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Abstract
We proposed and experimentally demonstrated a low loss modified Bezier bend for silicon and silicon nitride photonic integrated circuits. Both simulation and experimental results confirm that the modified Bezier bend can effectively reduce the bend loss for silicon and silicon nitride platform. At a bend radius of 1 µm, the reduction of bend loss from 0.367 dB/90° of circular bend and 0.35 dB/90° of traditional Bezier bend to 0.117 dB/90° of modified Bezier bend for silicon platform was experimentally demonstrated. For a 12-µm radius silicon nitride bend, the bend loss reduction from 0.65 dB/90° of circular bend and 0.575 dB/90° of traditional Bezier bend to 0.32 dB/90° was achieved. The proposed modified Bezier bend design can also be applied to other material systems, such as InP, LN, GaAs, etc., to effectively reduce the bend waveguide loss.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silicon and silicon nitride photonic integrated circuits (PICs) have attracted much attention owing to the compatibility with cost-effective complementary metal–oxide semiconductor (CMOS) technology. Nowadays, they have significant applications in data centers [1–4], sensing [5–8], lidar [9–11], and quantum techniques [12–15]. The refractive indexes of silicon and silicon nitride are 3.47 and 2 at 1550 nm, respectively, which are higher than the silica cladding (${n_{Si{O_\textrm{2}}}}$∼1.44 at 1550 nm). The high index contrast results in high optical confinement, enabling the realization of high-density photonic integration chip. The bend is a fundamental optical unit in complex PICs and reducing bend loss is one of the most important design aims for integrated optical devices. For example, the bend loss is a major issue in the small-size high Q micro-ring filters [16–18] or large-scale optical switching fabrics [19–21]. Therefore, it is significant to develop a small size low loss bend waveguide in the high-density PICs.
The optical loss in bends is mainly composed of four factors [22,23]: 1) material and surface absorption loss, 2) scattering loss caused by the roughness of the waveguide boundary, 3) radiation loss caused by the curvature of the waveguide, and 4) mode mismatch loss occurring between sections with different mode profiles, i.e., input/output straight waveguide and bent waveguide. When the radius of bends is reduced enough, bend loss is dominated by the mode mismatch loss. In recent years, various solutions have emerged to reduce bend loss. The lateral offset was first proposed to realize mode matches between the straight waveguide and bent waveguide for the reduction of bend loss [23,24]. However, the size of offset is very small so that it is difficult to fabricate. Replacing the lateral offset solution, the Euler curve [25,26] or Euler-Circular [27] waveguide bends can match the curvature of waveguide bend to the straight waveguide, effectively reducing the mode mismatch loss. At the same time, Bezier waveguide bend [28,29] was confirmed to be able to reduce the bend loss and a S-bend structure with optimal Bezier curve [30] has been found helpful for reducing loss. However, the bend loss of the Euler curve and the Bezier curve are higher than that of circular bends when bend radius is ultra-small [31]. The reverse design is currently employed to realize low loss ultra-small radius bends. The issue of the reverse design is that the linewidth is too small (∼120 nm), which makes it impossible for mass production [32,33].
In order to reduce optical loss of ultra-small radius bend, we present a novel modified Bezier bend structure optimized by the particle swarm optimization (PSO). Simulation and experiments confirm that the proposed design can significantly reduce bend loss on silicon and silicon nitride platforms. In addition, we found the newly proposed modified Bezier bend can effectively suppress the instability of the output light field, which can reduce the loss of PICs system.
This paper is organized as follows. In Section 2, we introduce the structure of modified Bezier bend and the corresponding design method. In Section 3, we display the simulation and experimental results of modified Bezier bend in the silicon platform. In Section 4, the simulation and experimental results of the proposed modified Bezier bend in the silicon nitride platform are presented. The further discussion and conclusion are given in Section 5 and Section 6.
