1 Introduction
At present, with the rapid integration and development of 5G, cloud computing [1-3], virtual reality [4, 5], artificial intelligence, blockchain [6], and other technologies, the metaverse [7, 8], which is known as the “next-generation internet”, has gradually emerged as the direction for future human development. As the entry point to the metaverse, virtual reality technology connects the physical world and digital world, providing people with an immersive experience of the digital world and an interactive experience between the physical and digital worlds. Many micro display products based on virtual reality technology, such as augmented reality head-up displays (AR-HUD) [9, 10], AR [11] glasses, head-mounted display [12, 13], and mobile projectors [14, 15], have undergone extensive research. The red-green-blue (RGB) beam combiner is an indispensable component in micro display products, which can be divided into three main types: prism beam combiner, fiber beam combiner, and optical waveguide combiner. Prism beam combiners are suitable for high-power fiber laser synthesis but are rarely used due to their weak dispersion capability [16, 17]. Meanwhile, fiber beam combiners currently face challenges in achieving high-power and high-quality beam output [18, 19]. Compared with the other two types, the optical waveguide combiner has the characteristics of simple, efficient transmission and high integration [20, 21], and therefore has attracted widespread attention. Table 1 provides a detailed comparison of the three types of beam combiners.
| Combiner type | Principle | Characteristic |
|---|---|---|
| Prism beam combiner [16, 17] | Refraction and reflection of prisms | Large size and little flexibility; high contamination susceptibility; high sensitivity to angle and position. |
| Fiber beam combiner [22-24] | Total reflection of optical fiber and beam coupling principle | Wide range of applications; coupling efficiency depends on high-quality alignment; good flexibility and customizable. |
| Optical waveguide combiner [20, 21] | Coupling and transmission properties of the optical waveguide | Small size and high integration; good flexibility and low cost; high multiplexing efficiency. |
Currently, the main problem of optical waveguide combiners is the low multiplexing efficiency, which affects the performance of micro display products. Thus, researchers have conducted extensive research on optical waveguide combiners. An RGB beam combiner formed by cascading two-mode interference (TMI) structures was reported [25]. The device has high multiplexing efficiency but a relatively complex structure. An RGB combiner based on multimode interference (MMI) was reported, which has a small size but low light multiplexing efficiency [26, 27]. An RGB beam combiner using a mode conversion waveguide was reported, which greatly shortened the size of the device, but the light multiplexing efficiency was low [28]. A directional coupler-based RGB beam combiner was reported [29]. Compared with other types of combiners, this type of combiner has a simpler structure and an average multiplexing efficiency of 96% for red, green, and blue light. However, the multiplexing efficiency of blue light is only 92.1%, leaving room for further improvement through parameter optimization. Therefore, in this paper, the performance of the RGB beam combiner is optimized from the perspective of parameter optimization. The RGB beam combiner is initially optimized by analyzing the relationship between individual parameters and the device performance. Then, the entropy weight-TOPSIS method is used to optimize the key parameters of the device from a multi-parameter perspective, and the optimal parameter scheme is determined, further improving the performance of the RGB beam combiner.
2 Theory and methods
2.1 Directional coupler theory
A directional coupler [30, 31] consists of two waveguides (waveguide 1 and waveguide 2), with a coupling region formed by two parallel straight waveguide sections, as shown in Figure 1. When the two waveguides are close to each other, interaction (synchronous coherent coupling) occurs between them. The evanescent field from one waveguide can enter the effective region of the other waveguide. At this point, energy transfer between the two waveguides is achieved. The indicator for evaluating the performance of the coupler is the coupling efficiency, which is the ratio of the optical power coupled out from the original waveguide to the total power.
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When light enters from the left end of waveguide 1, a portion or all of the optical power will transfer to waveguide 2 through the coupling region [32-34]. The corresponding powers within waveguide 1 and waveguide 2 can be represented as:
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where a is the exponential light attenuation coefficient, z is the length of the waveguide along the z-direction during the coupling process, and k is the coupling coefficient.
From the power equation within the waveguide, the varible z represents the length of the waveguide along the z-direction during the coupling process, denoted by L. To completely transfer power from one waveguide to another, the coupling length L needs to satisfy the following formula.
