## 2 Schematics  
It is well known that lithium niobate exhibits birefringence characteristics [15]. Each polarization axis of lithium niobate has a voltage efficiency difference of approximately three times that of the signal modulation [16]. The proposed technique uses this characteristic to apply different amplitude modulations to both polarization axes. First, an ideal MZM transfer curve was assumed. In this case, for an applied voltage V, the light component along one polarization axis (referred to as the \(X\)-axis) is modulated by the following equation:  
\[E_{out,X}=E_{in,X}e^{j\pi\cdot V/2V_{\pi}}+E_{in,X}e^{-j\pi\cdot V/2V_{\pi}}=E_ {in,X}\cos\pi V/2V_{\pi} \tag{1}\]  
where \(E_{in}\), \(E_{out}\) refer to the amplitude of the input and output E-fields, respectively, and \(V_{\pi}\) refers to the voltage that the MZM must apply when it modulates the intensity of the voltage-intensity transfer curve by \(\pi\). Assuming that the electro-light modulation efficiency of the other polarization component (\(Y\)-axis) of lithium niobate differs by exactly three times compared to the crystal axis, the light is modulated by the following equation:  
\[E_{out,Y}=E_{in,Y}e^{j\pi\cdot V/6V_{\pi}}+E_{in,Y}e^{-j\pi\cdot V/6V_{\pi}}=E _{in,Y}\cos\frac{\pi V}{6V_{\pi}} \tag{2}\]  
The overall scheme is represented in Figure 1.  
Figure 1: Overall schematic of the proposed scheme. Figure 2a,c show that the transfer curve of each polarization is different. Thus, different intensity signals can be modulated for each polarization by using the same voltage signal. If the eight-voltage point is set as the input symbol voltage, as depicted in Figure 2a,c, then the intensity of each polarization is modulated differently due to the birefringence of MZM. By adequately tuning the bias and points, one axis can be modulated as PAM4, and the other axis can be modulated as OOK. Figure 2b,d depict the expected eye diagrams of each polarization. In this case, the eight-voltage point is just an example. The modulation order could also be adjusted arbitrarily. MPAM could be modulated in the \(X\)-axis, and OOK could be modulated in the \(Y\)-axis. There are two issues associated with this method. The first is the power division. The optimal power rate for each polarization needs to be determined. The other is symbol mapping, which determines the optimal bias and voltage symbol points. These issues cannot be solved independently because both can affect the signal power of each polarization. Thus, these two issues must be optimized simultaneously. Figure 3 shows the eye diagrams and transfer curves when symbol mapping and power-dividing are changed. The blue and red arrows show the polarization rate change (power-dividing change), and the black arrow shows the symbol mapping change. As shown in Figure 3, the blue and red lines are inversely proportional to each other. This is because the total power is limited. Therefore, if the power allocated to the \(X\)-axis increases, the power allocated to the other axis decreases. The symbol mapping change, depicted as a black arrow, changes the signal power of each axis. If the eye of the \(Y\)-axis increases, the eye of the \(X\)-axis should decrease as both polarizations are modulated with a single input voltage signal. Thus, optimization of the symbol mapping change depends on the signal power. Figure 2: Transfer curve and expected eye-diagram for each polarization axis: (**a**) \(X\)-axis voltage vs. intensity transfer curve; (**b**) Expected \(X\)-axis eye diagram (**c**); \(Y\)-axis voltage vs. intensity transfer curve (**d**); Expected \(Y\)-axis eye diagram. Because one axis transmits the MPAM signal and the other transmits OOK, we assume that the total number of bits, N, is transmitted in the ratio X:Y = N-1:1.