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Abstract
Optical splitters are promising photonic devices for next-generation photonic integrated circuits, which enable signal distribution and routing between the different components, facilitating complex optical functionalities on a single chip. This research introduces what we believe is a novel numerical technique for enhancing optical network efficiency by incorporating a taper-based step-index (SI) Y-branch multimode interference (MMI) splitter with organic-inorganic hybrid polymer materials. The proposed device comprises a core width of 5 µm for the input and output waveguides to satisfy the single-mode conditions. We designed and optimized the MMI splitter using the beam propagation method (BPM). The splitter demonstrates the power splitting property with an efficiency of 86%. The excess losses for the MMI splitter are 0.52 dB and 0.50 dB for TE and TM modes, respectively, at 1.55 µm. The polarization dependence loss (PDL) and propagation loss (PL) are 0.015 dB and 0.00019 dB/µm, respectively.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The existing data transmission systems cannot meet the growing bandwidth demand for quick and efficient data transmission, particularly in cloud computing and high-performance computing (HPC) systems. Optical interconnects offer a crucial solution to address these challenges. It has the potential to revolutionize data transfer speeds, decrease delays, improve system reliability [1], and introduce a new era for optical communication systems. The optical communication systems transfer data with the speed of light, which is much higher than that of the traditional electrical interconnects [2]. In particular, optics possesses unique properties, and it has a wide bandwidth and experiences with minimal signal weakening over long distances. These characteristics make it a perfect fit for today's data transmission needs [3]. Additionally, optical interconnects exhibit less power consumption and generate less heat, which is environment-friendly [4]. Hence, optical interconnects can be the potential candidate devices for photonic integrated circuits (PICs).
The short-reach optical interconnects, particularly the polymer optical waveguides, significantly contributed to the next-generation HPC systems due to their low propagation loss, higher flexibility, and easy integration on printed circuit boards (PCBs) [5]. Polymer waveguides offer unique advantages that address critical challenges in contemporary optical communication systems. Polymer waveguides have distinct properties, including low propagation loss, accommodating tighter bending structures with small radii, and compact photonic devices [6]. Also, Polymer waveguides have a significant low propagation loss advantage over traditional silicon waveguides [6,7], overcome limitations associated with silicon waveguides, and allow precise control of the refractive index (RI) and dispersion [8]. These properties address the challenges of size constraints, fabrication tolerances, and wavelength compatibility [9–11]. All these unique benefits make polymer waveguides a promising candidate technology for next-generation optical circuitry.
Optical splitters have been demonstrated as excellent passive optical components realized with efficient power splitting for optical circuitry. Among them, multimode interferometers (MMIs) [12] draw much more attention as they have played essential roles in photonic devices. MMIs utilize the self-imaging principle for light propagation, enabling manipulation of optical signals within the multimode waveguides to achieve uniform power splitting and ensure uniformity between the outputs [13]. They offer the advantage of shorter lengths. However, the MMI splitters are designed for a specific wavelength to operate within a narrow band and exhibit polarization dependence properties [14,15]. The Y-branch splitter can also provide efficient power splitting, exhibit minimal sensitivity to wavelength variations, demonstrate polarization effects, and maintain a compact footprint [16–18]. However, the limitations of the Y-splitter are the scattering loss and non-uniform splitting [19]. The MMI splitters with Y-branch configuration are proposed to address this issue in Refs. [20,21]. Combining a Y-branch splitter with the MMI splitter reduces wavelength and polarization dependence and ensures a more stable splitting ratio. Many studies have demonstrated that Y-branch MMI splitters work well in many applications, such as optical sensors, optical coherence tomography, laser systems, spectroscopy, and interferometry [20–23]. However, these optical splitters still need further development to enhance the stability within a specific wavelength range and achieve greater polarization independence with minimal loss.
This paper presents a theoretical approach for designing a 1 × 6 power splitter employing two MMI couplers in a polymer waveguide architecture. We insert tapered waveguides at the input of the MMI couplers to reduce modal mismatch and ensure maximum output uniformity between the output ports. The optimization of this Y-branch MMI splitter offers suitable geometrical parameters to obtain the utmost efficiency. The Y-branch MMI splitters demonstrate uniform splitting and shallow polarization-dependent loss in a wavelength range from 1.5 µm to 1.6 µm. The proposed splitters also exhibit high tolerance ranges of the structural parameters to reduce fabrication complexity.
