Cladding-Pumped Erbium/Ytterbium Co-Doped Fiber Ampliﬁer for C-Band Operation in Optical Networks

: Space-division multiplexing (SDM) attracts attention to cladding-pumped optical ampliﬁers, but they suffer from a low pump power conversion efﬁciency. To address this issue, ytterbium (Yb 3+ ) and erbium (Er 3+ ) co-doping is considered as an effective approach. However, it changes the gain proﬁle of Er 3+ -doped ﬁber ampliﬁers and induces the gain difference between optical wavelengths in the C-band, signiﬁcantly limiting the effective band of the dense wavelength-division multiplexed (DWDM) system. This paper is devoted to a detailed study of a cladding-pumped Er 3+ /Yb 3+ co-doped ﬁber ampliﬁer (EYDFA) through numerical simulations aiming to identify a conﬁguration, before assembling a similar EYDFA in our laboratory premises that ensures the desired performance. The simulation model is based on a commercial double cladding EYDF whose parameters are experimentally extracted and fed to the EYDFA setup for the system-level studies. We investigate the wavelength dependence of the ampliﬁer’s characteristics (absolute gain, gain uniformity, noise ﬁgure) and bit error rate (BER) performance for several DWDM channels and their optical power. The obtained results show that a 7 m long EYDF and co-propagating pump direction is preferable for the EYDFA with a 3 W pump source at 975 nm and with the given gain medium characteristics for WDM applications. For instance, it ensures a gain of 19.7–28.3 dB and a noise ﬁgure of 3.7–4.2 dB when amplifying 40 DWDM channels with the input power of − 20 dBm per channel. Besides, we study EYDFA gain bandwidth and the maximum output power when operating close to the saturation regime and perform a sensitivity analysis showing how the doped ﬁber’s absorption and emission cross-sections impact the ampliﬁcation process through energy transfer from Yb 3+ to Er 3+ . Finally, we quantify the power penalty introduced by the EYDFA; the results show that it is not higher than 0.1 dB when amplifying 40 × 10 Gbps non-return-to-zero on-off keying signals from − 20 dBm/channel. sensitivity analysis for EYDF cross-sections shows how the energy transfer from Yb 3+ to Er 3+ ions impacts the ampliﬁer’s gain and noise ﬁgure values. Speciﬁcally, a ± 30% change in the cross-sections results in minor gain and noise ﬁgure changes—0.7 dB and 0.1 dB, respectively. The revealed characteristics are of importance for assembling and testing an in-house-made cladding-pumped EYDFA.

transmission over a 1500 km long 12-core MCF. A transoceanic distance of more than 8000 km is demonstrated in [17] where the authors used a 31.4 km long recirculation loop, consisting of a 19-core MCF and two cladding-pumped MC-EDFAs (for the C and the L bands separately) for the inline amplification of the dual-polarization quadrature phase-shift keying (DP-QPSK) signals. When it comes to long-haul transmission, amplifier characteristics, e.g., noise figure (NF), gain profile, etc., can significantly decrease the number of amplification spans a signal can traverse before impairments degrade its quality below a certain threshold. Using the transmission link configuration with an MC-EYDFA and with a standard EDFA, the authors in [5] investigate the impact that the IC-XT has on the maximum transmission distance (without regeneration) when operating with the 400G dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM). The investigation relies on the Gaussian noise (GN) model [19] to estimate the signal-to-noise ratio (SNR) after each 80 km long fiber span using the amplifier's NF and the IC-XT component. The results show that, for the considered scenario, the maximum transmission distance decreases from 11 spans to only eight spans when replacing the conventional inline EDFAs (NF = 4.5 dB) with the MC-EYDFAs (NF = 4.5 dB). For NF = 6.5 dB, the corresponding numbers are 11 and six spans, respectively. Therefore, the design of MC-EYDFAs should be carefully considered to reduce the impact on the maximum transmission distance while enabling cost and power savings. Yet, the impact that the design specifications of a cladding-pumped EYDFA (e.g., the length of Er 3+ /Yb 3+ co-doped fiber, pump power and propagation directions, and Er 3+ /Yb 3+ emission cross-sections) have on the amplifier's characteristics remain unclear, especially, when it comes to the wavelength dependence. This latter aspect is of importance for the use of such amplifiers to compensate optical losses in networks/links exploiting wavelength division multiplexing (WDM).
