# Dispersion Management and Pulse Characterization of Graphene-Based Soliton Mode-Locked Fiber Lasers
## 7 Results and Discussions
This justifies that the experimental value of the pulse repetition rate matches well with the computed pulse cavity round-trip time for each total cavity length that ranges from 11.4 to 15.4 m.  
Analysis of the pulse duration against different lengths of SMF-28 is made based on the graph plotted in Figure 10. The experimental findings show that a shorter pulse duration of the mode-locked EDFL is attained with a shorter cavity length, from the highest value of 820 fs at 4 m length additional SMF-28, to the lowest value of 710 fs at 0 m additional SMF-28. This agrees with the inverse correlation between pulse duration and spectral bandwidth of the mode-locked EDFL, as presented in Figure 8. The corresponding TBP value decreases gradually from 0.719 to 0.573, with increasing SMF-28 length from 0 to 4 m. All the obtained TBP values for all SMF-28 lengths are slightly higher from the expected transform-limited sech\({}^{2}\) pulse of 0.315, which indicates minor chirping in the pulse due to  
Figure 8: Spectral bandwidth of the laser output against different SMF-28 lengths. Figure 7: Mode-locked output characteristics; (**a**) optical spectrum, (**b**) autocorrelation trace, (**c**) pulse train, (**d**) RF spectrum at the fundamental frequency peak, and (**e**) RF spectrum at 200 MHz span. residual dispersions in the laser cavity. Since the TBP value decreases with SMF-28 length, the minor chirping is deduced to be inversely proportional to the length of SMF-28. The pulse stability of the mode-locked EDFL at different SMF-28 lengths is examined by analyzing the PER of the RF signal at the first-order pulse. In this measurement, the RF spectrum analyzer is set to a span of 1 MHz and a resolution bandwidth of 30 kHz. Figure 11 shows the recorded PER value based on different lengths of SMF-28 used. It is observed that the PER value fluctuates across 0 to 4 m range of the SMF-28 length, with the maximum value of 40.98 dB obtained at 2 m length, and the minimum value of 39.88 dB recorded at 0.5 m length. The development of the average output power and pulse energy against pump power for different additional SMF-28 lengths are shown in Figure 12a,b, respectively. From Figure 12a, it can be observed that after reaching the similar continuous wave (CW) lasing threshold of 12.8 mW, all the graphs exhibit a linear increment of the average output power with respect to the pump power. As for the case of pulse energy evolution in Figure 12b, starting from the mode-locking threshold of 27.1 mW, the pulse energy increases linearly with respect to pump power for all different lengths of the SMF-28. The mode-locking  
Figure 10: Pulse duration measurement at different additional SMF-28 lengths. Figure 9: Fundamental pulse repetition rate at various additional SMF-28 lengths. threshold achieved in this work is relatively low for a graphene-based mode-locked fiber laser in the C-band region [43; 44; 45], which is attributed to the low transmission loss of the fabricated graphene/PMMA thin film of 0.6 dB. From the perspective of the average output power and pulse energy variation with respect to the length of additional SMF-28, it can be deduced that the longer the fiber, the higher the resulting average output power and pulse energy. Based on the results, the value of maximum average output power, maximum pulse energy, and power slope efficiencies for each respective length of additional SMF-28 are tabulated in Table 2. The maximum average output power and maximum pulse energy increases from 4.93 to 5.99 mW and from 391.47 to 599.52 pJ, respectively, as the SMF-28 length increases from 0 to 4 m. It must be noted that the maximum average output power and pulse energy are not limited to these values, and higher values are expected to be obtained if a laser diode with a higher pump power is used. However, since this work is limited by a maximum available pump power of \(\sim\)100 mW, further demonstration of the average output power and pulse energy above that pump power could not be demonstrated.