Abstract

Tunable metasurfaces enable us to dynamically control light at subwavelength scales. Here, using phase change materials and transparent graphene heaters, a new structure is proposed to develop tunable metasurfaces which support first-order Mie-type resonance in the near-IR regime. In the proposed structure, by adjusting the bias voltages applied to transparent graphene heaters, the crystallization levels of the phase change materials are controlled, which in turn modifies the response of the metasurface. The proposed metasurface is able to modulate the phase of the reflected wave in the range of 0° to −270° at the telecommunication wavelength of λ = 1.55 µm. A comprehensive Joule heating analysis is performed to investigate the thermal characterizations of the proposed structure. The results of this analysis show that there is a suitable thermal isolation between adjacent unit cells, making individual control on unit cells possible. The potential ability of the proposed metasurface as a beam steering device is also demonstrated. By using the proposed unit cells, a beam-steering device is designed and numerically studied. This study shows that the device can reflect a light normally incident on it in the range of ±65° with reasonably low sidelobe levels. The proposed structure can be used in developing low-cost integrated LiDARs.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Achieving comprehensive light manipulation in a subwavelength scale is the primary goal of nanophotonics. By realization of this aim, one can develop a wide range of nanophotonic devices used in different applications such as free-space beam shaping [1], integrated subwavelength optical circuits [2], subwavelength imaging [3] and high-efficiency energy harvesting [4]. In recent years, artificial structures with subwavelength thickness, called metasurfaces, have shown promising results to achieve this goal. These structures that can be considered as the 2-dimensional version of metamaterials [57], consist of arrays of optical scatterers engineered to manipulate the wavefront of the transferred or reflected light. Unlike traditional bulky devices, metasurfaces are able to modulate light characteristics in a subwavelength resolution, and thanks to their subwavelength thickness, they can shape the desired wavefront in distances much less than a wavelength [811]. The scatterers are usually made of metals that change the electromagnetic wave parameters (amplitude, phase, polarization) via excitation of gap plasmon resnance. An alternative to metallic scatterers is high refractive index dielectric scatterers that do the same job via Mie-type resonances. The main advantage of dielectric scatterers is their significantly lower loss compared to metallic counterparts [12].

So far, numerous metasurface designs have been developed to operate at the near-IR region for different applications, such as holography [13], photonic topological insulators [14], focusing lenses [15], retroreflector [16], and efficient thin-film solar cells [17,18]. However, the vast majority of the previously developed structures are static, i.e., their behavior is fixed at the time of fabrication, limiting their use in applications that require tunability, such as active optical beam steering. Recently, there has been a significant interest among researchers around the world to realize tunable metasurfaces in which the specifications of the structure can be tuned and adjusted dynamically. The approaches taken to develop these structures vary for different ranges of the operation wavelength.

In the near-IR range, the tuning methods can be divided into two categories. In the first one, tuning methods are mechanical, e.g., tunable lens using Micro-Electro-Mechanical Systems (MEMS) [1,19] and stretchable metasurfaces [20]. These methods are suitable for applications in which a relatively low tuning speed is required and also when the metasurface is in a stable condition. Besides, in this category, tunable metasurfaces with independent control on each unit cell have not been demonstrated yet. In the second category, tunability is realized by incorporating active materials inside the unit cell structure. The optical properties of these materials can be controlled by an external stimulus, such as optical laser pulses, applied bias voltage, or heating. Liquid crystals [21], transparent conducting oxides, such as Indium Tin Oxide (ITO) [2224], phase transition materials (PTMs) such as Vanadium di Oxide (VO2) [2527], III–V multiple-quantum-wells [28], or phase change materials (PCMs), such as chalcogenide glasses (GST, GSST) [2932] are examples of active materials that fall in the second category. The methods in this category have a higher tuning speed, and also provide the opportunity to control each unit cell individually.

Among all of the mentioned methods, phase change materials (PCMs) have an optimum balance between the tuning speed and efficiency. By heating PCMs, their state transfer from fully amorphous (crystallization level = 0) to fully-crystallized (crystallization level = 1), which results in a significant variation in the refractive index of these materials in the visible and infrared range [33,34]. Their state can become amorphous again by heating them to the melting point for a few nanoseconds. Interestingly enough, the level of crystallization can be tuned to be any amount between 0 to 1 by heating the material to the corresponding temperature. This multi-level tunability, when used in the design of metasurfaces, provides the possibility of a continuous dynamic control on the parameters of the reflected or transferred electromagnetic wave. Based on this principles, numerous applications such as holography [29], beam steering [30], tunable absorbers [31], and metalenses [32], have been realized experimentally and theoretically.

There are different approaches to heat PCMs. Heating using laser pulses is a precise approach to change crystallization to the desired level. This method yields excellent results in experiments [29,31]. However, due to the need to scan a high-power laser through whole arrays of scatterers or using spatial light modulators for tuning a spatially variable phase profile, their utilization is limited in real-world environments. Another method for heating PCMs is Joule heating, also known as resistive heating. By incorporating an electric conductor into the unit cell structure and passing the electric current through it, the conductor acts as a heater, and the resultant heat changes the crystallization level of the PCM. Although this method seems to be more practical than laser pulses, the intrinsic loss of metallic heaters significantly decreases the metasurface efficiency [35]. An alternative to metallic heaters is transparent ones, such as transparent conducting oxides [36,37] and graphene [3841]. By using transparent heaters, the efficiency of the resultant metasurfaces can be significantly improved.

Graphene has been a popular material in designing tunable metasurfaces, mainly because of its voltage-controlled tunable surface conductivity in terahertz and mid-IR frequencies [42,43]. Moreover, this material also benefits from high thermal and electrical conductivity, in addition to transparency in visible and near-IR range. These material properties make graphene a great candidate as a transparent heater material for controlling the crystallization level of PCMs. Recently, some works has been done in this area to investigate this capability [44,45]. However, it has never been studied in complex structures such as tunable metasurfaces.

