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Research Article Realization of advanced passive silicon photonic devices with subwavelength grating structures developed by efficient inverse design a,b,† a,† a a a a,b,c, Jingshu Guo , Laiwen Yu , Hengtai Xiang, Yuqi Zhao, Chaoyue Liu, and Daoxin Dai * Zhejiang University, College of Optical Science and Engineering, International Research Center for Advanced Photonics, State Key Laboratory for Modern Optical Instrumentation, Hangzhou, China Zhejiang University, Jiaxing Research Institute, Intelligent Optics & Photonics Research Center, Jiaxing Key Laboratory of Photonic Sensing & Intelligent Imaging, Jiaxing, China Zhejiang University, Ningbo Research Institute, Ningbo, China Abstract. Compact passive silicon photonic devices with high performance are always desired for future large- scale photonic integration. Inverse design provides a promising approach to realize new-generation photonic devices, while it is still very challenging to realize complex photonic devices for most inverse designs reported previously due to the limits of computational resources. Here, we present the realization of several representative advanced passive silicon photonic devices with complex optimization, including a six- channel mode (de)multiplexer, a broadband 90 deg hybrid, and a flat-top wavelength demultiplexer. These devices are designed inversely by optimizing a subwavelength grating (SWG) region and the multimode excitation and the multimode interference are manipulated. Particularly, such SWG structures are more fabrication-friendly than those random nanostructures introduced in previous inverse designs. The realized photonic devices have decent performances in a broad bandwidth with a low excess loss of <1 dB, which is much lower than that of previous inverse-designed devices. The present inverse design strategy shows great effectiveness for designing advanced photonic devices with complex requirements (which is beyond the capability of previous inverse designs) by using affordable computational resources. Keywords: silicon photonics; inverse design; subwavelength grating structures; mode (de)multiplexers; wavelength (de) multiplexers; 90 deg hybrids. Received Dec. 6, 2022; revised manuscript received Jan. 22, 2023; accepted for publication Feb. 1, 2023; published online Feb. 24, 2023. © The Authors. Published by SPIE and CLP under a Creative Commons Attribution 4.0 International License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.APN.2.2.026005] 3–6 problem, inverse design provides a solution. An inverse de- 1 Introduction sign method translates the photonic design into finding the sol- Integrated photonics has been known as a key technology of ution for a black-box problem, in which the device structure is optoelectronics. By using on-chip light manipulations, the bulk generated according to the given objective function by using optical and optoelectronic systems can be integrated to compact computer-aided design methods [such as evolutionary algo- and robust photonic integrated circuits (PICs), bringing signifi- rithms (EAs) or artificial neural networks (ANNs) ]. Inverse de- cant advantages in cost, size, and power consumption. As the sign can break the limitation of the conventional (forward) integration intensity of the PICs increases, researchers have design methods, and thus potentially results in much more com- been devoted to developing advanced passive silicon photonic 9,10 2 pact footprints in contrast to the conventional devices. devices with high performance and compact footprints. For this For inverse design, the set of the to-be-decided geometry parameters is usually called an “individual.” An individual and *Address all correspondence to Daoxin Dai, dxdai@zju.edu.cn its corresponding set of the objective values consist of a “sample,” Jingshu Guo and Laiwen Yu contributed equally to this work. which can be used for the training of ANNs. All the possible Advanced Photonics Nexus 026005-1 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… individuals constitute the high-dimension search space. Similarly, As discussed in Ref. 22, the issue for the fully automatic in- all the objective-value set constitute the solution space whose di- verse design may be solved with the prior knowledge and intu- mension is the objective-value set dimension. As is well known, a ition of experienced designers, in which the computational costs multiobjective problem is widely recognized as a big challenge can be reduced by applying intelligent constraints and supplying in the field of computing mathematics. Currently, the inverse de- an exceptional initialization. Previously, we proposed a univer- sign of photonic devices is mainly limited to low-dimension sol- sal manipulation strategy of on-chip multimode excitations/ ution spaces, in which case only a few objective values are interferences by using all-dielectric metamaterial waveguides, allowed to be involved. When designing a photonic device with and mode exchangers were successfully designed with low a high-order scattering matrix, a large number of matrix elements computation cost. Fundamentally, various on-chip photonic should be optimized simultaneously, which makes the design op- devices for light manipulations with their amplitudes, wave- 25 26 17 27 timization pretty difficult. For example, there are few results of lengths, polarizations, phases, as well as modes can be demonstrating the inverse design of a 90 deg hybrid because the realized by appropriately manipulating the mode excitations optimization is challenging when both amplitude and phase re- and the mode interferences. sponses of all four output ports are considered. Similarly, the In this work, we propose a high-efficiency inverse design design complexity for mode (de)multiplexers increases signifi- approach for developing advanced passive silicon photonic de- cantly with the channel number, and thus currently the mode vices based on branch waveguides with subwavelength grating (de)multiplexers demonstrated with an inverse design still structures. Supervised by the theory of multimode excitations/ 12–14 have quite limited mode channels (no more than four). interferences, this geometry framework enables a high degree Therefore, it is still very desirable to develop an improved inverse 2 of freedom and low search space dimension of ∼10 to 10 design approach available for developing advanced passive sili- simultaneously. Importantly, it naturally supports a multistage con photonic devices with functional complexity. optimization strategy with manual intervention. Benefiting from To solve a black-box problem, a technical route is utilizing the experiences of traditional designs, the dimension of the optimization algorithms, such as the evolutionary algorithms search space increases minimally during the design process, 15 10 (EAs), the search algorithms (e.g., binary search algorithm ), which simultaneously enables fast convergence and high design and the gradient-based algorithms (e.g., gradient descent flexibility. Meanwhile, some advanced optimization algorithms 9 16 optimization and topology optimization ). The geometry [like covariance matrix adaptation evolution strategy (CMA- framework is usually a complete black box with a very high ES)] and