# Cladding-Pumped Erbium/Ytterbium Co-Doped Fiber Amplifier for C-Band Operation in Optical Networks
## 2 Experimental Setup and Principles
To estimate the EYDF absorption cross-section, we use Er\({}^{3+}\) and Yb\({}^{3+}\) ion absorption spectra obtained using a measurement setup consisting of Agilent's Cary 7000 Universal Measurement Spectrophotometer [21], FiberMate2 TM Fiber Optic Coupler system from Harrick Scientific Products Inc. [22], and two EYDF samples of different lengths. A 1 m long EYDF sample is used to perform the absorption spectra measurements around a 975 nm wavelength, whereas a 19 m long sample was used for wavelengths around 1550 nm. In such a way, we avoid the saturation effect that might distort the absorption spectra measurements. The absorption around 975 nm is attributed to \({}^{2}\)F\({}_{7/2}\) \(>\) \({}^{2}\)F\({}_{5/2}\) and \({}^{4}\)I\({}_{15/2}\) \(>\) \({}^{4}\)I\({}_{11/2}\) optical transitions of Yb\({}^{3+}\) and Er\({}^{3+}\), respectively. However, the impact of Er\({}^{3+}\) can be neglected since its absorption cross-section is significantly lower than that of Yb\({}^{3+}\)[23]. Furthermore, according to the specification, the EYDF has a 20 times higher Yb\({}^{3+}\) concentration compared to the Er\({}^{3+}\) concentration. The absorption cross-section is estimated using the measured absorption spectra, the ratio between the fiber's core and \begin{table}
\begin{tabular}{c c} \hline \hline  & **System Parameters** \\ \hline Bitrate and modulation & 10 Gbps non-return-to-zero on-off keying \\ \hline Number of channels (\(n\)) & 1, 2, 4, 8, 16, 32, 40, 64 (41–64 outside of C-band) \\ \hline The carrier frequency of the first/last channel & 191.6/195.5 THz \\ \hline Channel spacing & 100 GHz \\ \hline Single channel power & \(-25\) dBm/channel to \(-10\) dBm/channel \\ \hline \hline \multicolumn{3}{c}{**EYDFA Pump Parameters**} \\ \hline Pump wavelength & 975 nm at temperature = 25 \({}^{\circ}\)C \\ \hline Pump power & 3 W, (operational range 0.3–5 W) \\ \hline Direction & Co-/counter propagation \\ \hline \multicolumn{3}{c}{**Doped fiber parameters**} \\ \hline Length & 1–10 m \\ \hline Er\({}^{3+}\) concentration & \(1\times 10^{25}\) m\({}^{-3}\) \\ \hline Yb\({}^{3+}\) concentration & \(2\times 10^{26}\) m\({}^{-3}\) \\ \hline Er\({}^{3+}\)/Yb\({}^{3+}\) cross-relaxation coefficient & \(1\times 10^{-22}\) m\({}^{3}\)/s \\ \hline Core area/inner cladding area & 0.0058 \\ (A\({}_{\text{core}}\)/A\({}_{\text{inner cladding}}\)) & 0.9203 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the amplifier’s schematic parameters. inner cladding areas, its length, and Yb\({}^{3+}\)/Er\({}^{3+}\) concentrations. The emission cross-section is estimated using the McCumber relation [24] connecting emission and absorption spectra. Finally, the overlap factor is estimated using the RGB color approach that relies on the graphical post-processing of images of the doped fiber cross-section magnified by a microscope objective lens (see Figure 2). In general, the overlap factor (\(\Gamma\)) of double-cladding optical fiber is defined as a ratio between its core area (\(A_{c}\)) and inner cladding (\(A_{icl}\)) area [25]:  
\[\Gamma=\ \frac{A_{c}}{A_{icl}} \tag{1}\]  
Since the inner cladding is usually formed into a specific shape (e.g., star shape [25], D shape [26], or even flower shape [27]), the estimation of its area becomes a task in itself since fiber manufacturers tend to provide only overall geometrical dimensions, whereas parameters such as core and cladding areas and ion concentrations, which are crucial when building and analyzing doped fiber amplifiers (DFAs), remain unrevealed. Similarly, in our case, the manufacturer of the EYDF provides information only about its geometrical dimensions (see Figure 2a) and the ratio between Er\({}^{3+}\)/Yb\({}^{3+}\) concentrations. Therefore, the overlap factor is estimated using the proposed RGB approach. First, the gray-scale image from the microscope is used to identify the borders between the core, the inner cladding, and the outer cladding.