In this work, a new design for developing tunable metasurfaces is proposed and numerically studied. In the proposed structure, the tunability is realized by the germanium-antimony-tellurium (GST) phase change material, resulting in phase and amplitude modulation of the reflected wave. To dynamically control the crystallization level of the GST layer, a graphene heater is embedded inside the the unit cell structure. The applied bias voltage to the graphene layer is used as the controlling signal. The metasurface unit cell is designed and optimized in order to simultaneously provide a broad phase modulation range, high tuning speed, and low amplitude fluctuation. To illustrate the performance of the proposed structure, not only the electromagnetic parameters of the metasurface are numerically extracted, but also a comprehensive numerical Joule heating analysis is performed. In the joule healing analysis, both steady-state response and also the transient response of the structure are studied. Furthermore, the capability of the proposed metasurface for beam steering at the telecommunication wavelength of λ = 1.55µm is numerically investigated by analyzing an array of 80 tunable unit cells.

2. Structure of the proposed tunable metasurface

The unit cell of the proposed metasurface is shown in Fig. 1(A). As shown in this figure, the width of the unit cell (W1) is 490 nm, smaller than one-third of the operational wavelength (1550 nm). The tunability of the proposed structure comes from the 130 nm thick GST layer located at the center of the proposed resonator. GST is a phase change material (PCM) whose phase can continuously be altered from fully amorphous (crystallization level = 0) to fully-crystallized (crystallization level = 1) by adjusting its temperature [33]. The resonators are placed above a gold/SiO2 stack. The gold layer acts as a reflecting mirror, and the SiO2 acts as a low-index dielectric spacer between the resonators and the reflecting mirror. The SiO2 layer also adds a degree of freedom in designing the optical resonance mode. More specifically, its thickness affects the frequency and crystallization level in which the Mie resonance happens.

 figure: Fig. 1.

Fig. 1. Geometry of the proposed metasurface A: schematics of the proposed unit cell. The left image shows how the materials are stacked together. The middle image shows the unit cell after fabrication (as shown in this figure, the voltage difference is applied to both sides of the graphene layer), and the right image is the side view of the metasurface unit cell with W1= 490 nm, W2 = 305 nm, hSilicon= 75 nm, hGST= 130 nm, hSiO2= 150 nm, hAu= 300 nm. B: schematics of the proposed metasurface. The crystallization level of each unit cell can be tuned independently through voltages applied to the graphene layer in each unit cell. The input electromagnetic wave is assumed to be a plane wave with E-field perpendicular to the unit cell's length (in line with the x-axis). C: A suggested fabrication procedure for the proposed metasurface.

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Here, to control the temperature of the GST layer, a graphene layer is placed below the GST layer to produce the needed heat (see Fig. 1(A)). By applying a voltage difference to it, electrical current flows along the y-axis. According to Joule's law, the flowing current produces heat, which can be used to tune the crystallization level of the GST layer [44,45].

In the proposed structure, we have designed the GST layer as thin as possible in order to have a high tuning speed and also to ensure that the crystallization happens uniformly in the entire GST layer [36]. However, reducing the thickness in dielectric metasurfaces makes the Mie resonance occur in shorter wavelengths [46]. Therefore, in order to have the magnetic dipole resonance around the operation wavelength of 1550 nm, the PCM and graphene layers are encapsulated between two silicon layers (see Fig. 1(A)). Silicon has been chosen for this design since it has a low loss at the operating wavelength, and at the same time, it has a refractive index close to the GST. Furthermore, silicon is a chemically and physically stable material and can act as a protective layer in the proposed structure. It is worth noting that it would be possible to reduce the GST thickness further (less than 100 nm). However, numerical results show that it will result in lower efficiency, and also more fluctuation in the amplitude of the reflected wave.

A procedure similar to what reported in [38] can be taken to fabricate the structure. Figure 1(C) shows suggested fabrication steps. As shown in this figure, as the first step, material layers are deposited on a silicon wafer. The graphene layers are grown using chemical vapor deposition (CVD) (and then transferred onto the structure), while the GST layer is deposited via thermal evaporation. In the second step, the desired pattern is written on the coating layer via electron beam lithography, and in the third step, plasma etching is used to develop the desired pattern. Finally, in the last step, the coating remnants are washed up.

The effective permittivity of the GST material is a function of its crystallization level and can be approximated using the Lorentz-Lorenz relation [47,48]:

$$\frac{{{\varepsilon _{eff}}(\lambda )- 1}}{{{\varepsilon _{eff}}(\lambda )+ 2}} = m\frac{{{\varepsilon _c}(\lambda )- 1}}{{{\varepsilon _c}(\lambda )+ 2}} + ({1 - m} )\frac{{{\varepsilon _a}(\lambda )- 1}}{{{\varepsilon _a}(\lambda )+ 2}}$$
where λ is the operation wavelength, ɛeff is the permittivity of the GST at the crystallization level m, and, ɛc and, ɛa are permittivity of GST in fully crystallized and fully amorphous states, respectively. Figure 2(A) shows the permittivity variation as a function of temperature at the wavelength of λ = 1.55 µm [49], while Figs. 2(B) and (C) show the permittivity versus the wavelength and crystallization level [49]. As shown in Fig. 2(A), the real part of the GST's permittivity significantly varies when its crystallization level changes, resulting in a detectable shift in the Mie resonance frequency of the metasurface unit cell. That causes a significant variation in the amplitude and phase of the wave reflected by the metasurface.

 figure: Fig. 2.

Fig. 2. Optical material characterstics of the GST layer. A: The real (blue line) and imaginary (red dashed line) part of GST permittivity variation as a function of temperature at the telecommunication wavelength of λ = 1.55 µm. B,C: B shows The real part and C shows the imaginary part of the permittivity of the GST's layer as a function of crystallization level (m), and the wavelength. The data is measured in Ref. [49].