efficient electromagnetic (EM) simulation tools are ap- 3,9,10,12–14 search space dimension (e.g., 100–1000 ). The most plied to further improve the computational efficiency. Finally, popular geometry frameworks for the fully atomic inverse de- three representative devices are designed and fabricated, con- sign are the complete black-box structures, such as no-shape- firming the effectiveness of the present approach for handling 6,9,14 constraint topology optimization structures and pixel struc- complex multiobjective problems. Furthermore, the designed 10,12,13 tures, both of which have to introduce a high search space photonic devices presented here are based on subwavelength dimension (at a scale of ∼10 ). To design application-oriented grating structures and thus have good feature-size uniformity, photonic integrated devices with decent performances, the mul- which can be fabrication-friendly. tiobjective problems should be solved efficiently even when no reasonable initial individual is available. In this case, the opti- 2 Results mization convergence usually becomes very difficult due to the high-dimensional search space and the high-dimensional solu- 2.1 Theory and Strategy tion space, and huge computational resources are needed. Moreover, the region to be designed is usually very limited For an inverse design, there are two key points to improve the 9,10,12–14,17 (e.g., typically <10 μm × 10 μm ) in order not to intro- design efficiency. First, the search space dimension should be duce an unacceptable search space dimension (e.g., >10 ). minimized as much as possible. Second, the search space should However, the device performance might not be sufficiently ex- be well-defined so that the final optimal design is included. As a cellent for real applications due to the limited solution space. As result, in this paper, we propose an inverse design method with a result, the fully atomic inverse design usually cannot perform unique features that are useful for efficiently developing ad- well for complex functional devices of photonics, e.g., the ob- vanced passive silicon photonic devices, as described below. tained performance may not meet the application requirements. 2.1.1 Device geometry definition From the perspective of device fabrication, the device generated from the fully automatic inverse design usually has a very tiny The device structure is basically defined geometrically with feature size, and the structure might be highly nonuniform, some waveguide branches separated by subwavelength grating which makes the fabrication requirement very crucial. As an al- (SWG) metamaterial structures, as shown by the example given ternative, recently ANNs have provided another technical route in Fig. 1(a). Definitely, the devices with more ports have more 8,18 for inverse design. It has been reported that a well-trained branches. Here each branch [see the deep-blue part in Fig. 1(a) forward-modeling ANN may solve a nanophotonic particle which consists of several segments longitudinally, and each seg- inverse-design problem much more efficiently than optimization ment is defined by its corner locations (i.e., the black pillars in algorithms. However, the training of the ANN still requires a Fig. 1(a)]. As shown in Fig. 1(a), an SWG structure is usually large amount of computing resources. In Ref. 19, there are as defined by the period P and the fill factor Λ, which can be preset many as 50,000 samples needed to train a forward-modeling or adjusted freely as desired. The SWG structures enable the ANN for an eight-sample-dimension problem. Therefore, the dispersion engineering to realize broadband or wavelength-sen- 23,28 ANN inverse design mainly focuses on the specific grating de- sitive photonic devices when desired. These to-be-designed 8,18 sign problems with low search space dimension of <10 and, geometry parameters are included in the individual for the 20,21 23 consequently, it is highly desirable to reduce the dimension. optimization. Advanced Photonics Nexus 026005-2 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… Fig. 1 Proposed inverse design strategy for passive photonic devices. (a) The design framework is demonstrated by an example of a photonic device with one input port and two output ports. Here, the SWG has a period of P and a fill factor of Λ. (b) Design flow chart with manual interventions. (c) Typical manual intervention operations. This device geometry definition is derived from our previous approach has much higher capability for the optimization of work, where a universal strategy of on-chip multimode exci- complex photonic devices even with limited computational re- tation/interference was demonstrated. In this work, the optimi- sources than those of previous inverse design approaches. zation of the design region enables flexible mode manipulation 2.1.2 Iteration strategy with manual interventions and further realizes on-chip light manipulations. The present de- sign strategy is potentially useful as a universal approach for Figure 1(b) shows the design flow chart of the present inverse developing various optical functional devices even without design method, which is based on a multistage optimization iter- any special initialization. This is different from those previously ation strategy with manual interventions. One stage of optimi- reported works based on multisectional multimode interferences zation is terminated when the figure of merit (FOM) comes to a 24,29 (MMIs) optimized with appropriate initialization. In particu- standstill. The corresponding solution is then used to initialize lar, the multibranch structure proposed here as the initialization the next stage of optimization, and manual interventions may be can build up a relatively smooth connection between the input/ introduced in the initialization, the EM solver setting, or other output ports and the design region. As a result, it is possible to parameter setting. Figure 1(c) gives several kinds of typical achieve excess losses (ELs) lower than those of previous inverse manual intervention processes, which include the following design devices with random nanostructures. cases. (1) The search space dimension can gradually be in- Apparently, the search space dimension is decided by the creased as the optimization stage iterates. For example, as number of the lengthwise sections in the design region. Any shown in Fig. 1(c), a stage solution with two sections and 12 design region with n sections can be redefined with 2n sections definition corners can be used to derive new generation with when needed. Such flexibility in the design makes it convenient four sections and 20 definition corners. (2) When possible, to gradually adjust the search space dimension. For example, a one should first use the most efficient EM solver in the early low search space dimension with, e.g., n ¼ 10 only can be stages of optimization and then use a high-precision EM solver adopted at the first stage of the optimization, so that one can (which is usually time-consuming) for the final stages of optimi- achieve a suboptimal solution with a low computational cost. zation. (3) For a multiobjective problem with a high-solution The suboptimal solution can be further used to initialize the sec- space dimension, the definition of the FOM may also be modified