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Abstract
In this work, we design, fabricate, and characterize a different-mode (waveguide-connected) power splitter ((W)PS) by what we believe to be a novel multi-dimension direct-binary-search algorithm that can significantly balance the device performance, time cost, and fabrication robustness by searching the state-dimension, rotation-dimension, shape-dimension, and size-dimension parameters. The (W)PS can simultaneously generate the fundamental transverse electric (TE0) and TE1 mode with the 1:1 output balance. Compared with the PS, the WPS can greatly shorten the adiabatic taper length between the single-mode waveguide and the grating coupler. The measured results of the different-mode (W)PS indicate that the insertion loss and crosstalk are less than 0.9 (1.3) dB and lower than −17.8 (−14.9) dB from 1540 nm to 1560 nm. In addition, based on the tunable tap couplers, the different-mode (W)PS can be extended to multiple output ports with different modes and different transmittances.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The photonic integrated circuits (PICs) provide a scalable hardware platform to realize large-scale optical interconnects on a chip. In order to extend the transmission capacity further, a potential way is to use so-called mode-division multiplexing (MDM) that can carry multi-channel data by the orthogonal eigenmodes in the multi-mode optical waveguides [1,2]. Great efforts have been made to enhance various on-chip components, such as power splitters (PSs) [3,4], mode (de)multiplexers ((de)MUXs) [5,6], multi-mode bends [7,8], and multi-mode crossings [9,10], to manipulate higher-order modes better in the MDM system.
The integrated photonic PS has much wider scope of applications such as feedback circuits, tap-port power monitoring, or optical quantization because of the functionality of dividing the power into the output ports [11]. Previously, the PSs based on various structures have been demonstrated, including asymmetrical directional couplers [12], multimode interference coupler (MMI) [13], Y junction [14], and so on. Recently, the advanced intelligent algorithms, such as direct-binary-search (DBS) algorithm [15], genetic algorithm [16], objective-first design [17], and deep learning [18], have drawn more and more attentions due to the requirement of the high-density PICs. Based on a phased inverse design, Zhicheng Wang et al. simulated an ultra-broadband PS for the fundamental transverse electric (TE0) mode with the insertion loss (IL) of less than 0.2 dB from 1200 nm to 1900 nm [19]. In order to support high-order modes, the dual-mode and three-mode 3-dB PSs were demonstrated via the DBS algorithm, respectively [20,21]. Specially, Weiwei Chen et al. used the particle swarm optimization algorithm to design a multimode 3-dB PS with the measured ILs of less than 1.5 dB and the measured crosstalk (CTs) of lower than 14.1 dB for the TE0, TE1, TE2, TE3, and TE4 modes [22]. These PSs can split the multiple modes, but they can not simultaneously realize mode coversion. By the rotatable DBS (RDBS) algorithm, Hansi Ma et al. theoretically designed the mode-conversion 3-dB PSs that can efficiently convert the input TE0 mode into high-order modes [23]. However, the devices cannot provide different modes, which limits the further application in the MDM system. Besides, the grating coupling region is typically enlarged to 10 µm in the lateral direction. A long (hundreds of micrometers) taper is required to minimize the mode size mismatch effect, which increase the device footprint. Thus, the simple and effective provision of the different modes in the MDM system becomes challenging.
In this work, we first propose a novel multi-dimension DBS (MDBS) algorithm that can significantly balance the device performance, time cost, and fabrication robustness by searching the state-dimension, rotation-dimension, shape-dimension, and size-dimension parameters. Based on the unique algorithm, we design and experimentally demonstrate different-mode PS and waveguide-connected PS (WPS), which can simultaneously generate different modes with the 1:1 output balance. Compared with the PS, the WPS can greatly shorten the adiabatic taper length between the single-mode waveguide and the grating coupler. In addition, by combining the tunable tap couplers, the (W)PS can provide multiple different-mode and different-transmittance output points in the MDM system.
2. Multi-dimension direct-binary-search algorithm
Before introducing the MDBS algorithm, we briefly review the main concept of the DBS algorithm. This is meant for readers who might not be familiar with DBS algorithm. The interested reader is, however, urged to consult the standard DBS literature for more information. The device under consideration is discretized into silicon or air pillars, called ‘pixels’. The state of the randomly chosen pixel is switched and then a figure of merit (FOM) is calculated. The FOM digitalizes the device performance, which is very convenient to control the performance by the program. The pixel state is retained if the device performance goes up. Otherwise, this pixel returns to previous state and the algorithm proceeds to the next pixel. When all pixels are searched, a single iteration ends. The iteration continues until the device performance does not improve further. At the same time, it means that the algorithm ends.