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3. Electromagnetic response of the tunable unit cell

Here, we perform a full-wave numerical analysis to evaluate the electromagnetic response of the proposed metasurface. The numerical simulation is done using COMSOL RF module, a commercial solver based on finite element method. The simulation setup and boundary conditions are illustrated in Fig. 3(A). As shown in this figure, periodic boundary conditions are applied on the boundaries along the x-direction, and the structure is excited by a TE-polarized plane wave propagating in the -z direction. For the permittivity of the GST layer, the data shown in Figs. 2(B) and (C) are used. Silicon and SiO2 have an almost constant permittivity in the near IR range with the values of ɛsilicon = 12, ɛSiO2 = 2.08 The graphene layer is modeled as a 2D structure with a surface conductivity given by Kubo's formula [50]:

$$\begin{array}{l} \sigma (\omega ,\Gamma ,{\mu _c},T) ={-} j\frac{{{e^2}{k_B}T}}{{\pi {\hbar ^2}(\omega - j2\Gamma )}}(\frac{{{\mu _c}}}{{{k_B}T}} + 2ln({\textrm{exp}} ( - {\mu _c}/{k_B}T) + 1)) - \\ \frac{{j{e^2}(\omega - j2\Gamma )}}{{\pi {\hbar ^2}}}\int_0^\infty {\frac{{{f_d}( - \varepsilon ) - {f_d}(\varepsilon )}}{{{{(\omega - j2\Gamma )}^2} - 4{{(\varepsilon /\hbar )}^2}}}} d\varepsilon \: \end{array}$$
where ${f_d}(\varepsilon )$ is defined as:
$${f_d}(\varepsilon ) = {({\textrm{exp}} (\frac{{\varepsilon - {\mu _c}}}{{{k_B}T}}) + 1)^{ - 1}}\:\:\:\:\:$$
where e, ℏ and kB are the electron charge, the reduced Planck constant, and the Boltzmann constant, respectively, and T, Г and µc are the temperature, the scattering rate, and the chemical potential of the graphene layer, respectively.

 figure: Fig. 3.

Fig. 3. Electromagnetic response of the proposed unit cell with dimentiones mentioned in Fig. 1. A: simulation setup. B: Phase of the reflected wave as a function of wavelength and crystallization level, observed at one operating wavelength (1.55 µm) above the SiO2 surface C: amplitude ratio of the reflected wave as a function of wavelength and crystallization level. (D-G): Snapshot of spatial magnetic field distribution Hy (color map) and displacement current density (arrows) of the unit cell at the λ=1.55 µm for m = 0, m = 0.2, m = 0.4, and m = 0.6, respectively in the x-z plane. H: Amplitude (blue line) and phase (dashed red line) of the reflected wave at λ=1.55 µm as a function of crystallization level. I: Snapshot of spatial electric field distribution of the unit cell at the telecommunication wavelength for the crystallization level of m = 0.2 in the x-y plane. The color map shows the amplitude ${(E_x^2 + E_z^2)^{1/2}}$, and the arrows show the direction of the electric field.

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One of the fascinating features of phase change materials is that they are non-volatile, which means that they hold their crystallization state when their temperature drops down to the room temperature. Therefore, here we can assume that the bias voltage is first applied to the graphene heater to heat the GST layer, and then it is removed during the electromagnetic wave interaction with the metasurface. That means during the electromagnetic wave interaction with the metasurface, the metasurface and graphene will be at the room temperature, and the graphene layer would have a low chemical potential. Based on these conditions, we assume T = 300K, µc = 0 ev, Г = 5 ×1012 s−1 then we used Eq. (2) and Eq. (3) to calculate the surface conductivity of the graphene, which gave us σ = 60 – j0.06 µS at the wavelength of λ = 1.55 µm. This amount of surface conductivity (which is almost constant in 1–2 µm wavelength range) would have a negligible effect on the parameters of the reflected wave, which is consistent with previous reports that state graphene as a low loss and transparent heater in the near-IR region [40,41,44,45].

The results of this simulation are shown in Figs. 3(B)–3(I). As shown in Figs. 3(B) and (C), the first order Mie resonance, also known as magnetic dipole (MD) resonance, occurs in the vicinity of the operational wavelength of λ = 1.55 µm, leading to abrupt changes of the reflected wave parameters. These abrupt changes allow us to modulate the amplitude and phase of the reflected wave by adjusting the crystallization level of the GST layer. Figures 3(D)–3(G), and also Fig. 3(I), illustrate the field distribution inside the unit cell for different crystallization levels of the GST layer. The spatial distribution of intensified electromagnetic fields and circular shape of the displacement current in mentioned figures is another proof on the excitation of the first order Mie resonance at the wavelength of 1.55 µm and for the crystallization level of 0 to 0.6.

As the field intensity inside the unit cell increases, the slope of the phase variation also increases. Moreover, at the same time, the absorbance of the unit cell increases. These two phenomena are fundamentally related to each other by Kramers-Kronig relation [51]. In the design of phase gradient metasurfaces, it is favorable to have a high phase variation. However, the amplitude variation is not favorable at all, and we prefer to keep it as low as possible. Therefore, there is a trade-off here. To address this trade-off, we optimized the geometry parameters of the metasurface unit cells to have a balance between phase and amplitude variance at the desired wavelength (λ = 1.55 µm). As shown in Fig. 3(H), the phase variation range is 270°. This range could have been increased to the full phase range of 360°. However, the price of that would be drastic fluctuation in amplitude. So, we compromised to have both phase and amplitude variations in an acceptable range. Furthermore, the unit cell is designed to have the resonance at the low crystallization levels (specifically around m = 0.2); due to the fact that the GST layer has a relatively lower imaginary part for the permittivity in lower crystallization levels, which leads to a less absorption. At the mentioned crystallization level, imag (ɛeff) = 0.97, which is significantly lower than that of higher crystallization levels, e.g., imag (ɛeff) = 4.40, when m = 0.8 (see Fig. 2(C)).

4. Joule heating analysis

Since the crystallization level is controlled by the temperature, we need to perform Joule heating analysis to evaluate the performance of graphene heaters. Joule heating simulations have been performed by COMSOL Multiphysics heat transfer module, which solves the heat transfer equation [52]:

$$\rho {C_p}\frac{{\partial T}}{{\partial t}} - \nabla \cdot ({k\nabla \textrm{T}} )= {Q_e}$$
where ρ is density, Cp is the specific heat capacity at constant stress, T is the absolute temperature, t is time, k is thermal conductivity, and Qe is the heat source. Here, Qe is determined by Joule's law as ${Q_e} = {\bar{J}_{dc}}\cdot {\bar{E}_{dc}}$ [52], where ${\bar{J}_{dc}}$ is the current density and ${\bar{E}_{dc}}$ is the electrostatic field strength on the graphene layer. Table 1 shows the parameters used for Graphene and GST in the Joule heating analysis. Graphene layers are modeled as an electrically and thermally thin materials, which means that the electric current, heat flux and temperature difference along the thickness of the graphene are neglected, and only the tangential variations are considered. Due to the significant difference in electrical conductivity of graphene compared to other materials used in the metasurface, it is assumed that the electric current flows only through graphene layers. The length of unit cells along the y-axis is assumed to be 7µm, which is 4.51 times of the operational wavelength.