ond stage of optimization for which the search space dimension manually as the optimization stage iterates to balance the optimi- is improved to be with n ¼ ∼10 . In this way, the present zations of different objective values [Fig. 1(c)]. (4) When no Advanced Photonics Nexus 026005-3 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… gratifying solution is obtained after several stages of optimiza- In short, the present inverse design method combines the tions, the global settings of the computation need to be modified. search-space-dimension-control strategy, the advanced optimi- For example, the design region can be extended by the structure zation algorithm, and the flexible EM simulation strategy, so extension process. The preset parameters (like the input/output that it enables to solve efficiently multiobjective optimization waveguide locations) can also be changed, as shown in Fig. 1(c). problems. In the following sections, several advanced passive Assisted with some manual interventions, the present inverse silicon photonic devices are presented by utilizing this inverse design with the multi-stage optimization strategy has a high po- design method. In contrast, the design of these devices is very tential to realize high-performance functional photonic devices, challenging due to the complexity when using previous inverse since the search-space dimension for the final-stage optimiza- design methods. tion could be sufficiently high. Meanwhile, the optimization can be efficient because the geometry definition strategy is used 2.2 Realization of a Six-channel Mode (de)multiplexer to reduce the search-space dimension significantly. A mode (de)multiplexer is the fundamental device in mode- division-multiplexing systems. Typically, high-performance 2.1.3 Optimization algorithm mode (de)multiplexers are often realized by utilizing multi-stage We use the covariance matrix adaptation evolution strategy 36,37 asymmetric directional couplers. Recently, ultracompact (CMA-ES), which is known as an advanced optimization mode (de)multiplexers have been demonstrated by using the algorithm solving difficult black-box problems with large budg- 12–14 inverse design methods. However, these inverse-designed ets. CMA-ES and its variants have been found to outperform modes (de)multiplexers have no more than four channels. other optimization algorithms when the search space dimension The reason is that the inverse design becomes much more dif- 15,31 is high (e.g., >20). Currently, there have been few works ficult due to the increased complexity when it is desired to be using CMA-ES for the inverse designs of photonic integrated with more channels (more ports). devices. In this work, this advanced optimization algorithm Here, we propose and demonstrate a six-channel mode (de) is introduced to be helpful for efficient inverse designs. More multiplexer for the first time by utilizing the inverse design details about this algorithm are given in the Appendix, Sec. 4.1. method. As shown in Fig. 2(a), the initial geometry framework is based on an ordinary 1 × 6 branch configuration without spe- 2.1.4 EM simulation tool cial considerations. In the optimization region, there are six pol- ygon waveguides defined in the following way. Along the To evaluate the FOM, the EM simulation should be carried out lengthwise direction, there are n sections defined with the for each individual. The typical EM simulation tools include lengths L ¼½l ;l ; …;l . At the yz cross-sectional interface be- finite-difference time-domain (FDTD), finite-difference fre- 1 2 n 7 33 tween the (n − 1)’th and the n’th sections, the parameters D ¼ quency domain (FDFD), finite-element method (FEM), and n ½d ;d ; …;d define the lateral corner location in the y di- eigenmode expansion (EME). The EM-solving simulations n1 n2 n12 rection [see Fig. 2(a)]. The metamaterial SWG structure has a usually occupy most of the computational resource in inverse period P and a fill factor Λ. Specifically, here we choose P ¼ designs. Apparently, the simulation time usually increases with 200 nm and Λ ¼ 50%. For the input/output (I/O) waveguides, the device footprint. w and w respectively denote the waveguide widths, d and EME is also a frequency-domain algorithm whose computation in out in0 d respectively denote the positions of Port #1 and Port #7 in speed and precision depend on the number of the eigenmodes in- out0 the y axis, and d is the separation between the adjacent output volved and the number of the sections along the light propagation out waveguides. The parameter l (l ) denotes the length of the direction (rather than the device footprint). With EME, the total in out waveguide taper connecting the optimization region and the in- scattering matrix for all the ports of the device can be achieved in put (output) waveguide. The parameter set S to be optimized total one run. In this case, only one run is needed even for a six-channel can combine flexibly any related parameters. For example, one mode demultiplexer (DEMUX) (with six output ports). In con- might have S ¼½D ; D …D ; D or S ¼½D ; D … total 1 2 n nþ1 total 1 2 trast, one has to run the FDTD simulation six times for the six D ; D ; L;l ;l . n nþ1 in out mode channels one by one. Furthermore, an EME simulation For the scattering matrix of a photonic device, the element S ij may be much faster than a 3D FDTD simulation when the device denotes the coupling coefficient from mode #j to mode #i.For has a large footprint (e.g., the length > 10 μm). However, the the six-channel mode (de)multiplexer considered here, the bus EME method does not work well when there are sharp bends waveguide at Port #1 supports six modes (i.e., the TE − TE or nonwaveguide structures. Fortunately, the initialized structure 0 5 modes denoted as modes #1–#6). The output waveguides at is defined very well and thus intrinsically satisfies the requirement Ports #2–#7 support the corresponding TE modes (denoted of EME. 0 as modes #7–#12). Ideally, a six-channel mode (de)multiplexer Therefore, in this paper, the EME method is introduced as an should have the transmissions of jS j ¼ 1, where ji − jj¼ 6, important tool for the simulation. In the early stages of optimi- ij 1 ≤ i ≤ 6, and 7 ≤ j ≤ 12. The FOM for optimization is defined zations, EME is used to obtain a preliminary optimization solution, which is then used as a good initialization for the fol- by FOM ¼ − 20 lg jS j. Even though the optimiza- ðiþ6Þi 6 i¼1 lowing optimization stages with a 3D FDTD simulation. For tion was run with a single operation wavelength of λ ¼ example, when designing a six-channel mode DEMUX, the 1550 nm, fortunately, the optimized photonic device is very EME simulation takes 80.6 h only to improve the FOM from possible to work very well with a broad bandwidth, which is 10.94 to 0.42. The preliminary solution obtained by the EME attributed to the dispersion-insensitive multimode excitation/ simulation is already very close to the final optimization result. interference processes in the SWG waveguides, as demonstrated The introduction of efficient EME helps greatly to improve the previously. efficiency of our inverse design method for developing high- Figure 2(b) shows the FOM and the total computation time performance optical functional devices. cost as the iteration