On-Chip E00–E20 Mode Converter Based on Multi-Mode Interferometer

Mode converters is a key component in mode-division multiplexing (MDM) systems, which plays a key role in signal processing and multi-mode conversion. In this paper, we propose an MMI-based mode converter on 2%-Δ silica PLC platform. The converter transfers E00 mode to E20 mode with high fabrication tolerance and large bandwidth. The experimental results show that the conversion efficiency can exceed −1.741 dB with the wavelength range of 1500 nm to 1600 nm. The measured conversion efficiency of the mode converter can reach −0.614 dB at 1550 nm. Moreover, the degradation of conversion efficiency is less than 0.713 dB under the deviation of multimode waveguide length and phase shifter width at 1550 nm. The proposed broadband mode converter with high fabrication tolerance is promising for on-chip optical network and commercial applications.


Introduction
With the development of new generation communication technology and largecapacity signal processing technology, the demand for high-speed data transmission and large-capacity data processing is increasing. Various multiplexing methods have been proposed for this purpose, such as wavelength division multiplexing (WDM), space division multiplexing (SDM) and polarization division multiplexing (PDM) technologies [1][2][3][4][5][6][7][8]. Mode division multiplexing (MDM) has been considered as a promising technology [9,10] that can significantly improve the capacity of optical communication, on-chip interconnect, and computation [11,12]. Since the orthogonal eigenmodes of the same wavelength propagate in a single channel without inter-channel crosstalk, cooperation with WDM technology, MDM technology increases overall transmission capacity dramatically [13,14]. In MDM system, mode converter with broad bandwidth, low insertion loss, and high mode conversion efficiency is the key components between fundamental mode and higher-order modes at optical nodes [15][16][17][18][19][20]. Mode converters have been demonstrated on different structures, such as asymmetrical directional couplers (ADCs) [21], Y-branch [22], multimode interferometers (MMIs) [23,24]. Although ADCs convertors show low loss and high fabrication tolerant, they suffer from high wavelength dependence. Y-branch converters contribute high crosstalk between modes. Nowadays, slotted waveguide and etched metasurface waveguide converter show ultra-compact footprint and high efficiency of mode conversion [17,[25][26][27][28]. However, for commercial usage, large fabrication tolerances, in the micrometer range, are necessary. Compared with other kinds of mode conversion techniques, the mode converters based on MMIs shows broad bandwidth and large fabrication tolerance. 2 of 9 In this paper, we demonstrate an MMI-based mode converter on silica based planar lightwave circuits (PLC) platform with 2% refractive index difference(∆). The light of E 00 mode will be converted into E 20 after propagating through the device. We optimize the mode converter through beam propagation method (BPM). The simulation result shows a conversion efficiency of −0.083 dB at 1550 nm. After fabrication, the converter shows high mode conversion efficiency of −0.614 dB at 1550 nm. From 1500 nm to 1600 nm, the conversion efficiency exceeds −1.741 dB. Moreover, the degradation of conversion efficiency is less than 0.713 dB under the deviation of multimode waveguide length and phase shifter width at 1550 nm. Compared with other mode conversion techniques, our designed MMIbased mode converter reduces the device size while ensuring high conversion efficiency, which has the advantages of broad bandwidth and large fabrication tolerance. The mode converter is suitable for large scale and complex on-chip optical networks. The high fabrication tolerance contributes the devices are promising for commercial application.