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The coupling coefficient k can be expressed as:
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where W is the width of the waveguide; s is the spacing between waveguides, and the size of s influences the coupling efficiency of the coupler by altering the coupling coefficient k; h and β represent the propagation constants in the y and z directions respectively; and q is the extinction coefficient in the y direction. When s changes, the size of the coupling coefficient k is affected, consequently influencing the magnitude of optical power in waveguide 1 and waveguide 2.
From Eqs. (1)-(4), it can be seen that, under given waveguide material and optical wavelength, the coupling length L and the waveguide spacing s are the key parameters influencing the coupler’s coupling efficiency.
2.2 Entropy weight-TOPSIS method
The entropy weight-TOPSIS method is a comprehensive analytical method that combines the entropy weight method [35, 36] with the technique for order preference by similarity to an ideal solution (TOPSIS) method [37-40]. It can objectively evaluate each parameter scheme based on comprehensive multiple performance indicators to achieve optimization of multiple parameters, thereby improving the performance of the research object. The core idea of this method is as follows: First, construct the original data matrix based on the performance indicators of the given parameter scheme. Then, standardize the original matrix. Subsequently, calculate the weights of each indicator using the entropy weight method. Next, the TOPSIS method is used to weight the standardized matrix. Then, the maximum and minimum values in each column of the matrix are computed, and the best and worst parameter schemes are constructed from all the maximum and minimum values respectively. Following that, the distances D+ between each parameter scheme and the best scheme, and the distances D- between each parameter scheme and the worst scheme, are calculated respectively. Finally, the closeness Ci between each parameter scheme and the ideal scheme is calculated through Eq. (5). A higher Ci value indicates better performance of the parameter scheme.
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where i=1, 2, …, m; j=1, 2, …, n.
3 Design and parameter analysis of RGB beam combiner
In this section, a model of the RGB beam combiner based on directional couplers is constructed. The schematic diagram of the RGB beam combiner is shown in Figure 2. The overall structure of the RGB beam combiner is approximately symmetrical. It primarily consists of three directional couplers (Coupler 1, Coupler 2, Coupler 3), three input waveguides, and one output waveguide (excluding the structure enclosed by the dashed black lines). The structures of Coupler 1 and Coupler 2 both include waveguide L1, and waveguide L2 is one of the constituent structures of Coupler 3. R1, R2, and R3 respectively represent the radii of the curved waveguides in the RGB beam combiner. The waveguide cross-section size of the RGB beam combiner is 2 μm×2 μm, and it supports single-mode operation. The cladding material of the waveguide is silicon dioxide on an insulator, with a refractive index of 1.457@632.8 nm, and the core material is Ge-doped silica. The relative refractive index difference between the waveguide core and cladding is 0.75%. Red, green, and blue lights enter the RGB beam combiner from right to left, coupling through Coupler 1, Coupler 2, and Coupler 3 to combine in the central waveguide(GL), and are output from the central waveguide. During the transmission process, the red light is coupled by Coupler 2 and Coupler 3, the green light is coupled by Coupler 1 and Coupler 2, and the blue light is coupled by Coupler 1, Coupler 2, and Coupler 3. The multiplexing efficiency of light is used as the performance evaluation metric for the RGB beam combiner. Its value is the ratio of the output power of light from the central waveguide to the input power of light. The performance metrics of the RGB beam combiner include the multiplexing efficiency of red, green, and blue lights, as well as their average multiplexing efficiency. In this paper, R, G, B and Average are respectively used to denote the multiplexing efficiency of red, green, and blue lights, as well as their average multiplexing efficiency. The wavelengths of red, green, and blue lights are 638, 520 and 445 nm, respectively. Since there is no polarization requirement, the transverse electric (TE) mode of light is chosen for the design of the RGB beam combiner.