As mentioned above, the DBS algorithm only searches the state-dimension parameter (two pixel states), which greatly limits its potential. To extend the design degree of freedom of the DBS algorithm, we propose the RDBS algorithm [23]detailed in Sec. 1,Supplement 1. The RDBS algorithm added a rotation-dimension calculation by employing the rotatable triangular and rectangular holes. However, the round corner effect caused by the sharp corners of the holes is one of the typical etching errors [24]. Therefore, the first challenge we face is how to weaken the influence of the sharp corners during the fabrication process to the greatest extent. The simplest and most direct way is that we approximately treat the sharp corner as a rounding radius. However, as shown in Fig. 1(a), the too small rounding radius at the corners of the triangular hole are still sharp and difficult to be fabricated, and the same challenge also arises in other polygons, such as the rectangle in Fig. 1(c). On the contrary, if we assume too big rounding radii at the corners of the triangular hole, the shape could not only have a great impact on device performance, but also be close to the circle in Fig. 1(b). The more angles a polygon has, the closer it is to a circle, such as rectangle in Fig. 1(d). When a shape is close to a circle or is a circle, there is not much computational value in the rotation dimension, because when a circle is rotated around the center, it does not change. To thoroughly solve the issue, we came up with a racetrack-like hole consisting of two semicircles and one rectangle in Fig. 1(e). The racetrack-like hole has a very smooth and easily-fabricated boundary, and searches the rotation-dimension parameters with high computational value. In addition, we choose circle as the other hole shape to search the shape-dimension parameters. In this way, we determine the hole shapes that can significantly weaken the influence of the round corner effect.
Fig. 1. Different rounding radii at the corner of the different-shape holes. (a) Small rounding radius at the triangular corner. (b) Big rounding radius at the triangular corner. (c) Small rounding radius at the rectangular corner. (d) Big rounding radius at the rectangular corner. (e) Racetrack-like hole.
In addition to searching different states (state dimension), different rotational angles (rotation dimension), and different shapes (shape dimension), we increase a size-dimension calculation to further extend the searching degree of freedom. In other words, the MDBS algorithm can evaluate the hole-size impact on the performance. The other challenge, however, is coming that the calculation of the multi-dimensional parameters inevitably leads to increasing the time cost. To balance the time cost and degree of freedom, the MDBS algorithm only searches the size-dimension parameters of the circle instead of the size-dimension parameters of all shapes. In this way, we determine the reasonably multi-dimension searching scheme.
The building process for the MDBS algorithm is shown in Fig. 2. Like the DBS, the device design region is discretized into many pixels. The different-shape holes are at the pixel centers. We choose a random hole as staring point, and calculate the FOM after deleting it. The next step is to add racetrack-like hole and calculate FOMs corresponding to each rotation. Here, deleting hole and adding hole mean the material switching of the pixel between air and silicon. Then MDBS algorithm deletes racetrack-like hole and add circular hole to calculate the FOMs corresponding to each size change. The algorithm, at last, compares all the FOMs and selects the optimal one as hole parameters. All pixels are searched until the performance does not improve further. As described in the algorithm flow, the MDBS algorithm searches multi-dimension parameters, including state dimension (step 3, step 5 and step 8), rotation dimension (step 5 and step 6), shape dimension (step 5 and step 8), and size dimension (step 8 and step 9), which is the salient feature of the MDBS algorithm.
3. Designs and simulations
The different-mode PS is composed of one 0.5 µm-wide input waveguide, one 0.5 µm-wide output waveguide, one 0.9 µm-wide output waveguide, and one design region of 2.52 µm × 2.52 µm. The gap between two output ports is 1.12 µm. The design region is discretized into 16 × 16 square pixels and the size of each one is 150 nm × 150 nm. The pixels can either remain as silicon or be etched, and the etched shape is different-size circular or different-rotation racetrack-like holes at the pixel center. The circular hole radius varies form 45 nm to 60 nm, and the step is set as 5 nm. The racetrack-like hole consisting of two semicircles with 45 nm radii and one 90 nm × 30 nm rectangle can be rotated 180 degrees, and the step is set as 10 degrees. The etching depth is 220 nm. Obviously, the minimal gap between adjacent holes is 30 nm, which can be fabricated using the e-beam lithography (EBL).