Design and Simulation
Several material platforms have been investigated for integrated photonics circuits, including silicon-on-insulator (SOI), silicon nitride (SiN), polymer-based PLC and silicabased PLC. SOI and SiN waveguide devices are compact and promising for co-package optics. However, they suffer from low fabrication tolerant and high coupling loss with fiber. Polymer based PLC devices are attractive for thermo-optical switch and high-speed modulators. The stability of polymers is a major limitation to their commercial usage. Compared with other platforms, the silica-based PLC have advantages of low loss, good match of the optical mode field with an optical fiber, and is commercially available. However, the low thermal optical coefficient (TOC) of silica contributes to high power consumption when thermo-optical tuning is used. Therefore, the silica-based PLC platform is suitable for our passive converter. Figure 1a shows the cross section of single mode waveguide. The thickness is 4 µm. With different germanium oxide doping, the refractive index difference between claddings and cores is 2%. Refractive indices are 1.473 and 1.444 at 1550 nm, respectively. According to the calculated relationship between effective refractive indices and waveguide width shown in Figure 1b, we choose 4 µm as the height and width to maintain single mode propagation. In this paper, we demonstrate an MMI-based mode converter on silica based planar lightwave circuits (PLC) platform with 2% refractive index difference(Δ). The light of E00 mode will be converted into E20 after propagating through the device. We optimize the mode converter through beam propagation method (BPM). The simulation result shows a conversion efficiency of −0.083 dB at 1550 nm. After fabrication, the converter shows high mode conversion efficiency of −0.614 dB at 1550 nm. From 1500 nm to 1600 nm, the conversion efficiency exceeds −1.741 dB. Moreover, the degradation of conversion efficiency is less than 0.713 dB under the deviation of multimode waveguide length and phase shifter width at 1550 nm. Compared with other mode conversion techniques, our designed MMI-based mode converter reduces the device size while ensuring high conversion efficiency, which has the advantages of broad bandwidth and large fabrication tolerance. The mode converter is suitable for large scale and complex on-chip optical networks. The high fabrication tolerance contributes the devices are promising for commercial application.

Design and Simulation
Several material platforms have been investigated for integrated photonics circuits, including silicon-on-insulator (SOI), silicon nitride (SiN), polymer-based PLC and silicabased PLC. SOI and SiN waveguide devices are compact and promising for co-package optics. However, they suffer from low fabrication tolerant and high coupling loss with fiber. Polymer based PLC devices are attractive for thermo-optical switch and high-speed modulators. The stability of polymers is a major limitation to their commercial usage. Compared with other platforms, the silica-based PLC have advantages of low loss, good match of the optical mode field with an optical fiber, and is commercially available. However, the low thermal optical coefficient (TOC) of silica contributes to high power consumption when thermo-optical tuning is used. Therefore, the silica-based PLC platform is suitable for our passive converter. Figure 1a shows the cross section of single mode waveguide. The thickness is 4 μm.
With different germanium oxide doping, the refractive index difference between claddings and cores is 2%. Refractive indices are 1.473 and 1.444 at 1550 nm, respectively. According to the calculated relationship between effective refractive indices and waveguide width shown in Figure 1b, we choose 4 µm as the height and width to maintain single mode propagation. The schematic of the proposed MMI-based mode converter is demonstrated in Figure  2. The converter is constructed by input waveguide, tapered waveguide, 66% mode converter MMI, phase shifter waveguide, S-bend, and output waveguide. The fundamental mode is coupled into Port 1 ( in P ) through a tapered waveguide. The 66% E00 mode is The schematic of the proposed MMI-based mode converter is demonstrated in Figure 2. The converter is constructed by input waveguide, tapered waveguide, 66% mode converter MMI, phase shifter waveguide, S-bend, and output waveguide. The fundamental mode is coupled into Port 1 (P in ) through a tapered waveguide. The 66% E 00 mode is converted into E 10 at Port 2 (P 1 out ) after the first MMI. The light left propagates in fundamental mode through Port 3 (P 0 out ). A phase shifter is introduced to ensure π phase difference between converted into E10 at Port 2 ( 1 out P ) after the first MMI. The light left propagates in fundamental mode through Port 3 ( 0 out P ). A phase shifter is introduced to ensure π phase difference between E00 mode and E10 mode. When these lights meet at the second MMI, the mode of light is converted to E20 mode at Port 4 ( out P ).