Therefore, in this article, we investigate the characteristics of an EYDFA under different operating conditions to assess the suitability for operation in a metro-access segment of optical transport networks where the dense wavelength-division multiplexing (DWDM) solutions are normally used. To perform the analysis, we have developed a simulation framework, consisting of a DWDM transmission system with up to 64 × 10 Gbps DWDM channels allocated using the fixed 100 GHz grid and a single-core cladding-pumped EYDFA of our design. The amplifier's model is adjusted using the experimentally extracted characteristics (e.g., overlap factor, absorption, and emission cross-sections) of the commercial Er 3+ /Yb 3+ co-doped fiber. The fiber's core is rare-earth-doped phosphosilicate glass, the inner cladding is pure silica, and the outer cladding is fluorine-doped silica glass. The EYDFA performance is evaluated in terms of gain (G), noise figure (NF), and the output signal bit error ratio (BER). We analyze the wavelength dependence of these characteristics by varying the number of DWDM channels and their optical power levels and scaling the fiber's emission and absorption cross-sections. Furthermore, we quantify the power penalty due to the amplification of 40 × 10 Gbps non-return-to-zero on-off keying (NRZ-OOK)-modulated wavelength channels. Note that a single-core configuration of the cladding-pumped EYDFA is used throughout the research to exclude distortions related to inter-core crosstalk (IC-XT) and cross-gain modulation and build a reference cladding-pumped EYDFA model for further studies.
The rest of the article is organized as follows. The simulation setup, alongside the description of the measurements and estimations of the gain medium parameters, is described in Section II. Section III analyzes the amplifier's performance under different operating conditions (number of DWDM channels, input optical power, absorption and emission characteristics of the Er 3+ /Yb 3+ doping) and quantifies the induced power penalty. Finally, Section IV summarizes the research findings.

Experimental Setup and Principles
The simulation setup used to characterize the performance of the developed claddingpumped EYDFA is shown in Figure 1. It is realized using VPIphotonics Design Suite [20], yet the absorption and emission cross-sections of the Er 3+ /Yb 3+ co-doped phosphosilicate Appl. Sci. 2021, 11, 1702 4 of 12 glass double-cladding fiber are experimentally measured in our laboratory and fed as the input data to the simulation setup ( Figure 1b). Besides, the overlap factor is estimated using the proposed red, green, blue (RGB) color approach applied to the EYDF cross-section images taken by a fiber microscope ( Figure 2). As we assume that EYDFA will be operated in metro-access segments of optical transport networks, the multi-wavelength operation is considered. Consequently, the setup includes three parts: (i) n × 10 Gbps OOK WDM transmitters; (ii) the realistic model of our EYDFA, consisting of the EYDF itself, optical pump source (central wavelength λ p = 975 nm at 25 • C and output power 3-5 W), highpower optical combiners/splitters, and the amplifier's test unit for the evaluation of its characteristics (e.g., gain spectrum and noise figure (NF)); and (iii) WDM (de-)multiplexers and receivers for signal quality estimation (not shown in Figure 1).

Experimental Setup and Principles
The simulation setup used to characterize the performance of the developed cladding-pumped EYDFA is shown in Figure 1. It is realized using VPIphotonics Design Suite [20], yet the absorption and emission cross-sections of the Er 3+ /Yb 3+ co-doped phosphosilicate glass double-cladding fiber are experimentally measured in our laboratory and fed as the input data to the simulation setup ( Figure 1b). Besides, the overlap factor is estimated using the proposed red, green, blue (RGB) color approach applied to the EYDF cross-section images taken by a fiber microscope ( Figure 2). As we assume that EYDFA will be operated in metro-access segments of optical transport networks, the multi-wavelength operation is considered. Consequently, the setup includes three parts: (i) n × 10 Gbps OOK WDM transmitters; (ii) the realistic model of our EYDFA, consisting of the EYDF itself, optical pump source (central wavelength λp = 975 nm at 25 °C and output power 3-5 W), high-power optical combiners/splitters, and the amplifier's test unit for the evaluation of its characteristics (e.g., gain spectrum and noise figure (NF)); and (iii) WDM (de-)multiplexers and receivers for signal quality estimation (not shown in Figure 1).  The key component of this optical back to back (OB2B) setup is a fiber model. For our purposes, we use a stationary fiber model from VPIphotonics Design Suite [20] that can be used for Er 3+ /Yb 3+ co-doped cladding-pumped fiber amplifiers. According to its description, this model is based on the bidirectional propagation equations for signals and multilevel rate equations for ion populations. To tune this model with the respect to our EYDF, we use the measured cross-sections to specify the emission and absorption spectra, and the overlap factors to specify the WDM signal (~1550 nm) and the pump signal (~975 nm) coupling and their propagation (which depends on fiber profile and dimensions). The model is resolved in both the longitudinal and transverse directions considering the number of effects, e.g., Er 3+ /Yb 3+ energy transfer, cross-relaxation effects, excited-state absorption, Rayleigh scattering, and Kerr nonlinearity. The summary of the setup parameters is given in Table 1.  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. Although this process may include a certain error due to the ambiguous edge detection of the fiber's core and inner cladding [28], it has an insignificant impact on the estimated overlap factor. When all edges are identified, an RGB color is assigned to each segment and they are recolored (see Figure 2b). The number of red (outer cladding), green (inner cladding), and blue (core) pixels are counted and used for the estimations.
