## 4 Characterization of the Fiber Compound-Ring Lasers
### Coherent Beam Combining Efficiency  
The principle of the proposed passive coherent beam combining technique of two compound-ring-based fiber lasers with two adjustable output couplers (i.e., Sagnac loop mirrors) is based on a passive phase-locking mechanism due to spontaneous self-organization operation [56; 58]. Due to the wide bandwidth of the SOAs, the passive phase-locking mechanism allows the fields' self-adjustment to select common oscillating modes or resonant frequencies of the counter-propagating (i.e., clockwise and counter-clockwise) light beams in the two merged ring cavities and optimize their in-phase locking state conditions without any active phase modulating system. In order to determine the beam combining efficiency of the proposed fiber laser structure, we first used each individual SOA as gain medium in the common branch I of the compound-ring cavity and measured the output power produced by the fiber laser system at its both output couplers, OUT1 and OUT2. Then, we placed at the same time both SOAs, SOA\({}_{1}\) (Kamelian model) and SOA\({}_{2}\) (Thorlabs, S1013S), in the compound-ring cavities (branch I and II, respectively). Similarly, we measured the output power delivered at both output couplers of the proposed fiber laser. Note that the reflectivity \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SOA\({}_{1}\)\(I_{B1}\) (mA)** & **SOA\({}_{2}\)\(I_{B2}\) (mA)** & **P\({}_{OUT1}\) (dBm)** & **P\({}_{OUT2}\) (dBm)** & **3 dB-BW (nm)** \\ \hline
75 & 250 & 3.40 & 3.40 & 0.1985 \\
100 & 300 & 5.80 & 5.70 & 0.2075 \\
125 & 350 & 6.73 & 6.75 & 0.2122 \\
150 & 400 & 7.65 & 7.68 & 0.2131 \\
175 & 450 & 8.35 & 8.35 & 0.2157 \\
200 & 500 & 8.94 & 8.95 & 0.2182 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The 3-dB bandwidth (BW) at different bias current \(I_{B}\) (mA) levels and 1550-nm center wavelength with Sagnac loop mirror reflectivity set at <0.1%. Figure 4: Insertion losses (IL, shown by triangles, in dB), and full-width-half maximum (FWHM, shown by squares, in nm) spectra of the tunable optical filter. of the Sagnac loop mirrors, SLM\({}_{1}\) and SLM\({}_{2}\), was adjusted to maximum (i.e. >99.9%) and minimum (i.e., <0.1%), respectively. The tunable filter was manually adjusted from 1535 to 1565 nm and each semiconductor optical amplifier, SOA\({}_{1}\) and SOA\({}_{2}\), was driven and kept constant at its standard bias current, 200 and 500 mA, respectively. Figure 5 illustrates the passive coherent beam combining efficiency spectrum (right vertical axis) and the output power spectrum (left vertical axis) from the proposed fiber compound-ring laser operating with individual SOAs as well as both SOAs over the C-band tuning range of 30 nm. The beam combining efficiency (filled circles) was obtained by dividing the optical power measured at the output port (OUT2) when the fiber laser was operating with both SOAs by the power summation (unfilled triangles) of the same output port of the fiber laser while operating with individual SOA, SOA\({}_{1}\) (filled squares) and SOA\({}_{2}\) (unfilled circles), i.e., \(\eta=(P_{measured}/(P_{SOA1}+P_{SOA2}))\). The leakage optical power spectrum (unfilled squares) at the other output port (OUT\({}_{1}\)) remained below \(-\)28.5 dBm. The maximum output power delivered by the fiber laser operating with a single SOA, SOA\({}_{1}\) (Kamelian model) and SOA\({}_{2}\) (Thorlabs model), was +8.91 and +8.90 dBm at 1565 nm, respectively. On the other hand, when both SOAs were placed in the compound-ring cavities, the maximum measured output power obtained at the output port, OUT2, was +11.9 dBm at 1565 nm, which is almost double the output power obtained with either individual SOA placed in the fiber compound-ring laser cavity. Moreover, the maximum output power obtained by just adding the optical power from single SOA fiber laser operation at the output port, OUT2, was +11.91 dBm vs. +11.9 dBm measured output power from the fiber laser operating with both SOAs at 1565 nm wavelength.