Enhanced Power Distribution and Symmetry in Terahertz Waveguides Using Graphene-Based Power Dividers

Abstract

This paper investigates a graphene-on-insulator power divider designed for terahertz applications based on spoof surface plasmon polaritons. We optimize structural parameters to maximize signal transmission from input to output ports while achieving a uniform and symmetrical electric field distribution at the output cross-section. Our findings indicate that utilizing three graphene layers significantly enhances power distribution and symmetry at output ports. We demonstrate electrical control over waveguide transmission properties by modulating the graphene chemical potential from 0 to 0.5 eV. The proposed device holds promise for applications in plasmonic circuits and on-chip interconnects operating within the terahertz frequency range.

1. Introduction

Plasmonic power dividers are devices that split an optical signal into multiple output signals with adjustable power ratios. They use plasmonic waveguides capable of guiding and manipulating light at the nanoscale [1,2]. Plasmonic power dividers utilize surface plasmon polaritons (SPPs), which are collective oscillations of electrons at a metal-dielectric interface [3,4,5]. By managing the properties of plasmonic waveguides—such as their geometry, material composition, and coupling mechanisms—it is possible to achieve precise control over how power is divided among the output ports. These devices have various applications, including in telecommunications [6,7], integrated photonics [8,9,10], and optical computing [11]. They can be used for signal distribution, power splitting, and even for optical signal processing tasks, such as wavelength division multiplexing (WDM) or mode division multiplexing (MDM).

Electromagnetic waves propagating along the joint surface of a metal (or a semi-metal) and a dielectric give rise to the formation of plasmonic structures. Surface plasmon polaritons, typically manifest within the visible spectrum, are primarily achieved by utilizing noble metallic elements like gold or silver. However, it is noteworthy that composite materials can also sustain these surface plasmon polaritons at lower frequencies. This phenomenon attests to the versatility and potential applicability of plasmonic systems across a wide range of frequencies, serving as an intriguing domain of study in the realm of optics and optical engineering [12,13]. Surface plasmons have served as a basis for the development of nanophotonic devices [14], the integration of photonics and electronic fields at the nanoscale [15], and finding applications in various fields such as imaging [16,17] or sensing [18].

Graphene is a two-dimensional material characterized by its crystalline structure and atomically thin thickness. It offers several advantages, including high electron mobility, excellent thermal conductivity, a large surface area, an adjustable bandgap, and biocompatibility. These properties make graphene an ideal material for high-performance electronic devices that are thermally sensitive and require rapid switching [19,20,21,22,23,24]. The 2D structure of graphene provides a large surface area, which can be utilized in devices such as sensors, energy storage, and catalysis [25,26]. Graphene has unique plasmonic properties, such as a high tunability of the plasmon frequency, making it an attractive material for plasmonic-based devices [27]. Graphene provides excellent possibilities for dynamic tuning of electromagnetic waves [28,29]. Graphene possesses unique electrical properties that can be easily manipulated by applying an external magnetic or electrostatic field. This ability allows for the emission of surface plasmons in the terahertz and infrared frequency bands. Compared to traditional materials like silver or gold, surface plasmon polaritons on graphene offer significant advantages, including tunability, low loss, and enhanced confinement [30]. Recent years have witnessed significant progress in the development of graphene-based electromagnetic devices, expanding the potential applications of this versatile material. For instance, Shao et al. [31] conducted a comprehensive review of emerging applications and properties of graphene-derived microwave metamaterials and meta-devices. Their work highlights the unique capabilities of graphene in creating tunable and reconfigurable electromagnetic structures, opening new avenues for device miniaturization and performance enhancement in the microwave regime. In the realm of stealth technology, Li et al. demonstrated a groundbreaking graphene-based optically transparent metasurface for microwave and terahertz cross-band stealth [32]. This innovation showcases graphene’s potential in creating multifunctional electromagnetic devices that can operate across different frequency bands, a crucial advancement for next-generation communication and defense systems. The noteworthy point is that graphene polariton plasmon is emitted at the edges of graphene and graphene nanoribbons; recently, most attention has been focused on the properties of graphene polariton plasmon propagation [33,34].