2. Theoretical analysis
We design and demonstrate the Y-branch MMI splitters by using the RSoft CAD BeamPROP solver. Now, we explore the theoretical development to comprehensively understand this cutting-edge technology with the capabilities and functionality of the Y-splitters. We consider ${\textrm{F}_{\textrm{in}}}$, as the field intensity at the starting point of the tapered Y branch splitter, the splitter divides ${\textrm{F}_{\textrm{in}}}$ into two distinct output arms ${\textrm{F}_{\textrm{out} - 1}}$ and ${\textrm{F}_{\textrm{out} - 2}}$ having transmission coefficients ${\textrm{T}_1}$ and ${\textrm{T}_2}$, respectively, where $\textrm{T}_1^2 + \textrm{T}_2^2 = 1$. After traversing through the 1 × 2 MMI splitters, the field amplitudes [24] ${\textrm{F}_{\textrm{MMI} - 1}}$ and ${\textrm{F}_{\textrm{MMI} - 2}}$ in the two arms of the corresponding MMI regions can be mathematically represented in Eq. (1) as follows:
Here, $\textrm{T}.{\mathrm{\alpha }_{\textrm{MMI}}}$ indicates the transmission coefficient of the multimode splitter and $\textrm{T}.{\mathrm{\alpha }_{\textrm{MMI}}} = \frac{1}{2}$ is for equal splitting [24]. The MMI splitter demonstrates a distinctive intrinsic connection between the propagation constants of various modes, resulting in the achievement of the self-imaging principle [25] as input signals propagate through multimode waveguides. The polymer MMI splitters utilize this principle to divide the optical field by inducing the excitation of multiple modes [26]. These devices make the input field appear as a single or more images at regular intervals with the waveguide's propagation direction. The electric field profile [27] within the single-mode-based multimode waveguide splitter can be presented in Eq. (2) as follows:
Here, the variables ${p_n}$ and ${q_n}$ represent the transverse wave numbers of the nth mode within the core and cladding, respectively, and ${A_n}$ as the constant. The propagation constant demonstrates an almost quadratic relationship to the mode number in the SI multimode waveguide. The constant, ${\mathrm{\beta }_\textrm{n}}$ [28] can be approximated in Eq. (3) as follows:
In this equation, ${n_{eff}}$ represents the effective refractive index. The notion of the beat length is introduced to ensure optimal power distribution among multiple outputs [29], as defined in Eq. (4) as follows:
Here, ${\textrm{W}_{\textrm{MMI}}}$ represents the width of the MMI, while ${n_2}\; \textrm{and}\; {n_1}$ correspond to the refractive indices of the cladding and core materials, respectively. Additionally, the parameter $\mathrm{\sigma } = 0\;\textrm{or}\;1$ is contingent on the polarization mode [25]. We can calculate the length of the MMI coupler for the first N-fold image by using Eq. (6), as given by:
The symbol M represents the intrinsic periodic self-imaging property, and N indicates the number of outputs within this context. The transfer matrix corresponding to a MMI device [30], widely utilized for power splitting and combining in integrated photonics, is represented in Eq. (7) as follows:
The matrix represents the power distributions from the individual arm, governing the behavior of this MMI splitter. This splitter operates using two modes, and the matrix works on these modes. To practically apply this theory to the Y-branch splitter, we use RSoft CAD BPM software. The initial steps involve creating the layout of the splitter components, following the theoretical sequence, which includes the 1 × 2 MMI splitters and couplers. Then, the transfer matrices with relevant transmission coefficient values from mathematical formulations are assigned to each component. The simulation suggests how the optical field evolves through these elements. The simulation results are analyzed to gain insights into the MMI splitter and the specific characteristics of the output field for the proposed Y-branch MMI splitter configuration.
3. Design and optimization
3.1 Structural design
We designed a symmetrical geometrical structure of the Y-branch MMI splitter with a single input waveguide. This device is comprised of two S-bend waveguides through a Y-shaped configuration, as shown in Fig. 1. Figure 1(a) is a 3D representation of the Y-branch MMI splitter, and the parameters of the splitter are shown in Fig. 1(b). The input and output cross-sections are shown in Figs. 1(c) and 1(d), respectively. The outputs of this Y-branch waveguide are directly connected to the MMI waveguides with a taper and produce six outputs (each MMI waveguide demonstrates three outputs). The core width of the input, output, and S-bend waveguides are adjusted to satisfy the single-mode condition. We use NP-001L2 as the core material with a refractive index of 1.573 and NP-216 as the cladding material with a refractive index of 1.560 at 1550 nm [31]. The primary parameters of this splitter require optimization to get maximum efficiency. These parameters include the core width, length (Lmmi), and width (Wmmi) of the MMI region, along with the S-bend waveguides, pitch length, and taper waveguides. The optimization process will be discussed in the following sections. In addition, transverse electric (TE) and transverse magnetic (TM) polarizations are applied to observe the splitter's behavior in these modes. In TE polarization, the electric field is perpendicular to the direction of wave propagation, with the magnetic field also perpendicular to both the electric field and the direction of propagation. In TM polarization, the magnetic field is perpendicular to wave propagation, while the electric field is perpendicular to both the magnetic field and the direction of propagation.
