Integrated dual-mode 3 dB power coupler based on tapered directional coupler

A dual-mode 3 dB power coupler based on silicon-on-insulator platform for mode division multiplexing system is proposed and demonstrated. The device, which consists of a tapered directional coupler and two output bend waveguides, has a 50:50 coupling ratio around the wavelength of 1550 nm for both fundamental and first order transverse magnetic (TM0 and TM1) modes. Based on asymmetrical tapered structure, a short common coupling length of ~15.2 μm for both modes is realized by optimizing the width of the tapered waveguide. The measured insertion loss for both modes is less than 0.7 dB. The crosstalks are about −14.3 dB for TM0 mode and −18.1 dB for TM1 mode.

Scientific RepoRts | 6:23516 | DOI: 10.1038/srep23516 utilized to alleviated the issue of wavelength sensitivity and relax the precision of coupling length 13,22,23 . As shown in Fig. 1(b), half energy is coupled from the input waveguide to another waveguide through the coupling region for TM 0 and TM 1 modes, resulting in 3 dB power splitting for both modes. The length of the coupling region is defined as L, and other parameters are shown in Fig. 1(c). We use the multimode bend waveguides with radius R to separate the two output ports. The R is chosen to be 25 μm to avoid excess loss while not compromise the size of the device.
In the simulation, the width of the uniform waveguide w 1 is chosen to be 1 μm, which can stably support the TM 1 mode. The gap between the two waveguides is fixed to be 200 nm. The coupling length L, which is the least common 3 dB coupling length of the two modes, is determined based on the optimized result of waveguide width. The width w 2 is supposed to be w 1 − Δw while w 3 is w 1 + Δw. The effective index of TM 0 mode is almost invariable when the waveguide is tapered around 1 μm, while the one of TM 1 mode is dramatically changed, as indicated in Fig. 1(d). Therefore, the tapered directional coupler can be regarded as a conventional coupler for TM 0 mode but a tapered asymmetrical coupler for TM 1 mode. Hence, the coupling length L can be set as the 3 dB coupling length of TM 0 roughly, and Δw is optimized to mainly adjust the 3 dB coupling length of TM 1 mode, targeting to obtain a short common 3 dB coupling length. Considering the two modes simultaneously, the finally optimized width of tapered waveguide varies from w 2 = 0.93 μm to w 3 = 1.08 μm. The optimized coupling length L is 15.2 μm. The final results are presented as the red and green curves in Fig. 2. It is worth noting that the transmission spectra of both modes are almost the same and the coupling ratios are around 50:50 at the wavelength of 1550 nm. The simulated insertion losses of both modes are lower than 0.1 dB which can be neglected. The transmission spectra of conventional symmetrical directional couplers are calculated as a contrast, as shown by blue and pink dash curves  The results of (a) TM 0 mode and (b) TM 1 mode input. The conventional coupler for TM 0 consists of two strip waveguides whose widths are 1.0 μm and heights are 220 nm. The gap between the two waveguides is 200 nm. The parameters for TM 1 is the same except the coupling length.
in Fig. 2(a,b). One can find that, the coupling ratio dependency on wavelength of our scheme is slightly improved in the case of TM 0 mode input, and the improvement for TM 1 mode is obvious. The difference is accessible because the tapered asymmetrical structure mainly works on TM 1 mode. Figure 3(a,b) present the electric field distributions of TM 0 and TM 1 modes along the propagation direction at 1550 nm respectively, while the inserts are the mode distributions of the input and two output ports. The input TM 0 and TM 1 modes are evenly divided around the point of L = 15.2 μm. The inserts show that the output mode is the same with the input mode, qualitatively indicating a low crosstalk. Additionally, we utilize the mode expansion method to quantitatively calculate the crosstalk of the whole coupler with the output bend waveguides. The simulated results are shown in Fig. 4. The crosstalks, defined as the ratio of the sum of the interfering mode power to the desired mode power, are − 17.0 dB for TM 0 mode and − 18.9 dB for TM 1 mode. The higher crosstalk of TM 0 might be caused by the multimode bend waveguides 24,25 , which would introduce a crosstalk in transmission and can be reduced by increasing the radius or special design. As mentioned previously, the performance of the directional-coupler-based device is sensitive to geometric parameters. The fabrication tolerances to the deviations of coupling length, waveguide width and gap are investigated, as shown in Fig. 5. The same calculations for conventional scheme are also presented as references. Results indicate improvement on the fabrication tolerance compared with the conventional coupler.
Experimental results. Figure 6(a) shows the scanning electron micrograph (SEM) of the fabricated structure. Due to the lack of TM 1 source and other necessary facilities for high order mode, an extra mode multiplexer is designed for TM 1 signal inputting and another mode demultiplexer is utilized for output TM 1 measurement. The input TM 0 mode from Input 1 (marked in Fig. 6(a)) is converted to TM 1 mode by the multiplexer, and then the converted TM 1 mode divides evenly into the two output waveguides, which are finally converted to TM 0 modes and coupled out from the Output 1 and Output 3, respectively. On the other hand, the input TM 0 mode from the Input 2 propagates straightly to the 3 dB coupler and couples out from the Output 2 and Output 4 after division. In order to calibrate the insertion loss of the device we designed, a referenced MDM structure including a mode multiplexer and a demultiplexer is also fabricated, as shown in Fig. 6(b). The detailed SEM of the mode multiplexer is shown in Fig. 6(c). The mode multiplexer is based on asymmetrical directional coupler. The TM 0 -TM 1 coupling relies on the phase matching between the waveguides, which means that the effective index of the TM 0 mode of the narrow waveguide should be equal to that of the TM 1 mode of the wide waveguide. The optimized width of the single-mode and multimode waveguides are 0.5 μm and 1.23 μm respectively, while  the coupling length is 9.5 μm. Figure 6(d) shows the detail of the fabricated dual-mode 3 dB power coupler. The focusing grating couplers are used to couple TM 0 mode into and out of the chip 26,27 .
To evaluate the performance of the proposed device, a broadband light source assisted by the polarization controller and an optical spectrum analyzer (OSA) are used to measure the transmission spectra of the device. Figure 7(a) presents the measured coupling efficiency of the grating coupler. The coupling loss is about 4.3 dB for one port at 1550 nm. The experimental results of the mode multiplexer are shown in Fig. 7(b). The excess losses  are about 0.2 dB and 2.1 dB for TM 0 and TM 1 mode channels, respectively. Low crosstalks of −25 dB for the two mode channels are observed. The average transmission spectra of TM 0 and TM 1 are shown in Fig. 8(a,b), respectively. The insertion loss introduced by the coupling gratings and the MDM structure have been deducted. The experimental results almost conform to the simulated ones shown in Fig. 2(a,b). The insertion loss of the TM 0 mode is ~ 0.7 dB, while the one of TM 1 mode is ~0.2 dB. The difference is caused by the inconformity between the MDM structure used in the test structure and the referenced one, owing to the imperfect fabrication. The measured crosstalks for TM 0 and TM 1 transmissions are −14.3 dB and −18.1 dB, respectively.