Plasmonic power dividers are among the most commonly used devices in optoelectronics thanks to their waveguide properties, which enable efficient power transfer from one point to another. The amount of power transmitted to the output of a plasmonic power divider depends on several factors, including the materials used, their dimensions, and the arrangement of the structure. Graphene has gained significant attention among the various materials used in plasmonic power dividers, particularly in the infrared and terahertz ranges. In the terahertz frequency range, T-shaped plasmonic dividers can be utilized to create a 90-degree bend in environments with a continuous refractive index with the aid of graphene. Graphene is a promising material for effective surface plasmon conduction and propagation in components with such capabilities. These designs are promising schemes for the applications of devices capable of working in the terahertz range [35]. Graphene is a two-dimensional material that influences the properties of the substrate beneath it. This interaction affects various factors, including the carrier density on the surface of graphene, its chemical potential, and conductivity. These characteristics offer greater flexibility in the design and optimization of graphene-based waveguides.

Graphene nanoribbon waveguides represent one of the most advanced techniques for controlling the emission of surface plasmon polaritons. These waveguides take advantage of the unique properties of graphene surface plasmons, which are most effective on narrow graphene ribbons. By studying graphene waveguides, researchers can achieve exceptional surface plasmon propagation characteristics. Additionally, this design offers a broad bandwidth. Recent studies have proposed various designs for graphene-based plasmonic devices, including plasmonic right-angled waveguide bends and dividers using graphene and transformation optics. These studies highlight the potential of graphene-based plasmonic devices for various applications in plasmonic circuits and optoelectronics. Furthermore, they can be utilized in integrated circuits based on graphene [36]. They can be used for power distribution in integrated circuits in the infrared and terahertz ranges. The full-wave simulation results in the article reported by M. Romagnoli et al. show that graphene-type plasmonic dividers have no reflection in 90-degree bends, and the input power is well divided and transmitted at the output [36]. A recent study presented the design of a two-by-four graphene plasmonic divider that utilizes a silicon sub-layer and a silica layer. The design features two one-by-two dividers made from silica, all of which are covered with graphene. This configuration reduces losses and generates surface plasmons in the direction of propagation, ultimately enhancing transmission along the waveguide [37]. The paper demonstrates that increasing the chemical potential from 0.1 volts to 0.5 volts causes the waveguide to shift from a passive to an active state. This change in chemical potential results in several effects:

1.

enhanced electrical conductivity in graphene, which improves the material’s plasmonic properties;

2.

modulation of the plasmon’s wavelength and strength, facilitated by an ionic gel gate configuration.

For graphene-based plasmonic switches, theoretical calculations and rigorous coupled-wave analysis simulations have shown excellent control over plasmon energy, reaching near-infrared spectral ranges using realistic chemical potential values for graphene.

While graphene has garnered significant attention for its unique properties in controlling terahertz radiation, it is important to acknowledge other materials that also demonstrate responsiveness to external stimuli in this frequency range. These materials offer alternative approaches for manipulating terahertz waves and expand the toolkit available to researchers and engineers in this field. Liquid crystals, for instance, have shown promise in controlling terahertz radiation. As reported by Yang et al. [38], liquid crystals can be used to create tunable terahertz devices due to their ability to change their molecular orientation in response to external electric fields. This property allows for developing electrically controllable terahertz phase shifters and filters. Another material of interest is vanadium dioxide (VO₂), which undergoes a reversible phase transition from insulator to metal when subjected to temperature changes or electric fields. Zhu et al. [39] demonstrated that VO₂ can be used to create active terahertz metamaterials, enabling dynamic control over terahertz wave propagation and absorption. These examples highlight the diverse range of materials being explored for terahertz applications, each offering unique advantages and potential use cases. While our work focuses on graphene-based devices, it is crucial to recognize the broader landscape of materials research in this field, as it may inspire future hybrid or alternative approaches to terahertz wave manipulation.

In this paper, we investigated the performance of plasmonic power dividers within graphene nanoribbon waveguides, with a primary focus on whether bends and slits in the structure lead to reflections or reduce propagation losses. We used optimized specifications to design a low-loss and low-reflection divider to address this. We developed a one-to-two graphene waveguide on a dielectric substrate with a constant refractive index based on the proposed design. By incorporating bends to minimize losses and manage reflections, we created an optimized graphene plasmonic waveguide operating at a frequency of 33.4 THz. Moreover, the structural parameters are optimized to have a uniform and symmetrical electrical field distribution at the cross-section of output waveguides.