Figure 2.
Schematic of the MMI-based mode converter.
The first MMI coupler is a 3 × 3 MMI with outputs modified into two, one of which is for first-order mode output, another is for fundamental mode output. The length of the conventional 3 × 3 MMI is equal to the length of the 66% mode converter MMI, which is , with c L as the coupling length based on self-imaging property and it is given by [29]: λ is the operation wavelength, r n is the refractive index of the core waveguide and W is the effective width taking into account the Goos-Hänchen shifts at the ridge boundaries, whose displacement is very small, and can approximatively equal to the width of MMI ( MMI W ). For a conventional 3 × 3 MMI, when E00 mode is input from port in P , the powers at three output ports of E00 modes are equal. However, the phases of the three outputs are 11 0 5 / 3 ϕ ϕ π = + , 12 0 2 / 3 ϕ ϕ π = + and 13 0 ϕ ϕ π = + , respectively, where 0 ϕ is a constant phase. Therefore, the phase difference between the two fundamental modes at Port 2 is π. We combine these two fundamental modes to form E10 mode. As for of the E20 mode, we need a 2/3π phase shifter. With BPM calculating, the width and length of the phase shifter are , linearly. The gap between E10 mode port and E00 mode port is 4.85 µm. The length of these three tapered waveguides is 35 µm. There are 100-µm-length straight waveguides after E00 and E10 mode port. We use S-bend to connect Port 2 with output width. The arc radius of the S-bend is above 2 cm. The loss caused by S-bend could be neglected. The length of the straight waveguide that connects phase shifter and output waveguide is chosen to be 400 µm. The width of the output waveguide is set to be 15.9 µm. In our design, the width of the MMI (WMMI) is designed to be 22.25 µm, which is used to avoid coupling between E10 mode and E00 mode at ports 2 and 3. Therefore, the The first MMI coupler is a 3 × 3 MMI with outputs modified into two, one of which is for first-order mode output, another is for fundamental mode output. The length of the conventional 3 × 3 MMI is equal to the length of the 66% mode converter MMI, which is with L c as the coupling length based on self-imaging property and it is given by [29]: where β 0 is the fundamental mode propagation constant, β 1 the first-order mode propagation constant, λ 0 is the operation wavelength, n r is the refractive index of the core waveguide and W is the effective width taking into account the Goos-Hänchen shifts at the ridge boundaries, whose displacement is very small, and can approximatively equal to the width of MMI (W MMI ). For a conventional 3 × 3 MMI, when E 00 mode is input from port P in , the powers at three output ports of E 00 modes are equal. However, the phases of the three outputs are ϕ 11 = ϕ 0 + 5π/3, ϕ 12 = ϕ 0 + 2π/3 and ϕ 13 = ϕ 0 + π, respectively, where ϕ 0 is a constant phase. Therefore, the phase difference between the two fundamental modes at Port 2 is π. We combine these two fundamental modes to form E 10 mode. As for of the E 20 mode, we need a 2/3π phase shifter. With BPM calculating, the width and length of the phase shifter are W PS = 3.7 µm and L PS = 200 µm, respectively. Based on the above principle, we use BPM for the design and optimization of the device at 1550 nm. To reduce the loss caused by mode mismatch, tapered waveguides are introduced between MMI region and waveguides. Widths of tapers are transferred from W 1 = 4 µm, W 2 = 11.5 µm and W 3 = 4.5 µm to W 1 = 4.5 µm, W 2 = 10.4 µm, and W 3 = 4 µm, linearly. The gap between E 10 mode port and E 00 mode port is 4.85 µm. The length of these three tapered waveguides is 35 µm. There are 100-µm-length straight waveguides after E 00 and E 10 mode port. We use S-bend to connect Port 2 with output width. The arc radius of the S-bend is above 2 cm. The loss caused by S-bend could be neglected. The length of the straight waveguide that connects phase shifter and output waveguide is chosen to be 400 µm. The width of the output waveguide is set to be 15.9 µm. In our design, the width of the MMI (W MMI ) is designed to be 22.25 µm, which is used to avoid coupling between E 10 mode and E 00 mode at ports 2 and 3. Therefore, the calculated MMI coupler length is optimized to be L MMI = 730 µm. The length of the output waveguide is 800 µm. The total length of the mode converter is 2400 µm. Figure 3a shows the field distribution of the device at 1550 nm wavelength with fundamental mode is input. Figure 3b shows the fundamental mode field distribution of the input. The mode distributions of E 10 at port 2 and E 00 at port 3 of the mode converter MMI are shown in Figure 3c. Figure 3d shows the mode distribution of E 20 . From Figure 3a, the E 00 mode is successfully converted to the E 20 mode. In the simulation, we set the E 00 mode input power of port1 to 1 and simulated the conversion efficiency of the mode converter from 1500 nm to 1600 nm, as shown in Figure 3e. The conversion efficiency in percent (E p ) and dB (E d ) are calculated by Equations (2) and (3), respectively. Here, b is the propagation loss of the E 00 mode in the dB scale [30].