Fig. 1. The schematics of the Y-branch MMI splitter. (a) 3D representation of the splitter. (b) Top view of the Y-branch MMI splitter with parameters. (c) Input cross-sectional view. (d) Output cross-sectional view.
The schematic shown in Fig. 1(a) can be fabricated with the Imprint technique, as illustrated in [32]. We spread the cladding monomer on a glass epoxy substrate as a lower cladding layer. The grooves of the cores are formed on the lower cladding by pressing a stamp mold made of polydimethyl-siloxane (PDMS). The liquid lower cladding layer is cured by UV exposure. Next, the PDMS mold is peeled off, and we fill up the grooves with the liquid core monomer, followed by UV curing. Finally, the cladding monomer is coated on the core and lower cladding layer to act as an upper cladding layer and is cured by UV exposure.
3.2 Optimization of the core width
Since this splitter combines the single-mode input, outputs, and S-bend waveguides, it is imperative to determine the optimum core width of these waveguides to satisfy the single-mode conditions. This assessment is conducted within the core width range of 1 to 10 µm using the NP-001L2 and NP-216 materials combination, as shown in Fig. 2(a). This evaluation confirms that the core width for the single-mode waveguides should be less than 6 µm to satisfy the single-mode behavior. Figure 2(b) illustrates the tolerance range of the suitable core width depending on the output intensity, and the output intensity increases with the core width until reaching 4.5 µm. The tolerance ranges of the core width are obtained from 4.5 µm to 6 µm for achieving the maximum output intensity. To assess the uniformity of the output intensity between the outputs, we conducted a numerical investigation of the splitter by varying the core width within the 4-6.5 µm range, as shown in Fig. 2(c). Our investigation reveals that the optimal core width for this splitter is 5 µm, where the output intensity is almost uniform with maximum intensity, and we fix the core width for the single-mode waveguide as 5 µm. The splitter's input and output mode profiles exhibit single-mode conditions, achieved with a 5 µm core width, as shown in Fig. 2(d). Thus, this optimal core width demonstrates the maximum intensity with uniformity under the single-mode condition.
Fig. 2. (a) Investigation of the single-mode condition. (b) Intensity variation for the core width. (c) Uniformity among the outputs. (d) The mode profiles for the input and outputs.
3.3 Optimization of the length and width of the MMI coupler
The two critical parameters for achieving the performance of the MMI devices are Lmmi and Wmmi. To better understand these parameters and their significance, we investigate this splitter's output intensity, varying Wmmi and Lmmi simultaneously, as shown in Fig. 3. Figure 3(a) illustrates the MMI structure. Figure 3(b) presents diverse variations in output intensity for different color combinations. The vertical line on the right side of Fig. 3(b) reveals the intensity levels, where red demonstrates the highest intensity and purple indicates the lowest. This SI splitter, with Wmmi ranging from 30-50 µm and Lmmi ranging from 600-1100 µm, exhibits its highest intensity in the red color range. We thoroughly analyzed these intensity fluctuations and identified the optimal values for Lmmi and Wmmi. After a couple of preliminary investigations, we confirm that this MMI splitter exhibits maximum output intensity when the Wmmi and Lmmi are 50 µm and 960 µm, respectively.
3.4 Taper and pitch-length optimization
The taper waveguides are crucial in integrated optics, and the taper waveguides gradually adjust cross-sectional dimensions through the design to achieve efficient light transmission with minimum loss [33]. We conducted a comprehensive study to determine the optimum length of the tapered waveguide, as shown in Fig. 4. The solid sky-blue line and the dotted yellow line denotes the intensity variation between outputs 1 and 6, respectively. Likewise, the black and dotted green lines are for output 2 and output 5, while the solid pink and dotted purple lines are for output 3 and output 4. The intensity distribution among outputs 1 and 6, 2 and 5, and 3 and 4 overlaps each other because of their alignment based on the central position of the MMI coupler. All the lines intersect at 250 µm, which is selected as the optimal taper length. In addition, the pitch length between the two waveguides of the Y-branch is another crucial parameter to obtain maximum uniformity between the outputs. We examine the pitch length between the Y splitter varying from 44 to 74 µm, and the results are presented in Fig. 5, which reveals that the highest uniformity between the outputs is obtained at 60 µm. Hence, the optimal pitch length for this Y-branch splitter is determined to be 60 µm.
