Silicon-based on-chip optical interconnect has become an emerging technology for its unique advantages of high level of integration. Recently, research work to further increase the transmission capacity of wavelength division multiplexing (WDM) system has become a hot spot in the chip-scale optical communication systems. However, the capacity of WDM is limited by the small bandwidth of fiber amplifier and the low launched power due to fiber nonlinearity. To further increase the optical transmission capacity, various kinds of methods have been proposed, such as polarization multiplexing (PDM) and mode multiplexing (MDM) technologies . In addition, WDM interconnections which are compatible with MDM are achieved by using different types of mode de/multiplexer (DE/MUX), which are based on asymmetrical directional couplers (ADC) , adiabatic couplers  and asymmetrical Y-junctions  . However, the ADC structure requires additional phase section to realize mode conversion, leading to a limited fabrication tolerance. The adiabatic couplers can reach a low crosstalk, but at the expense of large footprints. The asymmetrical Y-junction has a small footprint, however, the relatively high insertion loss restricts its applications. In contrast, the multimode interference (MMI) combines the advantages of compact size, low crosstalk, large optical bandwidth, and large fabrication tolerance  ; thus, it may become a good scheme to achieve high-capacity WDM interconnections.
In this paper, we report a new silicon-based mode converter and demultiplexer structure by employing MMI and tapered phase shifter. As the wavelength is increased, the phase shift induced by tapered phase shifter becomes smaller while the phase shift introduced by MMI becomes larger. Therefore, combing the MMI with the tapered phase shifter, the crosstalk between adjacent wavelengths channels will be reduced substantially. The insertion loss and crosstalk of the presented device are simulated by using 3D finite-different time domain (FDTD) method. The simulated results show the total device has a low insertion loss of less than 1 dB, a crosstalk of better than −15 dB, and the footprint of ~2.7 μm × 43.7 μm (except the length of input/output).
2. Principle and Device Design
The structure of MMI based on the self-image principle has been proposed by Lucas B. Soldano , and the input image reproduced as mirror or direct images at the period intervals along the propagation direction. Lπ is defined as the beat length of the two lower-order modes:
where β represents the propagation constant of optical mode, nr and We is the effective reflective index and the width of MMI for wavelength in vacuum of λ0, respectively.
We propose a mode converter and demultiplexer structure for WDM transmission by employing the principle of MMI, and the wavelength signals are multiplexed into a mode converter and multiplexer structure, then transmitted through the symmetric structure and demultiplexed into the date channel respectively. The mode converter and demultiplexer structure consists of three parts, a symmetric interference MMI coupler (MMI1) as a mode converter, a tapered π/2 phase shifter and a 3 dB general interference MMI coupler (MMI2) as illustrated in Figure 1. The length of MMI1 and MMI2 are 3Lπ/4 and 3Lπ/2, respectively. The fundamental mode (TE0) is injected from Port1 and imaged in Port3 and Port6, then extracted from Port9. In addition, the first-order mode (TE1) will be spilt into two fundamental modes in the Port2 and Port4 with the same power and π phase difference. After transmitting through the tapered π/2 phase shifter and MMI2, the two modes will be converted into the TE0 mode through constructive interference in MMI2, and then output from Port8. Therefore, the TE0 mode will be directed out from Port9 while the TE1 mode will be converted into TE0 mode and coupled out from Port8, thus realizing the mode converter and demultiplexer.
In the design above, an SOI wafer with a 220 nm top silicon layer and 2 μm buried oxide (BOX) layer is considered as the fabrication platform, and the input width of Port1 is set to be 1 μm so that fundamental mode and first order mode can exist at the same time. The width of MMI1 is chosen to be 2.4 μm in consideration of the compact device size and fabrication requirement. Firstly, the effective reflective index of the fundamental mode in MMI1 at the wavelength of 1550 nm is numerically calculated to be ~2.83, and the length of the MMI1 is 10.5 μm according to Equation (1). As shown in Figure 2(a) that the optimal length of MMI1 is 9.2 μm when TE0 and TE1 mode injected into Port1 and analyze the power in Port2, Port3 and Port4 respectively, and produce a high transmission
Figure 1. Schematic diagram of the mode converter and demultiplexer structure.