Tables Icon

Table 1. Graphene and GST parameters used in the Joule heating analysis

The results of this analysis are shown in Fig. 4. Figures 4(A)–4(C) illustrate the stationary state results in which the temperature distribution has reached its final state, while Fig. 4(D) illustrate the transient response of the metasurface. In order to investigate the heat distribution in unit cells, Figs. 4(A) and 4(B) show the metasurface in the x-z and x-y plane, when a 14 Volts bias voltage is only applied to the graphene heater of the middle unit cell, and other unit cells doesn't experience any voltage differene. As seen in these figures, the isothermal curves show us that heat has been distributed uniformly inside the central GST layer. In addition, due to the appropriate distance between adjacent unit cells, the heat is centralized at the central unit cell and has not significantly transmitted to adjacent ones. Figure 4(C) shows the GST layer of the middle unit cell temperature, and also the nearest point of adjacent unit cells’ GST layers as a function of applied voltage. The points in which the temperature is measured are shown in Fig. 4(A) by red dots. As shown in Fig. 4(C), when the bias voltage of the middle unit cell increases, the temperature in the middle unit cell significantly increases, while adjacent unit cells don’t experience a significant change in their temperatures. This is another evidence of the existence of suitable thermal isolation between adjacent unit cells.

 figure: Fig. 4.

Fig. 4. The results of Joule heating analysis. A, B: Heat distribution of the proposed tunable unit cell when the bias voltage of Vb= 14 V is applied to the graphene heater of the central unit cell. The adjacent unit cells are assumed to be turned off (Vb = 0 V). The length of unit cells along the y-axis is 7 µm. In A, the inset lines show isothermal surfaces, and in B, the heat distribution of the surrounding air is hidden in order to the heat distribution in unit cells becomes visible. C: The temperature of GST material of the middle (black line) and highest temperature of adjacent unit cells (dashed red line) as a function of the applied bias voltage, Vb. Red dots in A show the points where this temperature is calculated. D: The temperature at the center of the GST material of the middle unit cell as a function of time for different bias voltages.

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In order to understand the thermal behavior of the structure before reaching the stationary state, Fig. 4(D) shows the temperature at the center of the GST layer in the middle unit cell as a function of time. The initial temperature is assumed to be 20 °C. As shown in this figure, it takes around 500 ns to reach up to 90% of the final temperature. Given that it is needed another 400–500 ns to reach to the desired crystallization level [60], this design enables us to tune the crystallization level of GST in time scales around 1 µs.

By merging the results of the Electromagnetic and Joule heating studies (see Figs. 3(H) and 4(C)) with the GST material characteristics (see Fig. 2(A)), the relation between applied voltage and reflected wave characteristics can be found. Figure 5 shows the reflected wave characteristics as a function of applied bias voltage, Vb. According to this figure, to tune the characteristics of the reflected wave, the bias voltage must be tuned in the range of 10.5 −13.6 V.

 figure: Fig. 5.

Fig. 5. Amplitude (blue line) and phase (dashed red line) of the reflected wave at operational wavelength of λ = 1.55 µm, as a function of applied bias voltage Vb.

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One of the important requirements to realize a true tunable metasurface using GST change materials is designing a mechanism for crystallized-to-amorphous transition, which is known as the reset process. For accomplishing the reset transition, the temperature of the material needs to be raised to 600 °C [33,60]. However, the required time for this transition is much shorter than the time needed for amorphous-to-crystallized transition. According to the results of Fig. 4(C), the reset process can be achieved by applying a bias voltage of Vb = 27 V to heaters. Another alternative would be using a combination of Joule heating enabled by graphene heaters, and laser-induced heating, to reset all the unit cells at once. This method is experimentally realized in [61] for an integrated photonic switch structure. Since there would be no need to scan through whole unit cells or using spatial light modulators, this method is also practical for the resetting transition.

Another consideration in thermal tuning process is maintaining graphene thermal stability. Although this material has an extremely high melting temperature (around 5000 °C [62]), experimental studies show that single layer graphene gets damaged in temperatures above 800 °C and loses its quality [63]. Fortunately, our thermal simulations show that the temperature of the graphene heater always remain below 800 °C; even during full electrical reset process.

5. Optical beam steering using the proposed metasurface

By adjusting the phase spatial distribution of a reflected wave from a tunable metasurface, numerous photonic devices and applications can be achieved. Among the potential applications, a high speed, wide range, and precise optical beam steering is one of the most precious applications. A versatile optical beam steering device can be used in low-cost light detection and ranging (LiDAR) sensors [64]. The conventional LiDAR sensors use mechanical beam steering, which makes them costly, bulky, and power-hungry. Introducing a non-mechanical beam steering method with mentioned specifications is a big step toward LiDAR sensors development.

Here, the capability of our proposed tunable metasurface as a beam steering device in the telecommunication wavelength is investigated. According to generalized Snell's law, for a phase gradient metasurface with the phase variation in the x-direction, the relation between the angle of incidence θi and angle of anomalous reflection (θr) is as [65]:

$$\frac{{d\phi }}{{dx}}\; = \frac{{{k_0}}}{n}[sin({\theta _r}) - sin({\theta _i})]$$
where $d\phi /dx$ is the phase gradient of the metasurface along the x-axis, n is the refractive index of the surrounding space, and k0 is the wavenumber in the free space. In our case, by assuming normal incidence (θi = 0), and the air as the surrounding material, and also by applying the discretization of the phase gradient, Eq. (5) leads to:
$${\theta _r} = si{n^{ - 1}}(\frac{{\Delta \phi }}{{{k_0}d}})\;$$
where Δϕ is the progressive phase difference between adjacent unit cells, and d is the width of unit cells (d = W1). Therefore, by adjusting the progressive phase difference Δϕ, we can manipulate the reflection angle θr to our desired amount. It is worth mentioning that Eq. (6) can also be derived from phased array theory by considering θr as the steering angle [66].

