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Abstract
An optical power coupler is one of the most well-used components in integrated photonics. Although couplers with an output power ratio 1:1 have been widely studied in the past, constructing asymmetric-ration optical power couplers is still an issue that is difficult to be addressed by using traditional Y-branch waveguides. Artificial intelligence (AI) assisted design is an effective technique for realizing complex optical structures. In this work, we have designed asymmetric-ration optical power couplers by using AI assisted design. Two couplers with the targeted splitting power ratio as 1:9 and 1:99 have been designed, respectively. In the AI assisted design, the coupler area was divided into discrete nano-pixels in the shape of circular holes with the same dimension. The AI controlled each pixel to be occupied by waveguide or air and trialed the occupation of each pixel one by one. In a 3.4 × 3.2 µm2 area, it took 1452 trials to obtain one optimized coupler. As a result, a splitting power ratio of 1:9.007 and 1:99.004 for the two couplers has been confirmed by using the finite-difference time-domain method. In addition, the waveguide configuration was further modified as the excess loss of the AI-designed coupler was a bit high, more than 3.50 dB. The way to reduce the loss is as follows: 1) positioning optimization of the output waveguide to avoid light scattering at the boundary between the coupler and the output waveguide, and 2) widening the output waveguide width to avoid insufficient light coupling. As a result, a scattering loss reduction of 1.7 dB by position optimization, and a coupling loss reduction of 1.6 dB by width widening were confirmed. The achieved design also exhibited a wide operation wavelength ranging from 1500–1600 nm in addition to sufficient fabrication tolerance of ±10 nm (± 11%).
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photonic integrated circuits (PICs) based on a silicon (Si) platform have attracted tremendous interest for constructing efficient optical devices and systems due to the high refractive index contrast and complementary metal-oxide-semiconductor compatibility [1–5]. In the development of PICs, a compact optical power coupler is one of the key components due to the requirements of power distribution among its building blocks [6–10].
Common couplers are with symmetric splitting ratio (output power ratio 1:1), which have been studied to some extent in the past [11–13]. Symmetric splitting ratio couplers are usually realized by using Y-branch waveguide or multi-mode interferometer (MMI) structure [11–14]. The symmetric couplers have been studied sufficiently and even widely applied in fiber to the home systems. In contrast, couplers with an asymmetric splitting ratio still have difficulties that are not easily addressed for practical applications because there is less matured design-theory. For realizing asymmetric splitting ratios, asymmetric Y-branch waveguides or directional couplers have to be implemented [12,14]. In the asymmetric Y-branch waveguides, the cross-section of the input waveguide is different from those of the output waveguides, so that it is difficult to realize optical mode-matching among the waveguides. This may cause a high coupling loss from the input waveguide to the output waveguides [12]. In the directional couplers, the coupling section is long and the operation wavelength bandwidth is limited [14]. For example, for a silicon channel waveguide directional coupler, the length of the coupling section is around 20 µm and the bandwidth is only 5 nm when the change of the splitting ratio is less than 5% [15]. On the other hand, if asymmetric optical power couplers can be easily designed, it is valuable for integrated optics. If a little amount of the light is able to be coupled out from some part of a densely integrated photonic circuit by using asymmetric couplers, the power or wavelength is monitored with less power-loss [16,17]. For example, the power and wavelength is needed to be detected in some sections of a PIC where a 50–100 mW laser is propagated. Since the common photo-detectors and optical spectrum analyzers have a limitation of the maximum detectable power, the power of the light coupled out of the PIC should be low enough. In this case, a 1:99 coupler may be useful, so that 0.5–1 mW light is coupled into the photo-detector or optical spectrum analyzer.