Discussion
In conclusion, we propose and design an on-chip dual-mode 3dB power coupler using an asymmetrical directional coupler built on the SOI platform. The device can be easily fabricated in a single step of exposure and etching. Simulated and experimental results show an even division for both TM 0 and TM 1 modes at the wavelength of 1550 nm, with insertion losses of about 0.7 dB and 0.2 dB. The measured crosstalks for TM 0 and TM 1 modes are about −14.3 dB and −18.1 dB, respectively. The fabrication tolerances to the deviations of coupling length, waveguide width and gap are also discussed, and the results show improvement compared with the conventional coupler. The coupler can accommodate the mode division multiplexed system and would be applied in future silicon based large capacity communication systems.

Methods
Simulation method. We use a three-dimension finite difference time domain (FDTD) method to simulate the proposed dual-mode 3 dB coupler. In order to save the simulation time, we firstly optimize the performance of the coupler without the two bend waveguides to obtain the rough parameters. It is to be noted that, there is still a  small coupling in the bend region, which is not considered in the simulation. So in the next step, we optimize the performance of the whole coupler by making a small change around the rough parameters.
Device fabrication and experimental method. The device is fabricated utilizing 248 nm deep ultraviolet photolithography and inductively coupled plasma (ICP) etching using SOI wafer with top silicon layer of 220 nm and silicon dioxide (SiO 2 ) substrate of 2 μm. The etched structures have a SiO 2 cladding layer by utilizing plasma-enhanced chemical vapor deposition. Due to the lack of TM 1 source and other necessary facilities for high order mode, an extra mode multiplexer is designed for TM 1 signal inputting and another mode demultiplexer is utilized for output TM 1 measurement. In order to calibrate the insertion loss of the device we designed, a referenced MDM structure including a mode multiplexer and a demultiplexer is also fabricated. Since the results are easily disturbed by a lot of factors, we test the device many times and average the results, aiming to reduce the measuring error and alleviate the influence introduced by environment.
Crosstalk calculation. We employ the mode expansion method to analyze the crosstalk of the dual-mode power coupler in the simulation. The mode expansion method is to calculate the power proportion of each mode inside one waveguide based on overlap integral, as explained by following formula: where the F x y ( , ) is the input mode field and the ψ x y ( , ) i is a set of modes that the waveguide supports.