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According to the working principle of the RGB beam combiner, it can be seen that the factors that affect its performance are mainly the coupling efficiency of Coupler 1, Coupler 2 and Coupler 3, and the transmission loss of light in the waveguide. According to the directional coupler theory, the main factors affecting the coupling efficiency of the coupler are the waveguide spacing and coupling length. Therefore, the waveguide spacing Gap1 and Gap2, as well as the coupling lengths L1 and L2, are key parameters that affect the performance of the RGB beam combiner. The transmission loss of light in waveguide includes transmission loss, radiation loss, and mode conversion loss. In this design, it is assumed that the waveguide in the RGB beam combiner is ideal, that is, there is no transmission loss caused by material defects. And the waveguide is single-mode light transmission, so mode conversion loss is not discussed. Therefore, this paper only discusses radiation loss in curved waveguide. The radiation loss mainly comes from the curved waveguide that plays a connecting role in the device, which is related to the radii R1, R2 and R3. The size of the GL determines the length of the RGB beam combiner, and the value of this parameter can be calculated after the values of the remaining parameters are determined. Therefore, the optimization of the RGB beam combiner primarily focuses on optimizing the seven parameters of the curved waveguide radii, i.e., R1, R2 and R3, the waveguide spacing Gap1 and Gap2, and the coupling lengths L1 and L2.
The optimization idea of the RGB beam combiner is as follows. Since the bending radii R1, R2 and R3 play the role of connecting the coupler and transmitting light in the device, their values determine whether the light can be constrained as much as possible and transmitted in the waveguide. Therefore, it is necessary to first optimize these three parameters. Then, the four parameters of the waveguide spacing (Gap1 and Gap2) and the coupling lengths (L1 and L2) are optimized. Additionally, in order to facilitate the construction of the RGB beam combiner model and optimize the parameters in simulation software, the waveguide structures enclosed by the dashed black lines are added on the basis of the RGB beam combiner structure, as shown in Figure 2. The initial values of the parameters of the RGB beam combiner are shown in Table 2.
| L1 | L2 | Gap1 | Gap2 | R1 | R2 | R3 |
|---|---|---|---|---|---|---|
| 580 | 600 | 1.25 | 1.83 | 13000 | 13000 | 13000 |
4 Optimization of RGB beam combiner
4.1 Optimization of bending radius
A curved waveguide model is established, as shown in Figure 3(a). Under the conditions of wavelengths of 638 nm (red light), 520 nm (green light), and 445 nm (blue light), the relationship between bending loss and bending radius at a bending angle of 90° is studied, respectively.
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The relationship between the bending loss and the bending radius is shown in Figure 3(b). When the radius increases from 2000 to 22000 μm, the bending loss shows a decreasing trend for wavelengths of 638, 520 and 445 nm. Among these, when the bending radius increases from 2000 to 9000 μm, the bending loss decreases significantly. When the bending radius exceeds 9000 μm, the rate of decrease in bending loss slows down. In this paper, the radius corresponding to a bending loss of 0.012 dB is defined as the minimum bending radius, which is 9000 μm. Since the bending radius affects the performance and integration of the RGB beam combiner, it is necessary to obtain appropriate values for the bending radii in the RGB beam combiner. Therefore, the relationship between the performance of the RGB beam combiner and R1, R2 and R3 is studied separately within the range of 9000 to 18000 μm, as shown in Figure 4.
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As can be seen from Figures 4(a)-(c), when R1 and R3 increase from 9000 to 18000 μm, respectively, the multiplexing efficiencies of red, green, and blue light gradually increase. When R2 increases from 9000 to 18000 μm, the multiplexing efficiencies of red and green light show an increasing trend, while the multiplexing efficiency of blue light first increases and then decreases. This indicates that an excessively large bending radius can reduce the device’s performance. This is because an excessively large bending radius affects the structural layout of the RGB beam combiner, thereby impacting the device’s performance. When R2 is 10800 μm, the multiplexing efficiency of blue light reaches its maximum value. It is appropriate to set R1, R2 and R3 at 18000, 10800 and 12000 μm, respectively. At this moment, the performance indicators of the device are shown in Table 3.
| Red | Green | Blue | Average |
|---|---|---|---|
| 90.60% | 94.05% | 96.39% | 93.68% |
4.2 Preliminary optimization of key parameters of RGB beam combiner
In this section, the relationship between the performance of the RGB beam combiner and individual key parameters is studied, as shown in Figure 5.