damental mode is input. Figure 3b shows the fundamental mode field distribution of the input. The mode distributions of E10 at port 2 and E00 at port 3 of the mode converter MMI are shown in Figure 3c. Figure 3d shows the mode distribution of E20. From Figure 3a, the E00 mode is successfully converted to the E20 mode. In the simulation, we set the E00 mode input power of port1 to 1 and simulated the conversion efficiency of the mode converter from 1500 nm to 1600 nm, as shown in Figure 3e. The conversion efficiency in percent (Ep) and dB (Ed) are calculated by Equations (2) and (3), respectively. Here, b is the propagation loss of the E00 mode in the dB scale [30].
At 1550 nm wavelength, the conversion efficiency is 96.2% (−0.083 dB). From 1500 nm to 1600 nm, simulation results show that the conversion efficiency exceeds −0.630 dB. In summary, we obtain a mode conversion from E00 to E20 at 1550 nm with a conversion efficiency of −0.083 dB.

Characterization and Discussion
The proposed mode converter was fabricated by the PLC foundry, SHIJIA, China. First, the bottom cladding of ~15 µm was thermally oxidized on silicon substrate. Second, we grew a 4-µm-thickness silica core layer above the bottom cladding by plasma enhanced chemical vapor deposition (PECVD). The waveguide was formed by etching through inductively coupled plasma etching (ICP) technique. Finally, PECVD was again used to deposit the upper cladding. Since the existing coupling test system is difficult to directly monitor the high-order mode power, a mode demultiplexer was introduced at the end of the output waveguide to convert the E20 mode to the E00 mode to indirectly characterize the higher-order mode power. The mode multiplexer/demultiplexer of E20 mode and a reference waveguide are fabricated simultaneously. The microscope images of the demonstrated converter are shown in Figure 4a-d.
In Figure 4a, the measured width of the MMI is 22 µm. The widths of the two output ports are measured in Figure 4b at 10 µm and 4 µm, respectively. The S bend is separated from the phase shifter by a large distance of 5 µm, which can be observed in Figure 4c. The width of the output waveguide is measured to be 16 µm in Figure 4d. At 1550 nm wavelength, the conversion efficiency is 96.2% (−0.083 dB). From 1500 nm to 1600 nm, simulation results show that the conversion efficiency exceeds −0.630 dB. In summary, we obtain a mode conversion from E 00 to E 20 at 1550 nm with a conversion efficiency of −0.083 dB.