In order to investigate the performance of the proposed tunable metasurface for beam steering application, the reflected wave of a metasurface consisting of 80 unit cells under the illumination of a normal TE plane wave, has been numerically calculated. For each unit cell, the phase of the reflected wave is tuned by adjusting the crystallization level of the GST layer (see Fig. 3(H)), which in turn is controlled by the voltage applied to the graphene heaters (see Fig. 5). Figure 6(A) shows the numerically calculated magnitude of the electric field of the reflected wave when the phase difference between unit cells are adjusted to be Δϕ = 60°. According to Eq. (6), for this value of phase difference, the reflection angle θr should be equal to 31.8°, which is more clearly shown in Fig. 6(B), that shows the radiation pattern of the metasurface when illuminated by a normally incident light. In this figure, the numerically calculated pattern is also compared with an ideal pattern, which is analytically calculated using the array factor formula [66]:

$$AF = \sum\limits_{n = 1}^{80} {{\textrm{exp}} (j(n - 1)({k_0}dcos(\theta ) + \Delta {\phi _n}))}$$

As shown in Fig. 6(B), the numerically calculated radiation pattern and the ideal analytically calculated one have the main lobe in the exact same direction. However, due to the coupling effect between adjacent unit cells with different crystallization levels, which is not considered in the array factor calculation, the numerically calculated radiation pattern of the metasurface shows slightly bigger side lobes when compared to the analytically calculated radiation pattern. Figure 6(C) shows the ideal and realizable metasurface phase distribution for the Δϕ = 60°. As shown in this figure, the realized reflection phase by the proposed tunable metasurface is very close to the ideal phase required for this application.

 figure: Fig. 6.

Fig. 6. Beam steering using the proposed tunable metasurface. A: Amplitude of the electric field of the reflected wave for the progressive phase difference of Δϕ = 60°. B: Polar plot of the normalized Intensity radiation pattern of the tunable metasurface consisted of 80 unit cell (blue line) and array factor of an Ideal metasurface with full phase coverage and constant reflection amplitude (dotted green line) for the progressive phase of Δϕ = 60°. C: Phase variation of the reflected wave of the tunable metasurface as a function of location. The black line shows the ideal phase variance, according to generalized Snell’s Law. The red dots show the realized phase variance by the proposed tunable metasurface. The plot belongs to Δϕ = 60°. D: Normalized Radiation pattern Intensities for different reflection angles, which corresponds to the different progressive phase difference.

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To illustrate the beam steering ability of the proposed structure, Fig. 6(D) shows the normalized radiation pattern intensity for different values of progressive phase difference Δϕ, which has been created by adjusting the applied voltage to graphene heaters (see Fig. 5). As shown in this figure, the main lobe of the reflected beam rotates from θr = 0° to θr = 65° as Δϕ increases from 0 to 105°. The highest obtained steering angle is θr = 65°. For bigger steering angles, sidelobe intensities would become comparable to the main lobe intensity. It is apparent that by adjusting Δϕ to negative values, beam turns to the opposite direction. Therefore, the proposed structure can provide the beam steering in the range of ±65°, which is quite enough for a wide range of applications. When steering the beam, the sidelobe level varies in the range of −13 dB (for Δϕ = 0°) to −6 dB (for Δϕ = 105°), and the half-power beamwidth increase from 2° (for Δϕ = 0°) to 6° (for Δϕ = 105°). However, the positive point about the side lobes is that the level of the side lobes adjacent to main lobes do not exceed −10dB within the range of θr = ±65°.

6. Conclusion

A tunable metasurface based on phase change materials and transparent graphene heaters was proposed. The unit cells consist of a thin GST and graphene layer sandwiched between 2 silicon layers. The proposed metasurface was both electromagnetically and thermally characterized using numerical simulations. Numerical simulations have shown that the proposed metasurface can modulate the phase of the reflected wave in the range of 0° to −270°, by tuning the crystallization level of the GST layers. In order to observe the performance of transparent graphene heaters, both stationary and time-dependent Joule heating analyses were performed. It was found out that by applying a DC bias voltage to the graphene heater, the temperature of the GST layer can be increased to the phase changing point in sub-microsecond time scales. Due to graphene transparency in the near-IR region, the impact of the graphene heater on optical response was insignificant. This transparency is the main reason for the superiority of graphene heaters over metallic heaters. Finally, a metasurface consisted of 80 unit cells as a beam steering device was designed, and its performance was studied through full-wave numerical simulations. It was shown that by individually tuning the crystallization level of GST layers which could be achieved by applying corresponding voltages to graphene heaters, the proposed metasurface could steer the reflected wave continuously in the range of θr = ±65°, while the adjacent sidelobe levels are less than −10 dB in the worst case. The findings of this study can help pave the way toward the development of low-cost electrically steering LiDARs.

Funding

Iran National Science Foundation.

Disclosures

The authors declare no conflicts of interest.

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2020 (4)

C. Zhang, J. Jing, Y. Wu, Y. Fan, W. Yang, S. Wang, Q. Song, and S. Xiao, “Stretchable All-Dielectric Metasurfaces with Polarization-Insensitive and Full-Spectrum Response,” ACS Nano 14(2), 1418–1426 (2020).
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G. K. Shirmanesh, R. Sokhoyan, P. C. Wu, P. C. Wu, H. A. Atwater, and H. A. Atwater, “Electro-optically Tunable Multifunctional Metasurfaces,” ACS Nano 14(6), 6912–6920 (2020).
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M. Julian, C. Williams, S. Borg, S. Bartram, and H. J. Kim, “Reversible optical tuning of GeSbTe phase-change metasurface spectral filters for mid-wave infrared imaging,” Optica 7(7), 746–754 (2020).
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J. Zheng, S. Zhu, P. Xu, S. Dunham, and A. Majumdar, “Modeling Electrical Switching of Nonvolatile Phase-Change Integrated Nanophotonic Structures with Graphene Heaters,” ACS Appl. Mater. Interfaces 12(19), 21827–21836 (2020).
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2019 (11)