2. Structure of modified Bezier bend waveguide
Once the wafer specification parameters are determined, the waveguide thickness is a fixed value. Therefore, from the perspective of layout, the waveguide is a planar figure, as well as two curves forming a wave-guided path (for example, a straight waveguide is equivalent to a pair of parallel straight lines). For avoiding the loss due to mode coupling and simplifying the design process, the width of the optical waveguide along the transmission direction is usually a fixed value and meets the single-mode condition. Therefore, most bend waveguide designs are based on optimizing the center of the fixed width bend waveguide. However, mode coupling in waveguide requires a long coupling length and huge structural birefringence to excite. As for bends with ultra-small bend radius and symmetrical cladding, the mode coupling loss of bends can be completely ignored. In this view, optimizing the two curves of the bend instead of only one waveguide center curve to increase design freedom is an important strategy to reduce bend loss. For a bend with a given input waveguide width and bend radius, the flexible cubic Bezier curve prefers to be the optimized curve. Different from the traditional Bezier bend [30], the width of the new proposed bend waveguide varies along the transmission direction. We call this novel bend structure as modified Bezier bend. The cubic Bezier curve equation for the modified Bezier bend is expressed as
- 1) Ensure that the junction between bent waveguide and the input/output straight waveguide curve is continuous (the first order derivative of curve is equal at the junction), and then, C1x = 0, C3x = 0, C2y = Reff + W/2, and C4y = Reff - W/2.
- 2) Ensure that the overall area of modified Bezier bend is same as the normal circular bend, and then, C2x ∈ [0, Reff + W/2], C4x ∈ [0, Reff - W/2], C1y ∈ [0, Reff + W/2], and C3y ∈ [0, Reff - W/2].
Fig. 1. (a) The schematic of modified Bezier bend structure. (b) the schematic of traditional Bezier bend structure (c) the three-dimensional schematic of modified Bezier bend
Therefore, the four parameters (C2x, C4x, C1y, and C3y) of the modified Bezier need to be optimized. If four-dimensional parameters were scanned step by step, and the amount of data would be too large, which leads to a long design period. For solving multi-objective problems, we select the PSO algorithm with high rate of convergence [34–36]. With the fixed number of particle (NP) and iterations (NI), the optimal parameter and loss can be obtained. The three-dimensional schematic of the modified Bezier bend is shown in Fig. 1(c). As shown in Fig. 1(b), the width of the traditional Bezier bend has no change along the transmission direction. The structure of the traditional Bezier bend with the lowest bend loss can be obtained by sweeping the control coefficient B.
3. Silicon modified Bezier bend
3.1 Design silicon modified Bezier bend for 1550 nm
The typical size for single-mode waveguide cross section of silicon on insulator (SOI) wafer is 500 nm × 220 nm (width × height). Therefore, we select this waveguide parameter for input/output waveguide to design the modified Bezier bend. Bend loss is solved based on three-dimensional finite-difference time-domain (FDTD) through commercial software Lumerical FDTD. Transverse electric (TE) mode light is selected as the input mode. We set the number of iterations to be 100 and the particle size to be 20, and the termination condition of the iteration is 0 dB insertion loss. The optimization process for silicon modified Bezier bend with 1-µm, 1.5-µm, and 2-µm radius is shown in Fig. 2(a). The optimal insertion loss values are 0.11 dB/90°, 0.029 dB/90°, and 0.013 dB/90°, respectively. The structural parameters of three different silicon modified bends under the lowest loss are listed in Table 1.
Fig. 2. (a) PSO optimization of silicon modified Bezier bend at 1-µm,1.5-µm and 2-µm radiuses. (b). Sweeping results of silicon traditional Bezier bend at 1-µm,1.5-µm and 2-µm radiuses.
Table 1. Optimal Parameters of Silicon Modified Bezier Bend
By sweeping the coefficient B of the silicon traditional Bezier bend, the lowest losses of the silicon traditional Bezier bend at radius of 1 µm, 1.5 µm and 2 µm are −0.34 dB/90° (B = 0.45), −0.075 dB/90° (B = 0.35) and −0.015 dB/90° (B = 0.3), respectively. The result of sweeping is shown in the Fig. 2(b). For comparison, we also simulated the circular bend loss and traditional Bezier bend loss which are shown in Table 2. It can be found that the modified Bezier bend loss is lower than others. Compared with silicon circular bend, the simulated losses of silicon modified Bezier bend with 1-µm, 1.5-µm and 2-µm radiuses are reduced by 0.24 dB, 0.136 dB and 0.062 dB, respectively. As for silicon traditional Bezier bend, the simulated losses of silicon modified Bezier bend are reduced by 0.23 dB and 0.046 dB for 1-µm and 1.5-µm bending radiuses. Compared with 2-µm radius silicon traditional Bezier bend, the loss reduction effect of modified Bezier bend is not obvious, because the bend loss is already too small and can be ignored.