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The relationship between the performance of the RGB beam combiner and waveguide L1 is shown in Figure 5(a). When the waveguide L1 increases from 525 to 725 μm, the multiplexing efficiencies of red, green, and blue light all exhibit a trend of initially increasing and then decreasing. The multiplexing efficiency of red light fluctuates between 77.47% and 99.11%. The multiplexing efficiency of blue light varies from 93.44% to 97.22%, while the multiplexing efficiency of green light ranges between 83.49% and 99.69%. It can be seen that the size of waveguide L1 significantly impacts the multiplexing efficiency of red, green, and blue light. This is because waveguide L1 is part of the structure composing Coupler 1 and Coupler 2. According to directional coupler theory, whether the length of waveguide L1 affects red, green, and blue light can be fully coupled and transmitted by Coupler 1 and Coupler 2, thereby impacting the performance of the RGB beam combiner. Figure 5(a) shows that the lengths of waveguide L1 required to achieve maximum multiplexing efficiency for red, green, and blue light in the RGB beam combiner are approximately 670, 640 and 625 μm, respectively. When the length of the waveguide L1 deviates from any of these three values, the corresponding light’s multiplexing efficiency will decrease. Therefore, the value of the waveguide L1 needs to be set to ensure that all three kinds of light maintain high multiplexing efficiency.
The relationship between the performance of the RGB beam combiner and the waveguide L2 is depicted in Figure 5(b). When the waveguide L2 increases from 550 to 750 μm, the multiplexing efficiency of red light changes from 94.16% to 97.48%. When the length of waveguide L2 is 630 μm, the multiplexing efficiency of red light reaches the maximum value of 97.48%. It is evident that the length of waveguide L2 significantly impacts the multiplexing efficiency of red light, which is attributed to the fact that waveguide 2 is part of the structure of Coupler 3. According to directional coupler theory, the size of waveguide L2 plays a crucial role in determining whether red light can be maximally coupled by Coupler 3 into the central waveguide. With variations in the length of waveguide L2, the multiplexing efficiency of green light remains essentially unchanged, consistently above 99.81%. This is because the transmission path of green light within the device does not require passage through Coupler 3. As the size of waveguide L2 increases, the blue light multiplexing efficiency gradually decreases from 97.54% to 96.18%. This is because the blue light coupled to the GL by Coupler 1 will be coupled by Coupler 3. According to directional coupler theory, as the waveguide length L2 increases, more blue light will be coupled by Coupler 3, thereby reducing the multiplexing efficiency of the blue light. In order to ensure better performance of the RGB beam combiner, the values of waveguide L2 should focus on ensuring high multiplexing efficiency of the red light while minimizing the impact on the multiplexing efficiency of blue light.
The relationship between the performance of the RGB beam combiner and the waveguide spacing Gap1 is shown in Figure 5(c). As Gap1 increases from 1.15 to 1.35 μm, the multiplexing efficiency of red, green, and blue light all exhibit a trend of first increasing and then decreasing. Small changes in Gap1 significantly impact the performance of the RGB beam combiner. This is because the waveguide spacing Gap1 is a parameter relevant to both Coupler 1 and Coupler 2. According to directional coupler theory, when Gap1 changes, the coupling coefficient k also changes accordingly. This variation affects the efficiency of red, green, and blue light coupled by Coupler 1 and Coupler 2, thus impacting the multiplexing efficiency of red, green, and blue light in the RGB beam combiner. The appropriate value of Gap1 ensures that Coupler 1 and Coupler 2 have high coupling efficiency for red, green, and blue light.
The relationship between the performance of the RGB beam combiner and the waveguide spacing Gap2 is shown in Figure 5(d). As Gap2 increases from 1.7 to 1.9 μm, the multiplexing efficiency of red light initially increases and then decreases, ranging from 89.99% to 99.23%. It can be seen that Gap2 has a significant impact on the multiplexing efficiency of red light. This is because red light needs to be coupled into the GL through Coupler 3. According to directional coupler theory, Gap2 affects the magnitude of the coupling coefficient k, thereby affecting the power of red light coupled by Coupler 3 into the middle waveguide. As Gap2 increases from 1.7 to 1.9 μm, the multiplexing efficiency of green light remains essentially constant at 99.60%. This is because Coupler 3 is not the transmission path of green light in the RGB beam combiner. With the increase in Gap2, the multiplexing efficiency of blue light rises from 94.36% to 95.33%. Certainly, the increase in Gap2 contributes to the enhancement of the blue light’s multiplexing efficiency. This is because when blue light is transmitted within the RGB beam combiner, a portion of it enters the central waveguide through Coupler 1, while the remaining light continues to propagate in the left waveguide and finally couples into the central waveguide through Coupler 2. The higher the coupling efficiency of Coupler 3 for blue light, the less the blue light transmitted in the middle waveguide, thereby reducing its multiplexing efficiency. Therefore, the selection of the value of Gap2 needs to consider reducing the coupling efficiency of Coupler 3 for blue light.
