## 2 Materials and Methods  
### EO-Combs with a DD-MZM  
To generate wideband EO-combs with a DD-MZM, we apply an asymmetric drive condition. The electro-optic transfer function [16] of an DD-MZM is represented as a function of an applied modulation voltage \(V(t)\), which is given by  
\[T_{MZM}=\frac{P_{out}(t)}{P_{in}(t)}=\frac{IL}{2}\bigg{[}1+\cos(\pi\frac{V(t)}{ V_{\pi}}+\phi_{0})\bigg{]} \tag{1}\]  
where \(V_{\pi}\) is the voltage applied to generate a phase drift of \(\pi\) between both arms as the half-wave voltage [28]. In practice, \(V_{\pi}\) is diverse between DC and RF. \(IL\) is the insert loss. The phase drift resulting from an internal path length differences between the two arms of the MZM is expressed as \(\phi_{0}\). Usually, as the other modulators have independent electrodes for RF and DC, the modulation voltage and the constant bias voltage \(V_{bias}\) provided at the DC electrode are independent of each other. \(V_{RF}(t)\) provided at the RF electrode is the time-varying modulation voltage. If the \(V_{RF}(t)\) is supposed as a sinusoidal voltage, the modulation voltage \(V(t)\) can be represented as  
\[V(t)=V_{bias}+V_{RF}(t)=V_{bias}+V_{e}\cos\big{[}\omega_{e}t+\phi_{e}(t)\big{]} \tag{2}\]  
where \(\phi_{e}(t)\) expresses a stochastic process that shows the phase fluctuations interpreted as a parasitic phase modulation with the RF signal. \(\omega_{e}\) and \(V\) are, respectively, the angular frequency \((\omega_{e}=2\pi\phi_{e})\) and the voltage amplitude of the RF driving signal.hus, the electro-optic transfer function [29] of the DD-MZM can be extended to  
\[T_{MZM}=\frac{IL}{2}\bigg{[}1+\cos\bigg{(}\pi\frac{V_{RF}(t)}{V_{\pi,RF}}+\pi \frac{V_{bias}}{V_{\pi,DC}}\bigg{)}+\phi_{0}\bigg{]} \tag{3}\]  
Supposing the optical carrier is linearly polarized and aligned to the electro-optic modulator's polarization state axis, the electric field expression of input optical wave \(E_{in}(t)\) is in scalar type as  
\[E_{in}(t)=E_{0}*\cos[\omega_{0}t+\phi_{0}(t)] \tag{4}\]  
where \(\phi\) is the phase of the light. If \(\phi=0\), the output power is the largest; and if \(\phi=\frac{\pi}{2}\), the light fields in the two branches are eliminated by interfering with each other. The output power is the smallest, which is zero in the ideal case. Now, assuming the input optical carrier is supported to the input port of the DD-MZM practically, the mathematical expression of the output optical signal modulated is given by  
\[\begin{split} E_{out}(t)&=E_{0}*\cos[\omega_{0}t+ \phi_{0}(t)]\\ &\cos\bigg{\{}\frac{\phi_{DC}}{2}+\frac{\pi}{2V_{\pi,RF}}V_{e}\cos [\omega_{e}t+\phi_{e}(t)]\bigg{\}}\end{split} \tag{5}\]  
where  
\[\phi_{DC}=\pi\frac{V_{bias}}{V_{\pi,DC}}+\phi_{0} \tag{6}\]Clearly, diverse spectral comb lines will be generated due to the nonlinearity of the electro-optic converse function, which determined on the static phase offset \(\phi_{DC}\) caused by the bias voltage and on the magnitude \(V_{e}\) of the signal modulated.In order to well comprehend the modulated spectrum, the Bessel functions is used in mathematical Equation (5), which is given by  
\[\begin{split}& E_{out}(t)=E_{0}\cos\left(\frac{\phi_{DC}}{2}\right)J _{0}(m)\cos[\omega_{0}t+\phi_{0}(t)]\\ &+E_{0}\cos\left(\frac{\phi_{DC}}{2}\right)\bigg{\{}\sum_{n=1}^{ \infty}J_{2n}(m)\\ &\left[\begin{array}{l}\cos[\omega_{0}t+\phi_{0}(t)-2n(\omega_{e }t+\phi_{e}(t))+n\pi]\\ +\cos[\omega_{0}t+\phi_{0}(t)+2n(\omega_{e}t+\phi_{e}(t))-n\pi]\end{array} \right]\bigg{\}}\\ &+E_{0}\sin\left(\frac{\phi_{DC}}{2}\right)\bigg{\{}\sum_{n=1}^{ \infty}J_{2n-1}(m)\\ &\left[\begin{array}{l}\cos[\omega_{0}t+\phi_{0}(t)-(2n-1)(\omega_{e}t+\phi _{e}(t))+n\pi-\frac{\pi}{2}]\\ +\cos[\omega_{0}t+\phi_{0}(t)+(2n-1)(\omega_{e}t+\phi_{e}(t))-n\pi+\frac{\pi}{ 2}]\end{array}\right]\bigg{\}}\end{split} \tag{7}\]  
According to Equation (6) [28], the two RF signals with reversal phase drive the DD-MZM, i.e., \(|V_{1}(t)|=|-V_{2}(t)|=V\); thus, \(\Delta\phi=2\pi V/V_{\pi}\), and a flat OFC can be generated.