# Dispersion Management and Pulse Characterization of Graphene-Based Soliton Mode-Locked Fiber Lasers
## 7 Results and Discussions  
With appropriate PC adjustment, a stable self-starting mode-locked fiber laser is achieved at the pump power of 27.1 mW. Figure 7 shows the mode-locked characteristics of the fiber laser taken for 2 m length of additional SMF-28 at a pump power of 80 mW. As measured from the OSA, the mode-locked output spectrum has a central wavelength of 1556.2 nm, which matches the gain profile of the EDF [42], and a 3-dB bandwidth of 7.47 nm, as shown in Figure 7a. The existence of multiple Kelly's sidebands validates that the pulse belongs to conventional soliton. By using a sech\({}^{2}\) fitting in the autocorrelation trace, the full width at half maximum pulse duration (\(t_{\text{FWHM}}\)) is 730 fs (Figure 7b). The experimental result agrees well with the theoretical sech\({}^{2}\) curve fitting, with no indication of pulse breaking or pulse pair generation, thus confirming the soliton-like operation of the mode-locked pulse. The corresponding time-bandwidth product (TBP) is estimated to be 0.676. The pulse train measured from the oscilloscope is shown in Figure 7c, where the pulse repetition rate and the time interval between pulses are 11.19 MHz and 0.0894 us, respectively. The absence of spectral modulation proves that the Q-switching instability does not exist, thus verifying good stability of the mode-locked pulse operation. From the RF measurement, the peak-to-pedestal extinction ratio (PER) at the fundamental repetition rate is approximately 41 dB, which is measured with about 1 MHz frequency span and 30 kHz resolution bandwidth, as shown in Figure 7d. The central frequency of the fundamental pulse is about 11.19 MHz, which is tallied with the value obtained from the oscilloscope trace. The RF spectrum with a span of 200 MHz is shown in Figure 7e, which indicates an evenly spaced frequency interval of approximately 11.19 MHz, thus further verifying the stability of the mode-locked pulse operation. Similarly, we experimentally investigate the mode-locked output characteristics at other lengths of the SMF-28. The spectral bandwidth of the optical spectrum for every different length of the SMF-28 is measured, and the results are divided into three distinct regions according to a degree of the wideness of the spectral bandwidth, as shown in Figure 8. Each region corresponds to a certain range of spectral bandwidth, with only slight variation between one another. Region 1 has the broadest spectral bandwidth of more than 8 nm, which is achieved when employing the additional SMF-28 length of 0 m and 0.5 m. A narrower spectral bandwidth of approximately 7.5 nm is measured in Region 2, which consists of 1 to 2.5 m of the additional SMF-28. The narrowest spectral bandwidth is acquired between 5.5 and 6 nm when the SMF-28 length is above 3 m, as shown in Region 3. This infers that the spectral bandwidth increases when the SMF-28 length decreases, corresponding to the increment of the net GVD negative value. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{3}{c}{**Fiber Length (m)**} & \multicolumn{3}{c}{**Fiber GVD (ps\({}^{2}\))**} & \multicolumn{2}{c}{**Net GVD (ps\({}^{2}\))**} \\ \hline
**SMF-28** & **EDF** & **Hi-1060** & **SMF-28** & **EDF** & **Hi-1060** & \\ \hline
10.4 & & & \(-\)0.23 & & & \(-\)0.121 \\
9.9 & & & & \(-\)0.22 & & & \(-\)0.110 \\
9.4 & & & & \(-\)0.21 & & & \(-\)0.099 \\
8.9 & & & & \(-\)0.2 & & & \(-\)0.088 \\
8.4 & 5 & 1 & \(-\)0.19 & 0.115 & \(-\)0.007 & \(-\)0.077 \\
7.9 & & & & \(-\)0.17 &The pulse repetition rate behavior for different SMF-28 lengths taken at the same pump power of 80 mW is plotted in Figure 9. A decreasing pattern of the pulse repetition rate from 12.5 to 10.0 MHz is observed, with a consistent interval of about 0.3 MHz for every increase of 0.5 m length SMF-28.