3.5 Optimization of the S-bend and input-output waveguides
The S-bend in a Y-branch splitter is a curved waveguide shape that helps efficiently split incoming light into two output paths, ensuring equal intensity distribution. We calculate the output intensity varying the S-bend radii (from 14000 µm to 19000 µm) and the S-bend length (from 1150 µm to 1300 µm) of the Y-splitter, as shown in Fig. 6. The results demonstrate that the maximum output intensity is obtained at the radius of 16097 µm, while the S-bend length is 1211 µm. The tolerance range for the maximum output intensity is obtained with a radius between 15500 µm and 16500 µm and a length between 1200 µm and 1225 µm. After optimizing the Y-branch splitter, we investigated the input and output waveguides of the overall Y-branch MMI splitter, as presented in Fig. 7. In this figure, we can observe the four possible cases: both input and outputs in straight waveguides, both input and outputs in taper waveguides, input in straight and outputs in tapered waveguides, and input in tapered and outputs in straight waveguides. Our analysis reveals that the configuration with a taper waveguide-based input and a straight waveguide-based output exhibits the maximum output uniformity among the six outputs, surpassing the other three cases. In contrast, the other configurations show nonuniformity between the outputs. Consequently, we selected the configuration with a taper-based input and a straight output for this Y-branch MMI splitter.
3.6 Optimization of the Y-branch MMI splitter
After conducting a couple of investigations, we successfully obtained an optimized configuration for our proposed Y-branch MMI splitter, having a single input and six outputs, shown in Fig. 8. The optimized parameters of the 1×6 Y-branch MMI splitter are shown in Table 1. Figure 8(a) illustrates the field intensity distribution among these six outputs, which are almost constant peak intensity at 1.55 µm. It also provides a two-dimensional representation of the intensity distribution across the six outputs, showing closely aligned peak values. Figure 8(b) shows a three-dimensional view, providing the peak intensity among the splitter outputs. Since the optical signal enters the MMI splitter, it undergoes the self-imaging principle [34] within the MMI region. This phenomenon results in uniform splitting among the output ports. The MMI waveguides facilitate the interference of optical modes [35], ensuring the optical intensity is distributed into multiple outputs. In the 1 × 6 Y-branch MMI splitter, the optical power distribution across its six distinct output ports is contingent upon the geometric dimensions of the waveguides within the MMI region. The output uniformity of this Y-branch MMI splitter is obtained at the propagation length of 3260 µm at 1.55 µm, as in Fig. 8(c). The splitter demonstrates the input signal into the six outputs with remarkable uniform values within the wavelength range of 1.5 µm to 1.6 µm, as shown in Fig. 8(d).
Table 1. Optimal Parameters of the 1 × 6 Polymer Y-Branch MMI Splitter
Fig. 8. Optimized Y-branch MMI splitter. (a) Intensity distribution among outputs. (b) The 3D view of the intensity distribution, (c) Variation in intensity distribution along the propagation direction. (d) The uniformity between the outputs with wavelength variation.
4. Results and siscussion
4.1 Index profile
The index profile is a fundamental concept in optics, representing the variation of the refractive index across the cross-section of the optical waveguide. This profile plays a pivotal role in the behavior of light propagation in the waveguide, influencing aspects such as mode confinement and propagation characteristics [36]. The SI index profile demonstrates a sudden change in refractive index from core to cladding interface, and the SI splitter is vividly depicted in Fig. 9, offering a visual insight into the light propagation characteristics within the SI profile. This comprehensive illustration underscores the remarkable index uniformity maintained consistently throughout the core region, where the same distinct red color permeates every segment. This visual representation is an invaluable tool for understanding the uniform index distribution that characterizes the SI profile of the waveguide.
4.2 Loss analysis
4.2.1 Insertion loss
The insertion loss (IL) is a crucial parameter in characterizing the performance of the splitters. It quantifies the reduction in signal power as it traverses through the splitter, indicating the power transfer efficiency between input and output ports [37]. Keeping this crucial aspect in focus, we carefully determine the IL for this splitter using the equation provided as follows:
Here, Po represents the output power, and Pi denotes the input power of the splitter. This study presents a comprehensive performance exploration of this splitter, spanning a wide range of wavelengths (1.30 to 1.70 µm) and propagation lengths (from 2000 to 3260 µm) centered around our operating wavelength of 1.55 µm, as depicted in Fig. 10.