As shown in Figure 5, L1 and Gap1 significantly affect the multiplexing efficiency of red, green, and blue light. Meanwhile, L2 and Gap2 have the greatest effect on the multiplexing efficiency of red light, with a lesser effect on blue light and almost no effect on green light. In addition, small changes in Gap1 and Gap2 greatly affect the performance of the device. Based on the above analysis and research, the key parameters of the RGB beam combiner can be initially optimized to achieve preliminary optimized performance. When L1=670 μm, L2=630 μm, Gap1=1.23 μm, and Gap2=1.84 μm, the preliminary optimized performance of the RGB beam combiner can be obtained, as shown in Table 4.
| Red | Green | Blue | Average |
|---|---|---|---|
| 95.88% | 96.95% | 94.81% | 95.88% |
4.3 Optimization of key parameters using entropy weight-TOPSIS method
In this section, the key parameters of the RGB beam combiner are optimized using the entropy weight-TOPSIS method. Firstly, based on the relationship between the performance of the RGB beam combiner and individual key parameters, the range of values for each key parameter is determined to ensure that all performance indicators of the device exhibit good performance. And reasonable step sizes are set for each key parameter, as shown in Table 5.
| Parameter | Minimum value/μm | Maximum value/μm | Step size/μm |
|---|---|---|---|
| L1 | 613 | 693 | 20 |
| L2 | 603 | 723 | 30 |
| Gap1 | 1.17 | 1.25 | 0.02 |
| Gap2 | 1.80 | 1.88 | 0.02 |
Next, a certain number of parameter schemes and their corresponding performance indicators are provided. Because the parameter schemes generated by orthogonal experimental design [41] are uniformly distributed and representative among all parameter schemes, they avoid redundant parameter schemes and reduce the cost of parameter optimization. Therefore, based on the orthogonal experimental design (four factors, five levels) and Table 5, 25 sets of parameter schemes are provided. Subsequently, using the beam propagation method, the performance indicators of the RGB beam combiner under the 25 parameter schemes are calculated, as shown in Table 6.
| Scheme | L1/μm | L2/μm | Gap1/μm | Gap2/μm | Performance indicator | |||
|---|---|---|---|---|---|---|---|---|
| R | G | B | Average | |||||
| 1 | 613 | 583 | 1.17 | 1.80 | 0.9747 | 0.9213 | 0.9059 | 0.9340 |
| 2 | 613 | 603 | 1.19 | 1.82 | 0.9898 | 0.9625 | 0.9387 | 0.9637 |
| 3 | 613 | 633 | 1.21 | 1.84 | 0.9947 | 0.9893 | 0.9597 | 0.9812 |
| 4 | 613 | 663 | 1.23 | 1.86 | 0.9851 | 0.9965 | 0.9703 | 0.9840 |
| 5 | 613 | 693 | 1.25 | 1.88 | 0.9617 | 0.9793 | 0.9713 | 0.9708 |
| 6 | 633 | 583 | 1.19 | 1.84 | 0.9687 | 0.9313 | 0.9252 | 0.9417 |
| 7 | 633 | 603 | 1.21 | 1.86 | 0.9816 | 0.9727 | 0.9532 | 0.9692 |
| 8 | 633 | 633 | 1.23 | 1.88 | 0.9832 | 0.9950 | 0.9697 | 0.9826 |
| 9 | 633 | 663 | 1.25 | 1.80 | 0.9692 | 0.9925 | 0.9639 | 0.9752 |
| 10 | 633 | 693 | 1.17 | 1.82 | 0.9387 | 0.8801 | 0.8773 | 0.8987 |
| 11 | 653 | 583 | 1.21 | 1.88 | 0.9496 | 0.9466 | 0.9544 | 0.9502 |
| 12 | 653 | 603 | 1.23 | 1.80 | 0.9917 | 0.9849 | 0.9416 | 0.9727 |