In previous study, we have demonstrated the possibility of designing asymmetric optical power couplers via artificial intelligence (AI) assisted design [18]. Though the asymmetric splitting ratio has been realized, the excess loss and the match between the input and output waveguides still needs to be improved. In this work, two asymmetric couplers with a splitting power ratio of 1:9 and 1:99 have been designed via AI assisted inversely design method. To realize the asymmetric ratios, the coupler region was divided into discrete nano-pixels in the shape of circular holes with the same dimension. AI program was utilized to decide the material of each hole to be waveguide or air one by one and FDTD simulation was introduced to evaluate the performance of the AI designed couplers. After 1452 trials, the splitting power ratio of 1:9.007 and 1:99.004 has been realized in the two couplers with a same footprint of 3.4 × 3.2 µm2. In addition, the positions and widths of the output waveguides were further optimized as the excess loss of the AI-designed coupler is a bit high of more than 3.50 dB. Through the optimization of the configuration, a scattering loss reduction of 1.7 dB by position optimization, and a coupling loss reduction of 1.6 dB by width widening were confirmed. The achieved design exhibited an operation wavelength from 1500–1600 nm and a sufficient fabrication tolerance of ±10 nm (± 11%).
2. Artificial intelligence assisted inversely designed optical power couplers
As shown in Fig. 1(a), the optical coupler consists of two sections: input/output waveguides and coupler section. The coupler section is composed of discrete nano-pixels in the shape of circular holes with the same dimension. The widths of the input/output waveguides are initially set as 0.5 µm to ensure the single-mode condition around the wavelength of 1550 nm. The couplers are constructed on the Si high-mesa waveguide [16] as shown in Fig. 1(b). The waveguide is based on a silicon-on-insulator wafer with a device layer of 100 nm, a top SiO2 cladding of 2 µm and a bottom SiO2 cladding of 3 µm. The bottom cladding is etched with a thickness of 1 µm. In our previous work [16], we have demonstrated that the fabrication of the waveguide was able to be completed in single step etching process and the propagation loss of the waveguide was as low as 0.2 dB/cm. Considering the light propagated in photonic circuits (especially in Si photonics) is usually in the TE polarization and the common semiconductor-lasers are also in the TE polarization, the designed couplers work in TE mode for future integration.
Fig. 1. AI designed optical power couplers: (a) Schematic diagram: input light is divided into two output waveguides by the coupler and (b) 100 nm Si high-mesa waveguide cross-section.
Traditionally, the design of photonic devices relies on human knowledge. It includes the physical insights revealed by the study of simple systems, the experience obtained from previous practice and the intuitive reasoning. Traditional tools to solve a photonic design problem include finite-difference time-domain (FDTD) method, finite element method (FEM) and beam propagation method (BPM). The simulated results are evaluated by the designer and the optical structure is updated repeatedly by adjusting some parameters until the specified performance is approached. Nevertheless, optimization of the photonic devices by human knowledge is not only computationally costly, but also less likely to match the desired performance directly. In contrast, the recent blossoming of AI has revolutionized many realms of science and engineering [19,20]. As a kind of junior AI, inverse design tackles the design task in a different manner. Without the need of physical principles for the initial guess, intended photonic functionalities are obtained by optimization in the design parameter space based on advanced algorithms and combined simulations.
In this work, AI assisted inverse design approach [21–26] is employed to realize the desired splitting ratio in the coupler section. The optimization processes proceed in several stages as shown in Fig. 2(a). The process is outlined as (1) an initial area as the coupler section; (2) the area is divided into discrete nano-pixels in the shape of circular holes with the same dimension; (3) carry out optimization process, where each pixel of the designed region can be occupied by waveguide or air. If the set targets are satisfied, the coupler area is shrunk in order to check whether a much compact coupler area exists; (4) if the targets are not satisfied, the pixels will be set smaller and step (3) is repeated again; (5) if the targets are still not satisfied even with smaller pixels, the coupler area size will be changed and steps (2)–(4) are repeated again until the structure is generated. According to the experience from previous Refs. [27] and [28], the diameter of the hole as 90 nm is accurate enough to control the light around the wavelength of 1550 nm. In order to reduce the amount of the calculations, the diameter of the hole is set as a fixed value of 90 nm in this work. As shown in Fig. 2(b), the size of the pixels is controlled in the optimization process, so the space of the holes is also adjusted at the same time as the pixel size varies. If the targets are not satisfied at the larger pixels (the space of the holes is d1), the pixels will be set smaller and the space is also reduced to d2 (d2<d1). The nonlinear direct-binary-search (DBS) optimization algorithm [29] is utilized to vary the material (waveguide or air) of each pixel. The objective of the optimization is to find the structures that satisfy the required splitting power ratio (1:9 and 1:99 in our case) with an excess loss α (α < 0.5 dB in our case) and a broadband performance from 1500–1600 nm. Here, α is the total loss between input waveguide and output waveguides, defined as:
Fig. 2. Overview of AI assisted inverse design of the coupler section (a) The whole AI design process and (b) the adjustment of the hole spacing during the AI design.