generation updates. The computation time Advanced Photonics Nexus 026005-4 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… Fig. 2 Inverse design of a six-channel mode (de)multiplexer on silicon. (a) Top view (xy plane), 3D view, and cross-sectional view (yz plane) at the interface between section n − 1 and section n (not to scale). (b) FOM and the simulation time cost as functions of the iteration generation for air- slot and SiO -slot devices. Inset: the milestone structures in the optimization flow. (c) and (d) The 3D FDTD simulation performance of the designed SiO -filled mode (de)multiplexer including the transmissions (c) and the light propagation fields for different input modes at 1550 nm (d). Modes #1 to #6 are, respectively, the TE to TE modes supported by the bus waveguides (Port #1), and 0 5 modes #7 to #12 are, respectively, the TE mode of Ports #2 to #7. Here the silicon photonic waveguides with a 220-nm-thick silicon core and a SiO upper-cladding are used. was evaluated on an ordinary personal computer (PC; details in designs, manual intervention processes were carried out. For ex- Appendix, Sec. 4.2). The milestone structures generated during ample, the section number n changes from 6 to 24. More details the optimization are also depicted in Fig. 2(b). One can see that are given in Sec. S1 in the Supplementary Material. The two an ordinary branch waveguide structure is used as the initial types of devices have similar theoretical performances, provid- individual. In terms of the fabrication process, the SiO filling ing excellent options for the labs/fabs with different fabrication in the SWG slots usually depends on the SiO deposition tech- technologies. In the following section, we focus on SiO -filled 2 2 nology. In the design, we consider the cases with air slots or devices regarding the fabrication technologies available. SiO slots. The air-slot device was designed first with a regular According to the high-precision 3D FDTD simulations with linear initial structure [Fig. 2(b)]. The EME method was used at very fine meshes (26 mesh points per effective-wavelength the early stages, and the FOM reaches 0.42 dB after 384 gen- scale), the designed SiO -filled device (with detail geometric erations of iteration (80.6 h). The FDTD simulation with two parameters in Table S2 in the Supplementary Material) has a types of mesh precision (see the details in Table S1 in the footprint as compact as 7.5 × 18 μm , low ELs from 0.53 to Supplementary Material) was then used in the following stages 1.03 dB, and low cross talks (CTs) < − 15.1dB in the wave- of optimization. Finally, the FOM is about 0.69 dB, obtained length range from 1500 to 1600 nm for all mode channels, as with 104 generations (41.5 h). This corresponding design shown in Fig. 2(c). In Fig. 2(d), the simulated light propagation was then used as the initialization for further optimizing the at 1550 nm is given, showing impressive mode (de)multiplexing air-slot and SiO -filled devices with high-precision FDTD sim- behaviors. The devices were fabricated by the regular processes ulation. As shown in Fig. 2(b), the optimization of the air-slot from Applied Nanotools Inc. (details in Appendix, Sec. 4.3). device finishes at the 507th generation with an FOM of 0.55 dB, Figure 3 shows the experimental results. Here the measured PIC costing 247.1 h in total. And the optimization of the SiO -filled consists of a pair of mode (de)multiplexers and fiber-to-chip device finishes at the 590th generation with an FOM of 0.62 dB, grating couplers [see Fig. 3(a)]. Figure 3(b) shows the scanning costing 419.2 h in total (including the 122.1 h for the optimi- electron microscope (SEM) image of the fabricated device, and zation of the air-slot device initially). For such multistage the normalized transmissions of the PIC are shown in Fig. 3(c). Advanced Photonics Nexus 026005-5 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… Fig. 3 Fabricated devices and measured results. (a) Microscope picture for the fabricated silicon PIC consisting of a pair of mode (de)multiplexers with six input ports (I − I ) and six output TE0 TE5 ports (O − O ). (b) SEM image of a mode (de)multiplexer. (c) Normalized transmissions of TE0 TE5 different port pairs. It can be seen that all channels for the fabricated mode (de)mul- correlation of these target values is weak in the optimal design tiplexers have a low EL of < ∼ 1dB and low CT of < − 10 dB of a 90 deg hybrid. Specifically, the amplitude-target-value-set in the wavelength range from 1520 to 1610 nm experimentally. fjS j ;j ¼ 1g for Port #1, the amplitude-target-value-set ij The slight ripples in the transmission spectrums may be attrib- fjS j ;j ¼ 2g for Port #2 and the phase-target-value-set fθ − ij 3 uted to the nonzero reflection of the mode (de)multiplexers. θ ; θ − θ ; θ − θ g have almost no correlation among them. In 6 4 6 5 6 this case, the optimization is often likely to be trapped locally, and it is hard to reach the globally optimal design. Nevertheless, 2.3 Realization of a 90 deg Hybrid the present high-efficiency inverse design works well and gives a high-performance 90 deg hybrid successfully. As shown by A 90 deg hybrid is the key device in optical coherent commu- the details in Sec. S2 in the Supplementary Material, the nication systems. Basically speaking, a 90 deg hybrid has two FOM definition can be adjusted manually in the multistage op- input ports [i.e., Port #1 for the signal and Port #2 for the local timization process to ensure global optimization for all the target oscillator (LO)] and four output ports (#3, #4, #5, and #6), as values. shown in Fig. 4(a). Generally speaking, the optimal design of a Finally, the 90 deg hybrid is designed with a footprint 90 deg hybrid is pretty challenging because not only the ampli- of ∼13 × 5 μm (with detail geometric parameters in Table tude responses but also the phase responses at the four ports S3 in the Supplementary Material), and one has fθ ; θ ; θ ; should be considered. 3 4 5 θ g ≈ f0 deg;−180 deg; 90 deg;−90 deggþ 133 deg.Asa For a 90 deg hybrid, the scattering matrix of the electric field result, Ports #3 and #4 are the in-phase (I) channels, while amplitude should satisfy eight requirements of jS j ¼ 1∕4 ij Ports #5 and #6 are the quadrature (Q) channels. Figure 4(b) (j ¼ 1, 2; i ¼ 3, 4; 5, 6), while the phase differences between shows the simulated light propagation when the TE modes with the output ports should satisfy the condition of fθ − θ ; 3 6 different phase differences Δθ are, respectively, injected into θ − θ ; θ − θ g¼f−90 deg; 90 deg; 180 degg, where 4 6 5 6 the two input ports. One can clearly see that the interference θ ¼ argðS Þ − argðS Þði ¼ 3, 4; 5, 6. In this problem, there i i2 i1 cancellation happens at one of the four output ports according are 11 target values, including eight amplitude requirements to the phase difference. It proves that the present design method and three phase requirements. One should notice that the Advanced Photonics Nexus 026005-6 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… Fig. 4 Inverse design of a 90 deg hybrid on silicon. (a) The 3D schematic diagram. LO, local oscillator. (b)–(f) The simulated performances of the final design (SiO slot device): the simulated light propagation fields with varied