Table 2. Simulation Results Comparison for Silicon Bend Loss
Furthermore, we compare the optical field propagation of modified Bezier bend, traditional Bezier bend and circular bend at 1-µm, 1.5-µm, and 2-µm radiuses. As shown in Fig. 3, the optical field propagate in the modified Bezier bend with a better confinement, resulting in weaker radiated light field than those of the circular bend and traditional Bezier bend. This is the main reason why the proposed modified Bezier bend can reduce the bend loss. It can also be found that the output optical field from circular bend has a strong instability. This instability exhibits periodical offset around the central waveguide during the light propagation. The smaller the radius is, the stronger this instability is. Therefore, the instability is mainly caused by the mode mismatch between the input/output straight waveguide and bent waveguide. The Bezier curve has the gradually varying curvature, so modified Bezier bend can solve the mode mismatch problem and further effectively suppress this instability. At 2-µm bend radius, the optical instability of circular bend is obvious. However, the output light field of modified Bezier bend is as stable as the input field. Although traditional Bezier bend structure exhibits the ability to inhibit this instability, there is still a more radiation in the bend area compared with modified Bezier bend. Different from the traditional Bezier bend, the modified Bezier bend optimizes both boundary Bezier curves at the same time, so the modified Bezier bend can obtain better results.
Fig. 3. Optical field propagation in the silicon modified Bezier bend, traditional Bezier bend and circular bend
Figure 4 compare the three structures of the modified Bezier bend, the traditional Bezier bend and the circular bend at 1.5-µm radius. It can be found that the width of the modified Bezier waveguide along the propagation direction changes from W to W0 (W0 > W) and then back to W. With the same waveguide thickness, a wider waveguide has a larger effective refractive index and a stronger optical confinement. Therefore, the radiation field in the modified Bezier bend is weaker. As more optical field on the sidewalls of the wide waveguide will be weakened compared to the narrow waveguide, the wide waveguide can effectively reduce the scattering loss caused by the rough sidewall, which also allows the fabrication to be more tolerant. Since only the fundamental TE mode is input, both input and output waveguides are single-mode waveguides and the optimization target is to reduce the loss of this mode, whether the width of bent waveguide satisfies the single-mode condition can be ignored.
Fig. 4. Structure comparison of the modified Bezier bend, the traditional Bezier bend and the circular bend at 1.5-µm bend radius. W is width of input waveguide.
3.2 Experiments
The silicon device was fabricated based on 220-nm-thick top silicon and 3-µm-thick buried oxide (BOX) SOI wafers. Using plasma enhanced chemical vapor deposition (PECVD) of SiH4/N2O to deposit a 2-µm-thick silicon dioxide for the upper cladding. The silicon layer was patterned with electron-beam lithography (EBL) and was etched by a reactive ion etch (RIE) of C4F8/SF6/O2. The fully-etched uniform grating coupler of 567 nm pitch and 0.6 duty ratio was used for testing. The measurement setup consists of single mode fiber, polarization-maintaining fiber, polarization controller, spectrometer (Yokogawa AQ2211) and wavelength tunable C-band source (Santec TSL-500).
Figure 5 shows the experiment results of the silicon bend losses at 1550 nm obtained by the cut-back method. The measured bend losses are listed in Table 3. It can be found that among the tested bends, the modified Bezier bend have the lowest bend loss. When Reff = 1 µm, the experimental results are consistent with the simulation results. At 1-µm radius, the loss of the circular bend and the traditional Bezier bend are 0.367 dB/90° and 0.35 dB/90° in experiment, respectively. The loss of the modified Bezier bend is only 0.117 dB/90° in experiment. When Reff = 1.5 µm and Reff = 2 µm, the measured losses are slightly larger than the simulated results which may be caused by the fabrication process. At the same time, when Reff =2 µm, the traditional Bezier loss and the modified Bezier loss are almost equal, which is also consistent with the simulation results, so the experimental results are agreeable with the simulated results. Figure 5(d) shows the scanning electron microscope image of the 2-µm radius fabricated modified Bezier silicon bend. Each silicon bend is connected by a 0.5-µm long straight waveguide.
Fig. 5. Experimental results of silicon bend losses at 1550 nm when (a) Reff = 1 µm, (b) Reff = 1.5 µm and (c) Reff = 2 µm. (d) Scanning electron microscope (SEM) image of modified silicon Bezier bend at 2-µm radius.