2. Graphene Plasmon-Polariton Mode Characteristics

Graphene is usually modeled in two dimensions. The thickness of graphene is considered equal to d = 0.35 nm. The control of graphene depends on the surface conductivity, which is modeled by Kubo’s formula as follows:

$$\sigma ={\sigma }_{intra}+{\sigma }_{inter}.$$

(1)

The first and the second terms are written as follows, respectively [36]:

$${\sigma }_{intra}\left(\omega \right)={\displaystyle \frac{i{e}^2{k}_{B}T}{\pi {\hslash }^2(\omega +i2\Gamma )}}[{\displaystyle \frac{{\mu }_c}{k_{B}T}}+2ln(e^{-{\displaystyle \frac{{\mu }_c}{k_{B}T}}}+1)].$$

(2)

$${\sigma }_{inter}\left(\omega \right)={\displaystyle \frac{i{e}^2}{4\pi \hslash }}ln{\displaystyle \frac{2|{\mu }_c|-(\omega +i2\mathsf{\Gamma })\hslash }{2|{\mu }_c|+(\omega +i2\mathsf{\Gamma })\hslash }}.$$

(3)

where $\omega$ is the angular frequency, $T=300$ K, temperature in Kelvin, e is the electric charge of an electron, ℏ is Planck’s constant, $K_B$ is Boltzmann’s constant, ${\mu }_c$ is the graphene chemical potential that in our proposed structure is changed from 0 to 0.5 electron volts, and $\mathsf{\Gamma }$ is the rate of scattering parameter, which is considered to be 0.00011 electron volts. When the imaginary part of the conductivity is positive, graphene acquires metallic properties that can emit the TM mode.

3. Proposed Structure of Graphene Plasmonic Divider

Plasmonic waves are generated at the interface between a metal (or semiconductor) and a dielectric material. In the proposed structure, we consider a dielectric with a refractive index of n = 2. The design is three-dimensional, with dimensions of x = 600 nm, y = 600 nm, and a height of z = 400 nm. Since graphene is used as a shell on the surface, its dimensions are defined only in the two-dimensional x and y directions. Figure 1 provides a schematic representation of the proposed waveguide design and the overall dimensions of the structure.

In this study, we designed graphene waveguides to function as a one-to-two power divider. The design allows light to enter through an input port and exit from two output ports labeled Output1 and Output2. The thickness of the graphene in this structure is 0.35 nm, representing a single layer, and it comprises four graphene waveguides.

The first component, referred to as waveguide1, serves as the input for the entire structure. The second waveguide, named waveguide2, forms the central part of the design, while the third waveguide, known as waveguide3, is where the first output is obtained at the end of this section. The fourth waveguide, designated waveguide4, is where the second output is extracted.

Simulation Methodology

The dimensions of the structure used for the simulation are accurately illustrated in Figure 1, with additional simulation parameters provided in Section 2 and Section 3. The dimensions are defined as $x=y=600\mathrm{nm}$ and the height $z=400\mathrm{nm}$, corresponding to the substrate. A single layer of graphene, with a thickness of $0.35\mathrm{nm}$, is placed on the substrate and treated as a two-dimensional material in the design, while the simulation is conducted in three dimensions.

The graphene waveguide is segmented into four distinct waveguides on the substrate. Waveguide 1 (input) measures $275\mathrm{nm}$ in length (x-direction) and $70\mathrm{nm}$ in width (y-direction). Waveguide 2 has dimensions of $50\mathrm{nm}$ in the x-direction and $260\mathrm{nm}$ in the y-direction. Waveguide 3 measures $275\mathrm{nm}$ in the x-direction and $50\mathrm{nm}$ in the y-direction, with Waveguide 4 having the identical dimensions as Waveguide 3, differing only in coordinates. The distance between the two output ports is calculated based on the dimensions of the waveguides, resulting in a distance of 160 nm.