phase difference Δθ between Ports 2 and 1 at (b) 1550 nm, (c) the transmissions, (d) CMMRs, (e) the Els, and (f) phase errors (f). Here the transmission is given by the S parameter (i.e., S channel is given by 20 log jS j). CMMR, common mode re- ij 10 ij jection ratio. is effective even when both the amplitude and phase responses range from 1530 to 1570 nm is within the range from are required to be considered. Figures 4(c) and 4(d) show the −14.90 deg to 10.63 deg. simulated amplitude and phase responses in the wavelength range from 1530 to 1570 nm. It can be seen that the transmission losses 2.4 Realization of a Two-channel Flat-top are 6.6 to 7.4 dB and the ELs of the signal- and LO-ports Wavelength-Division (De)multiplexer are <0.96 dB, while all the phase errors are within −4.6deg A wavelength (de)multiplexer is a key element to separate/ ∼4.6deg, and the common mode rejection ratio (CMMR ) combine different wavelength channels in wavelength division are >26.3dB for all I∕Q channels. multiplexing (WDM) systems. Here, a two-channel wavelength Figure 5 shows the measurement results of the fabricated (de)multiplexer is designed optimally with the present inverse 90 deg hybrid. In our experiments, the transmissions were mea- design method. Currently, there have been several inverse de- sured with the testing PIC [Fig. 5(a)], while the CMMRs and the signs for the wavelength (de)multiplexers with two channels, ELs are extracted from the measured transmissions. As shown in 33,40,41 42 Fig. 5(b), the measured transmissions are −4.8 ∼ −9.0dB in three channels, and six channels, and most of them are the wavelength range from 1530 to 1570 nm. The CMMRs narrowband. As it is well known, a flat-top response is often of both I∕Q channels are below −10.2dB, and the measured desired in practice because it becomes tolerant of some random ELs are below 1 dB, as shown in Fig. 5(c). The phase responses wavelength variation. For the design of a wavelength (de)multi- were measured by the testing PIC consisting of a 1 × 2 power plexer with a flat-top spectral responses, the inverse design is splitter, a pair of asymmetric interference arms, a 90 deg hybrid, usually challenging because it is required to include multiple as well as grating couplers (see Fig. S1 in Sec. S2 in the objective values. In this example, the two wavelength-channels Supplementary Material), which has been widely used before. from 1290 to 1330 nm and 1470 to 1570 nm are considered. The measured transmissions at the four outports are presented Basically, the two-channel wavelength (de)multiplexer has in Fig. 5(d), and the extracted phase errors are given in an input Port (#1) and two output Ports (#2 and #3), as shown Fig. 5(c), which shows that the phase error in the wavelength in Fig. 6(a). The 1550 nm channel and the 1310 nm channel are Advanced Photonics Nexus 026005-7 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… Fig. 5 Experimental results of the fabricated 90 deg hybrid. (a) Measured transmissions. (b) Measured CMMRs. (c) Measured ELs. (d) The port-to-port optical transmission are spectra measured by the phase-test PIC. (e) Phase error extracted from the measured results of the phase-test PIC. Fig. 6 The inverse-designed two-channel wavelength multiplexer on silicon. (a) 3D schematic diagram. (b) Simulated light propagation in the designed devices. (c) Calculated transmissions. (d) Measured transmissions. Inset: SEM image of the fabricated wavelength demultiplexer. Advanced Photonics Nexus 026005-8 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… Advanced Photonics Nexus 026005-9 Mar∕Apr 2023 Vol. 2(2) Table 1 Summary of the state-of-the-art mode (de)multiplexers, 90 deg hybrids, and wavelength (de)multiplexers on silicon. a b EL (dB) CT/ER/CMMR/IM (dB) Bandwidth (nm) Special indicators Footprint Device Type, year (μm ) Sim. Exp. Sim. Exp. Sim. Exp. Sim. Exp. Ref. Mode (de) Dual-core adiabatic ∼33×471 NA <1.8 NA CT<-14 140 80 10 Channels 37 multiplexer tapers, 2018 (5TE+5TM) Tilt waveguide 2 × 50 <1 <1.29 CT<-17.4 CT<-14.4 60 60 4 Channels 43 junctions, 2022 @1.55 μm) @1.55 μm ANN-Inverse 2 × 17.5 <1.1 <2.4 CT<-10 CT<-10 90 70 3 Channels 44 design, 2021 @1.55 μm) Inverse design, 2020 5.4 × 6 <2 (∼1 <1.5 CT<-18 CT<-16 60 60 4 Channels 13 Inverse design, 2021 6.5 × 6.5 NA 0∼10 NA CT<-14 NA 60 4 Channels 14 @1.55 μm Inverse design, 2022 4.8 × 4.8 <5 (<1.1 ) <2.5 CT<-12 CT<-12 100 40 4 Channels 12 Inverse design 7.5 × 18 <1.03 <∼1 CT<-15.12 CT<-10 100 90 6 Channels This work 90 deg hybrid MMIs + phase 21.6 × 27.9 <0.45 <0.5 CMMR>30 CMMR>30 35 35 - PE < 3 29 shifter, 2017 @1.55 μm a) Inverse design, 2022 4.8 × 4.2 <2 (<0.5 ) <2.1 −2∼2.4 (IM) ∼±2 (IM) 100 40 PE < 70 PE < 27 12 @1.55 μm @1.55 μm (<6.5 ) (<10 ) Inverse design 4.71 × 13.03 <0.96 <1 CMMR > 26.33 CMMR>10.2 40 40 PE<4.6 PE<14.9 This work @1.55 μm (<5 ) IM < 0.37 IM=-2.82∼1.5 @1.3/1.55 μm WDM Inverse design, 2015 2.8 × 2.8 ∼1.7 >1.8/2.4 ER >∼ 13 ER>11 100/170 100/170 2 Channels, Flat-top 9 Inverse design, 2018 5.5 × 4.5 1.56/1.68/1.35 2.82/2.55/2.29 ER > 15 ER>10.7 NA NA 3 Channels, Non-flat-top 41 Inverse design, 2019 1.4 × 1.8 0.36/0.09/0.76 1.87/1.49/3.47 ER > 6.23 ER>8.51 NA NA 3 Channels, Non-flat-top 33 Inverse design, 2020 2.8 × 2.8 0.3/0.54 NA ER > 15.29 NA NA NA 2 Channels, Non-flat-top 42 4.6 × 2.8 ∼1.9 ER = ∼ 13 4 Channels, Non-flat-top 6.95 × 2.8 0.31∼2.12 ER > 15.86 6 Channels, Non-flat-top Inverse design, 2022 6.2 × 5.4 ∼0.8 1.2 ER > 17 ER > 15 >30 >30 3 Channels, Flat-top 40 Inverse design 3.07 × 12.46 <1 <1 ER > 10 ER > 10 80/140 88/109 2 Channels, Flat-top This work The superscript “@ λ ” denotes that the result is only for the central wavelength λ (similarly hereinafter). 0 0 For the wavelength (de)multiplexer, the bandwidth of each channel of the flat-top devices is given. For Ref. 9, the simulated bandwidth condition is EL < 4dB and ER > ∼13 dB, while the ex- perimental bandwidth condition is EL < 5.4dB and ER > 11 dB. In our work, the bandwidth is for achieving EL < 1dB and ER > 10 dB. Here, the special indicators are listed including simulated and experimental results, e.g., the channel numbers of mode (de)multiplexer and wavelength (de)multiplexer, the phase error of 90 deg hybrid, the flat-top feature. Abbreviation definitions: EL, excess loss; CT, cross talk; ER, extinction ratio; CMMR, common mode rejection ratio; IM, imbalance; PE, phase error; Sim., simulated result; Exp., experimental result; NA, not available; PBS, polarization beam splitter; WDM, wavelength (de)multiplexer. Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… 2 29 launched from Port #1 and are then separated to Port #2 and 21.6 × 27.9 μm . In contrast, the present 90 deg hybrid has a Port #3, respectively. Here we choose several key wavelengths footprint shrunk by ∼tenfold and similar performances, includ- with a spacing of 20 nm for each channel, and the condition ing low ELs, high CMMRs, low phase errors, and large band- for the optimization is given by jS ðλ Þj ¼ 1, λ ∈ width. Our present 90 deg hybrid has shown much better 21 a a f1470,1490,1510,1530,1550,1570g nm and jS ðλ Þj ¼ 1, performance on the EL, the imbalance, the phase error, and 31 b the bandwidth than those of inverse-designed 90 deg-hybrid λ ∈ f1290,1310,1330g nm. The optimization costs 302.5 h with 2D code structures. The broadband characteristic of (see more details in Sec. S3 in the Supplementary Material). our 90 deg hybrid also reflects the high-efficiency capability Finally, the designed device has a compact footprint of of our approach for the optimization with a large number of ob- 3.1 × 12.5 μm (with detail geometric parameters in Table S4 jective values (e.g., with multiple wavelengths involved). in the Supplementary Material). Figure 6(b) shows the simu- Nowadays, there have been many wavelength (de)multi- lated light propagation for the two central wavelengths by using plexers designed conventionally, in which high performance the 3D FDTD method. As shown in Fig. 6(c), the designed and footprint compactness usually conflict. As shown in wavelength (de)multiplexer has ELs of < 1dB and ERs of > Table 1, the two-channel flat-top wavelength (de)multiplexers 10 dB in the wavelength ranges from 1250 to 1330 nm and 1470 designed with conventional methods are usually based on to 1610 nm. The ELs at 1310 and 1550 nm are, respectively, 45 46 Mach–Zehnder interferometers, waveguide Bragg gratings, 0.67 and 0.36 dB, while the corresponding ERs are, respec- or wavelength-selective waveguide couplers, and they have tively, 15.02 and 30.33 dB. The fabricated wavelength (de)mul- lengths in scale of ∼10 μm. In contrast, the inverse-designed tiplexer [see the inset in Fig. 6(d)] was then measured with the wavelength (de)multiplexer in this work has an ultracompact help of the PICs with different grating couplers working at the footprint of 3.07 × 12.46 μm . In recent years, there have been corresponding wavelength bands of 1310 and 1550 nm. From 9,33,40–42 several inverse-designed wavelength (de)multiplexers. the measured transmissions shown in Fig. 6(d), it can be seen 33,41,42 However, they most are nonflat-top. The inverse-designed that the EL is <1dB and the ER is >10 dB in the wavelength wavelength (de)multiplexer in Ref. 9 is indeed flat-top while the ranges from 1256 to 1344 nm and 1482 to 1591 nm. EL is higher than 1.8∕2.4dB for the central wavelengths of 1.31∕1.55 μm. In contrast, our device has flat-top responses 2.5 Comparisons and Perspective as well as a low EL of <1dB. More recently, a three-channel flat-top wavelength (de)multiplexer was reported with a band- Table 1 gives a summary of various related silicon photonic width of ∼30 nm for an EL of ∼1dB and an ER of >15 dB. In devices reported. The state-of-the-art devices developed by con- contrast, our wavelength (de)multiplexer enables flat-top re- ventional (forward) design methods and inverse design methods sponses with an ultrabroad bandwidth from 80 to 110 nm. are listed. Here, the devices are evaluated by their performance Furthermore, the present devices can be scaled easily for more within the whole bandwidth except those non-flat-top wave- channels by structure cascading when needed. length (de)multiplexers and those labeled with “@ λ .” Here, In summary, for practical applications (e.g., optical “@ λ ” is for the performance at the central wavelength λ . 0 0 1,2 interconnects ), the devices are often required to have decent The conventional (forward) design methods usually have advan- performance with low losses, high extinction ratios, multiple tages in device performance and the design scalability. For these channels, broad bandwidths, etc. As shown in Table 1, the pre- devices, however, the difficulty of footprint shrinking is the key viously reported inverse design devices usually cannot satisfy issue. In contrast, inverse designs have natural advantages in the requirement with ELs of <1dB in a broad bandwidth, footprint compactness, while the bottleneck is the design effi- which fortunately can be achieved in this work. Our designs ciency for complex functional devices with a large number need computation time of ∼200 h (see Supplementary of to-be-optimized objective values, such as multichannel Material) when using a single PC. This computation resource devices or flat-top wavelength-selective devices. As shown in requirement is affordable even for the six-channel mode (de) Table 1, the present mode (de)multiplexer exhibits high theoreti- multiplexer and 90 deg hybrid, which are beyond the capability cal performances of low ELs, low CT, and large bandwidths of previous inverse designs with regular computational resour- comparable to or even better than those of conventional mode 37,43 ces. As shown in Table 1, the experimental results for the CT/ (de)multiplexers. The measured CT for the fabricated mode ER/CMMR/IM are usually inferior to the simulation ones, (de)multiplexers is slightly inferior to conventional mode (de) mainly due to fabrication errors. In our case, all the geometry multiplexers, and the footprints depend on the channel numbers. parameters including D ¼½d ;d ; …;d and the SWG n n1 n2 n12 More recently, a four-channel mode (de)multiplexers using feature size are chosen to be sufficiently large (e.g., >80 nm) tilt waveguide junctions was reported with footprint of 2 43 according to the fabrication technology. Unfortunately, there ex- 2 × 50 μm , which represent the state-of-the-art level of the ist some acute-angle structures at some corners, which leads to conventional methods. Definitely, the device footprint will in- some performance degradation for the fabricated devices. In the crease greatly if the channel number increases from 4 to 6. future work, the device performance (e.g., the CT) could be pos- Furthermore, the performance degradation may occur as usual. sibly improved by introducing smoothened subwavelength To the best of our knowledge, we present the first six-channel structures. The optimization efficiency should be improved fur- mode (de)multiplexers developed with inverse design, owing to ther for realizing the devices with very high complexity, such as the high efficiency of our inverse design strategy. Moreover, our the mode/wavelength (de)multiplexers with many channels. devices have advantages in the performances of the EL and the bandwidth when compared to the other inverse design coun- 3 Conclusion terparts. For conventional 90 deg hybrids, the state of the art is with an We have proposed a high-efficiency inverse design method for EL below 0.5 dB, a CMMR over 30 dB, and phase errors below developing advanced passive silicon photonic devices with high 3 deg in the C-band (1530 to 1565 nm) while the footprint is performance and compact footprints. Multistage optimizations Advanced Photonics Nexus 026005-10 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… with manual intervention processes are carried out based on seg- effective for the nonseparable, illconditioned black-box prob- mented geometry-definition assisted by SWG structures. lems with high dimensionality. In this work, the start sample ð1Þ ð1Þ Thanks to the manual intervention processes, the search space is assigned to m , the initial step size σ is set from 2 to ð1Þ dimension increases gradually under control to realize fast con- 7 nm, depending on the specific problems, and C is an iden- vergence and high design degrees of freedom simultaneously. tity matrix. Meanwhile, the flexible setting of EM simulation tools and the efficient optimization algorithm CMA-ES further enable a 4.2 Electromagnetic Field Numerical Simulation Details high design efficiency for our