## 4 System Modeling and Performance  
Based on the above modeling and simulation work of the discrete devices, the system-level simulation of the optical transmitter is carried out using the commercially available software of Lumerical Interconnect. The schematic diagram of the system modeling is shown in Figure 12a. As can be seen, the optical transmitter is characterized channel by channel using a tunable continuous wave laser (CWL). As mentioned before, two grating designs are used for the modulators. By substituting the S-parameter matrix of the bidirectional grating coupler (BGC), performance of different wavelength channels can be obtained. An optical network analyzer (ONA) is utilized to obtain the optical transmission spectra where the optical loss can be evaluated. For the dynamic performance, a PRBS generator, symbol mapper for NRZ and PAM4 modulation format and eye diagram analyzer (EYE) were added in the simulation for data transmission test. An optical spectrum analyzer (OSA) is also added to the optical output of the transmitter for frequency-domain analysis of the modulated optical signal. The optical loss of the optical transmitter determines the signal-noise ratio of the modulated signal and largely affects the complexity of the receiver circuit. Figure 12b shows the optical loss of the optical transmitter under NRZ and PAM4 modulation format. For the NRZ modulation format, the optical loss of the transmitter is (4.86-6.72) dB. For the PAM4 modulation format, the optical loss is (5.38-7.27) dB. Due to the bias condition difference, the optical loss of PAM4 modulation is about 1 dB below that of NRZ modulation. Nevertheless, the optical loss is kept well below 8 dB for all wavelength channels, which is acceptable for the silicon transceiver applications. Figure 13a,b shows the calculated frequency spectra of the eight-channel modulated optical signals with NRZ and PAM4 modulation format. The modulated optical signal shows good uniformity between different channels. The channel isolation is below \(-60\) dB  
Figure 11: (**a**) The simulated optical transmission spectra of the MZI optical interleaver. (**b**) The simulated optical transmission curve of the eight output channels of the interleaved AMMI device. Figure 12: (**a**) Schematic diagram of the system-level simulation of the optical transmitter for eye diagram test and dynamic performance characterization. (**b**) The optical loss of the transmitter under NRZ modulation and PAM4 modulation format. for both modulation formats. Obviously, the signal integrity for 100 Gb/s NRZ signal is expected to be better than 50 GBaud/s PAM4 after optical filtering or demultiplexing. Figure 14 shows the NRZ modulation format eye diagram test results of the optical transmitter with data rate of 100 Gbps and input optical power of 10 dBm. Benefiting from the high performance of the bidirectional grating couplers, clear open eyes were obtained for eight channels. The modulation depth is about 6.7 dB. By replacing the NRZ signal generator with a PAM4 signal generator, the eye diagram test of PAM4 modulation format can be carried out. Compared with the NRZ signal, the optical signal with PAM4 pattern is more sensitive to noise. Thus, the requirement for signal quality is more rigorous. To achieve good linearity and symmetry of eye diagrams, bias conditions for working wavelength and driving voltage levels are carefully chosen. Figure 15 shows the simulated eye diagram test results of eight channels. Small ripples can be clearly seen, which is mainly due to the optical and electrical reflections within the photonic link. Notably, the eye diagrams do not show obvious deterioration at the edge channels. The extinction ratio is about 4.54 dB. For PAM4 eyes, the level separation mismatch ratio (RLM) is an important concern which is directly related to the BER. The RLM of eight-channel PAM4 eye diagrams are analyzed. According to our calculations, the RLM is above 0.94 for all the wavelength channels, which should be able to meet most of the PAM4 specifications.