized plane wave is normally incident. (e) Electric field of the reflected light at the wavelength of 1127 nm, plotted in a polar coordinate system (black solid dots). The phases of the black solid dots are marked with red solid dots on the same plots to show them clearly. The dots, when plotted clockwise starting from 189°, correspond to the data when V_Gold = [-4, −3, −2, −1, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 2, 3, 4] V. (f) Distribution of the electric field’s x component in the resonator at the wavelength of 1127 nm when V_Gold = 4 V. (g) The same distribution when V_Gold = −4 V.

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Furthermore, the operating wavelength of the actively tunable metasurface can be modulated in a range extending approximately from 850 to 1150 nm by varying the diameter of the nanodisk, d_Si, in the range of 180 ~280 nm, as given in Fig. 5. The periodic distance of the resonators in the metasurfaces, Λ_x ( = Λ_y), is chosen for each d_Si based on the condition in which the reflectance at resonance is minimized when V_Gold = 0 V. However, Λ_x (or Λ_y) can be changed to suit various uses, and any operating wavelength in the near-infrared region can be achieved by precisely controlling d_Si, Λ_x, and Λ_y. In addition, the modulation magnitude of the metasurface can be manipulated. According to the permittivity dispersion of ITO for various V_Gold shown in Fig. 3(c), ITO’s permittivity change increases as the wavelength increases. For this reason, the maximum amplitude and phase modulation increase as the metasurface operates at longer wavelengths; this is shown in Fig. 5(b), in which the maximum phase shifts of the metasurface for V_Gold from −4 to 4 V increases from 218.5° to 272.9° as the operating wavelength increases from 880 nm to 1127 nm.

Fig. 5 (a) Calculated reflectance and (b) phase shift for the 2-D periodic array of active tunable resonators with diameter (d_Si) in the range of 90 ~140 nm and with V_Gold ranging from −4 to 4 V, with a step of 1 V. The periodic distance of the resonator (Λ_x = Λ_y) for each d_Si is determined at the resonance condition of the resonator.

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Although the device structure presented in this work is not easy to be fabricated, the device performance is less susceptible to imperfections in fabrication. According to the results of the simulations performed with a wide range of parameter variations, at a fixed periodic distance of the resonators, more than 80% of the optimum values of the reflection and phase modulation can still be achieved even if the diameter of the silicon nanodisk is changed by 20 nm. Note that the height variation of the silicon nanodisks and surface roughness in a nanometer range have negligible effect on the device performance. This level of fabrication accuracy can be obtained by recent advances in the silicon nanofabrication techniques [19–21]. In addition, the internal structure consisting of Au/HfO₂/ITO affects the modulation of the optical response rather than the resonance characteristics of the nanodisk. Therefore, the shape of the inner structure can be modified to be easily fabricated as long as sufficient change in the complex refractive index of ITO is ensured in the region where the optical electric field is concentrated.

4. Conclusion

In conclusion, a novel electrically tunable metasurface is proposed, and the feasibility of the device is demonstrated based on TCAD and FDTD simulations. The metasurface is composed of a 2-D periodic array of Si nanodisks. To individually manipulate the optical response of the disk-shaped dielectric resonators using external applied bias, ITO is incorporated as an active material in the middle of the Si nanodisks, where a concentrated optical electric field is generated at the resonance wavelength. To control the active material’s complex permittivity, the gold post electrode covered by a thin layer of HfO₂ is embedded in the middle of the ITO. By applying bias to the gold electrode, the electron density of the ITO near the HfO₂/ITO interface can be modulated, enabling substantial manipulation of the ITO’s complex permittivity at near-infrared wavelengths. According to the results of the electrical and optical simulations, a reflectance shift from 61% to 8% at λ = 1111 nm and a phase shift of 272.9° at λ = 1127 nm can be achieved with applied voltage in the range of −4 ~4 V, when d_Si = 280 nm and Λ_x = Λ_y = 970 nm. Furthermore, the performance can be improved by optimizing the geometrical parameters of the resonator or by replacing the materials (Si, HfO₂, and gold) with other appropriate materials. The operating wavelength of the metasurface and the modulation magnitude of the optical responses can also be adjusted simply by choosing the proper geometrical parameters (such as d_Si, Λ_x, and Λ_y.) for the resonators.

Funding

This work was supported by 2017 Korea Aerospace University Faculty Research Grant.

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Electrically tunable two-dimensional metasurfaces at near-infrared wavelengths

Abstract

1. Introduction

2. Device structure

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (5)

Equations (2)

Optics Express