method. Using this method, three The 3D FDTD simulations and EME simulations were performed types of advanced passive silicon photonic devices have been by using Lumerical FDTD Solutions and Mode Solutions. In this demonstrated, including a six-channel mode (de)multiplexer, work, the simulation time was tested on a personal computer a 90 deg hybrid, and a two-channel flat-top wavelength (de)mul- (CPU: Inter Core i7-11700 @2.5 GHz, RAM: 64 G). The EME tiplexer. In contrast to the previous inverse design methods, our solver was carried with configuration of one process and 16 method has the advantage of handling multiobjective problems threads. The SWG metamaterial is equivalent to homogeneous and shows great potential to be applied widely for various ad- anisotropic metamaterials. The FDTD solver was carried with vanced passive photonic devices. For instance, it enables the configuration of four processes and one thread. The final perfor- realization of the first six-channel mode (de)multiplexer de- mance confirmations of the devices were performed with dense signed by inverse design method, to the best of our knowledge. meshes (i.e., mesh accuracy index of 6 or 8, corresponding to 26 The first broadband 90 deg hybrid has also been realized with or 34 mesh points per effective-wavelength scale). our inverse design, which is very challenging because there are 55 objective values involved. Furthermore, the present devices 4.3 Device Fabrication usually have low loss of <1dB, enabling the possibility of de- vice cascading when needed. Our designs need affordable com- All the devices were fabricated on a silicon-on-insulator (SOI) putational resources (total computation time of ∼200 h when wafer with a 220 nm-thick top-silicon layer and a 2 μm-thick using a single PC). The demonstrated devices show decent theo- buried dioxide layer. The silicon photonic waveguides were pat- retical and experimental performances comparable to their state- terned by the processes of electron-beam lithography and induc- of-the-art counterparts designed conventionally. Meanwhile, tively coupled plasma dry-etching. Then the 2.2-μm-thick their footprints are reduced greatly by twofold to tenfold. silicon dioxide cladding was deposited by using chemical vapor The present work can be extended easily to III–V and lithium deposition. niobate systems. As a summary, this inverse design method is very helpful for the development of advanced passive photonic Acknowledgments devices with high performance, design universality, and foot- print compactness, which may be useful for realizing next-gen- This work was supported by the National Major Research and eration high-intensity PICs. In the future, further efforts in Development Program (Grant No. 2018YFB2200200); the design strategy and computation algorithms should be made National Science Fund for Distinguished Young Scholars to achieve performance improvements and footprint com- (Grant No. 61725503); the National Natural Science pressions. Foundation of China (Grant Nos. 62175216, 61961146003, 91950205); Zhejiang Provincial Natural Science Foundation 4 Appendix: Methods (Grant No. LR22F050001); The Fundamental Research Funds for the Central Universities; The Leading Innovative and 4.1 Covariance Matrix Adaptation Evolution Strategy Entrepreneur Team Introduction Program of Zhejiang (Grant (CMA-ES) No. 2021R01001). The authors declare no conflicts of interest. CMA-ES is based on a multi-individual search in which the Code, Data, and Materials Availability search individuals of each generation are sampled from multi- variate normal distributions. The individuals with good FOMs Supplementary Material is available. Additionally, the data that are used for guiding the evolution of the normal distribution support the findings of this study are available from the corre- parameters. The introduction of normal distribution follows sponding author upon reasonable request. the maximum entropy principle, making this algorithm power- ful. The algorithm flow is described as follows. The individuals References of each generation are obtained by sampling of the normal dis- ðgÞ 2ðcÞ ðgÞ ðgÞ ðgÞ ðgÞ tribution Nðm; ðσ Þ Þ m þ σ Nð0;C Þ, where m is 1. N. Margalit et al., “Perspective on the future of silicon photonics ðgÞ the mean value of the search distribution at generation g, σ and electronics,” Appl. Phys. Lett. 118(22), 220501 (2021). ðgÞ is the step-size, and C ∈ R , is the covariance matrix of 2. W. Bogaerts and L. Chrostowski, “Silicon photonics circuit de- n×n ðgÞ sign: methods, tools and challenges,” Laser Photonics Rev. the normal distribution Nð0;C Þ at generation g. The FOM 12(4), 1700237 (2018). of each individual is evaluated by EM solving and then ranked. 3. S. Molesky et al., “Inverse design in nanophotonics,” Nat. After that, part of the individuals with good FOMs (usually Photonics 12(11), 659–670 (2018). the better 50%) are used for updating the parameters 4. Z. A. Kudyshev, V. M. Shalaev, and A. Boltasseva, “Machine ðgþ1Þ ðgþ1Þ ðgþ1Þ ½m ; σ ;C by covariance matrix adaptation algo- learning for integrated quantum photonics,” ACS Photonics rithm for next-generation computation (details in Ref. 30). 8(1), 34–46 (2021). As the generation increases, the population (including the mean 5. G. Genty et al., “Machine learning and applications in ultrafast value and the sampled individuals) will approach to the prom- photonics,” Nat. Photonics 15(2), 91–101 (2021). ising area covering good solutions. CMA-ES has been known as 6. A. Y. Piggott et al., “Inverse-designed photonics for semiconduc- one of the most efficient evolutionary approaches, which is tor foundries,” ACS Photonics 7(3), 569–575 (2020). Advanced Photonics Nexus 026005-11 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… 7. M. M. R. Elsawy et al., “Numerical optimization methods for 31. D. Molina et al., “An insight into bio-inspired and evolutionary metasurfaces,” Laser Photonics Rev. 14(10), 1900445 (2020). algorithms for global optimization: review, analysis, and lessons 8. P. R. Wiecha et al., “Deep learning in nano-photonics: inverse de- learnt over a decade of competitions,” Cogn. Comput. 10(4), 517– sign and beyond,” Photonics Rev. 9(5), B182–B200 (2021). 544 (2018). 9. A. Y. Piggott et al., “Inverse design and demonstration of a 32. Y. Miyatake et al., “Computational design of efficient grating cou- compact and broadband on-chip wavelength demultiplexer,” plers using artificial intelligence,” Jpn. J. Appl. Phys. 59(SG), Nat. Photonics 9(6), 374–378 (2015). SGGE09 (2020). 10. B. Shen et al., “An integrated-nanophotonics polarization beam- 33. Z. Liu et al., “Integrated nanophotonic wavelength router based on splitter with 2.4×2.4 μm footprint,” Nat. Photonics 9(6), 378– an intelligent algorithm,” Optica 6(10), 1367–1373 (2019). 382 (2015). 34. B. Luyssaert et al., “A compact photonic horizontal spot-size con- 11. B. Li et al., “Many-objective evolutionary algorithms: a survey,” verter realized in silicon-on-insulator,” IEEE Photonics Technol. ACM Comput. Surv. 48(1), 1–35 (2015). Lett. 17(1), 73–75 (2005). 12. H. Zhou et al., “Dielectric metasurfaces enabled ultradensely in- 35. A. W. Snyder and J. D. Love, Optical Waveguide Theory, tegrated multidimensional optical system,” Laser Photonics Rev. Chapman & Hall, London, UK (1983). 