# Advanced Modulation Formats for 400 Gbps Optical Networks and AI-Based Format Recognition
## 2 Materials and Methods  
### System Structure and Setup  
The structure of the 4 \(\times\) 100 Gbps Apol-CRZ-FSK signal transmitters proposed in this study for optical networks is shown in Figure 1a. Each channel adopts a dual-light-source scheme, which involves two lasers generating two optical signals with the same intensity and a frequency spacing of 100 GHz to distinguish between digital signals 0 and 1. The two lasers for the first channel are denoted as CW1 and CW2, and similarly, the lasers for the second, third, and last channels are represented as CW3, CW4, CW5, CW6, CW7, and CW8, respectively. Taking the modulation process of the first channel as an example, the two laser signals CW1 and CW2 are combined through a 3 dB coupler and then modulated by MZM1, Variable optical attenuator (VOA) is used to adjust the power level of the transmitter. First, the input 100 Gbps binary pseudo-random sequence data1\(\{b_{n}\}\) is differentially encoded to obtain a binary relative code sequence \(\{d_{n}\}\). The generation principle of the relative code sequence \(\ d_{n}\) is as follows [3]:  
\[d_{n}=b_{n}\oplus d_{n-1} \tag{1}\]  
Here, \(\oplus\) is known as the XOR gate in digital circuits. The bias voltage of the MZM1 modulator is set at \(V_{bias}=V_{\pi}\), and the input signal is the differentially encoded pseudo-random NRZ signal \(V_{in}(t)=V_{\pi}a(t)\), \(a(t)=\pm 1\). The phase difference between the code \"0\" and the code \"1\" of the signal is 180 degrees, suppressing the discrete components in the signal spectrum. The output modulated optical signal can be expressed as [3]:\[E_{out}(t)=j\cdot E_{in}(t)\cdot\sin\Bigl{[}\frac{\pi}{2}a(t)\Bigr{]} \tag{2}\]  
\[P_{out}(t)\ =\ \frac{P_{in}(t)}{2}\cdot\{1-\cos[\pi a(t)]\}=P_{in}(t) \tag{3}\]  
Subsequently, the signal is demodulated in the MZDI 1 with a 1-bit delay. The output of the MZDI1 exhibits periodically varying comb-filter characteristics. When the CW1 and CW2 signals with a frequency spacing of 100 GHz are modulated to the peak and trough of the transmission curve of the MZDI1, respectively, the waveforms of the two frequencies outputted on the same interference arm are opposite, resulting in a phase difference of 180 degrees, which creates interference patterns of cancellation and enhancement between them. This allows the data of CW1 and CW2 with different frequencies to be demodulated as intensity-modulated signals on \"1\" and \"0\", respectively. The demodulation output of MZDI 1 exhibits complementary optical power on the two interference arms. Although these two demodulated signals are derived from the same source, they are logically opposite and complementary in power. In the time-domain optical intensity, they manifest as continuous light, while the optical frequency hops between two wavelengths as the information changes. Therefore, it can generate FSK signals that carry optical pulses in every bit interval. MZM2 performs pulse slicing on the FSK signal with the bias point set at V\(\pi\)/2, and the amplitude and frequency of the clock signal are V\(\pi\)/4 and B, respectively. The phase difference between the two clock signals is \(\pi\). A phase modulator1 is added afterwards to control the pre-chirp amount, which can generate the CRZ-FSK signal as shown in Figure 1b. If the CRZ-FSK signal is further processed through a polarization alternating device, an Apol-CRZ-FSK signal will be generated. The CRZ-FSK optical signal is divided into two optical signals with the same intensity and orthogonal polarization states by a 45-degree polarizing beam splitter (PBS). One of the signals is phase-modulated to vary its phase between 0 and \(\pi\). The two polarization signals are then coupled by a polarizing beam combiner (PBC) to obtain the Apol-CRZ-FSK signal for channel 1 with orthogonal polarization states for adjacent bits, as shown in Figure 1c. Similarly, signals for the other three wavelength channels are generated. This project is implemented by VPI9.3 simulation.