P. Guo, A. Sarangan, and I. Agha, “A Review of Germanium-Antimony-Telluride Phase Change Materials for Non-Volatile Memories and Optical Modulators,” Appl. Sci. 9(3), 530 (2019).
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C. Wu, H. Yu, H. Li, X. Zhang, I. Takeuchi, and M. Li, “Low-Loss Integrated Photonic Switch Using Subwavelength Patterned Phase Change Material,” ACS Photonics 6(1), 87–92 (2019).
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F. Liu, M. Wang, Y. Chen, and J. Gao, “Thermal stability of graphene in inert atmosphere at high temperature,” J. Solid State Chem. 276, 100–103 (2019).
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W. Bai, P. Yang, J. Huang, D. Chen, J. Zhang, Z. Zhang, J. Yang, and B. Xu, “Near-infrared tunable metalens based on phase change material Ge2Se2Te5,” Sci. Rep. 9(1), 1–9 (2019).
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P. C. Wu, R. A. Pala, G. Kafaie Shirmanesh, W.-H. Cheng, R. Sokhoyan, M. Grajower, M. Z. Alam, D. Lee, and H. A. Atwater, “Dynamic beam steering with all-dielectric electro-optic III–V multiple-quantum-well metasurfaces,” Nat. Commun. 10(1), 3654 (2019).
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A. Forouzmand, M. M. Salary, G. Kafaie Shirmanesh, R. Sokhoyan, H. A. Atwater, and H. Mosallaei, “Tunable all-dielectric metasurface for phase modulation of the reflected and transmitted light via permittivity tuning of indium tin oxide,” Nanophotonics 8(3), 415–427 (2019).
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Y. Kim, P. C. Wu, R. Sokhoyan, K. Mauser, R. Glaudell, G. Kafaie Shirmanesh, and H. A. Atwater, “Phase Modulation with Electrically Tunable Vanadium Dioxide Phase-Change Metasurfaces,” Nano Lett. 19(6), 3961–3968 (2019).
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P. Salami and L. Yousefi, “Far-Field Subwavelength Imaging Using Phase Gradient Metasurfaces,” J. Lightwave Technol. 37(10), 2317–2323 (2019).
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T. Mohamadi and L. Yousefi, “Metamaterial-Based Energy Harvesting for Detectivity Enhanced Infrared Detectors,” Plasmonics 14(4), 815–822 (2019).
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A. L. Holsteen, A. F. Cihan, and M. L. Brongersma, “Temporal color mixing and dynamic beam shaping with silicon metasurfaces,” Science 365(6450), 257–260 (2019).
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M. Honari-Latifpour and L. Yousefi, “Topological plasmonic edge states in a planar array of metallic nanoparticles,” Nanophotonics 8(5), 799–806 (2019).
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2018 (10)

M. A. Shameli and L. Yousefi, “Absorption enhancement in thin-film solar cells using an integrated metasurface lens,” J. Opt. Soc. Am. B 35(2), 223 (2018).
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M. A. Shameli, P. Salami, and L. Yousefi, “Light trapping in thin film solar cells using a polarization independent phase gradient metasurface,” J. Opt. (Bristol, U. K.) 20(12), 125004 (2018).
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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. S. Faraji-Dana, and A. Faraon, “MEMS-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812–819 (2018).
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S. M. Choudhury, D. Wang, K. Chaudhuri, C. DeVault, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Material platforms for optical metasurfaces,” Nanophotonics 7(6), 959–987 (2018).
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P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
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S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
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A. Forouzmand, M. M. Salary, S. Inampudi, and H. Mosallaei, “A Tunable Multigate Indium-Tin-Oxide-Assisted All-Dielectric Metasurface,” Adv. Opt. Mater. 6(7), 1701275 (2018).
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A. Forouzmand and H. Mosallaei, “Dynamic beam control via Mie-resonance based phase-change metasurface: A theoretical investigation,” Opt. Express 26(14), 17948–17963 (2018).
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M. D. Goldflam, I. Ruiz, S. W. Howell, J. R. Wendt, M. B. Sinclair, D. W. Peters, and T. E. Beechem, “Tunable dual-band graphene-based infrared reflectance filter,” Opt. Express 26(7), 8532–8541 (2018).
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A. Sarangan, J. Duran, V. Vasilyev, N. Limberopoulos, I. Vitebskiy, and I. Anisimov, “Broadband Reflective Optical Limiter Using GST Phase Change Material,” IEEE Photonics J. 10(2), 1–9 (2018).
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2017 (7)

M. C. Sherrott, P. W. C. Hon, K. T. Fountaine, J. C. Garcia, S. M. Ponti, V. W. Brar, L. A. Sweatlock, and H. A. Atwater, “Experimental Demonstration of >230 ° Phase Modulation in Gate- Tunable Graphene − Gold Reconfigurable Mid-Infrared Metasurfaces,” Nano Lett. 17(5), 3027–3034 (2017).
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Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically Reconfigurable Metadevice Employing Nanostructured Phase-Change Materials,” Nano Lett. 17(8), 4881–4885 (2017).
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H. Lin, Y. Song, Y. Huang, D. Kita, S. Deckoff-Jones, K. Wang, L. Li, J. Li, H. Zheng, Z. Luo, H. Wang, S. Novak, A. Yadav, C. C. Huang, R. J. Shiue, D. Englund, T. Gu, D. Hewak, K. Richardson, J. Kong, and J. Hu, “Chalcogenide glass-on-graphene photonics,” Nat. Photonics 11(12), 798–805 (2017).
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E. Ganz, A. B. Ganz, L. M. Yang, and M. Dornfeld, “The initial stages of melting of graphene between 4000 K and 6000 K,” Phys. Chem. Chem. Phys. 19(5), 3756–3762 (2017).
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A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
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N. Raeis-Hosseini, J. Rho, N. Raeis-Hosseini, and J. Rho, “Metasurfaces Based on Phase-Change Material as a Reconfigurable Platform for Multifunctional Devices,” Materials 10(9), 1046 (2017).
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H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and Applications of Metasurfaces,” Small Methods 1(4), 1600064 (2017).
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2016 (8)