In the design process, AI controlled each pixel to be occupied by waveguide or air and trialed the occupation of each pixel one by one. In each trial, finite-difference time-domain (FDTD) method was used to simulate the light propagation in the couplers. The input light is set as TE polarization, so that only the TE mode is excited in the couplers. In the FDTD simulation, optical power detectors are set in the input and two output waveguides, so the splitting power ratio is able to be calculated based on the power projected on the detectors. Figure 3(a) shows the splitting power ratio versus times of trial in a 3.4 × 3.2 µm2 area for the 1:9 coupler. At the beginning, the ratio is far from the target because the pixels are randomly arranged. Subsequently, AI will change the occupied material of each pixel automatically and calculate the splitting power ratio. If the ratio is getting close to the target 1:9, the changed material will be reserved. Otherwise, the pixel goes back to the original material. In this way, the ratio is gradually becoming close to the target as the curve shown in Fig. 3(a). At the 1250-time trial, the ratio is 1:8.972 and the slope of the curve starts to become flat, which means the optimization is quite close to the optimization. After 1452 times, the ratio of 1:9.007 is accordance with our target and the optimization process terminates. The total computing time of the 1452 trials was around 16 hours (CPU: Intel Xeon 4114, 40 cores). For the 1:99 coupler, the process is similar, which takes 1452 trials to realize a 1:99.004 splitting ratio. The finally optimized couplers have a footprint of 3.4 × 3.2 µm2. There are totally 576 pixels consisting of circular air holes with an identical diameter of 90 nm randomly located in the coupler area. Figures 3(b) and 3(c) show the simulated optical fields in the 1:9 and 1:99 coupler, respectively. The color bar at the right side of the simulated results indicates the normalized light intensity profile, where different color stands for different light intensity, for example the dark blue means no light. The above results verify that the 1:9 and 1:99 couplers have been successfully realized by using the AI assisted inverse design method, which overcomes the difficulty that there is less matured design-theory for asymmetric couplers.
Fig. 3. AI assisted inverse design process and results: (a) Splitting power ratio versus times of trial in the 3.4 × 3.2 µm2 coupler area for 1:9 coupler (the curve of the 1:99 coupler is similar) and simulated light field in the finally (1452 trial) optimized (b) 1:9 and (c) 1:99 coupler.
3. Analysis and reduction of excess loss
For the 1:9 and 1:99 coupler as shown in Figs. 3(b) and 3(c), the estimated α were 3.7 and 3.62 dB, respectively at the wavelength of 1550 nm, which are higher than our target (α<0.5 dB). It is therefore necessary to carried out analysis and reduction of α for future applications in photonic integrated circuits. For the light coupling between two optical waveguides, the mismatch of the waveguide center and the model field usually leads to a high optical loss [30,31]. In our case, as shown in Figs. 3(b) and 3(c), we can see that the optical field at the edge of the optical coupler section is obviously larger than the width of the output waveguide (0.5 µm). This will cause a serious mismatch of the waveguide center and the model field, which is the main reason of the excess loss α.
In order to reduce α, the positions and widths of the output waveguides are optimized for the two couplers. Figure 4(a) shows the influence of the 0.5 µm wide output waveguide locations on the excess loss. The deviation σ is defined as σ > 0 for an outward deviation and σ< 0 an inward deviation [as shown in the inset of Fig. 4(a)]. In the simulation, the width of the input waveguide is Winput = 0.5 µm and the detector locates at the edges of the two output waveguides. From the simulated results, we can see that σ = −0.25 µm is the best location for the 1:9 and 1:99 couplers and α has a reduction of 1.7 dB compared with the original position σ = 0 µm. α with different output waveguide width Woutput is examined as shown in Fig. 4(b). The results indicate the optimized Woutput = 1 µm for both 1:9 and 1:99 couplers. After the width optimization, α has a further decrease of 1.6 dB at the wavelength of 1550 nm for the both couplers. The significant α reduction reveals that the waveguide centers and model fields between the output waveguide and the coupler section have been matched each other much better.