We use the MDBS algorithm to facilitate the device optimization. The finite-difference time domain, a method of approximately solving Maxwell’s equations, is used for the numerical simulation. The mesh step of dx = 30 nm, dy = 30 nm, dz = 30 nm is used. Since the MDBS algorithm makes use of the various-radius circular hole and various-angle racetrack-like hole, the device strcture can be properly resolved in the simulations. The three-dimensional diagram and top view of the optimized structure are illustrated in Fig. 3(a) and Fig. 3(b), respectively. Based on the self-imaging in the MMIs, the different-size circular and different-rotation racetrack-like holes, determined by the MDBS algorithm, collectively alter the electric field distribution and tune the image formation so that the target performance can be obtained. The simulated electric field distributions of xy-plane at z = 0 are displayed in Fig. 3(c), where the black lines are the device profiles. When the TE0 mode is launched from the input port, the TE0 and TE1 modes can be obtained simultaneously in the port 1 and port 2, respectively. In order to get an approximately 1: 1 output balance in the optimization process [25], the FOM is defined as:
Fig. 3. Design and simulated results of the different-mode PS. (a) Three-dimensional diagram. (b) Top view. (c) Simulated electric field distribution. (d) Simulated transmission spectra.
To match the mode field of the standard single-mode fiber, the longitudinal size of the ordinary grating coupler is often on the scale of 10 µm. For the sake of realizing low loss interconnection between single-mode waveguide and 10 µm-wide grating coupler, an adiabatic taper with a length of hundreds of micrometers will be needed. Complex nanophotonic structures allow one to design a single device that can implement multiple functions. We integrate one 10 µm-wide waveguide and one different-mode PS into a functional module to significantly shorten the adiabatic taper length. As is shown in Fig. 4(a), the different-mode WPS is composed of one 10 µm-wide input waveguide, one 0.5 µm-wide output waveguide, one 0.9 µm-wide output waveguide, and one design region of 4 µm × 10 µm. The gap between two output ports is 4.3 µm. The design region is discretized into 25 × 65 square pixels and the size of each one is 150 nm × 150 nm. After optimization of the MDBS algorithm, the top view of optimized structure is shown in Fig. 4(b). The simulated electric field distributions in Fig. 4(c) demonstrate that the different-mode WPS can simultaneously generate the TE0 and TE1 modes with great uniformity. Meanwhile, the simulated results in Fig. 4(d) indicate that the device is capable of providing both the IL of less than 0.7 dB and the CT of lower than −27.6 dB from 1540 nm to 1560 nm.
Fig. 4. Design and simulated results of the different-mode WPS. (a) Three-dimensional diagram. (b) Top view. (c) Simulated electric field distribution. (d) Simulated transmission spectra.
Fig. 5. Simulated transmission spectra under the diameter variations from −10 nm to 10 nm. (a) Radius variations. (b) Simulated transmission spectra of the different-mode PS. (c) Simulated transmission spectra of the different-mode WPS.
We have to consider the tolerances to the fabrication errors because of the ineluctable and random fabrication factors in practice. We take the diameter of the circular hole and the semicircle of the racetrack-like hole as a single variable, as show in Fig. 5(a). Under the diameter variation from −10 nm to 10 nm, the transmission spectra of the different-mode PS and WPS are plotted in Fig. 5(b) and in Fig. 5(c), respectively. The transmission curves of the different-mode PS become slightly fluctuated after imposing the diameter variations. The IL is still less than 0.5 dB under diameter variations from −10 nm to 10 nm. The transmission curves of the different-mode WPS become greatly fluctuated because of the large footprint, but the IL is still less than 2 dB under diameter variations from −5 nm to 5 nm. In conclusion, the fabrication tolerance guarantees the good fabricability of the devices designed by the MDBS algorithm.
4. Fabrications and measurements
The designed structures are fabricated and demonstrated experimentally. The devices are patterned on SOI substrate with 220 nm top silicon and 2 µm-thick buried oxide by the EBL system. An inductively coupled plasma etcher is used to transfer the pattern to the silicon device layer. An extra reference circuit with a back-to-back mode (de)MUX is fabricated to normalize the transmission and to extract the losses of our devices. The design of the mode (de)MUX is detailed in Sec. 2, Supplement 1. The mode (de)MUX is composed of two 0.5 µm-wide branch waveguides, one 0.9 µm-wide bus waveguide, and one design region of 3.12 µm × 2.52 µm. The scanning electron microscope (SEM) image of the back-to-back mode (de)MUX is illustrated in Fig. 6(a). Figure 6(b) and Fig. 6(c) show the detailed SEM images of the fabricated mode (de)MUXs. A fiber laser source (ASE-CL-100-T-B) and an optical spectrum analyzer (Yokogawa AQ6370D) are utilized to measure the transmission spectra. When the light is launched from the I1 and I2 ports, the normalized transmission spectra measured in the O1 and O2 ports are plotted in in Fig. 6(d). Here, the curves represent the losses of a single (de)MUX. The measured ILs and CTs of the single (de)MUX for both TE0 and TE1 modes are less than 1.4 dB and lower than –14.2 dB from 1540 nm to 1560 nm, respectively.
