# Impact of Intracavity Power Variations toward Ultrashort Pulse Generation
## 5 Pulse Laser Performance  
In this work, nine sets of experiments were conducted to determine the efficiency of generating ultrashort pulses. From these, four sets of experiments that used 60%, 70%, 80% and 90% arms as the output coupling ratio cannot produce stable lasers. Therefore, only five sets of experiments that generated stable lasers are analyzed throughout this report. Figure 7a shows the laser output for a 30% output coupling ratio at 99 mW pump power as an example of the analysis. The central wavelength of the laser is about 1557.5 nm, which indicates moderate population inversion of the erbium system. Its spectral bandwidth of 3.78 nm is obtained from this arrangement. It is important to note that the laser spectrum consists of symmetrical Kelly sidebands as the indication of mode-locked pulse formation in the cavity. We also confirm this pulse phenomenon with the presence of a pulse train in the oscilloscope that is measured simultaneously. Figure 7b depicts the central lasing wavelength and associated spectral bandwidth from 10% to 50% output coupling ratio. The pulse formation is also confirmed by the appearance of a pulse train in the oscilloscope, as previously explained. For the analysis of spectral bandwidth, the largest value of 3.78 nm is observed using a 30% output coupling ratio. While the lowest value of 2.31 nm is recorded using a 10% output coupling ratio. Furthermore, the spectral bandwidth value is also decreased to 2.66 nm. The lasing bandwidth is associated with the strength of the soliton mode-locking mechanism that is influenced by the balance of dispersion and nonlinearity. However, the former factor is almost negligible because the total length and type of fiber are kept constant throughout the experiment. Thus, the latter factor is the main contributor to this observation, which can be explained by the dynamics of light amplification in the EDF. In this case, the 30% output coupling ratio is the optimum condition to harness the widest spectral bandwidth that leads to the shortest pulse formation. Figure 6: Experimental setup of mode-locked EDFL with GNP-SA (**a**) schematic diagram and (**b**) actual layout. To explain the lasing wavelength properties, it is important to relate this phenomenon with the condition of population inversion level in the EDF. Based on the Giles parameter in the classical optical amplifier model, the gain coefficient \(G_{c}(\lambda)\) of the EDF is governed by the following equation [50]:  
\[G_{c}(\lambda)=\eta(g(\lambda)+\alpha(\lambda))-\alpha(\lambda) \tag{2}\]  
where \(\eta\) is the population inversion factor, \(g(\lambda)\) and \(\alpha(\lambda)\) are the wavelength-dependent emission and absorption coefficient, respectively. The population inversion value is the key parameter to determine the peak gain that determines the lasing wavelength in a cavity. To relate between the gain coefficient and intracavity power associated to this work, a schematic diagram is drawn, as illustrated in Figure 8a. To simplify, we present two conditions of intracavity power: low (X) and high (Y). Similarly, in this case, X and Y represent high and low output coupling ratios, respectively. Referring to Figure 6, the EDF is injected by the 0.98 \(\upmu\)m pump light in a forward-pumping scheme. The circulating light (1.53-1.56 \(\upmu\)m) and 0.98 mm pump light propagate in the same direction at the EDF input as illustrated in Figure 8b. The pump energy is absorbed at the input end of the EDF, and most of the electrons are excited to a higher energy level. However, the number of photon counts for X and Y are different. For Y, since the intracavity power is larger, more photons are generated through stimulated emission processes. Under this condition, more energy at the pump light is absorbed. Towards the end of EDF, the pump energy is absorbed faster which leads to a greater length of pump depletion region represented by the shaded area.