# 10 Gb/s Bidirectional Transmission with an Optimized SOA and a SOA-EAM Based ONU
## 2 Optimizing the Performance of an SOA  
This section shows the effects of input power and bias current on the gain and noise figure (NF) of an SOA in detail, via a small-signal model analysis. By adjusting the variable optical attenuator (VOA) and direct current (DC), the input power and bias current of the SOA are transformed, respectively. The equation for NF measurement is as follows [21]:  
\[\mathrm{NF}\;=\;10\log_{10}[1/\mathrm{Gain}(\mathrm{P}_{\mathrm{ASE}}/\mathrm{ hv}\mathrm{B}_{0}+1)]\;(\mathrm{dB}) \tag{1}\]  
where h is the Planck constant, \(\mathrm{v}\) is the center frequency of the optical signal, and \(\mathrm{B}_{0}\) is the frequency bandwidth of a spectrometer; they remain unchanged under constant external conditions. We can infer that NF is proportional to the ratio of amplified spontaneous emission (ASE) power to gain. The parameters used for the simulation are listed in Table 1.  
Figure 1a depicts the effect of input power on the characteristics of the SOA. The increasing power of gain goes to the nearly flat region between \(-45\) dBm and \(-20\) dBm and the linear descent region from \(-20\) dBm to \(0\) dBm. The increasing power of NF goes to the almost flat region between \(-45\) dBm and \(-20\) dBm, the linear descent region from \(-20\) dBm to \(-10\) dBm, and the linear ascent region from \(-10\) dBm to \(0\) dBm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Active length & \(0.0011\) m \\ Active layer width & \(0.4\) μm \\ Active layer height & \(0.4\) μm \\ Optical confinement factor & \(0.45\) \\ Recombination coefficient A & \(3.6\times 10^{8}\) s\({}^{-1}\) \\ Recombination coefficient B & \(5.6\times 10^{-16}\) m\({}^{3}\)/s \\ Recombination coefficient C & \(3\times 10^{-41}\) m\({}^{6}\)/s \\ Group velocity & \(7.5\times 10^{7}\) m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters chosen for the simulation of the semiconductor optical amplifier (SOA). The SOA consumes a spot of carriers at a low level of input power, which can fully amplify the optical signal. Therefore, the gain remains a constant substantially because the output power increases with the input power correspondingly. With the input power increases, the rate of carrier consumption caused by stimulated radiation increases, leading to a new balance of carrier concentration in the active region at a lower level. Accordingly, the gain of the SOA decreases with the reduction of the magnification ability. Under the gain-flat region, the NF remains the same at first since the stimulated and spontaneous radiation increase accordingly. Then, the NF decreases in that the output ASE decreases and the output OSNR increases under the gradual saturation of the SOA. Lastly, the NF rises with the decreases in the OSNR as a result of the intense gain saturation of the SOA. Figure 1b depicts the influence of bias current on the characteristics of the SOA. The gain function is almost in linear ascent in the region of the bias current from 60 to 80 mA and nearly flat in the region between 80 mA and 200 mA. The NF with the input power from \(-15\) dBm to \(-45\) dBm is nearly flat and from 0 dBm to \(-15\) dBm is almost linear in descent in the region of the bias current from 60 to 100 mA and nearly flat in the region between 100 mA and 200 mA. The bias current has nothing to do with NF approximately at low input power. Figure 1: _Cont._  
There is a little gain due to the low carrier concentration of the SOA, and there is a high NF since the low carrier concentration makes the stimulated radiation weaker at small bias current. As shown in Figure 1b, the gain increases monotonically at first and then maintains the same level as the bias current level--which is because the carrier density of the SOA increases, and the system is restrained by the recovery time of the carrier density. The increase in carrier concentration enhances the stimulated emission, which leads to the decrease in NF.