Characterization and Discussion
The proposed mode converter was fabricated by the PLC foundry, SHIJIA, China. First, the bottom cladding of~15 µm was thermally oxidized on silicon substrate. Second, we grew a 4-µm-thickness silica core layer above the bottom cladding by plasma enhanced chemical vapor deposition (PECVD). The waveguide was formed by etching through inductively coupled plasma etching (ICP) technique. Finally, PECVD was again used to deposit the upper cladding. Since the existing coupling test system is difficult to directly monitor the high-order mode power, a mode demultiplexer was introduced at the end of the output waveguide to convert the E 20 mode to the E 00 mode to indirectly characterize the higher-order mode power. The mode multiplexer/demultiplexer of E 20 mode and a reference waveguide are fabricated simultaneously. The microscope images of the demonstrated converter are shown in Figure 4a-d.
In Figure 4a, the measured width of the MMI is 22 µm. The widths of the two output ports are measured in Figure 4b at 10 µm and 4 µm, respectively. The S bend is separated from the phase shifter by a large distance of 5 µm, which can be observed in Figure 4c. The width of the output waveguide is measured to be 16 µm in Figure 4d.  Micromachines 2023, 14, x FOR PEER REVIEW 5 of 9 The E00 mode is coupled into the device by edge coupling system. The spectra of the reference straight waveguide and the mode multiplexed/demultiplexer for the E20 mode are shown in Figure 5a. The normalized spectral response of the E00 to E20 mode converter experimental measure data is shown in Figure 5b  (b) Conversion efficiency of the mode converter from E00 to E20 in the wavelength range from 1500 nm to 1600 nm. Output mode taken from output port at (c) 1500 nm, (d) 1550 nm and (e) 1600 nm.
We fabricate proposed device with different lengths of MMI and widths of phase shifter to perform fabrication tolerant. The key components, MMIs and phase shifters, influence the conversion efficiency of the device a lot. We study the fabrication tolerance by changing length and width of MMI and phase shifter, and observe the output power of E20. The deviations are 0 and ±10 µm for LMMI and 0 and ±0.2 µm for WPS. The simulation result is shown in the Figure 6. We can see that when LMMI move away from their optimal values, the conversion efficiency of E00-E20 has different degrees of degradation at wavelength 1550 nm., which means that the change of LMMI will cause an impact on the conversion efficiency of the device. At 1550 nm, the conversion efficiency varies from −0.083 dB to −0.234 dB.
Similarly, the influence of WPS on the conversion efficiency of the device is simulated. Figure 7 shows the dependence of the E00-E20 conversion efficiency on the WPS. We use the optimal value LMMI = 730 µm as the length of MMI. It can be seen that the change of WPS does have a certain impact on the conversion efficiency of the mode converter. At the wavelength of 1550 nm, the conversion efficiency of the mode converter varies from −0.083 dB to −0.155 dB. Compared with LMMI, the device is more sensitive to WPS. The E 00 mode is coupled into the device by edge coupling system. The spectra of the reference straight waveguide and the mode multiplexed/demultiplexer for the E 20 mode are shown in Figure 5a. The normalized spectral response of the E 00 to E 20 mode converter experimental measure data is shown in Figure 5b  The E00 mode is coupled into the device by edge coupling system. The spectra of the reference straight waveguide and the mode multiplexed/demultiplexer for the E20 mode are shown in Figure 5a. The normalized spectral response of the E00 to E20 mode converter experimental measure data is shown in Figure 5b  We fabricate proposed device with different lengths of MMI and widths of phase shifter to perform fabrication tolerant. The key components, MMIs and phase shifters, influence the conversion efficiency of the device a lot. We study the fabrication tolerance by changing length and width of MMI and phase shifter, and observe the output power of E20. The deviations are 0 and ±10 µm for LMMI and 0 and ±0.2 µm for WPS. The simulation result is shown in the Figure 6. We can see that when LMMI move away from their optimal values, the conversion efficiency of E00-E20 has different degrees of degradation at wavelength 1550 nm., which means that the change of LMMI will cause an impact on the conversion efficiency of the device. At 1550 nm, the conversion efficiency varies from −0.083 dB to −0.234 dB.