The scattering parameters for graphene are set at $\mathsf{\Gamma }=0.11$ meV and the ambient temperature is maintained at $300\mathrm{K}$. Meshing parameters are established with $\mathsf{\Delta }x=\mathsf{\Delta }y=3.5\mathrm{nm}$ and $\mathsf{\Delta }z=4\mathrm{nm}$, alongside a minimum mesh size of $0.1\mathrm{nm}$ for graphene. The excitation mode used for this simulation is Transverse Electric (TE), with the frequency of excitation varying from 1 to $40\mathrm{THz}$. Due to the presence of graphene, the simulation leverages Maxwell’s equations in three dimensions using the Finite Difference Time Domain (FDTD) method. The FDTD is a powerful numerical technique used to solve Maxwell’s equations, which describe the behavior of electromagnetic fields. It is particularly useful for modeling the interaction of light with materials and structures, making it a cornerstone in various fields like photonics, electromagnetics, and optics [40,41,42,43,44]. The simulation time is set to $1900\mathrm{fs}$ in the FDTD window, with the environment maintained at $300\mathrm{K}$ under perfectly matched layer (PML) and symmetric boundary conditions. To analyze the results, DFT monitors are positioned at the output ports to capture the intensity of the electric and magnetic fields, as well as the power and transmission levels. Additionally, monitors are installed over the entire structure at the height of $z=5\mathrm{nm}$ to observe the electric and magnetic field profiles. In these monitors, the number of sampling points and the sampling rate are uniformly distributed with 1000 points across the frequency range of 1 to $40\mathrm{THz}$.

4. Results and Discussion

This study’s main point of interest is the change in graphene’s behavior on the underlying material, which creates plasmonic properties in it. The field profile in these areas must be calculated to observe the distribution of surface plasmons and transition plasmons at both output ports. By introducing input light into the waveguide of the structure and varying the chemical potential of graphene from 0 to 0.5 eV, we can investigate the propagation and transmission of plasmonic waves. We divide the incoming light radiation, with a frequency range of 1–40 THz, into 1000 points to calculate the field profile at different frequencies. For each frequency irradiated onto the structure, we can observe changes in the field as the frequency varies, which allows us to select the most suitable mode for plasmonic waveguide operation. Given the variability in graphene’s behavior at different light frequencies, we should analyze both the real and imaginary parts, as illustrated in Figure 2a and Figure 2b, respectively.

Figure 2 shows the behavior of graphene’s real and imaginary parts with increasing frequency. Figure 2a shows the real part of graphene conductivity from the frequency of 1 to 40 THz. In the range before 2.5 THz, it can be seen that, with the increase in the frequency, the real part of graphene conductivity decreases until it almost reaches 2.5 THz. As the frequency increases, the real part of graphene’s conductivity also increases, causing light to diverge within the structure. Conversely, the imaginary part of graphene’s conductivity, which indicates light absorption in the material, decreases with rising frequency. The chemical potential of graphene can be independently controlled to modulate the plasmonic properties of waveguides. When the chemical potential of graphene is set close to zero electron volts, the propagation and transmission of plasmonic waves are effectively inhibited. This claim is supported by the results shown in Figure 3, where a zero chemical potential results in the absence of propagated plasmonic waves within the structure. The $E_z$ field distribution profile can be seen at the entrance edge of the first waveguide, while no transmission and propagation is observed in Waveguides 2, 3, and 4.

The waveguide can be regarded as inactive because the maximum radiated field occurs at the entrance of the structure. However, the field is not emitted towards the edges or the waveguide shell at the output ports. In the next phase of our study, we will examine the propagation properties of plasmonic waves within the structure as the chemical potential of graphene is varied from 0 to 0.5 eV. Figure 4 illustrates the real and imaginary parts of graphene’s conductivity at a chemical potential of 0.5 eV across a frequency range of 1–40 THz.

Figure 4a,b illustrate the real and imaginary parts of graphene conductivity, respectively. It is evident that both the real and imaginary components decrease from frequencies of 1–40 THz. The real part of the material’s conductivity influences the behavior of the refractive index of light in graphene, which decreases as the light frequency increases. Conversely, the imaginary part indicates the extent of absorption within the material. As shown in Figure 4, the amount of absorption in graphene diminishes with increasing frequency.

In this context, we also examine the characteristics of graphene waveguides. Figure 5 presents the field profile for a frequency of 33.4 THz at the cross-section of the output waveguides. This figure demonstrates that the input light is effectively transmitted to the output ports in the graphene plasmonic waveguides through the designed power divider, provided that the chemical potential of graphene is set to 0.5 eV.

In Figure 5, the distribution of the electric field in the $E_x$ view can be seen based on the comparative pattern of the field and its distribution in the waveguide. Compared to Figure 3, where the light was not coupled in the structure. As can be seen in Figure 5, the field at the edges and the graphene shell are being transferred and propagated to the output port. Graphene waveguides generally have losses, but in T-shaped graphene waveguides, if the ratio of input and output ports arm size ($d_{in}$ and $d_{out}$) are appropriately selected, the transmission of waveguides can be controlled and adjusted to the desired value at a specific frequency. The field profile in the direction of $E_z$ through the structure is demonstrated in Figure 6 for the frequency of 33.4 THz.