For our EYDF, Ac = 658 pixels, Aicl = 112,828 pixels, and the outer cladding area Aocl = 122,598 pixels, which gives us Γ = 0.0058 and Aicl/Aocl = 0.9203. Both these parameters are further used as input to the simulation setup.

Results and Discussion
In this section, we reveal how the EYDFA's configuration parameters, such as the Er 3+ /Yb 3+ co-doped fiber's length, its absorption and emission cross-sections, and the pump signal direction, impact its wavelength-dependent characteristics, namely, gain uniformity, noise figure, and maximum output power. Before the evaluation of an EYDFA-induced power penalty, we characterize its performance for a multiwavelength scenario by varying the number of DWDM channels and their power levels. The goal of these simulations is to find the most appropriate amplifier configuration that introduces the least distortion while ensuring the most uniform gain spectrum possible. Throughout the analysis, we use an optical pump source operating at λp = 975 nm and 3 W of output power. These values are selected based on the specifications of our high-power light source in the laboratory. We consider both the co-propagation and counter-propagation directions for the pump signal.
To select the length of the EYDF and the direction of the pump signal, we use the curves obtained for a 40-channel WDM system showing how the amplifier gain, noise  The key component of this optical back to back (OB2B) setup is a fiber model. For our purposes, we use a stationary fiber model from VPIphotonics Design Suite [20] that can be used for Er 3+ /Yb 3+ co-doped cladding-pumped fiber amplifiers. According to its description, this model is based on the bidirectional propagation equations for signals and multilevel rate equations for ion populations. To tune this model with the respect to our EYDF, we use the measured cross-sections to specify the emission and absorption spectra, and the overlap factors to specify the WDM signal (~1550 nm) and the pump signal (~975 nm) coupling and their propagation (which depends on fiber profile and dimensions). The model is resolved in both the longitudinal and transverse directions considering the number of effects, e.g., Er 3+ /Yb 3+ energy transfer, cross-relaxation effects, excited-state absorption, Rayleigh scattering, and Kerr nonlinearity. The summary of the setup parameters is given in Table 1. The simulation model includes parameters that specify both the WDM system and the EYDFA under test. In this case, we operate with a 10 Gbps NRZ-OOK signal whose central frequencies are arranged across the C-band (1530-1565 nm) using a 100 GHz grid. Although we consider the WDM configuration with the total number of channels up to n = 64, channels 41-64 are outside of the C-band (f c > 195.6 THz). They are used to highlight the wavelength dependence of the amplifier's gain and noise figure characteristics, especially for high (>−10 dBm/channel) and low (<−25 dBm/channel) input signal powers. The category "EYDFA pump parameters" provides details about the optical pump source and its direction with respect to the signal propagation. Finally, the category "doped fiber parameters" includes the measured, estimated, and given characteristics of our EYDF used to build the EYDFA in the laboratory.
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 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 (Γ) of doublecladding optical fiber is defined as a ratio between its core area (A c ) and inner cladding (A icl ) area [25]: 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. Although this process may include a certain error due to the ambiguous edge detection of the fiber's core and inner cladding [28], it has an insignificant impact on the estimated overlap factor. When all edges are identified, an RGB color is assigned to each segment and they are recolored (see Figure 2b). The number of red (outer cladding), green (inner cladding), and blue (core) pixels are counted and used for the estimations.