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, and O. Boyraz, “Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces,” J. Opt. Soc. Am. B 33(2), 189–194 (2016).
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Q. Wang, E. T. F. Rogers, B. Gholipour, C. M. Wang, G. Yuan, J. Teng, and N. I. Zheludev, “Optically reconfigurable metasurfaces and photonic devices based on phase change materials,” Nat. Photonics 10(1), 60–65 (2016).
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J. Rensberg, S. Zhang, Y. Zhou, A. S. McLeod, C. Schwarz, M. Goldflam, M. Liu, J. Kerbusch, R. Nawrodt, S. Ramanathan, D. N. Basov, F. Capasso, C. Ronning, and M. A. Kats, “Active Optical Metasurfaces Based on Defect-Engineered Phase-Transition Materials,” Nano Lett. 16(2), 1050–1055 (2016).
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M. Kim, J. Jeong, J. K. S. Poon, and G. V. Eleftheriades, “Vanadium-dioxide-assisted digital optical metasurfaces for dynamic wavefront engineering,” J. Opt. Soc. Am. B 33(5), 980 (2016).
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D. Schall, M. Mohsin, A. A. Sagade, M. Otto, B. Chmielak, S. Suckow, A. L. Giesecke, D. Neumaier, and H. Kurz, “Infrared transparent graphene heater for silicon photonic integrated circuits,” Opt. Express 24(8), 7871–7878 (2016).
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L. Yu, Y. Yin, Y. Shi, D. Dai, and S. He, “Thermally tunable silicon photonic microdisk resonator with transparent graphene nanoheaters,” Optica 3(2), 159–166 (2016).
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A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
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C. H. Chu, M. L. Tseng, J. Chen, P. C. Wu, Y. H. Chen, H. C. Wang, T. Y. Chen, W. T. Hsieh, H. J. Wu, G. Sun, and D. P. Tsai, “Active dielectric metasurface based on phase-change medium,” Laser Photonics Rev. 10(6), 986–994 (2016).
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2015 (5)

Y. Chen, X. Li, Y. Sonnefraud, A. I. Fernández-Domínguez, X. Luo, M. Hong, and S. A. Maier, “Engineering the phase front of light with phase-change material based planar lenses,” Sci. Rep. 5(1), 8660 (2015).
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S. A. Peng, Z. Jin, P. Ma, D. Y. Zhang, J. Y. Shi, J. Bin Niu, X. Y. Wang, S. Q. Wang, M. Li, X. Y. Liu, T. C. Ye, Y. H. Zhang, Z. Y. Chen, and G. H. Yu, “The sheet resistance of graphene under contact and its effect on the derived specific contact resistivity,” Carbon 82(C), 500–505 (2015).
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J. Sautter, I. Staude, M. Decker, E. Rusak, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Active tuning of all-dielectric metasurfaces,” ACS Nano 9(4), 4308–4315 (2015).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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M. Shoaei, M. K. Moravvej-Farshi, and L. Yousefi, “All-optical switching of nonlinear hyperbolic metamaterials in visible and near-infrared regions,” J. Opt. Soc. Am. B 32(11), 2358 (2015).
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2014 (3)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22(21), 26212 (2014).
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2013 (1)

A. N. Sidorov, D. K. Benjamin, and C. Foy, “Comparative thermal conductivity measurement of chemical vapor deposition grown graphene supported on substrate,” Appl. Phys. Lett. 103(24), 243103 (2013).
[Crossref]

2012 (1)

E. Pop, V. Varshney, and A. K. Roy, “Thermal properties of graphene: Fundamentals and applications,” MRS Bull. 37(12), 1273–1281 (2012).
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2011 (2)

J. Kang, H. Kim, K. S. Kim, S. K. Lee, S. Bae, J. H. Ahn, Y. J. Kim, J. B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11(12), 5154–5158 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
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2010 (2)

B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

A. Kabiri, L. Yousefi, and O. M. Ramahi, “On the fundamental limitations of artificial magnetic materials,” IEEE Trans. Antennas Propag. 58(7), 2345–2353 (2010).
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2009 (2)

H. T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nat. Nanotechnol. 4(12), 861–867 (2009).
[Crossref]

2008 (3)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

I. M. Park, J. K. Jung, S. O. Ryu, K. J. Choi, B. G. Yu, Y. B. Park, S. M. Han, and Y. C. Joo, “Thermomechanical properties and mechanical stresses of Ge2Sb2Te5 films in phase-change random access memory,” Thin Solid Films 517(2), 848–852 (2008).
[Crossref]

A. Redaelli, A. Pirovano, A. Benvenuti, and A. L. Lacaita, “Threshold switching and phase transition numerical models for phase change memory simulations,” J. Appl. Phys. 103(11), 111101 (2008).
[Crossref]

2007 (1)

J. P. Reifenberg, M. A. Panzer, S. Kim, A. M. Gibby, Y. Zhang, S. Wong, H. S. P. Wong, E. Pop, and K. E. Goodson, “Thickness and stoichiometry dependence of the thermal conductivity of GeSbTe films,” Appl. Phys. Lett. 91(11), 111904 (2007).
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Abdollahramezani, S.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alù, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 1.ahead-of-print (2020).

Adibi, A.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alù, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 1.ahead-of-print (2020).

Agha, I.

P. Guo, A. Sarangan, and I. Agha, “A Review of Germanium-Antimony-Telluride Phase Change Materials for Non-Volatile Memories and Optical Modulators,” Appl. Sci. 9(3), 530 (2019).
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Ahn, J. H.

J. Kang, H. Kim, K. S. Kim, S. K. Lee, S. Bae, J. H. Ahn, Y. J. Kim, J. B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11(12), 5154–5158 (2011).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
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Alam, M. Z.

P. C. Wu, R. A. Pala, G. Kafaie Shirmanesh, W.-H. Cheng, R. Sokhoyan, M. Grajower, M. Z. Alam, D. Lee, and H. A. Atwater, “Dynamic beam steering with all-dielectric electro-optic III–V multiple-quantum-well metasurfaces,” Nat. Commun. 10(1), 3654 (2019).
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Alexeev, A. M.

C. R. de Galarreta, I. Sinev, A. M. Alexeev, P. Trofimov, K. Ladutenko, S. G.-C. Carrillo, E. Gemo, A. Baldycheva, V. K. Nagareddy, J. Bertolotti, and C. D. Wright, “All-Dielectric Silicon/Phase-Change Optical Metasurfaces with Independent and Reconfigurable Control of Resonant Modes,” https://arxiv.org/abs/1901.04955 .

Alù, A.

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alù, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 1.ahead-of-print (2020).

Anisimov, I.