Fig. 4. Influence of the waveguide widths and locations on the excess loss: (a) Excess loss at different waveguide locations (insets show the schematics of the simulation) and (b) Output waveguide widths versus excess loss.
Figures 5(a) and 5(b) show a comparison of the calculated excess loss α for the output waveguides with a width of 0.5 and 1 µm from the wavelength 1500 nm to 1600 nm. The reduction of α (Δα) is 3.4 and 3.35 dB for the 1:9 and 1:99 coupler at the wavelength of 1550 nm, respectively. The reduction of α indicates that the optimization of the output waveguide positions and widths is effective to improve the coupling efficiency between the coupler section and the output waveguides.
Fig. 5. Comparison of the excess loss as the output waveguide with a width of 0.5µm and 1 µm, (a) 1:9 coupler and (b) 1: 99 coupler.
4. Input/output waveguide geometry unification
The widths of the input and output waveguides after the loss reduction are different from each other, which are 0.5 and 1µm respectively. In order to match waveguide width and benefit for future application, we design a mode size converter also based on AI assisted inversely designed nano-pixel structure. To be brief, we do not give the details of the simulation and calculation. The design process is similar to that of the above design of the optical power couplers [refer to Fig. 1(a)]. The finally optimized device is shown in Fig. 6, which consists of the optical power coupler and the mode converter. The mode converter occupies a space of 1 × 2 µm2, which is much more compact compared with the traditional tapered waveguides. There are 74 holes with an identical diameter of 90 nm randomly located in the mode converter.
Fig. 6. Schematic of the coupler after adding a mode converter to match the input and output waveguide
Figure 7 shows the simulated optical filed in the device with a splitting ratio of 1 (output 1) : 9.006 (output 2) at the wavelength of 1550 nm. The color bar at the right side of the simulated results indicates the normalized light intensity profile, where different color stands for different light intensity. In the device, the light propagated in the 1 µm-wide waveguide firstly enters into the 1 × 2 µm2 mode converter, which in turn gradually becomes narrow in order to be coupled into the 500 nm-wide waveguide. Compared with the 1 µm-wide waveguide, the light intensity is enhanced in the 500 nm-wide waveguide, which is because the area of confining light is smaller. Subsequently, the light from the 500 nm-wide waveguide is launched into the optical power coupler based on nano-pixel structure. The inversely designed optical power coupler as described in section 2 gradually divides the light into two beams and finally transforms it into 1:9.006 in the output waveguides.
The coupler with a splitting power ratio as 1:99.003 is shown in Fig. 8 by using the same mode converter and just modifying the positions of the nano-pixels in the coupler section. This result verifies that flexible splitting ratios are realized in the same area just through optimizing positions of the nano-holes.
Fig. 8. In the same area, 1 (output 1) : 99 (output 2) beam splitter is realized by modifying the positions of the nano-piexls.
5. Performance of optical power couplers
For a nano-photonic device, there are two general requirements to be fulfilled to easily fabricate the device: alignment/etching steps and fabrication tolerance [32,33]. In our designed beam couplers, the waveguide and holes are with the same etching thickness, so the device is able to be fabricated in only single-step etching procedure. The single-step etching avoids critical and complex alignments in electro-beam or photolithography, improving the accuracy of fabrication. Consequently, the most critical technological parameter with the largest contribution to the coupler performance is the sizes of the holes. The influence of the diameter on the splitting ratio has been calculated. For our devices, it is able to be fabricated by using electron-beam lithography with a resolution as high as sub-10 nm. Considering this resolution, the diameter has been varied with a tolerance of ± 10 nm (± 11%) in the calculation, while keeping the other parameters constant. In the calculation, the number of the pixels is a fixed value as 576 in the 3.4 × 3.2 µm2 coupler area, so the size of a pixel is 137.5×137.5 nm2. When we change the diameter of the hole from 80 to 100 nm, therefore, the space of the holes is simultaneously adjusted from 57.5 to 37.5 nm. Figure 9 shows the calculated split power ratio with different diameters. We can see that the variation of the splitting ratio is sufficiently low with a tolerance of ±10 nm (±11%). The splitting ratio is 1:99.1 and 1:9.1 at the diameter of 80 nm, and 1:98.9 and 1:8.9 at 100 nm. In addition, according to our simulations, the splitting power ratio is a little far from the targets when the diameter of the hole is outside of the 80–100 nm. At the diameter of 70 and 108 nm, the splitting power ratio deviates to 1:8.12 and 1:94.28 for the 1:9 and 1:99 coupler, respectively. The insensitivity of the splitting ratio performance to the diameters of the holes predicts excellent robustness of the device against fabrication imperfection.
