Ultrahigh-speed graphene-based optical coherent receiver

Graphene-based photodetectors have attracted significant attention for high-speed optical communication due to their large bandwidth, compact footprint, and compatibility with silicon-based photonics platform. Large-bandwidth silicon-based optical coherent receivers are crucial elements for large-capacity optical communication networks with advanced modulation formats. Here, we propose and experimentally demonstrate an integrated optical coherent receiver based on a 90-degree optical hybrid and graphene-on-plasmonic slot waveguide photodetectors, featuring a compact footprint and a large bandwidth far exceeding 67 GHz. Combined with the balanced detection, 90 Gbit/s binary phase-shift keying signal is received with a promoted signal-to-noise ratio. Moreover, receptions of 200 Gbit/s quadrature phase-shift keying and 240 Gbit/s 16 quadrature amplitude modulation signals on a single-polarization carrier are realized with a low additional power consumption below 14 fJ/bit. This graphene-based optical coherent receiver will promise potential applications in 400-Gigabit Ethernet and 800-Gigabit Ethernet technology, paving another route for future high-speed coherent optical communication networks.


Supplementary Note 1. Design and optical simulations of the 90-degree optical hybrid and the graphene-on-plasmonic slot waveguide photodetector.
For an ideal optical coherent receiver (OCR), the 90-degree optical hybrid should meet the following transmission matrix: Here, the 90-degree optical hybrid utilizes a common 4×4 multimode interference (MMI) coupler, which works in the self-imaging principle 1 to control the phase of the output-port light. The structure diagram of the MMI coupler is shown in Supplementary Fig. 1. In this case, the optical phase changes of the signals in the 4×4 MMI coupler are given as the following equations.
For rs + is odd, In the proposed OCR, the signal light is input from the input port 4, and the LO light is input from the input port 2. According to Equations (3) and (4), the phase shifts between the input ports and output ports are shown in Table S1. The corresponding transfer function of the 4×4 MMI coupler is given as follows, And Equation (5) The simulated power imbalance (<1.5 dB) and phase deviation (<7.5) of the MMI coupler are shown in Supplementary Fig. 2.
Supplementary Table 1. The phase shifts between input ports and output ports of the 44 MMI coupler. S stands for the numbering of the output port. Fig. 2 Simulated MMI coupler as a 90-degree optical hybrid. a Simulated power imbalances of the optical hybrid. Port 4/2 represents the input port, CH1/2/3/4 stands for the output port. b Simulated phase deviations between different output ports of the optical hybrid, as the light simultaneous input into the input port 4 and 2.
The design and optical simulations of graphene-on-plasmonic slot waveguide (PSW) photodetector (PD) are similar to the previous work 2 , and a surface conductivity model is treated for graphene. Here, we mainly define the active detection area of the graphene-on-PSW PD more accurately. The in-graphene-plane field component is responsible for the absorption by graphene. 3 As shown in the Supplementary Fig. 3b, the distribution of the in-plane electric field |Ex, y| at the graphene boundary is calculated, which is the white line signed in the simulated in-plane electric field Supplementary   Fig. 3a). And we calculate the 2 , || xy E which is proportional to the absorption and plot it in the Supplementary Fig. 3c. By doing the line integration in the 100-nm gap and outside the gap, we obtain the absorption portions in two areas to be 98.9% and 1.1%, respectively.
Thus, we define the active detection width of graphene is equivalent to ~100 nm. As mentioned above, the active detection area of the graphene-on-PSW PD is 15 μm100 nm.

Supplementary Note 4. The state-of-the-art optical coherent receivers
Supplementary  Supplementary Table 2. The graphene-based PD adopted in the graphene-based OCR suffers from a large dark current (~2-3 mA) due to the biased photoconductive effect, but combines high-speed operation with a simple fabrication process and control. The shot noise caused by the dark current of this graphene-based PD may reduce the sensitivity of the OCR, and a higher input optical power is required to improve the SNR. In the future, the dark current can be vanished by using the unbiased photothermoelectric effect-based graphene PD 8 with a little complex fabrication process. Moreover, by optimizing the optical power of the LO and signal light, we have obviously improved the SNR of the OCR, and demonstrated high-speed and high-quality receptions of advanced modulation formats in the graphene-based OCR for the first time.