For our EYDF, A c = 658 pixels, A icl = 112,828 pixels, and the outer cladding area A ocl = 122,598 pixels, which gives us Γ = 0.0058 and A icl /A ocl = 0.9203. Both these parameters are further used as input to the simulation setup.

Results and Discussion
In this section, we reveal how the EYDFA's configuration parameters, such as the Er 3+ /Yb 3+ co-doped fiber's length, its absorption and emission cross-sections, and the pump signal direction, impact its wavelength-dependent characteristics, namely, gain uniformity, noise figure, and maximum output power. Before the evaluation of an EYDFAinduced power penalty, we characterize its performance for a multiwavelength scenario by varying the number of DWDM channels and their power levels. The goal of these simulations is to find the most appropriate amplifier configuration that introduces the least distortion while ensuring the most uniform gain spectrum possible. Throughout the analysis, we use an optical pump source operating at λp = 975 nm and 3 W of output power. These values are selected based on the specifications of our high-power light source in the laboratory. We consider both the co-propagation and counter-propagation directions for the pump signal.
To select the length of the EYDF and the direction of the pump signal, we use the curves obtained for a 40-channel WDM system showing how the amplifier gain, noise figure, and the maximum output power change with the EYDF length (see Figure 3). The results show that the maximum gain is reached for an 8 m long EYDF regardless of the pump direction (Figure 3a). A longer EYDF does not result in a higher gain, which is explained by the depletion of the pump radiation. A further increase in doped fiber length not only cannot produce additional gain, but the amplified signal power also starts to decrease due to the attenuation of the EYDF itself. Furthermore, the amplifier becomes noisier, especially for the configuration where the signal and the pump are launched in the counter-propagating directions (Figure 3b). Otherwise, the noise figure is not larger than 4.5 dB (co-propagation) and 6 dB (counter-propagation). Finally, Figure 3c shows the maximum gain difference detected for Channels 1 to 40 (Ch1-Ch40) in the 40-channel DWDM system with the input optical power of −20 dBm/channel. Appl. Sci. 2021, 11, 1702 7 of 12 than 4.5 dB (co-propagation) and 6 dB (counter-propagation). Finally, Figure 3c shows the maximum gain difference detected for Channels 1 to 40 (Ch1-Ch40) in the 40-channel DWDM system with the input optical power of −20 dBm/channel. The gain uniformity is an important characteristic, especially for systems with several amplification spans. Unless all DWDM channels are amplified equally, the power difference increases with every span, limiting the maximum transmission distance. The smallest gain difference (∆G < 9 dB) is obtained for a 7 m long EYDF for both the co-propagation and counter-propagation of the 975 nm pump signal. It is significantly larger for shorter and longer EYDF segments, which indicates that an appropriate level of ion population inversion is achieved for this specific combination of the pump power (3 W) and the EYDF length (7 m). Therefore, we keep these parameters unchanged. Finally, we choose to use the pump signal in the co-propagation direction. Although the counter-propagation ensures a 0.9-1 dB higher gain, its cost is a higher noise figure, which is almost 1 dB higher compared to the co-propagation case. Therefore, we choose a lower noise figure over a higher gain. Figure 4a shows the output (parametrized) spectrum, whereas Figure 4b shows the individual gain and noise figure of each EYDFA-amplified DWDM channel. Due to the wavelength-dependent gain and noise figure of the amplifier, the output spectrum is not uniform. Specifically, the amplifier's output power levels change from 0.1 to 8.3 dBm per channel (dBm/channel, see Figure 4a), resulting in a gain difference of 19.7-28.3 dB, and the noise figure changes from 3.7 dB to 4.2 dB (Figure 4b). The input optical power (pIN) was set to −20 dBm/channel in all 40 WDM channels considered. The gain uniformity is an important characteristic, especially for systems with several amplification spans. Unless all DWDM channels are amplified equally, the power difference increases with every span, limiting the maximum transmission distance. The smallest gain difference (∆G < 9 dB) is obtained for a 7 m long EYDF for both the co-propagation and counter-propagation of the 975 nm pump signal. It is significantly larger for shorter and longer EYDF segments, which indicates that an appropriate level of ion population inversion is achieved for this specific combination of the pump power (3 W) and the EYDF length (7 m). Therefore, we keep these parameters unchanged. Finally, we choose to use the pump signal in the co-propagation direction. Although the counter-propagation ensures a 0.9-1 dB higher gain, its cost is a higher noise figure, which is almost 1 dB higher compared to the co-propagation case. Therefore, we choose a lower noise figure over a higher gain. Figure 4a shows the output (parametrized) spectrum, whereas Figure 4b shows the individual gain and noise figure of each EYDFA-amplified DWDM channel. Due to the wavelength-dependent gain and noise figure of the amplifier, the output spectrum is not uniform. Specifically, the amplifier's output power levels change from 0.1 to 8.3 dBm per channel (dBm/channel, see Figure 4a), resulting in a gain difference of 19.7-28.3 dB, and the noise figure changes from 3.7 dB to 4.2 dB (Figure 4b). The input optical power (p IN ) was set to −20 dBm/channel in all 40 WDM channels considered.