Fig. 6. Fabrication and experimental results of the two-mode (de)MUX. (a) SEM image of the back-to-back mode (de)MUX. (b) and (c) Detailed SEM images of the mode (de)MUXs. (d) Measured transmission spectra.
The SEM image of the fabricated different-mode PS is shown in Fig. 7(a). The detailed SEM images of the fabricated different-mode PS and mode (de)MUX are illustrated in Fig. 7(b) and Fig. 7(c), respectively. When the light is launched from the I1 port, the normalized transmission spectra measured in the O1, O2, and O3 ports are plotted in Fig. 7(d). Here, the losses induced by the mode (de)MUX are deducted, and represent the performance of the different-mode PS. The Measured results indicate that the IL and CT of the different-mode PS are less than 0.9 dB and lower than −17.8 dB from 1540 nm to 1560 nm, respectively. At the same time, the SEM image of the fabricated different-mode WSP is shown in Fig. 7(e), and the detailed SEM images are illustrated in Fig. 7(f) and Fig. 7(g). Compared with the taper waveguide between the grating coupler and the PS in Fig. 7(a), the length of the taper waveguide between the grating coupler and the WPS is shortened by about 300 µm. The measured IL and CT of the different-mode WPS in Fig. 7(h) are less than 1.3 dB and lower than −14.9 dB from 1540 nm to 1560 nm, respectively. The experimental results agree generally with the simulation predictions on the device bandwidth, but there is a discrepancy between the measured CTs and the theoretical results. This discrepancy may be caused by the inevitable expansion or contraction of the etched pattern contour in practice.
Fig. 7. Fabrication and experimental results of the different-mode PS and WPS. (a) SEM image of the different-mode PS. (b) Detailed SEM image of the different-mode PS. (c) and (g) Detailed SEM images of the mode (de)MUXs. (d) Measured transmission spectra of the different-mode PS. (e) SEM image of the different-mode WPS. (f) Detailed SEM image of the different-mode WPS. (h) Measured transmission spectra of the different-mode WPS.
5. Discussions
5.1 Different-mode (W)PS with multiple output ports
By the optical phase-change-material-based (PCM-based) tap coupler, as shown in Fig. 8, the different-mode (W)PS can be extended to multiple output ports with different modes and different transmittances. The tap coupler composed of one bus waveguide and one tap waveguide harnesses an optical PCM, Ge2Sb2Se4Te1 (GSST) to optically modulate a directional coupler [26]. The bus waveguides are the output waveguides of the different-mode (W)PS. The GSST strip is deposited on the surfaces of the tap waveguide. The phase-matching condition in the amorphous (a-GSST) state is employed, because the a-GSST with low loss matches the refractive index of silicon very well. The tap waveguide can extract a fraction of optical power from the bus waveguide in the a-GSST state (“on” state) and be switched “off” in the crystalline (c-GSST) state. The tap couplers with different coupling lengths can get the different coupling efficiencies. Therefore, the tap-coupler-based (W)PS can dynamically provide multiple output points with different modes and different transmittances.
The widths of the bus waveguide, tap waveguide, and gap of the TE0-mode tap coupler are 0.5 µm, 0.444 µm, and 0.2 µm. The widths of the bus waveguide, tap waveguide, and gap of the TE1-mode tap coupler are 0.9 µm, 0.821 µm, and 0.2 µm. The thicknesses of the GSST strips are 40 nm. The tap couplers are detailed in Sec. 3, Supplement 1. We use the simulated results here to discuss the tap-coupler-based (W)PS with multiple output ports. Changing the coupling length can get the desired coupling efficiency in the a-GSST state. For example, the tap-coupler-based PS is composed of one different-mode PS, one tunable TE0-mode tap coupler with 25 µm coupling length, and one tunable TE1-mode tap coupler with 21 µm coupling length. The simulated electric field distributions of the tap-coupler-based PS are shown in Fig. 9(a). The simulated results in Fig. 9(b) indicate that when the GSST is amorphous, the ILs for the TE0 and TE1 modes in the TE0-mode and TE1-mode tap waveguides are about 7.1 dB and 9.8 dB at 1550 nm, respectively. In other words, the tap-coupler-based PS can output about 20% TE0 mode and 10% TE1 mode in the MDM system. In addition, when the GSST is crystalline, the ILs for the TE0 and TE1 modes in the TE0-mode and TE1-mode bus waveguides remains below 3.2 dB and 3.3 dB at 1550 nm, respectively. The tunable transmittances in the a-GSST state and low loss in the c-GSST state enables the tap-coupler-based (W)PS to dynamically provide multiple output points with different modes and different transmittances.