Figure 2. The transmit efficiency varies with (a) the MMI1 length, (b) the MMI2 length.
efficiency for both TE0 and TE1 modes. For the 3 dB coupler, MMI2 has a width of 2.7 μm. Similarly, as TE0 mode injected in Port8 and Port9 and analyzing the power in Port5, Port6 and Port7, respectively, the optimal length of MMI2 is 25 μm through FDTD simulations, as exhibited in Figure 2(b).
In order to obtain high transmission efficiency as much as possible, we design and optimize the width of W1, W3, W5 and W6. As shown in Figure 3(a), we fix the width and length of MMI1, then injected TE1 mode from Port1 and calculated the power in Port2 (the same power in Port2 and Port4) with the change of the width of W1. From the figure we can find that the transmission loss can be reduced to minimum in the case of W1 = 0.5 μm. Similarly, we injected TE0 mode in Port1 and analyzed the transmission efficiency varied with the width of W3, as shown in Figure 3(b), the width is optimized as W3 = 0.9 μm. In order to avoid the coupling between Port2, Port3 and Port4, we set the width of W4 and W7 as 0.5 μm, which can only support the fundamental mode, and the length of L2 and L4 is set as 2 μm and 5 μm. In order to optimize the widths of W5 and W6, we fix the size of MMI1 and MMI2, then inject TE0 and TE1 mode from Port1 and change the widths of W5 and W6 from 0.3 μm 1.3 μm, respectively. As shown in Figure 3(c) and Figure 3(d), we find the maximum transmission power in Port9 and Port8 in the case of W5 = 0.9 μm and W6 = 0.9 μm respectively.
When designing the tapered phase shifter, the length of L is chosen as 9.5 μm and the width of W2 is 0.8 μm. Then we scan the phase shift of tapered phase shifter of different length L1, as shown in Figure 4. The result shown a π/2 phase shifter at 1550 nm with the length of L1 = 7.6 μm. Moreover, we get the phase difference with different wavelength of 1530 nm, 1550 nm and 1570 nm in Figure 4,
Figure 3. The transmit efficiency varies with the width of (a) W1, (b) W2, (c) W5, (d) W6 at 1550 nm.
which indicates a variation range of lower than two degrees difference range over the whole C band wavelength (1530 nm to 1570 nm).
Then we calculate the phase difference when TE0 mode injects from Port8 then transmits through MMI2 and phase shifter with wavelength varying from 1530 nm to 1570 nm, as shown in Figure 5(a). The results clearly show that the phase shift induced by phase shifter is inversely proportional to the wavelength shift, which means a reduction of phase shift when wavelength increases. Nevertheless, the phase difference caused by MMI2 becomes larger with the increase of wavelength. Furthermore, we also analyze the total phase difference of these two components, as exhibited in Figure 5(b). It is obvious that the total phase difference is between −0.025 and 0.025 rad when wavelength varying within C band. Such small phase difference may enhance the transmission performance of the device.
Figure 4. The phase difference of 1530 nm, 1550 nm and 1570 nm as function of length L1.
Figure 5. (a) The phase difference of phase shifter and MMI2 as function of wavelength, (b) the total phase difference of MMI2 and phase shifter as function of wavelength.
3. Results and Discussion
The total device is simulated by way of 3D FDTD method. To demonstrate the mode converter and multiplexer of TE0-TE0, TE0-TE1, we simulate the optical field distributions, and the results are shown in Figure 6(a) and Figure 6(d). The TE0 mode injected in center-port (Port9 in Figure 1) will keep TE0 mode transmission to the output port. However, the TE0 mode injected in under-port (Port8 in Figure 1) will be converted into TE1 mode with high conversion efficiency. Additionally, for the mode demultiplexer, the light output from Port9 for the TE0 mode input, and the light output from Port8 for TE1 mode input. One should note that both output modes are TE0 modes, as displayed in Figure 6(b) and Figure 6(e). Then we simulate the transmission field distributions of the mode multiplex and de/multiplex structure, as shown in Figure 6(c) and Figure 6(f), there is an obvious and direct correspondence between the input port and the output port.
For a multiplexer and de/multiplexer structure, the two most important parameters are insertion loss (IL) and crosstalk (CT). Here we analyze the relationship between transmission efficiency and wavelength by calculated the IL and CT of the device. Figure 7 shows the result of two modes multiplex, demultiplex and mode multiplex and de/multiplex. Numerical calculation results show
Figure 6. Transmission field distributions of (a), (d) the mode multiplexer with TE0 injected in Port9 and Port8, respectively. (b), (e) the mode demultiplexer structure with TE0 and TE1 injected in Port1, and (c), (f) the mode multiplexer and de/multiplexer with TE0 injected in Port9 and Port8, respectively.