A. Sarangan, J. Duran, V. Vasilyev, N. Limberopoulos, I. Vitebskiy, and I. Anisimov, “Broadband Reflective Optical Limiter Using GST Phase Change Material,” IEEE Photonics J. 10(2), 1–9 (2018).
[Crossref]

Arbabi, A.

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. S. Faraji-Dana, and A. Faraon, “MEMS-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812–819 (2018).
[Crossref]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
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Arbabi, E.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, M. S. Faraji-Dana, and A. Faraon, “MEMS-tunable dielectric metasurface lens,” Nat. Commun. 9(1), 812–819 (2018).
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S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
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A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
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Atwater, H. A.

G. K. Shirmanesh, R. Sokhoyan, P. C. Wu, P. C. Wu, H. A. Atwater, and H. A. Atwater, “Electro-optically Tunable Multifunctional Metasurfaces,” ACS Nano 14(6), 6912–6920 (2020).
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ACS Nano (3)

C. Zhang, J. Jing, Y. Wu, Y. Fan, W. Yang, S. Wang, Q. Song, and S. Xiao, “Stretchable All-Dielectric Metasurfaces with Polarization-Insensitive and Full-Spectrum Response,” ACS Nano 14(2), 1418–1426 (2020).
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ACS Photonics (1)

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Figures (6)

Fig. 1.
Fig. 1. Geometry of the proposed metasurface A: schematics of the proposed unit cell. The left image shows how the materials are stacked together. The middle image shows the unit cell after fabrication (as shown in this figure, the voltage difference is applied to both sides of the graphene layer), and the right image is the side view of the metasurface unit cell with W1= 490 nm, W2 = 305 nm, hSilicon= 75 nm, hGST= 130 nm, hSiO2= 150 nm, hAu= 300 nm. B: schematics of the proposed metasurface. The crystallization level of each unit cell can be tuned independently through voltages applied to the graphene layer in each unit cell. The input electromagnetic wave is assumed to be a plane wave with E-field perpendicular to the unit cell's length (in line with the x-axis). C: A suggested fabrication procedure for the proposed metasurface.
Fig. 2.
Fig. 2. Optical material characterstics of the GST layer. A: The real (blue line) and imaginary (red dashed line) part of GST permittivity variation as a function of temperature at the telecommunication wavelength of λ = 1.55 µm. B,C: B shows The real part and C shows the imaginary part of the permittivity of the GST's layer as a function of crystallization level (m), and the wavelength. The data is measured in Ref. [49].
Fig. 3.
Fig. 3. Electromagnetic response of the proposed unit cell with dimentiones mentioned in Fig. 1. A: simulation setup. B: Phase of the reflected wave as a function of wavelength and crystallization level, observed at one operating wavelength (1.55 µm) above the SiO2 surface C: amplitude ratio of the reflected wave as a function of wavelength and crystallization level. (D-G): Snapshot of spatial magnetic field distribution Hy (color map) and displacement current density (arrows) of the unit cell at the λ=1.55 µm for m = 0, m = 0.2, m = 0.4, and m = 0.6, respectively in the x-z plane. H: Amplitude (blue line) and phase (dashed red line) of the reflected wave at λ=1.55 µm as a function of crystallization level. I: Snapshot of spatial electric field distribution of the unit cell at the telecommunication wavelength for the crystallization level of m = 0.2 in the x-y plane. The color map shows the amplitude ${(E_x^2 + E_z^2)^{1/2}}$, and the arrows show the direction of the electric field.
Fig. 4.
Fig. 4. The results of Joule heating analysis. A, B: Heat distribution of the proposed tunable unit cell when the bias voltage of Vb= 14 V is applied to the graphene heater of the central unit cell. The adjacent unit cells are assumed to be turned off (Vb = 0 V). The length of unit cells along the y-axis is 7 µm. In A, the inset lines show isothermal surfaces, and in B, the heat distribution of the surrounding air is hidden in order to the heat distribution in unit cells becomes visible. C: The temperature of GST material of the middle (black line) and highest temperature of adjacent unit cells (dashed red line) as a function of the applied bias voltage, Vb. Red dots in A show the points where this temperature is calculated. D: The temperature at the center of the GST material of the middle unit cell as a function of time for different bias voltages.
Fig. 5.
Fig. 5. Amplitude (blue line) and phase (dashed red line) of the reflected wave at operational wavelength of λ = 1.55 µm, as a function of applied bias voltage Vb.
Fig. 6.
Fig. 6. Beam steering using the proposed tunable metasurface. A: Amplitude of the electric field of the reflected wave for the progressive phase difference of Δϕ = 60°. B: Polar plot of the normalized Intensity radiation pattern of the tunable metasurface consisted of 80 unit cell (blue line) and array factor of an Ideal metasurface with full phase coverage and constant reflection amplitude (dotted green line) for the progressive phase of Δϕ = 60°. C: Phase variation of the reflected wave of the tunable metasurface as a function of location. The black line shows the ideal phase variance, according to generalized Snell’s Law. The red dots show the realized phase variance by the proposed tunable metasurface. The plot belongs to Δϕ = 60°. D: Normalized Radiation pattern Intensities for different reflection angles, which corresponds to the different progressive phase difference.

Tables (1)

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Table 1. Graphene and GST parameters used in the Joule heating analysis

Equations (7)

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ε e f f ( λ ) 1 ε e f f ( λ ) + 2 = m ε c ( λ ) 1 ε c ( λ ) + 2 + ( 1 m ) ε a ( λ ) 1 ε a ( λ ) + 2
σ ( ω , Γ , μ c , T ) = j e 2 k B T π 2 ( ω j 2 Γ ) ( μ c k B T + 2 l n ( exp ( μ c / k B T ) + 1 ) ) j e 2 ( ω j 2 Γ ) π 2 0 f d ( ε ) f d ( ε ) ( ω j 2 Γ ) 2 4 ( ε / ) 2 d ε
f d ( ε ) = ( exp ( ε μ c k B T ) + 1 ) 1
ρ C p T t ( k T ) = Q e
d ϕ d x = k 0 n [ s i n ( θ r ) s i n ( θ i ) ]
θ r = s i n 1 ( Δ ϕ k 0 d )
A F = n = 1 80 exp ( j ( n 1 ) ( k 0 d c o s ( θ ) + Δ ϕ n ) )

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