The field profile shown in Figure 6 indicates that the plasmonic field intensity is unevenly distributed throughout the structure. This suggests that, while light enters the first waveguide (input port) and propagates towards the second waveguide, only a very small amount of this field couples to the third and fourth waveguides (output waveguides). Consequently, the structure exhibits a low transmission coefficient.

To address this issue and enhance the transmission coefficient, shortening the length of the second waveguide equally from both the top and bottom is proposed. As illustrated in Figure 7, the middle waveguide will be shortened by 45 nm from both the top and bottom, making the average wavelength size equal to 170 nm. This adjustment will bring the third and fourth waveguides closer together in the Y-direction coordinates.

The key point is that the dimensions of the first, third, and fourth waveguides, as well as the substrate, remain unchanged. Additionally, the coordinates of the first waveguide are fixed. Due to a reduction of 45 nm at the lower part of the second waveguide, the fourth waveguide will be shifted upwards by the same amount. As a result, the third and fourth waveguides are now closer to each other.

Next, we examine the effect of light coupling on the entrance waveguide of the structure and the propagation of plasmonic waves within it. For this analysis, we assume the chemical potential of graphene to be 0.5 eV. We introduce a light source with a frequency of 33.4 THz at the input. According to Figure 8, it is evident that stronger electric fields are generated at a frequency of 33.4 THz compared to what is shown in Figure 6. This stronger field produces more plasmonic waves, which subsequently reach the third and fourth waveguides (the output ports).

The field profile distribution through the structure and the light intensity at the output ports are the most important parameters in the design of a waveguide. As shown in Figure 5 and Figure 8, the field intensity at the external edge of output ports is much higher than it is at its internal edge. This unsymmetrical field distribution at the output ports negatively affects the next stage, which will receive the output light and degrade its performance. Therefore, it was necessary to redesign the structure to solve this problem. In this research, the thickness of the graphene layer is considered to solve the problem, and its impact on the light distribution through the output waveguides and the light intensity at the output ports were studied. Figure 9a shows the field distribution at the output ports of the structure for a device with one, two, and three layers of graphene. This figure shows that the structure with one layer of graphene has a very unsymmetrical and non-uniform field distribution at its output ports. In this structure, the light intensity at the external edge of output ports is twofold more than the light intensity at its internal edge. Moreover, the cross-section of the output ports has a non-uniform light intensity. In the next stage, the number of graphene layers was increased to two layers, and the optical characteristics of the structure were investigated. Figure 9b shows the field distribution at the output of this schema, which has improved considerably the unsymmetrical field distribution at the output ports, and both edges have almost equal light intensity, but, in this design, the light intensity at the output ports is lower than the structure with one-layer graphene. A structure with three layers of graphene was also studied to achieve a more optimum result. As shown in Figure 9b, the output cross sections have a symmetrical light distribution at both edges, with increased intensity compared to the former schemes.

Following the approach in [45], we evaluated our device’s insertion loss (IL) and power splitting ratio (PSR):

$$\mathrm{IL}=-10{log}_{10}\left(\right|S_{21}{|}^2+|S_{31}{|}^2)$$

(4)

$$\mathrm{PSR}={\displaystyle \frac{|S_{21}{|}^2}{|S_{31}{|}^2}}$$

(5)

where $S_{21}$ and $S_{31}$ are the transmission coefficients to the two output ports. Figure 10 shows the transmission characteristic of the designed device from each ports and total transmission at the output ports. Our simulations show that the proposed device has 44% transmission at each port and achieves an average insertion loss of 4.1 dB over the frequency range of 1–33.4 THz. The power splitting ratio remains within 1 over the operational bandwidth, indicating an excellent balance between the output ports.

Inspired by [46], we conducted a detailed bandwidth analysis. Our device exhibits a −3 dB bandwidth of 33.4 THz.