Similarly, the influence of WPS on the conversion efficiency of the device is simulated. Figure 7 shows the dependence of the E00-E20 conversion efficiency on the WPS. We use the optimal value LMMI = 730 µm as the length of MMI. It can be seen that the change of WPS does have a certain impact on the conversion efficiency of the mode converter. At the wavelength of 1550 nm, the conversion efficiency of the mode converter varies from −0.083 dB to −0.155 dB. Compared with LMMI, the device is more sensitive to WPS. We fabricate proposed device with different lengths of MMI and widths of phase shifter to perform fabrication tolerant. The key components, MMIs and phase shifters, influence the conversion efficiency of the device a lot. We study the fabrication tolerance by changing length and width of MMI and phase shifter, and observe the output power of E 20 . The deviations are 0 and ±10 µm for L MMI and 0 and ±0.2 µm for W PS . The simulation result is shown in the Figure 6. We can see that when L MMI move away from their optimal values, the conversion efficiency of E 00 -E 20 has different degrees of degradation at wavelength 1550 nm., which means that the change of L MMI will cause an impact on the conversion efficiency of the device. At 1550 nm, the conversion efficiency varies from −0.083 dB to −0.234 dB.  We summary the spectra of all samples and separate in four groups, as shown in Figure 8a-d. It can be seen that at the wavelength of 1550 nm, the conversion efficiency degradation of the device is less than 0.713 dB when changing LMMI and WPS. However, the conversion efficiency of the converter proposed is lower than others. So there are still some cases that need to be discussed for the MMI-based mode converter we designed. First of all, during the simulation, we initially expected the conversion efficiency to be −0.083 dB (97%) at 1550 nm. However, the actual test results show that the conversion efficiency of the mode converter can only reach −0.614 dB (87%) at 1550 nm. The reason is the differences in geometry and refractive index of cores with respect to design parameters. The device has good repeatability, parameter scanning will help but only if you also have good repeatability. This problem is solved by parameter scanning while fabrication. Secondly, in Figure 8a,d, we note that when LMMI = 720 µm the normalized transmission may exceed 0, which is caused by the normalization procedure owing to the vibration of the reference waveguide. Similarly, the influence of W PS on the conversion efficiency of the device is simulated. Figure 7 shows the dependence of the E 00 -E 20 conversion efficiency on the W PS . We use the optimal value L MMI = 730 µm as the length of MMI. It can be seen that the change of W PS does have a certain impact on the conversion efficiency of the mode converter. At the wavelength of 1550 nm, the conversion efficiency of the mode converter varies from −0.083 dB to −0.155 dB. Compared with L MMI , the device is more sensitive to W PS .  We summary the spectra of all samples and separate in four groups, as shown in Figure 8a-d. It can be seen that at the wavelength of 1550 nm, the conversion efficiency degradation of the device is less than 0.713 dB when changing LMMI and WPS. However, the conversion efficiency of the converter proposed is lower than others. So there are still some cases that need to be discussed for the MMI-based mode converter we designed. First of all, during the simulation, we initially expected the conversion efficiency to be −0.083 dB (97%) at 1550 nm. However, the actual test results show that the conversion efficiency of the mode converter can only reach −0.614 dB (87%) at 1550 nm. The reason is the differences in geometry and refractive index of cores with respect to design parameters. The device has good repeatability, parameter scanning will help but only if you also have good repeatability. This problem is solved by parameter scanning while fabrication. Secondly, in Figure 8a,d, we note that when LMMI = 720 µm the normalized transmission may exceed 0, which is caused by the normalization procedure owing to the vibration of the reference waveguide. We summary the spectra of all samples and separate in four groups, as shown in Figure 8a-d. It can be seen that at the wavelength of 1550 nm, the conversion efficiency degradation of the device is less than 0.713 dB when changing L MMI and W PS . However, the conversion efficiency of the converter proposed is lower than others. So there are still some cases that need to be discussed for the MMI-based mode converter we designed. First of all, during the simulation, we initially expected the conversion efficiency to be −0.083 dB (97%) at 1550 nm. However, the actual test results show that the conversion efficiency of the mode converter can only reach −0.614 dB (87%) at 1550 nm. The reason is the differences in geometry and refractive index of cores with respect to design parameters. The device has good repeatability, parameter scanning will help but only if you also have good repeatability. This problem is solved by parameter scanning while fabrication. Secondly, in Figure 8a,d, we note that when L MMI = 720 µm the normalized transmission may exceed 0, which is caused by the normalization procedure owing to the vibration of the reference waveguide.