Fig. 9. Calculated split power ratio versus hole diameter (a) 1: 9 and (b) 1:99 coupler, which predicts excellent robustness of the device against fabrication imperfection.
Another important factor for the couplers application is wavelength dependent performance shift. Figures 10(a) and 10(b) show the splitting ratio of the two couplers from 1500–1600 nm, which indicates that the device has a quite low wavelength dependent performance shift in the range of 1500–1600 nm. In addition, we find that the splitting ratio starts to deviate the targeted values rapidly when the operation wavelength is <1500 or > 1600 nm. At the wavelength of 1480 nm and 1618 nm, the splitting ratio is 1:7.96 and 1:93.21 for the 1:9 and 1:99 coupler, respectively. Figure 10(c) exhibits the relationship of the excess loss α and working wavelength. Though α increases when the wavelength is out of the optimum value of 1550 nm, it still keeps < 0.8 dB at this broad wavelength range. The wavelength independent performance proves a broadband application in future integrated photonic circuits.
Fig. 10. Wavelength dependent device performance: Calculated split ratio versus wavelength for the (a) 1:9 and (b) 1:99 coupler, and (c) Excess loss versus wavelength.
Though the optical power coupler exhibits a broadband application, the bandwidth of the mode converter will also affect the properties of the whole device. We have therefore investigated the excess loss in the mode converter for wavelengths ranging from 1500 to 1600 nm. Here, the excess loss α of the converter is defined as the optical power reduction as the light propagates through the converter. Figure 11 shows the calculated α versus wavelength, which predicts that the excess loss is below 0.1 dB for the entire wavelength range. The excess loss α of the mode converter incudes the scattering loss and reflection loss caused by the holes. Based on our simulations, 68% of the α is from the reflection loss, and 32% from the scattering. Combining the results of Fig. 10 and Fig. 11, we can see that the AI assisted inversely designed device including the mode converter and optical power coupler has a wide bandwidth. We also check the fabrication tolerance of the mode converter and just give the obtained results (to be brief). The mode converter possesses the same fabrication tolerance with the coupler, i. e. diameter of the holes ±10 nm.
6. Conclusions
We have designed optical power couplers with a splitting power ratio 1:9 and 1:99. The different ratios are realized via AI optimizing nano-pixels. The coupler performance of every trial is evaluated by FDTD method. Each coupler takes 1452 trials (around 16 hours) to realize the targeted splitting ratio. The optimization of the output waveguide positions and widths was applied to reduce α. After the optimization, α was effectively reduced from 3.7 to 0.3 and 3.62 to 0.27 dB for the1:9 and 1:99 coupler, respectively. In order to enhance the applicability, the output and input waveguides should have the same width, so a mode size converter is designed also via AI design at the input side to widen the 0.5 µm -wide waveguide to 1 µm. The converter demonstrates a loss of 0.045 dB, a footprint of 1×2 µm2. The whole devices have an operation wavelength from 1500 to 1600 nm with a fabrication tolerance of ± 10 nm (± 11%). Recently, there have been some other works published about the inversely designed power splitters [27,28,34–36]. Though the optical waveguide structures are different, a flexible splitting ratio has been successfully realized and the promising potential of the application in integrated photonic circuits has been demonstrated. Inspired by these progresses and the results in this work, we believe that couplers with arbitrary splitting power ratio are possible via the AI assisted inverse design.
Funding
Secom Science and Technology Foundation (501100004298).
Disclosures
The authors declare no conflicts of interest.
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