To contextualize our results, we present a comparison with recent terahertz power dividers. Our work demonstrates a bandwidth of 33.4 THz, an insertion loss of 4.1 dB, and offers tunability. In comparison, the device reported in [45] operates at 1.5 THz with a bandwidth of 0.5 THz and an insertion loss of 3 dB, but lacks tunability. The device presented in [46] functions at 2.0 THz with a bandwidth of 0.3 THz and an insertion loss of 2.5 dB, and offers tunability. Our device demonstrates competitive performance in terms of bandwidth and insertion loss while offering the additional advantage of tunability through graphene’s chemical potential. To further contextualize our results, we present a comparison with recent terahertz power dividers in

Table 1. Comparison of Graphene-Based Devices.

Structure	Operating Frequency (THz)	Transmission Efficiency (%)	${\mathit{\mu }}_{\mathit{c}}$ (eV)	Ref
Graphene Nanoribbon Rectangular Ring Resonator	21	0.83	0.25–0.35	[47]
Graphene Plasmonic Crystal	31	0.99	0.1–0.5	[48]
Graphene on Power Divider Structure	15	0.95	0.3–0.9	[49]
Graphene-on-Insulator	33.4	0.57	0.1–0.5	This work

:

Our device demonstrates competitive performance in terms of bandwidth and insertion loss while offering the additional advantage of tunability through graphene’s chemical potential.

Experimental Feasibility and Challenges

In this subsection, we discuss the experimental feasibility of implementing the graphene-based power divider design presented in this paper, along with the challenges that must be addressed for successful realization.

1.

Material Synthesis and Availability: The primary material utilized in our design is graphene, which has become increasingly accessible due to advancements in synthesis techniques such as chemical vapor deposition (CVD) and liquid-phase exfoliation. These methods enable the production of high-quality graphene sheets suitable for integration into photonic devices. However, ensuring uniformity and scalability during fabrication remains a significant challenge that must be overcome.

2.

Integration with Existing Photonic Technologies: Our design aims to leverage graphene’s unique plasmonic properties within existing terahertz systems. Integrating these devices with conventional silicon-based photonic platforms could enhance their practical application. Nevertheless, achieving efficient coupling between graphene and traditional materials poses challenges, particularly in minimizing losses at the interfaces.

3.

Fabrication Techniques: The fabrication of nanoscale structures, as proposed in our simulations, necessitates precise lithography techniques. Current methods, such as electron-beam lithography (EBL) or nanoimprint lithography, can achieve the required resolutions but are often time-consuming and costly. Developing more efficient and cost-effective fabrication processes will be essential for practical applications.

4.

Characterization and Testing Protocols: Once fabricated, it is crucial to characterize the performance of these devices under operational conditions. This includes measuring transmission efficiency and power distribution while assessing the impact of environmental factors such as temperature and humidity on device performance. Establishing robust testing protocols will be necessary to validate simulation results and ensure reliability.

5.

Future Research Directions: While our study lays a solid foundation for theoretical exploration, further research is needed to address these challenges comprehensively. Future work could focus on prototyping physical devices based on our simulations, followed by iterative testing and optimization using empirical data. This will not only validate our findings but also contribute to refining the design for practical applications.

In conclusion, while our proposed graphene-based power divider shows promising theoretical results through simulation, translating these findings into practical implementations will require addressing several challenges related to material synthesis, integration with existing technologies, fabrication techniques, and thorough testing protocols. Ongoing advancements in nanotechnology and materials science are expected to facilitate overcoming these hurdles in future research endeavors.

5. Conclusions

Power dividers are waveguides that transmit power to designated output ports. The amount of light transmitted to these output ports is influenced by several factors, including the waveguide’s length, the materials used in the design, the operational frequency, and the structural symmetry. Most dividers aim to equally divide power within a system.

In this research, we designed a one-to-two plasmonic divider operating in the terahertz range. The design consists of a patterned graphene layer on an insulating substrate with a refractive index of 2, illuminated by a light source with frequencies ranging from 1 to 40 terahertz. By depositing graphene on the substrate, we create a plasmonic waveguide. Adjusting the chemical potential of the graphene within the waveguide from 0 to 0.5 eV allows for electrical modulation of the waveguide’s transmission properties.

In this study, we determined that the optimal condition for plasmon propagation and transmission occurs at a graphene chemical potential of 0.5 eV at a frequency of 33.4 THz. We investigated how the structural dimensions affect the transmission characteristics of the waveguide and reported the design that achieved maximum transmission. Additionally, we examined the influence of graphene thickness on light intensity and distribution at the output cross-section, ultimately presenting a structure that yields maximum intensity and symmetrical distribution at the output ports.