Figure 7. Wavelength dependence of (a) the mode multiplexer when the input is the TE0 in Port9 and Port8, (b) the mode demultiplexer structure with TE0 and TE1 injected in Port1, and (c) the mode multiplexer and de/multiplexer when the input is the TE0 in Port9 and Port8, respectively.
the IL are below 1 dB in multiplex and de/multiplex structure over the whole C band (1530 nm to 1570 nm), while the IL of the whole structure of multiplex and de/multiplex is below 2 dB as shown in Figure 7(c). It can be seen that the CT of mode multiplexer and de/multiplexer structure is lower than −14 dB and the designed two-mode multiplexer is below −15 dB within the bandwidth from 1530 nm to 1570 nm. Such simulated results show that the proposed structure is potential to be applied in practical silicon photonic integrated circuits.
At last, we calculate the fabrication tolerance of the proposed structure. It is clear that there is a quadratic curve relation between the beat length of MMI and the effective width of MMI, in other words, the performance of the device is much sensitive to the width of MMI. Therefore, we set the two mode demultiplexer structure with TE0 and TE1 mode injected into Port1, respectively. Then we analyze the normalized power with the MMI width varying from −50 nm to 50 nm at the wavelength of 1530 nm, 1550 nm and 1570 nm, respectively. As illustrated in Figure 8(a), when MMI width varies from −10 nm to 10 nm, the insertion loss is lower than 1.5 dB.
For the phase shifter, its performance highly sensitive to dimensional variations, we simulate the transmission characteristics when the total length varies at the wavelength of 1530 nm, 1550 nm and 1570 nm. It can be easily observed from Figure 8(b) that the maximum transmission occurs when ΔL is 0 nm at 1550 nm, and the transmission efficiency decreases whether the ΔL increases or decreases. In the practical fabrication craft, the length variation can be selected from −30 nm to 30 nm, which can provide much convenience.
Figure 8. Fabrication tolerance of the (a) transmission efficiency varies with MMI width, (b) transmission efficiency varies with phase shifter length at the wavelength of 1530 nm, 1550 nm and 1570 nm.
We propose and simulate a SOI-based mode converter and demultiplexer structure for WDM optical interconnection and transmission by employing MMI and tapered phase shifter structure. The simulation results indicate that such a structure has a broad bandwidth of over the whole C band, a low transmission loss of less than 1 dB and a low crosstalk of less than −15 dB. A compact mode converter and demultiplexer of less than 2.7 μm × 43.7 μm is achieved and the fabrication tolerance is ~10 nm which can meet the demand of the practical fabrication. Such structure may provide a valuable selection in silicon photonic integrated circuits (PICs).
This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 61875063).
 Dai, D., Wang, J., Chen, S., Wang, S. and He, S. (2015) Monolithically Integrated 64-Channel Silicon Hybrid Demultiplexer Enabling Simultaneous Wavelength and Mode Division Multiplexing. Laser and Photonics Reviews, 9, 339-344. https://doi.org/10.1002/lpor.201400446
 Driscoll, J.B., Grote, R.R., Souhan, B., Dadap, J.I., Lu, M. and Osgood, R.M. (2013) Asymmetric Y Junctions in Silicon Waveguides for On-Chip Mode-Division Multiplexing. Optics Letters, 38, 1854-1856. https://doi.org/10.1364/OL.38.001854
 Han, L., Liang, S., Zhu, H., Qiao, L., Xu, J. and Wang, W. (2015) Two-Mode De/Multiplexer Based on Multimode Interference Couplers with a Tilted Joint as Phase Shifter. Optics Letters, 40, 518-521. https://doi.org/10.1364/OL.40.000518
 Guo, F., Lu, D., Zhang, R., Wang, H., Liu, S., Sun, M., Kan, Q. and Ji, C. (2016) An MMI-Based Mode (DE) MUX by Varying the Waveguide Thickness of the Phase Shifter. IEEE Photonics Technology Letters, 28, 2443-2446. https://doi.org/10.1109/LPT.2016.2599934
 Soldano, L.B. and Pennings, E.C. (1995) Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications. Journal of Lightwave Technology, 13, 615-627. https://doi.org/10.1109/50.372474