## 4 Theoretical Modeling of RSOA-FCL  
In this section, we use the theoretical model of the RSOA-FCL developed in [21] to understand the improvements brought by an RSOA-FCL compared to an ASE spectrum-sliced source. A simplified simulation schematic is given in Figure 4. The RSOA is modeled as a bidirectional SOA as described in [29, 30]. The notations \(\vec{E}_{\text{out,RSOA}}^{(i)}(\text{v})\) and \(\vec{E}_{\text{in,RSOA}}^{(i)}(\text{v})\) represent the frequency domain optical field leaving and entering the RSOA, respectively, on the \(i^{th}\) round trip in the long cavity. \(H_{\text{fr}}(\text{v})\) is the fiber cavity frequency response that includes both the effects of chromatic dispersion and attenuation, (see [21]). The optical bandpass filter (OBPF) mimics the WGR filter and has a super Gaussian shape. It is given by \(H_{\text{OBPF}}(\text{v})\). \(R_{\text{RN}}\) and \(\eta_{\text{crp}}\) represent the remote node (RN) mirror reflectivity and the coupler output ratio, respectively. The overall cavity loss \(\alpha_{\text{VOA}}\) is determined by the variable optical attenuator (VOA). Figure 3: Operation principle of the RSOA-FCL. (**a**) RSOA-FCL with the three functions of the RSOA: (1) direct modulation; (2) amplification and (3) modulation suppression; (**b**) Output power and (**c**) gain _vs._ input power for RSOA. The RSOA static characteristics have two regions: a linear region where the input and output powers are linearly related (the gain is flat) and a nonlinear region where the output power does not change for increasing input power (the gain is suppressed for higher input power). Driving the RSOA in the nonlinear region allows operation such that modulation is suppressed. The optical field output \(E_{\text{out}}^{(i)}(\upsilon)\) of a signal emitted from the RSOA on the \(i^{\text{\tiny{th}}}\) cavity round trip is given by  
\[E_{\text{out}}^{(i)}(\upsilon)=\sqrt{\eta_{\text{\tiny{Cpr}}}}\cdot a_{\text{ \tiny{VOA}}}\cdot H_{\text{\tiny{GBPF}}}\big{(}\upsilon\big{)}\cdot H_{\text{ \tiny{Br}}}\big{(}\upsilon\big{)}\cdot\tilde{E}_{\text{\tiny{out,RSOA}}}^{(i)}(\upsilon) \tag{1}\]  
The reflected seeding optical field is given by  
\[E_{\text{\tiny{in,RSOA}}}^{(i)}(\upsilon)=\sqrt{R_{\text{\tiny{RN}}}(1\!-\! \eta_{\text{\tiny{Cpr}}})}\times\big{(}a_{\text{\tiny{VOA}}}\times H_{\text{ \tiny{GBPF}}}\big{(}\upsilon\big{)}\times H_{\text{\tiny{br}}}\big{(}\upsilon \big{)}\big{)}^{2}\times\tilde{E}_{\text{\tiny{out,RSOA}}}^{(i\!-\!1)}(\upsilon) \tag{2}\]  
The details of the model have been presented in [21]. Now we use this model in Figure 4 to show how placing a simple mirror behind the OBPF provides a higher power for the RSOA-FCL compared to a simpler ASE spectrum-sliced scheme. In the initial model, we consider the simplest case of a 15 m fiber cavity. We simulated the output power of the RSOA-FCL by varying the RN mirror reflectivity \(R_{\text{\tiny{RN}}}\) from \(-60\) dB to \(0\) dB. A \(R_{\text{\tiny{RN}}}\) of \(-60\) dB reflectivity is very low and thus represents the case of the ASE spectrum slicing (no mirror). Figure 5 plots the output optical power for different values of \(R_{\text{\tiny{RN}}}\) when the VOA is swept from \(5\) to \(32\) dB to mimic different cavity losses. Figure 4: Simplified RSOA-FCL simulation schematics: the RSOA mirror and a remote mirror with reflectivity \(R_{\text{\tiny{RN}}}\) form the fiber Fabry-Perot resonator cavity. The optical bandpass filter (OBPF) and the variable optical attenuator (VOA) represent the WDM filter and the cavity losses, respectively. Figure 5: Impact of RN mirror reflectivity \(R_{\text{\tiny{RN}}}\) and cavity loss on the optical output power of the RSOA-FCL. Depending on the \(R_{\text{\tiny{RN}}}\) and the losses, the source could be an ASE spectrum-sliced source (dashed blue line) or a RSOA-FCL laser (dashed red line). It is clearly visible that the output power follows one of two lines, either the dashed red or blue line.