| 13 | 653 | 633 | 1.25 | 1.82 | 0.9917 | 0.9976 | 0.9663 | 0.9852 |
| 14 | 653 | 663 | 1.17 | 1.84 | 0.9172 | 0.8274 | 0.8537 | 0.8661 |
| 15 | 653 | 693 | 1.19 | 1.86 | 0.9555 | 0.8934 | 0.8999 | 0.9163 |
| 16 | 673 | 583 | 1.23 | 1.82 | 0.9779 | 0.9661 | 0.9470 | 0.9637 |
| 17 | 673 | 603 | 1.25 | 1.84 | 0.9899 | 0.9948 | 0.9652 | 0.9833 |
| 18 | 673 | 633 | 1.17 | 1.86 | 0.8690 | 0.7673 | 0.8269 | 0.8211 |
| 19 | 673 | 663 | 1.19 | 1.88 | 0.9185 | 0.8450 | 0.8798 | 0.8811 |
| 20 | 673 | 693 | 1.21 | 1.80 | 0.9336 | 0.9162 | 0.9084 | 0.9194 |
| 21 | 693 | 583 | 1.25 | 1.86 | 0.9674 | 0.9835 | 0.9609 | 0.9706 |
| 22 | 693 | 603 | 1.17 | 1.88 | 0.7997 | 0.7013 | 0.7974 | 0.7661 |
| 23 | 693 | 633 | 1.19 | 1.80 | 0.8745 | 0.7947 | 0.8471 | 0.8388 |
| 24 | 693 | 663 | 1.21 | 1.82 | 0.9233 | 0.8741 | 0.8940 | 0.8971 |
| 25 | 693 | 693 | 1.23 | 1.84 | 0.9603 | 0.9400 | 0.9291 | 0.9431 |
Then, the performance indicators corresponding to the 25 sets of parameter schemes in Table 6 are used to form the original data matrix, which is then subjected to standardization processing. Afterward, the entropy (ej) and weights (wj) of each performance indicator are calculated, with the results shown in Table 7.
| Beam | ej | wj |
|---|---|---|
| Average | 0.9994 | 0.2302 |
| Red | 0.9996 | 0.1423 |
| Green | 0.9988 | 0.4587 |
| Blue | 0.9996 | 0.1687 |
Subsequently, the standardized matrix undergoes weighted processing. Then, based on the processed weighted matrix, the distances D+ between each parameter scheme and the ideal scheme, as well as the distances D- between each parameter scheme and the negative ideal scheme, can be calculated separately. According to Eq. (5), the closeness Ci between each parameter scheme and the ideal scheme can be calculated. The 25 sets of parameter schemes can then be ranked based on the magnitude of Ci, as shown in Table 8.
| Scheme | L1/μm | L2/μm | Gap1/μm | Gap2/μm | D+ | D- | Ci | Rank |
|---|---|---|---|---|---|---|---|---|
| 1 | 613 | 583 | 1.17 | 1.8 | 0.0083 | 0.0242 | 0.7438 | 16 |
| 2 | 613 | 603 | 1.19 | 1.82 | 0.0038 | 0.0287 | 0.8823 | 12 |
| 3 | 613 | 633 | 1.21 | 1.84 | 0.0009 | 0.0316 | 0.9709 | 5 |
| 4 | 613 | 663 | 1.23 | 1.86 | 0.0003 | 0.0323 | 0.9903 | 2 |
| 5 | 613 | 693 | 1.25 | 1.88 | 0.0022 | 0.0304 | 0.9330 | 9 |
| 6 | 633 | 583 | 1.19 | 1.84 | 0.0072 | 0.0253 | 0.7797 | 15 |
| 7 | 633 | 603 | 1.21 | 1.86 | 0.0027 | 0.0298 | 0.9168 | 10 |
| 8 | 633 | 633 | 1.23 | 1.88 | 0.0005 | 0.0321 | 0.9861 | 4 |
| 9 | 633 | 663 | 1.25 | 1.8 | 0.0011 | 0.0317 | 0.9672 | 6 |
| 10 | 633 | 693 | 1.17 | 1.82 | 0.0130 | 0.0196 | 0.6011 | 19 |
| 11 | 653 | 583 | 1.21 | 1.88 | 0.0055 | 0.0270 | 0.8294 | 13 |
| 12 | 653 | 603 | 1.23 | 1.8 | 0.0018 | 0.0309 | 0.9456 | 7 |
| 13 | 653 | 633 | 1.25 | 1.82 | 0.0002 | 0.0324 | 0.9937 | 1 |
| 14 | 653 | 663 | 1.17 | 1.84 | 0.0185 | 0.0140 | 0.4312 | 22 |
| 15 | 653 | 693 | 1.19 | 1.86 | 0.0112 | 0.0213 | 0.6544 | 18 |
| 16 | 673 | 583 | 1.23 | 1.82 | 0.0035 | 0.0290 | 0.8937 | 11 |
| 17 | 673 | 603 | 1.25 | 1.84 | 0.0004 | 0.0321 | 0.9878 | 3 |
