## 2 Basic Theory  
### The Double Sideband with Carrier Suppression (DSB-CS) Modulation Method  
Microwave carriers can be generated by means of DSB-CS modulation method with the advantages of input wavelength independence and microwave frequency tunability/doubling. In addition, the optical signal power generated at different wavelength regions after the MZMs can be calibrated by adjusting the input light power and the DC bias of the modulators. This provides convenience in comparing the photonics-generated microwave power at different wavelengths based on the same photodiode. Here, it is assumed that a single drive Mach-Zehnder Modulator (MZM) was used to generate the microwave carriers. Then, the input optical carrier electric field of the MZM is expressed as Equation (1). \[E_{in}(t)=E_{0}exp(j\omega_{c}t) \tag{1}\]  
where \(E_{in}(t)\) is the input optical carrier electric field, \(E_{0}\) represents the amplitude of the optical carrier electric field, and \(\omega_{c}\) represents the angular frequency of the input optical carrier. Being loaded on the single-driving MZM, the RF modulation signal is expressed in Equation (2). \[V_{RF}(t)=V_{RF}\sin(\omega_{RF}t+\varphi) \tag{2}\]  
where \(V_{RF}(t)\) represents the RF modulation signal, \(V_{RF}\) represents the voltage of the RF modulation signal, \(\omega_{RF}\) represents the angular frequency of the RF modulation signal, and \(\varphi\) is the phase of the sinusoidal modulated electrical signals generated by the signal generator. When the optical separation ratio of the Y-branches of the MZM is set as 0.5/0.5, after outputting the combined Y-branch of the MZM, the optical signal \(E_{MZMout}(t)\) is expressed by Equation (3), which is expanded based on the first kind of Bessel function. \[ \begin{array}{l}E_{MZMout}(t)\\ =\frac{E_{0}}{2}\left\{\sum\limits_{-\infty}^{+\infty}I_{n}\left(\frac{\pi V_{ RF}}{2V_{\pi}}\right)exp(j\omega_{c}t+jn\omega_{RF}t+jn\varphi)\left[exp \left(j\frac{\pi V_{DC}}{2V_{\pi}}\right)+(-1)^{n}exp\left(-j\frac{\pi V_{DC}} {2V_{\pi}}\right)\right]\right\}\\ =\frac{E_{0}}{2}\left\{\sum\limits_{-\infty}^{+\infty}J_{n}(m)exp(j\omega_{c} t+jn\omega_{RF}t+jn\varphi)\left[exp(j\Phi_{DC})+(-1)^{n}exp(-j\Phi_{DC}) \right]\right\}\end{array}  \tag{3}\]  
where \(V_{\pi}\) represents the half-wave voltage of the MZM. \(V_{DC}\) is the DC bias voltage of the MZM. \(m=\left(\pi V_{RF}\right)/\left(2V_{\pi}\right)\) is the modulation index of the MZM. \(\Phi_{DC}=\left(\pi V_{DC}\right)/\left(2V_{\pi}\right)\) is the optical phase changes caused by the DC bias voltage of the MZM, and \(\Delta\Phi_{DC}=\left(\pi V_{DC}\right)/V_{\pi}\) is the optical phase difference between the upper and lower channels of the Y-branch caused by the DC bias voltage of the MZM. When the DSB-CS modulation method is applied, the value of \(\Delta\Phi_{DC}\) is maintained as \(\pi\) by adjusting the DC bias voltage of the MZM to \(V_{\pi}\). At this moment, the power of the optical carrier is kept at a minimum as zero. The electric field of the high-order optical sidebands can be ignored because of the properties of the Bessel function. Then, Equation (3) is simplified to Equation (4) based on Euler's Formula. \[ \begin{array}{l}E_{MZMout}(t)=\frac{E_{0}}{2}\left\{\sum\limits_{-\infty}^{+ \infty}J_{n}(m)exp(j\omega_{c}t+jn\omega_{RF}t+jn\varphi)\cdot\left[j-(-1)^{n }j\right]\right\}\\ =E_{0}J_{1}(m)exp\left(j\omega_{c}t+j\omega_{RF}t+j\varphi+j\frac{\pi}{2} \right)+E_{0}J_{-1}(m)exp\left(j\omega_{c}t-j\omega_{RF}t-j\varphi+j\frac{\pi} {2}\right)\end{array}  \tag{4}\]  
As shown in Equation (4), the DSB-CS modulation is realized with the suppressed optical carrier power (\(n=0\)) demonstrating an optical carrier wavelength independent property. Additionally, the first-order optical sidebands (\(n=\pm 1\)) with the paired angular frequency of (\(\omega_{c}+\omega_{RF}\)) and (\(\omega_{c}-\omega_{RF}\)) are maintained. Then, the optical signal power \(P_{MZMout}(t)\) illuminated on photodetector can be expressed in Equation (5). \[