Fig. 9. Simulated results of the different-mode PS based on the tap couplers. (a) Simulated electric field distributions. (b) Simulated transmission spectra.
5.2 Robust analysis to fabrication errors
To guarantee the robustness to fabrication errors, adding regularization constraints on topological structures are considered [27,28]. The fabricated devices achieve a minimum feature size mainly by imposing the curvature constraint on hole boundary and the size constraint on silicon wall. As shown in Fig. 6 and Fig. 7, the hole boundaries of these fabricated devices are very smooth, because the etched patterns of the circular and racetrack-like shapes with a curvature radius lager than 45 nm can avoid the sharp angles in the MDBS algorithm.
On the other hand, many silicon walls along the device borders and between two adjacent holes, may be etched through because of the inevitable and random expansion or contraction of the etched pattern contour in practice. To prevent the damage of device borders, we add additional silicon walls with the widths of larger than 60 nm (the orange area) outside the design regions of the different-mode PS in Fig. 10(a) and different-mode WPS in Fig. 10(b). In addition, when the radius of two adjacent circular holes is 60 nm in Fig. 10(c), or when the long symmetrical axes of two adjacent racetrack-like holes are in a straight line in Fig. 10(d) or when the long symmetrical axis of the racetrack-like hole passes through the center of an adjacent circular hole with a radius of 60 nm in Fig. 10(e), the 30 nm-wide silicon walls between adjacent holes are the smallest. The 30 nm-wide silicon wall can be fabricated theoretically by using EBL, but the inevitable fabrication error may easily cause silicon walls to be etched through, and further lead to the hole fusion. Wider silicon wall can prevent the hole fusion effectively. Although directly increasing the pixel size can increase the silicon-wall width, it will lead to a decrease in the number of pixels in the same-size design region. In the MDBS algorithm, the circular-hole diameter and racetrack-like-hole rotation angle are variable but not fixed, which lead to the variable widths of the silicon walls between the adjacent holes. The MDBS algorithm can provide wider silicon walls between adjacent holes with high probability by rotating the racetrack-like hole and resizing the circular holes, such as the size change of the circular hole in Fig. 10(f), the racetrack-like-hole rotation in Fig. 10(g), and both the size change of the circular hole and the racetrack-like-hole rotation in Fig. 10(h). Therefore, by adding regularization constraints on the topological structures, the structures designed by the MDBS algorithm are greatly robust to fabrication errors.
Fig. 10. Robust analysis to fabrication errors. (a) Different-mode PS with an outside silicon wall. (b) Different-mode WPS with an outside silicon wall. (c) Minimum silicon wall between two adjacent circular holes. (d) Minimum silicon wall between two adjacent racetrack-like holes. (e) Minimum silicon wall between adjacent racetrack-like hole and circular hole. (f) Size change of the circular hole. (g) Racetrack-like-hole rotation. (h) Both the size change of the circular hole and the racetrack-like-hole rotation.