Table 3. Comparison for Measured Silicon Bend Losses
4. Silicon nitride modified Bezier bend
4.1. Design silicon nitride modified Bezier bend for 1550 nm
In order to verify the universality of the proposed modified Bezier bend structure, we further designed and experimentally studied the bend loss in the silicon nitride platform. We selected 1200 nm × 400 nm (width × height) silicon nitride waveguide as the input waveguide. Compared to silicon, silicon nitride bend has a larger bend radius due to relatively low refractive index. Optimization is achieved at 8-µm, 10-µm and 12-µm radiuses based on PSO algorithm and FDTD. Since the size of silicon nitride bend is large, the number of optimization iterations is increased to 300. The result of the optimization is shown in Fig. 6(a). The optimal insertion loss values of 8-µm, 10-µm and 12-µm bend are 0.95 dB/90°, 0.41 dB/90°, and 0.23 dB/90°, respectively. The structural parameters of three different radius silicon nitride modified bends with the lowest loss are listed in Table 4.
Fig. 6. (a) PSO optimization of silicon nitride modified Bezier bend at 10-µm,15-µm and 20-µm radiuses. (b) Sweeping result of silicon nitride traditional Bezier bend at 10-µm,15-µm and 20-µm radiuses.
Table 4. Optimal Parameters of Silicon Nitride Modified Bezier Bend
In the following, we swept the coefficient B of the silicon nitride traditional Bezier bend to obtain the lowest bend losses at the radiuses of 8 µm, 10 µm and 12 µm and the corresponding bend lowest losses are 1.46 dB/90° (B = 0.4), 0.67 dB/90° (B = 0.4) and 0.35 dB/90° (B = 0.35) respectively. The result of sweeping is shown in Fig. 6(b). Simulated bend loss comparison between the silicon nitride modified Bezier bend, traditional Bezier bend and circular bend is listed in Table 5. Compared with silicon nitride circular bend, the simulated losses of silicon nitride modified Bezier bend with 8-µm, 10-µm and 12-µm radiuses are reduced by 0.68 dB, 0.42 dB and 0.29 dB, respectively. As for traditional Bezier bend, the simulated losses of silicon nitride modified Bezier bend are reduced by 0.51 dB, 0.26 dB and 0.12 dB for 8-µm, 10-µm and 12-µm bending radiuses. Obviously, silicon nitride modified Bezier bend has lower loss than others. It is shown that the modified Bezier model can also effectively reduce the bend loss in the silicon nitride platform.
Table 5. Simulation Results Comparison for Silicon Nitride Bend Loss
We also investigate the optical field propagation in three different types of silicon nitride bend, which is shown in Fig. 7. At each bend radius, there are different degrees of optical field leakage at the junction between the input straight waveguide and the bent waveguide, which is caused by mode mismatch. Compared to other types, the silicon nitride modified Bezier bend has less leakage, which is the main reason for the large reduction in bend loss. At the same time, we can also observe that there is instability in the output optical field from the silicon nitride circular bend as well as silicon circular bend. The discontinuity in traditional Bezier is obvious at 8-µm and 10-µm radiuses, however, this phenomenon disappears at 12 µm. The optical field simulation results of silicon and silicon nitride bends confirm that this discontinuity may exist in the ultra-small bending radius for any material system. As for silicon nitride modified Bezier bend, the output optical field is uniform without discontinuity in all three bending radiuses, which shows that modified Bezier bend can effectively suppress the output instability from bend. We further discuss the effect of this instability in the following discussion section.
Fig. 7. Optical field propagation among the silicon nitride modified Bezier bend, traditional Bezier bend and circular bend
4.2. Experiments design of silicon nitride modified Bezier bend for 1550 nm
Using a 500-µm-thick silicon wafer, a 3-µm-thick silicon oxide was grown for the under cladding. Then, the silicon nitride was deposited by low-pressure chemical vapor deposition (LPCVD). Using PECVD to deposit a 2-µm-thick silicon dioxide for the upper cladding. The silicon nitride layer was patterned with EBL and was etched by a RIE of CHF3/SF6. The fully-etched uniform grating coupler of 1.16-µm pitch and 0.5 duty ratio was used for testing. The measurement equipment for silicon nitride is the same as for the above silicon devices.