Discussion
In order to clearly demonstrate the mode converter, Table 1 illustrates the performance comparisons between the reported E00-E20 mode converters. The compact siliconon-insulator based device using a 1 × 4 Y-junction and 4 × 4 MMI couplers can realize 16 different input-output mode conversions in C-band [31]. The mode converter with a cascaded tapers structure exhibits balanced performances [32]. The mode converter designed in Ref. [33] with phase change material inlaid in multimode waveguide has a large bandwidth and high conversion efficiency. However, the mode converters in these reports only have simulation results and are not actually fabricated. Owing to the low fabrication tolerance of the SOI platform, the device is hard to fabricate with the designed characteristics. Moreover, the SOI device is fixed after fabrication. To obtain a flexible and reconfigurable device, mode switching is necessary for the MDM system. The mode switch based on phase change materials or van der Waals materials can be used to achieve low power consumption and higher-order reconfigurable mode conversion [33][34][35]. In ref. [36], a mode converter based on cascaded long-period waveguide grating is mentioned, which uses the UV-curable polymer material EPO as the design material. The conversion efficiency of the device can be estimated to be more than 90% at 1550 nm. The polymer-based PLC is a lowcost platform. The design method could be verified on polymer. The design method is also inspiring for silica-based PLC. After comparison, the device proposed shows high conversion efficiency, high tolerance and large bandwidth, which has a good application prospect in MDM system.

Discussion
In order to clearly demonstrate the mode converter, Table 1 illustrates the performance comparisons between the reported E 00 -E 20 mode converters. The compact silicon-oninsulator based device using a 1 × 4 Y-junction and 4 × 4 MMI couplers can realize 16 different input-output mode conversions in C-band [31]. The mode converter with a cascaded tapers structure exhibits balanced performances [32]. The mode converter designed in Ref. [33] with phase change material inlaid in multimode waveguide has a large bandwidth and high conversion efficiency. However, the mode converters in these reports only have simulation results and are not actually fabricated. Owing to the low fabrication tolerance of the SOI platform, the device is hard to fabricate with the designed characteristics. Moreover, the SOI device is fixed after fabrication. To obtain a flexible and reconfigurable device, mode switching is necessary for the MDM system. The mode switch based on phase change materials or van der Waals materials can be used to achieve low power consumption and higher-order reconfigurable mode conversion [33][34][35]. In ref. [36], a mode converter based on cascaded long-period waveguide grating is mentioned, which uses the UV-curable polymer material EPO as the design material. The conversion efficiency of the device can be estimated to be more than 90% at 1550 nm. The polymer-based PLC is a low-cost platform. The design method could be verified on polymer. The design method is also inspiring for silica-based PLC. After comparison, the device proposed shows high conversion efficiency, high tolerance and large bandwidth, which has a good application prospect in MDM system.

Conclusions
In this work, we proposed an MMI-based mode converter that has the capability to efficiently convert E 00 mode to E 20 mode. The experimental results show that the fabricated device has high tolerance and high conversion efficiency, and the efficiency of the fabricated mode converter is −0.614 dB at 1550 nm wavelength. The degradation of conversion efficiency is less than 0.713 dB within the range of fabricate deviation. This paper provides a solution for efficient conversion in MDM systems.