16(4), 2100521 (2022). 36. C. Li, D. Liu, and D. Dai, “Multimode silicon photonics,” 13. H. Xie et al., “Highly compact and efficient four-mode multiplexer Nanophotonics 8(2), 227–247 (2019). based on pixelated waveguides,” IEEE Photonics Technol. Lett. 37. D. Dai et al., “10-Channel Mode (de) multiplexer with dual polar- 32(3), 166–169 (2020). izations,” Laser Photonics Rev. 12(1), 1700109 (2018). 14. K. Y. Yang et al., “Inverse-designed multi-dimensional silicon pho- 38. “NanoSOI Fabrication Service,” https://www.appliednt.com/ tonic transmitters,” arXiv:2103.14139, pp. 1–19 (2021). nanosoi-fabrication-service (accessed January 2021). 15. N. Hansen et al., “Comparing results of 31 algorithms from the 39. D. Liu et al., “Silicon photonic filters,” Microw. Opt. Technol. black-box optimization benchmarking BBOB-2009,” in Proc. Lett. 63(9), 2252–2268 (2021). 12th Annu. Conf. Companion on Genetic and Evol. Comput., 40. G. Zhang et al., “Experimental demonstration of robust nanopho- pp. 1689–1696 (2010). tonic devices optimized by topological inverse design with energy 16. M. P. Bendsoe and O. Sigmund, Topology Optimization: Theory, constraint,” Photonics Res. 10(7), 1787–1802 (2022). Methods, and Applications, Springer (2003). 41. L. Su et al., “Inverse design and demonstration of a compact on- 17. R. Halir et al., “High-performance 90° hybrid based on a silicon- chip narrowband three-channel wavelength demultiplexer,” ACS on-insulator multimode interference coupler,” Opt. Lett. 36(2), Photonics 5(2), 301–305 (2018). 178–180 (2011). 42. Y. A. Yilmaz et al., “Inverse design of efficient and compact 1×N 18. J. Jiang, M. Chen, and J. A. Fan, “Deep neural networks for the wavelength demultiplexer,” Opt. Commun. 454, 124522 (2020). evaluation and design of photonic devices,” Nat. Rev. Mater. 6(8), 43. X. Guo et al., “Scalable and compact silicon mode multiplexer via 679–700 (2021). tilt waveguide junctions with shallow etched slots,” J. Lightwave 19. J. Peurifoy et al., “Nanophotonic particle simulation and inverse Technol. 40, 4682–4688 (2022). design using artificial neural networks,” Sci. Adv. 4(6), eaar4206 44. Z. Wang et al., “Compact silicon three-mode multiplexer by re- (2018). fractive-index manipulation on a multi-mode interferometer,” 20. D. Melati et al., “Mapping the global design space of nanopho- Opt. Express 29(9), 13899–13907 (2021). tonic components using machine learning pattern recognition,” 45. H. Xu, D. Dai, and Y. Shi, “Low-crosstalk and fabrication-tolerant Nat. Commun. 10, 4775 (2019). four-channel CWDM filter based on dispersion-engineered Mach- 21. Y. Kiarashinejad, S. Abdollahramezani, and A. Adibi, “Deep Zehnder interferometers,” Opt. Express 29(13), 20617–20631 learning approach based on dimensionality reduction for design- (2021). ing electromagnetic nanostructures,” NPJ Comput. Mater. 6(1), 12 46. D. Liu, M. Zhang, and D. Dai, “Seismic noise attenuation using (2020). unsupervised sparse feature learning,” IEEE Trans. Geosci. 22. S. D. Campbell et al., “Review of numerical optimization tech- Remote Sens. 57(12), 9709–9723 (2019). niques for meta-device design,” Opt. Mater. Express 9(4), 47. E. S. Magden et al., “Transmissive silicon photonic dichroic filters 1842–1863 (2019). with spectrally selective waveguides,” Nat. Commun. 9, 3009 23. J. Guo et al., “Ultra-compact and ultra-broadband guided-mode (2018). exchangers on silicon,” Laser Photonics Rev. 14(7), 2000058 Jingshu Guo is a research fellow at the College of Optical Science and (2020). Engineering, Zhejiang University. He received his BE and PhD degrees 24. Y. Zhang et al., “A compact and low loss Y-junction for submicron from Huazhong University of Science and Technology in 2012 and 2017, silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013). respectively. He has published over 15 papers in peer-reviewed journals. 25. Y. Hu et al., “Wavelength division (de)multiplexing based on His current research interests include silicon photonics for photodetection dispersive self-imaging,” Opt. Lett. 36(23), 4488–4490 (2011). and light manipulation. 26. B.-K. Yang, S.-Y. Shin, and D. Zhang, “Ultrashort polarization splitter using two-mode interference in silicon photonic wires,” Laiwen Yu is currently pursuing his PhD at the College of Optical Science IEEE Photonics Technol. Lett. 21(7), 432–434 (2009). and Engineering, Zhejiang University. He received his BE degree from 27. T. Uematsu et al., “Design of a compact two-mode multi/ Xidian University in 2019. His research interest focuses on silicon/2D demultiplexer consisting of multimode interference waveguides material photodetectors and advanced passive photonic devices. and a wavelength-insensitive phase shifter for mode-division mul- tiplexing transmission,” J. Lightwave Technol. 30(15), 2421–2426 Hengtai Xiang is currently pursuing his PhD at the College of Optical (2012). Science and Engineering, Zhejiang University. He received his BE de- 28. R. Halir et al., “Waveguide sub-wavelength structures: a review of gree from Huazhong University of Science and Technology in 2021. principles and applications,” Laser Photonics Rev. 9(1), 25–49 His research interest focuses on silicon integrated low-dimensional (2015). material photodetectors. 29. H. Guan et al., “Compact and low loss 90° optical hybrid on a silicon-on-insulator platform,” Opt. Express 25(23), 28957– Yuqi Zhao is currently a BE degree student at the College of Optical 28968 (2017). Science and Engineering, Zhejiang University. His academic pursuits 30. N. Hansen, “The CMA evolution strategy: a tutorial,” and research interests lie in the design and development of advanced arXiv:1604.00772, pp. 1–39 (2016). Advanced Photonics Nexus 026005-12 Mar∕Apr 2023 Vol. 2(2) Guo et al.: Realization of advanced passive silicon photonic devices with subwavelength grating structures developed… silicon-based photonic devices and their applications in the fields of op- from the Royal Institute of Technology, Stockholm, Sweden, in 2000 tical communications and optical interconnects. and 2005, respectively. Currently, he is the QIUSHI Distinguished Professor at ZJU and mainly works on silicon photonics. He has pub- lished >260 refereed international journal papers. He is one of the most Chaoyue Liu received his BE and PhD degrees from Harbin Institute of cited Chinese researchers in 2015–2021 (Elsevier). He has given >100 Technology in 2017 and Zhejiang University in 2022, respectively. He cur- plenary/tutorial/keynote/invited talks for prestigious international confer- rently works as R&D engineer at Changguang Chenxin Microelectronics ences (e.g., OFC) and also serves as the general/TPC (co) chair for many Co., Ltd. His research interests include silicon integrated photodetectors conferences, including OECC 2023 and ACP 2022. He is a Fellow of the and optical architecture design. Optica Society (formerly OSA). Daoxin Dai received his BEng degree from the Department of Optical Engineering, Zhejiang University (ZJU), Hangzhou, China, and his PhD Advanced Photonics Nexus 026005-13 Mar∕Apr 2023 Vol. 2(2)
Advanced Photonics Nexus – SPIE
Published: Mar 1, 2023
Keywords: silicon photonics; inverse design; subwavelength grating structures; mode (de)multiplexers; wavelength (de)multiplexers; 90 deg hybrids
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