Design of a Low Power Hybrid Electro-Optic Plasmonic Modulator Based on ITO and Graphene

: In this paper, a hybrid plasmonic modulator based on ITO and graphene has been proposed and designed. Graphene and ITO are used in the active region, which increases the light-matter interaction and reduces the device's operating voltage in the proposed modulator. As a result, it increases the extinction ratio (ER), reduces power consumption and device footprint in the proposed modulator compared to similar modulators. The values of 14 dB/µm and 5.4 fJ are obtained for ER and power consumption, respectively. The time-domain finite-difference (FDTD) method is used to simulate the modulator. The integration of a modulator with high light-matter interaction and low power consumption in the silicon-on-insulator platform has significant potential for broadband, compact and efficient communication interconnects and circuits.


Introduction
One of the key elements in optical electronics is the silicon-based optical modulator, connecting the two fields of photonics and electronics by converting an electrical signal into an optical signal. The key characteristics of the optical modulator are low power consumption, compact size, high extinction ratio (ER), and low insertion losses. Therefore, designing optical modulators with optimum parameters is essential. The architecture of typical modulators such as silicon-based structures [1,2], high-quality resonant structures [3,4], and Mach Zehnder structures [5,6] are rarely able to optimize all modulator parameters simultaneously. Such structures have drawbacks such as narrow bandwidth, high-energy consumption as well as large size. Development of new modulators with compact size and broadband is required [7]. Metal oxide semiconductor-based hybrid plasmonic waveguides are used to design compact, broadband silicon-based optical modulators. These waveguides use doped silicon, Indium Tin Oxide (ITO), vanadium dioxide, or graphene [7][8][9][10][11]. A fundamental characteristic of these materials is adjusting the density of carriers and injecting charge into the material by applying an electric field [12][13][14][15][16]. Recently, directional coupler-based devices have been investigated [8,9,17]. In these structures, by changing the density of plasmonic material carriers in the coupler, the coupling rate and attenuation coefficient change, and the input signal can be modulated.
Plasmonic structures enhance light-matter interaction in optical devices and forming a strong local field interaction with plasmonic resonances. Based on this, combined plasmonic waveguide modulators (HPW) [12,16,[18][19][20] and Metal-Insulator-Metal (MIM) [21,22] have been introduced. In these structures, high confinement of the optical field leads to increasing interaction of light and matter. In recent years, the use of graphene as an active element in optical modulators has been considered. Graphene has unique properties such as a unique linear energy band, high carrier mobility at room temperature, and controllable light transmission and carrier density by applying electric media. These properties have led to the widespread use of graphene in electro-optical modulators from the visible range to terahertz [23][24][25][26][27][28]. However, these structures suffer from low ER due to poor interaction between graphene and light-wave. Therefore, increasing the interaction between optical signals with graphene is very important to achieve optical devices that use graphene adjustability [29].
On the other hand, ITO-based modulators have high ER but suffer from high operating voltages and high power consumption. The ITO layer can be used in graphene plasmonic waveguides to increase graphenebased modulator and optical signal interaction [29,30].
In this paper, a plasmonic modulator based on ITO and graphene is proposed and designed. The modulator structure consists of two silicon waveguides which a coupler is coupling these two waveguides. The coupler consists of Si/Graphene/HfO2/ITO/HfO2/Graphene vertical stack. The use of ENZ properties of both graphene and ITO materials has led to the design of modulators with low operating voltage and high resolution. The optical properties of the proposed modulator are investigated using the FDTD method.  Figure 1 shows the proposed modulator structure, which consists of three waveguides. Two of them are silicon waveguides, and one is a plasmonic waveguide, which the plasmonic waveguide placed between the two silicon waveguides. The plasmonic waveguide is composed of ITO and multilayer graphene separated by HfO2 dielectric and two silicon layers. The ITO and graphene layers are sandwiched between two layers of silicon.