Appl. Sci. 2021, 11, 1702 7 of 12 than 4.5 dB (co-propagation) and 6 dB (counter-propagation). Finally, Figure 3c shows the maximum gain difference detected for Channels 1 to 40 (Ch1-Ch40) in the 40-channel DWDM system with the input optical power of −20 dBm/channel. The gain uniformity is an important characteristic, especially for systems with several amplification spans. Unless all DWDM channels are amplified equally, the power difference increases with every span, limiting the maximum transmission distance. The smallest gain difference (∆G < 9 dB) is obtained for a 7 m long EYDF for both the co-propagation and counter-propagation of the 975 nm pump signal. It is significantly larger for shorter and longer EYDF segments, which indicates that an appropriate level of ion population inversion is achieved for this specific combination of the pump power (3 W) and the EYDF length (7 m). Therefore, we keep these parameters unchanged. Finally, we choose to use the pump signal in the co-propagation direction. Although the counter-propagation ensures a 0.9-1 dB higher gain, its cost is a higher noise figure, which is almost 1 dB higher compared to the co-propagation case. Therefore, we choose a lower noise figure over a higher gain. Figure 4a shows the output (parametrized) spectrum, whereas Figure 4b shows the individual gain and noise figure of each EYDFA-amplified DWDM channel. Due to the wavelength-dependent gain and noise figure of the amplifier, the output spectrum is not uniform. Specifically, the amplifier's output power levels change from 0.1 to 8.3 dBm per channel (dBm/channel, see Figure 4a), resulting in a gain difference of 19.7-28.3 dB, and the noise figure changes from 3.7 dB to 4.2 dB (Figure 4b). The input optical power (pIN) was set to −20 dBm/channel in all 40 WDM channels considered. Next, we explore the EYDFA characteristics (namely gain, maximum gain difference, and noise figure) under different operating conditions by varying the number of DWDM channels and their optical power levels. During the analysis, we consider a DWDM configuration with 1, 2, 4, 8, 16, 32, 40, and 64 channels, whose power levels are set between −25 and −10 dBm/channel, see Figure 5. The output power curves (Figure 5a) show that the higher the number of DWDM channels, the smaller the output power difference. The amplifier saturates and eventually it fails to amplify more than 40 DWDM channels even if their power is as low as −25 dBm/channel. When analyzing the output power curve for p IN = −25 dBm/channel, we have noticed that the output power levels increase by 3.5 dB when the number of DWDM channels is increased from two to four. However, the corresponding number is 4.3 dB when the number of DWDM channels is increased from 16 to 32 channels. Such behavior indicates that low-power optical signals (i.e., with low input power and/or a small number of channels) are not able to completely exploit the population inversion generated in the gain media. Consequently, the unused portion of the population inversion eventually generates an excessive amount of amplified spontaneous emission (ASE) noise, which results in a poor noise figure, see Figure 5c. On the contrary, high input power consumes the achieved population inversion, in such a way that the obtained gain is reduced and the output power reaches its limit. For instance, the output power increases by 0.3 dB when an additional eight channels (p IN = −25 dBm/channel) are added to a DWDM system with 32 channels, and it remains similar even when the number of channels is increased to 64. A higher pump signal power also does not result in a higher gain or a higher output power. Even if a 4 W pump signal is used, the output power increases by not more than 0.  