5.3 Algorithm analysis
We use the DBS and RDBS algorithms to design the same-functionality different-mode PSs with the same footprint to show the algorithm comparisons. The 2.52 µm × 2.52 µm design region is discretized into 16 × 16 square pixels. The size of each pixel is 150 nm × 150 nm with a center air hole. After about 10 hours computation on the 28 core desktop, the optimized structure designed by the DBS algorithm can be gained in Fig. 11(a). The air holes are circular shape with the radius of 60 nm. The IL and CT of the DBS-based different-mode PS in Fig. 11(b) are less than 0.6 dB and lower than –19.4 dB from 1540 nm to 1560 nm, respectively. In addition, after about 150 hours computation on the 28 core desktop, the optimized structure designed by the RDBS algorithm is shown Fig. 11(c). This design region simultaneously contains the regularly triangular hole with side length of 104 nm and rectangular hole of 104 nm × 60 nm. The IL and CT of the RDBS-based different-mode PS in Fig. 11(d) are less than 0.3 dB and lower than –21.9 dB from 1540 nm to 1560 nm, respectively. Compared with the DBS-based and RDBS-based different-mode PSs, after about 110 hours computation on the 28 core desktop, the MDBS-based structure in Fig. 3 can exhibit the IL of less than 0.2 dB and the CT of lower than –25.7 dB from 1540 nm to 1560 nm, respectively. The MDB algorithm takes more time than the DBS algorithm, but one can accelerate the optimization of the MDBS algorithm by increasing the search step, such as 7.5 nm radius step of the circular hole and 20 degrees rotation step of the racetrack-like hole. The performances of the different-mode PSs designed by the RDBS and MDBS algorithms are 7% and 10%, respectively, higher than that of the device designed by the DBS algorithm. Although the performances of the RDBS-based and MDBS-based devices is close, the MDBS-based device is not only time-saving but also great robust to fabrication error of the round corner effect.
Fig. 11. Different-mode PSs designed by the DBS and RDB algorithms. (a) Top view of the DBS-based device. (b) Simulated transmission spectra of the DBS-based device. (c) Top view of the RDBS-based device. (d) Simulated transmission spectra of the RDBS-based device.
The comparisons for the DBS, RDBS, MDBS algorithms are shown in Table 1. In column 2, each pixel in the DBS algorithm has two states, including silicon and etched states, and is calculated twice. In column 3, the RDBS algorithm can search many pixel shapes, such as triangle and rectangle. The triangle and rectangle are rotated 120 degrees and 180 degrees in steps of 10 degrees, respectively. Each pixel is calculated 31 times, including 1 deleted state and 30 rotation-dimension parameters. In column 4, the MDBS algorithm can search the racetrack-like and circular pixel shapes. The racetrack-like shape is rotated 180 degrees in steps of 10 degrees, and the circular diameter varies from 90 nm to 120 nm in steps of 10 nm. Each pixel is calculated 23 times, including 1 deleted state, 18 rotation-dimension parameters, and 4 size-dimension parameters. Compared with the DBS algorithm, the RDBS and MDBS algorithms calculate more samples and pays more time cost, but searches higher degrees of freedom which can provide more potentials for the ultra-compact and effective device. At the same time, since MDBS algorithm does not search the rotation-dimension parameters of the circular hole, it calculates fewer samples and save more time than the RDBS algorithm. In addition, the devices designed by the MDBS algorithm are strongly robust to fabrication errors because of the reasonable pixel shape and pixel size. In conclusion, the MDBS algorithm can greatly balance device performance, time cost, and fabrication robustness.
Table 1. Comparisons of the different algorithms
6. Conclusion
In this work, we firstly proposed the MDBS algorithm that can significantly balance the device performance, time cost, and fabrication robustness by searching the state-dimension, rotation-dimension, shape-dimension, and size-dimension parameters. Based on this novel method, we design, fabricate, and characterize the different-mode (W)PS. The different-mode PS with one 0.5 µm-wide input waveguide, one 0.5 µm-wide output waveguide, one 0.9 µm-wide output waveguide, and one footprint of 2.52 µm × 2.52 µm, can simultaneously generate the TE0 and TE1 modes with the 1:1 output balance. The measured results of the different-mode PS indicate that the IL and CT are less than 0.9 dB and lower than –17.8 dB from 1540 nm to 1560 nm. The different-mode WPS with one 10 µm-wide input waveguide, one 0.5 µm-wide output waveguide, one 0.9 µm-wide output waveguide, and one footprint of 4 µm × 10 µm, can not only simultaneously generate the TE0 and TE1 modes, but also greatly shorten the adiabatic taper length between the single-mode waveguide and the grating coupler. The measured results of the different-mode WPS indicate that the IL and CT are less than 1.3 dB and lower than –14.9 dB from 1540 nm to 1560 nm. In addition, the different-mode (W)PS can be extended to multiple output ports with different modes and different transmittances.
Funding
Program for New Century Excellent Talents in University (NCET-12-0142); Natural Science Foundation of Hunan Province (13JJ3001); Foundation of NUDT (JC13-02-13, ZK17-03-01); China Postdoctoral Science Foundation (2018M633704); National Key Research and Development Program of China (2022YFF0706005); National Natural Science Foundation of China (12272407, 60907003, 61805278, 62275269, 62275271).
Disclosures
The authors declare no conflict 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.
Supplemental document
See Supplement 1 for supporting content.
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