The measurement results of the silicon nitride bends are shown in Fig. 8(a), (b) and (c). Measured bend losses are listed in Table 6. It can be observed that the bend loss decreases as the radius increases, which is in accordance with the simulation. Among the three types of bends, the modified Bezier bend has the lowest bend loss. Compared with silicon nitride circular bend, the measured losses of silicon nitride modified Bezier bend with 8-µm, 10-µm and 12-µm radiuses are reduced by 0.625 dB, 0.775 dB and 0.33 dB, respectively. The measured bend losses of the silicon nitride modified Bezier bend are 1.25 dB, 0.775 dB and 0.255 dB lower than those of silicon nitride traditional Bezier bend for 8-µm, 10-µm and 12-µm bending radiuses. The measured losses are a little larger than simulation results in all three types of bend. This phenomenon can be attributed to the difference between the fabrication and the design layout. Due to the large feature size of silicon nitride waveguide, exposure was selected under a higher beam current for EBL, and the process deviation is from −60 nm to −100 nm. The narrowing of the waveguide width leads to weaker optical confinement, which explains why the loss of the silicon nitride bent waveguide is larger than expected. Comparing the difference between the simulation and experimental results, it is obvious that the deviation between design result and experimental result of modified Bezier bend is the smallest among all, which means that its fabrication process tolerance is largest due to the broadened waveguide width. The fabricated 12-µm radius modified Bezier silicon nitride bend is shown in Fig. 8(d). Each silicon nitride bend is connected by a 10-µm long straight waveguide.
Fig. 8. Experimental results of silicon nitride bend losses at 1550 nm of (a) modified Bezier bend, (b) traditional Bezier bend and (c) circular bend. (d) microscope image of modified Bezier silicon nitride bend at 12-µm radius.
Table 6. Comparison for Measured Silicon Nitride Bend Losses
5. Discussion
For the entire optical chip system, not only the optimization of discrete device is necessary, but analysis of the impact of discrete device on the entire optical system is very important. In usual, we focus on the characteristic of single optical device in the spectrum and ignored the output mode field, which may have a serious impact on the whole optical system. At a small bend radius, the output light field from circular bend is often instability (as shown in Fig. 3 and Fig. 7). The main manifestation of this instability is the output optical field oscillation, which seriously increases the system loss. As shown in Fig. 9(a), we use the cascading method to demonstrate the oscillation effects. The adjacent waveguides are connected by LC-length straight waveguides. As shown in Fig. 9(b), not only the 1.5-µm circular bend has a lot of loss, but also the loss has the tendency of periodical variation with LC. This effect is extremely obvious in the cascading process of even number of bends. The circular bend exhibits 0.35 dB and 0.46 dB peak-to-peak loss changes in the 2 and 4 cascade bends, respectively. This cascading is very common in large-scale optical switching and racetrack micro-rings (typically 4 cascaded bends). Therefore, suppressing the oscillation caused by the instability output can effectively reduce the system loss and improve the quality factor of the racetrack micro-ring. We found the modified Bezier bend can significantly suppress this instability. As shown in Fig. 9.(c), the modified Bezier bend exhibits 0.02 dB and 0.035 dB peak-to-peak loss changes in the 2 and 4 cascade bends, respectively. Therefore, the proposed modified Bezier bend is of great significance to promote the overall system performance and enhance the Q value of the racetrack resonator. In most PICs platforms, TE mode usually has lower loss, so TE mode was selected for demonstration in the paper. If loss optimization for TM mode or multi-order mode is required, the input and monitoring targets need to be changed to the desired mode, and then a corresponding low loss bend waveguide will be created. It is worth noting that C3y vanishes and C4x saturates at the ultra-small bent radius, indicating that the optimal shape of the inner curve for waveguide bend is a straight line.
Fig. 9. (a) Schematic diagram of cascaded bends. (b) Silicon circular bend loss of different bend amount at 1.5-µm radius versus LC. (c) Silicon modified bend loss of different bend amount at 1.5-µm radius versus LC
6. Conclusion
In this paper we propose a new modified Bezier bend for reducing the bend waveguide loss. Experimental measurements confirm that the modified Bezier bend can effectively reduce the bend loss compared with other bend structure for silicon and silicon nitride photonic platform. The measured loss of 1-µm radius silicon bend reduces from 0.367 dB/90° to 0.117 dB/90° by modified Bezier bend at 1550 nm. As for 12-µm silicon nitride bend, modified Bezier bend can experimentally reduce the loss from 0.575 dB/90° to 0.32 dB/90°. The proposed modified Bezier bend can also be applied to other material system, such as InP, LN, GaAs, etc., for reducing the bend waveguide loss. The new modified Bezier bend can also effectively suppress the instability of the output light from the ultra-small bend which can promote the overall system performance and enhance the Q value of the racetrack resonator.
Funding
National Key Research and Development Program of China (2020YFB2008803); National Natural Science Foundation of China (61905217).
Disclosures
The authors declare no conflicts of interest.
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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