In Fig. 10(a), the graph showcases the variation of IL with wavelength. This splitter exhibits optimal performance within a wavelength range from 1.5 µm to 1.6 µm, where minimal loss is observed. Thus, it can deliver better performance within this wavelength range. Figure 10(b) elucidates the IL behavior by depicting its variation with propagation length at 1.55 µm. This graph demonstrates the IL values of this splitter of 0.52 dB and 0.50 dB for the TE and TM modes, respectively, at 1.55 µm.
4.2.2 Polarization-dependent loss
The polarization-dependent loss (PDL) refers to the differences in IL experienced by TE and TM polarization modes. In this Y-branch MMI splitter, the significance of PDL becomes evident, as it influences the device's performance and practical applicability. We calculate the PDL [38] by using the following equation:
Fig. 11. (a) Polarization-dependent loss as a function of wavelength and (b) polarization-dependent loss as a function of propagation length at 1.55 µm.
4.2.3 Propagation loss
The propagation loss (PL) occurs due to the various factors such as absorption and imperfections in the material [39]. In the Y-branch MMI splitter, understanding and analyzing propagation loss is crucial because it directly affects the efficiency and performance of the device. We calculate the PL for this Y-branch MMI splitter by varying the wavelength along the direction of propagation at 1.55 µm by using the Eq. (11) [40] as follows:
where, ${P_{out}}$ represents the output power, ${P_{in}}$ denotes the input power, and L corresponds to the length of the waveguide. This formula quantifies the waveguide's signal power reduction per unit length in µm. We investigate the variation of PL across a wavelength range of 1.3-1.7 µm, as illustrated in Fig. 12(a). The graphical representation reveals a distinct trend wherein PL initially decreases, reaching a minimum at approximately 1.5 µm to 1.6 µm, and subsequently increases beyond this wavelength. This behavior underscores the optimal performance of this splitter within the specified wavelength range for both TE and TM modes, exhibiting minimum PL. Again, we calculate PL in the direction of propagation at 1.55 µm. First, the PL increases and then decreases from the propagation at 2800 µm, as illustrated in Fig. 12(b). The minimum PL for this splitter is 0.00019 dB/µm for both TE and TM modes, respectively.Fig. 12. (a) Propagation loss as a function of wavelength. (b) Propagation length vs. propagation loss at 1.55 µm.
4. Tolerance analysis
The tolerance analysis refers to the acceptable variation of the parameters in a desired value range in a device or system [41]. We investigate the tolerance range of the following parameters: Lmmi, Wmmi, and the gap between output ports for this Y-branch MMI splitter. These parameters can fluctuate without causing any alterations to the performance attributes of this device. Figure 13 illustrates the acceptable variations of the parameters for the Y-Branch splitter. Figure 13(a) shows the variation in the tolerance range of Lmmi, encompassing a range from 600 to 1200 µm, and the tolerance range of Lmmi for this Y-branch splitter is 900-1000 µm. Similarly, Figs. 13(b) and 13(c) present visual representations of the variation of Wmmi and the distance between output ports to find the optimum tolerance range. Within these representations, Wmmi ranges from 44 to 56 µm, and the distance between output ports fluctuates within the 10-26 µm range. The optimum tolerance range for Wmmi lies within 49-51 µm, while the gap between output ports varies between 15-18 µm for the splitter.
Fig. 13. Tolerance range analysis: (a) the tolerance range of Lmmi, (b) the tolerance range of Wmmi, and (c) the tolerance range of the distance between the output ports.
5. Conclusion
We have successfully demonstrated the optimization and performance analysis of the taper-based single-mode polymer Y-branch MMI splitters. This splitter yields a remarkable power-splitting efficiency of 86%. The insertion losses of this splitter are 0.52 dB and 0.50 dB for TE and TM modes, respectively, while the PDL is 0.025 dB at 1.55 µm. This splitter demonstrates the propagation loss of 0.00019 dB/µm and exhibits the tolerance ranges of the parameters related to the MMI waveguide. Thus, these Y-branch MMI splitters could be excellent evidence to fabricate these types of devices in the photonics industry and could be novel devices for next-generation computing systems.
Disclosures
The authors have no conflicts of interest to declare.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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