Next, we explore the EYDFA characteristics (namely gain, maximum gain difference, and noise figure) under different operating conditions by varying the number of DWDM channels and their optical power levels. During the analysis, we consider a DWDM configuration with 1, 2,4,8,16,32,40, and 64 channels, whose power levels are set between −25 and −10 dBm/channel, see Figure 5. The output power curves (Figure 5a) show that the higher the number of DWDM channels, the smaller the output power difference. The amplifier saturates and eventually it fails to amplify more than 40 DWDM channels even if their power is as low as −25 dBm/channel. When analyzing the output power curve for pIN = −25 dBm/channel, we have noticed that the output power levels increase by 3.5 dB when the number of DWDM channels is increased from two to four. However, the corresponding number is 4.3 dB when the number of DWDM channels is increased from 16 to 32 channels. Such behavior indicates that low-power optical signals (i.e., with low input power and/or a small number of channels) are not able to completely exploit the population inversion generated in the gain media. Consequently, the unused portion of the population inversion eventually generates an excessive amount of amplified spontaneous emission (ASE) noise, which results in a poor noise figure, see Figure 5c. On the contrary, high input power consumes the achieved population inversion, in such a way that the obtained gain is reduced and the output power reaches its limit. For instance, the output power increases by 0.3 dB when an additional eight channels (pIN = −25 dBm/channel) are added to a DWDM system with 32 channels, and it remains similar even when the number of channels is increased to 64. A higher pump signal power also does not result in a higher gain or a higher output power. Even if a 4 W pump signal is used, the output power increases by not more than 0.2-0.3 dB for a 40-channel configuration with pIN = −20 dBm/channel. Therefore, the maximum output power of the proposed EYDFA is limited to approximately 22 dBm. The maximum gain difference curves (Figure 5b) show the following trend-the higher the input power, the smaller the gain difference in a DWDM system with 4-32 channels. The main reason is that a higher portion of population inversion is consumed to achieve similar levels of amplification for higher input power signals. Therefore, at a certain level of population inversion, optical signals with higher power get less amplified The maximum gain difference curves (Figure 5b) show the following trend-the higher the input power, the smaller the gain difference in a DWDM system with 4-32 channels. The main reason is that a higher portion of population inversion is consumed to achieve similar levels of amplification for higher input power signals. Therefore, at a certain level of population inversion, optical signals with higher power get less amplified and the gain difference between the channels becomes smaller. However, the opposite situation is observed for 40 DWDM channels, where the gain difference becomes higher for higher input signal powers (e.g., compare −25 dB/channel and −10 dBm/channel curves). Such behavior occurs because higher power signals drain the ion population inversion more efficiently. The increase in the DWDM channel count to 40 in the case of a −25 dBm input signal changes the average level of population inversion throughout the EYDF to a value that provides more equal gain in the transmission system frequency band. Therefore, we observe a more uniform gain (amplification) of all 40 DWDM channels with p IN = −25 dBm/channel, whereas for −10 dBm/channel, the population inversion is drained much faster before the similar uniformity is achieved. A similar tendency is observed for the EYDFA's noise figure (Figure 5c). For channels with p IN ≥ −20 dBm/channel, the noise figure first decreases with every additional DWDM channel until the number of channels (and their combined power level) reaches a certain optimum point, exceeding which the noise figure starts increasing. For fewer power channels, the noise figure first increases by 0.5-1 dB and then starts decreasing, reaching 4-4.5 dB for 32-40 DWDM channels. The insets in Figure 5b,c show that the gain difference and the noise figure increasing dramatically when the number of DWDM channels exceeds 40, which confirms the bandwidth limitations of the amplifier. Signals outside the operation band get absorbed by the EYDF.
