## 3 Experimental Results
### Frequency Fiber Channel Response Analysis  
We continue by analyzing the measured frequency response after different lengths of SMF. The frequency responses were measured by again using the ONA. The frequency responses shown in Figure 3 were obtained by extracting the frequency response measured  
Figure 2: Measured E/O response of the 10G-class DML with different bias currents of the DML \(i_{b}\) in C-band (1550 nm). in Figure 2 with \(i_{b}\) = 60 mA, i.e., with 0 km fiber, to show the overall frequency response including SMF and DML chirp effects. The channel frequency response of SMF in a DML based IM-DD system can be theoretically evaluated using Equation (1) [33; 34]:  
\[H(\omega)=\sqrt{\alpha+1}cos\Big{(}\theta+tan^{-1}\alpha\Big{)}+j\frac{\alpha \kappa P_{0}}{\omega}sin\theta \tag{1}\]  
where \(\alpha\) is the enhancement linewidth factor, \(\kappa\) is the adiabatic chirp factor (the DML chirp parameters), \(P_{0}\) in W is the average output power of the DML (i.e., \(P_{TX}\)), \(\omega=2\Gamma f\) (where \(f\) is the frequency in Hz), \(\theta=D\lambda^{2}\omega^{2}L/4\Gamma lc\) (where \(\lambda\) is the wavelength of the signal in m), \(D\) is the CD parameter in s/m\({}^{2}\), \(L\) is the fiber length in m, and \(c\) in m/s is the speed of light in vacuum. The black solid lines with circles show the measured frequency responses. On top of the experimental graph, the red lines specify the theoretical responses by using Equation (1), obtained after a fitting procedure on the free parameters [35]. Please note that the DML parameters \(\alpha\) and \(\kappa\) are not normally available on the DML datasheet, so we used simulations and experimental measurements to evaluate them. In the fitting procedure, \(\alpha\), \(\kappa\) and \(D\) were set as three free parameters. After the fitting procedure, we obtained \(\alpha\) = 2.1, \(\kappa\) = 3.3 GHz/mW, and \(D\) = 16.64 ps/(nm\(\cdot\)km) (which were obtained from fitting procedure performed in this section) as well as \(P_{0}\) = 8.5 dBm (which Was measured at the output of the DML by using an optical power meter). The measured frequency responses are remarkably consistent with the theoretical ones calculated by using Equation (1) for all three different fiber lengths \(L\) = 25 km, 75 km, and 118 km. As shown in Figure 3, we can observe several frequency notches. For instance, as shown in Figure 3b, the three frequency notches are at around 10 GHz, 14 GHz, and 18 GHz. Figure 3: _Cont._  
Figure 3: Frequency response of SMFs with different fiber length \(L\) in C-band (1550 nm) and with bias current of the DML \(i_{b}=60\) mA. Solid line and circle: measured response. Solid line: theoretical response obtained by using Equation (1). (**a**) \(L=25\) km, (**b**) \(L=75\) km, and (**c**) \(L=118\) km. In Equation (1), the first and second terms are caused by the transient chirp and adiabatic chirp of the DML, respectively. In Figure 4, we present the total frequency responses (extracted from the theoretical response in Figure 3) with different fiber lengths. The total frequency response can be decomposed into transient chirp and adiabatic chirp. From the ideas of [24], we can observe that the first notch induced by the transient chirp (in blue dashed curves) can be partially compensated by the adiabatic chirp (in green solid curves). As a result, at the frequency \(f_{1}\) (where first notch induced by the transient chirp appears), the total frequency response (in red solid line) does not suffer the notch at frequency \(f_{1}\). However, the notches induced by the transient chirp appearing after frequency \(f_{1}\) cannot be compensated by the adiabatic chirp, since the notches induced by the transient and adiabatic chirp appear at almost the same frequency. Therefore, we can observe 1, 3, and 6 notch(es) with 25 km, 75 km, and 118 km fiber respectively (within the measurable frequency window).