Configuration and Characterization of hybrid plasmonic waveguide
The height and width of the two outer silicone waveguides HSi and WSi are assumed. The width and height of the middle waveguide are WPL and HPL, respectively. The height of the ITO layer is HITO, and the height of the HfO2 layer is HHfO2.
To investigate the epsilon near zero (ENZ) effect of two materials (ITO and graphene), we model the ITO and graphene using the Drude-Lorentz model and the Kubo formula, respectively.
At first, the refractive index of graphene will be investigated, which is related to its dynamic conductivity. The conductivity of graphene can be described using the Kobo equation, which includes intraband and the interband ( int int ra er    ), as follows [23,31,32]: Where kB is the Boltzmann constant, T is the temperature, is the Fermi-Dirac distribution, h is the reduced Planck's constant, μc is the chemical potential, 1   is the charged particle scattering rate, and ω is the angular frequency.
The relationship between voltage and chemical potential is defined Surface permittivity is obtained using graphene conductivity ( , at room temperature and λ = 1.55 μm: is the effective thickness of graphene [31,32]. The real part of the permittivity changes from positive to negative values as the chemical potential increased [31]. An ITO layer has been used in the plasmonic waveguide to increase the interaction between the graphene and optical fields [33]. The ITO permittivity is described using the Drude-Lorentz model (equation 1) [34,35]. ). It causes significant confinement of the electrical field in the ITO and dielectric interface, and it improves the interaction of light and matter. to the ENZ effect in graphene and the other to the ENZ effect in the ITO. The first peak is affected by the chemical potential of graphene, and the second peak is related to the ITO. Because the impact of ENZ on graphene has occurred at a lower voltage, if the two peaks are combined by increasing the number of graphene layers, a lower operating voltage is achieved. Modulators with this effect could have higher efficiency and lower energy consumption [39]. As the number of graphene layers increases, the two peaks propagation loss due to the effect of ENZ on graphene and ITO merged, and the propagation loss at voltage 0.62 V increases (figure 2 (c)). Also, The use of a large number of graphene layers will cause the properties of graphite, and the effect of ENZ will be attenuation. Therefore, we consider 8 layers of graphene.
The intensity of the guided mode in on state (0 V) and in the off state (0.62 V) is shown in figure 3(b) and 3(c), respectively. The intensity of the guided mode in 0 V is distributed in the active layers in the coupling region ( Figure 3(b)). In the 0.62 V, it is concentrated in the ITO and graphene layer (Figure 3(c)), and high losses occur due to the ENZ effect.

Design and Simulation of modulator
The device was simulated with the FDTD method in 1.55 µm wavelength. The refractive index of the materials is assumed to be: 3 [40]. WSi=300nm and HSi=250 nm are assumed to have a device with a compact size. For smaller sizes (WSi<300 nm), the guided mode did not support.
The effective index of silicon and plasmonic waveguides should be matched to increase the coupling rate between waveguides and reduce the insertion loss [41,42]. The coupling length (Lc) is calculated by coupling theory [34,43,44]. The device propagation mode has been found with cross-section simulation. n1, n2, and n3 are the effective index of the eigenmodes, which are symmetric mode (mode 1), asymmetric mode (mode 2), and symmetric mode (mode 3), respectively. Eigenmodes modes should apply to equation 6 to achieve maximum output power in V=0 [34,35,44]: The effective index of eigenmode modes for different values of the gap (distance between the waveguides) is shown in figure 4 (b). g = 30nm has been considered based on figure 4 (b) and equation 6.
The coupling length is obtained by the following equation [34,35,44]: Lc is equal to = 4.9 (in the λ = 1.55µm). Figure 5 shows the coupling length with voltage change.
By changing the voltage, the coupling length shows the dynamic behavior that results from the change of the real and imaginary parts of the effective index. Changing the coupling length disrupts the power coupling and thus has a role in attenuating the output power.

Properties of the hybrid plasmonic modulator
The device performance's main characteristics are presented in this section. Modulation speed, power consumption, propagation loss, and extinction ratio (ER) are investigated. The on/off extinction ratio is about 14 dB/µm; ER equals the difference between the propagation loss at the zero voltage and 0.62 V (ER=Loss0.62V-Loss0V) [31]. Loss in zero voltage is 1.6 dB/µm; also, we set the device length equal to coupling length. Figure 6 shows the ER and propagation losses for different wavelengths. The proposed modulator's ER is better than modulators in [31,45]. The resistance and capacitance of the device limit the modulation speed of the optical modulator. Power consumption is also related to modulation voltage and capacitance.
Capacitance is calculated by equation 8. The capacitors are modeled with a parallel plate structure (graphene/ HfO2/ITO interface) [31,44]. With this definition, there are two capacitors in the structure.

Conclusion
The optical modulator based on coupling between waveguides with vertical plasmonic structure was proposed and designed. The graphene and ITO were used in the plasmonic region of the modulator to decrease the operating voltage and increase the light-matter interaction. The modulator had a high ER (14 dB/µm), a compact size (4.9 µm), and low power consumption of (5.4 fJ). The modulator also had a broadband performance. The modulator characteristic in comparison to other similar modulators showed significant improvement. This plasmonic modulator with high ER, relatively low IL, and broadband could be used compact size, energy-efficient and potentially fast on-chip communication interconnects for the photonic integrated circuit.

Conflicts of interest/Competing interests
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Authors' contributions
The authors' contributions are equal. Figure 1 3D view of the proposed structure  The coupling length with voltage change Figure 6 ER as a function of wavelength