In Er 3+ /Yb 3+ co-doped fibers, Yb 3+ absorb the pump radiation and then resonantly transfer a portion of their energy to Er 3+ for signal amplification. We perform a sensitivity analysis showing how the absorption and the emission cross-sections of our EYDF impact the amplification process. For this purpose, we assume the cross-sections to be 70% (k = 1) and 130% (k = 1.3) of the initially estimated values (k = 1). Figure 6 shows the differences in the performance characterized using the excited ion percentage (Figure 6a), per channel gain, and noise figure (Figure 6b). We observe that, for k = 0.7, the peak of the excited Yb 3+ percentage becomes smaller (approximately by 5%) and moves further into the EYDF by changing its axial position. Consequently, the depletion of the population inversion is smoothed out on all energy levels, allowing the amplified signal to accumulate a certain part of the pump energy and therefore improving its ability to consume larger portions of the population inversion. This extends the length of the EYDF where the signal amplification occurs effectively, leading to a higher gain (by~0.7 dB) and a lower noise figure (by~0.1 dB). On the contrary, for larger cross-sections (k = 1.3), the Yb 3+ peak moves towards the signal/pump source (axial position = 0.7 m) and gets smoothed out, which brings a lower gain and a higher noise figure. and the gain difference between the channels becomes smaller. However, the opposite situation is observed for 40 DWDM channels, where the gain difference becomes higher for higher input signal powers (e.g., compare −25 dB/channel and −10 dBm/channel curves). Such behavior occurs because higher power signals drain the ion population inversion more efficiently. The increase in the DWDM channel count to 40 in the case of a −25 dBm input signal changes the average level of population inversion throughout the EYDF to a value that provides more equal gain in the transmission system frequency band. Therefore, we observe a more uniform gain (amplification) of all 40 DWDM channels with pIN = −25 dBm/channel, whereas for −10 dBm/channel, the population inversion is drained much faster before the similar uniformity is achieved. A similar tendency is observed for the EYDFA's noise figure (Figure 5c). For channels with pIN ≥ −20 dBm/channel, the noise figure first decreases with every additional DWDM channel until the number of channels (and their combined power level) reaches a certain optimum point, exceeding which the noise figure starts increasing. For fewer power channels, the noise figure first increases by 0.5-1 dB and then starts decreasing, reaching 4-4.5 dB for 32-40 DWDM channels. The insets in Figure 5b,c show that the gain difference and the noise figure increasing dramatically when the number of DWDM channels exceeds 40, which confirms the bandwidth limitations of the amplifier. Signals outside the operation band get absorbed by the EYDF.
In Er 3+ /Yb 3+ co-doped fibers, Yb 3+ absorb the pump radiation and then resonantly transfer a portion of their energy to Er 3+ for signal amplification. We perform a sensitivity analysis showing how the absorption and the emission cross-sections of our EYDF impact the amplification process. For this purpose, we assume the cross-sections to be 70% (k = 1) and 130% (k = 1.3) of the initially estimated values (k = 1). Figure 6 shows the differences in the performance characterized using the excited ion percentage (Figure 6a), per channel gain, and noise figure (Figure 6b). We observe that, for k = 0.7, the peak of the excited Yb 3+ percentage becomes smaller (approximately by 5%) and moves further into the EYDF by changing its axial position. Consequently, the depletion of the population inversion is smoothed out on all energy levels, allowing the amplified signal to accumulate a certain part of the pump energy and therefore improving its ability to consume larger portions of the population inversion. This extends the length of the EYDF where the signal amplification occurs effectively, leading to a higher gain (by ~0.7 dB) and a lower noise figure (by ~0.1 dB). On the contrary, for larger cross-sections (k = 1.3), the Yb 3+ peak moves towards the signal/pump source (axial position = 0.7 m) and gets smoothed out, which brings a lower gain and a higher noise figure. Finally, the BER performance is evaluated for a 40-channel configuration of the DWDM system with and without the EYDFA (see Figure 7). The BER values are obtained for four channels: Ch1 with fc = 191.6 THz (the beginning of the C-band), Ch16 with fc = 193.1 THz (the anchor frequency of the DWDM grid), Ch26 with fc = 194.1 THz (gives the peak gain), and Ch40 with fc = 195.5 THz (the end of the C-band), but Figure 7 shows the largest BER at a particular value of the received power. To obtain statistically reliable results, we use a 2 15 -1 uniquely seeded pseudorandom binary sequence (PRBS) to obtain 2 13 bits used for the simulations and BER estimation that relies on the stochastic signal and noise representation. Specifically, the noise is added to the signal and the probability density function of the detected signal is approximated with the chi-square function. The EYDFA parameters remain unchanged (7 m EYDF, 3 W, 975 nm, co-propagation), and the input optical power is set to −20 dBm per WDM channel.