| 18 | 673 | 633 | 1.17 | 1.86 | 0.0251 | 0.0075 | 0.2293 | 24 |
| 19 | 673 | 663 | 1.19 | 1.88 | 0.0165 | 0.0160 | 0.4930 | 21 |
| 20 | 673 | 693 | 1.21 | 1.8 | 0.0092 | 0.0233 | 0.7175 | 17 |
| 21 | 693 | 583 | 1.25 | 1.86 | 0.0018 | 0.0307 | 0.9443 | 8 |
| 22 | 693 | 603 | 1.17 | 1.88 | 0.0325 | 0.0000 | 0.0000 | 25 |
| 23 | 693 | 633 | 1.19 | 1.8 | 0.0221 | 0.0103 | 0.3183 | 23 |
| 24 | 693 | 663 | 1.21 | 1.82 | 0.0135 | 0.0190 | 0.5853 | 20 |
| 25 | 693 | 693 | 1.23 | 1.84 | 0.0064 | 0.0261 | 0.8044 | 14 |
From Table 8, it is evident that the parameter scheme in Series 13 exhibits the highest closeness degree Ci. Under this scheme, all performance indicators reach relatively high levels. Therefore, this parameter scheme is finalized as the key parameter configuration for the RGB beam combiner. The performance of the RGB combiner under Scheme 13 is detailed in Table 9. And the transmission process of red, green, and blue light in the RGB beam combiner is shown in Figure 6.
| Red | Green | Blue | Average |
|---|---|---|---|
| 99.17% | 99.76% | 96.63% | 98.52% |
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Combining the parameters provided in Table 6, the actual layout of the RGB beam combiner is depicted in Figure 7, with dimensions of 4.768 mm×0.062 mm. The RGB beam combiner designed in previous research is compared with our device, as shown in Table 10. As can be seen from Table 10, our RGB beam combiner performs better in performance and size.
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| RGB beam combiner | Size | Performance indicater/% | |||
|---|---|---|---|---|---|
| Red | Green | Blue | Average | ||
| An RGB beam combiner based on TMI [25] | 30 mm×0.02 mm | 96.00 | 99.00 | 98.00 | 97.67 |
| An RGB beam combiner based on MMI [26, 27] | Length of 0.3 mm | 67.00 | 65.00 | 75.00 | 69.00 |
| An RGB beam combiner with mode conversion waveguide [28] | 8.2 mm×0.5 mm | 75.86 | 93.33 | 93.33 | 87.51 |
| An RGB beam combiner based on directional coupler [29] | 7.8 mm×0.06 mm | 97.80 | 98.10 | 92.10 | 96.40 |
| This work | 4.768 mm×0.062 mm | 99.17 | 99.76 | 96.63 | 98.52 |
5 Conclusions
In this paper, an RGB beam combiner based on directional couplers is established. By exploring the relationship between bending waveguide loss and bending radius, the values of the radii R1, R2 and R3 are determined to be 18000, 10800 and 12000 μm, respectively. By analyzing the relationship between the performance and the key parameters of the RGB beam combiner, the initial optimization of the device’s key parameters is carried out. The entropy weight-TOPSIS method is introduced for further optimization of these key parameters, establishing the optimal scheme and further improving the performance indicators of the RGB beam combiner. The results demonstrate improved multiplexing efficiencies for red (99.17%), green (99.76%), and blue (96.63%) light, with an overall average efficiency of 98.52%. The size of the optimized RGB beam combiner is 4.768 mm×0.062 mm.
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