193.1 THz (the anchor frequency of the DWDM grid), Ch26 with fc = 194.1 THz (gives the peak gain), and Ch40 with fc = 195.5 THz (the end of the C-band), but Figure 7 shows the largest BER at a particular value of the received power. To obtain statistically reliable results, we use a 2 15 -1 uniquely seeded pseudorandom binary sequence (PRBS) to obtain 2 13 bits used for the simulations and BER estimation that relies on the stochastic signal and noise representation. Specifically, the noise is added to the signal and the probability density function of the detected signal is approximated with the chi-square function. The EYDFA parameters remain unchanged (7 m EYDF, 3 W, 975 nm, co-propagation), and the input optical power is set to −20 dBm per WDM channel.
The results in Figure 7 shows the power penalty below 0.1 dB at the reference level of BER = 10 −9 compared to the configuration without the amplification. Such distortion levels can be considered as negligible. However, its gain spectra should be flattened out, e.g., by using gain flattening filters or several amplification stages, before such amplifiers can be efficiently used for optical loss compensation in WDM transmission systems. However, this aspect deserves separate attention and thus will be addressed in future work.

Conclusions
The performance of the cladding-pumped EYDFA is characterized using the developed measurement data-based simulation framework. Through the analysis of the amplifier's gain, noise figure, and power penalty, we assess its suitability for operation in metroaccess optical transport networks where DWDM techniques are normally deployed. First, we experimentally characterize the double cladding Er 3+ /Yb 3+ co-doped fiber used as a gain medium for our amplifier to come up with the realistic model of the EYDF. Next, we test different EYDFA configurations under different operating conditions (including various doped fiber lengths, pump propagation directions, signal input power, etc.) to reveal parameter settings ensuring the best amplification characteristics, namely, high and uniform gain, and low noise figure. Finally, its power penalty is quantified using 40 × 10 Gbps NRZ-OOK signals and the DWDM system configuration with and without the EYDFA. The results show that the amplifier configuration with a 3 W pump source at 975 nm requires a 7 m long EYDF (with the obtained physical parameters) and a co-propagation pumping direction for WDM applications. Considering a reasonably low input signal power (~ −20 dBm/channel), the EYDFA can be used to amplify up to 40 DWDM channels The results in Figure 7 shows the power penalty below 0.1 dB at the reference level of BER = 10 −9 compared to the configuration without the amplification. Such distortion levels can be considered as negligible. However, its gain spectra should be flattened out, e.g., by using gain flattening filters or several amplification stages, before such amplifiers can be efficiently used for optical loss compensation in WDM transmission systems. However, this aspect deserves separate attention and thus will be addressed in future work.

Conclusions
The performance of the cladding-pumped EYDFA is characterized using the developed measurement data-based simulation framework. Through the analysis of the amplifier's gain, noise figure, and power penalty, we assess its suitability for operation in metro-access optical transport networks where DWDM techniques are normally deployed. First, we experimentally characterize the double cladding Er 3+ /Yb 3+ co-doped fiber used as a gain medium for our amplifier to come up with the realistic model of the EYDF. Next, we test different EYDFA configurations under different operating conditions (including various doped fiber lengths, pump propagation directions, signal input power, etc.) to reveal parameter settings ensuring the best amplification characteristics, namely, high and uniform gain, and low noise figure. Finally, its power penalty is quantified using 40 × 10 Gbps NRZ-OOK signals and the DWDM system configuration with and without the EYDFA. The results show that the amplifier configuration with a 3 W pump source at 975 nm requires a 7 m long EYDF (with the obtained physical parameters) and a co-propagation pumping direction for WDM applications. Considering a reasonably low input signal power (~−20 dBm/channel), the EYDFA can be used to amplify up to 40 DWDM channels across the C-band, ensuring a maximum output power of +22 dBm, a gain of 19.7-28.3 dB, a noise figure of 3.7-4.2 dB, and a power penalty (with respect to a system without amplification) below 0.1 dB at a BER level of 10 −9 . Finally, the performed sensitivity analysis for EYDF cross-sections shows how the energy transfer from Yb 3+ to Er 3+ ions impacts the amplifier's gain and noise figure values. Specifically, a ±30% change in the cross-sections results in minor gain and noise figure changes-0.7 dB and 0.1 dB, respectively. The revealed characteristics are of importance for assembling and testing an in-house-made cladding-pumped EYDFA.