## 4 Theoretical Modeling of RSOA-FCL
These two dashed lines represent one of two states of operation: the lasing source state (red), and ASE spectrum-sliced source state (blue), respectively. For \(R_{\text{RN}}\) = 60 dB (blue solid line), the output power stays close to the blue dashed line. As \(R_{\text{RN}}\) increases to 0 dB, the optical power increases and reaches the red dashed line that shows lasing. The transition from the ASE source operation to the lasing operation occurs when the RSOA gain is able to compensate for the cavity losses. Therefore, if the source is designed as a RSOA-FCL it will have a power advantage of \(\thicksim\)8 dB over an ASE spectrum-sliced source. Another difference between the RSOA-FCL is in the optical spectrum, which is narrower compared to that of an ASE spectrum-sliced source. To understand this, we followed (in simulation) the output optical field from the time it was launched to the 80\({}^{th}\) round trip. One round trip time is given by 2\(nL/c\), where \(L\), \(c\) and \(n\) are the cavity length, the speed of light in a vacuum and the refractive index of standard single mode fiber (SMF). For this initial exemplary case with 15 m cavity, the round trip time is \(\thicksim\)0.145 ns. We then plotted the 10 dB spectral width shown in Figure 6a (which is derived from [21]). Initially, the spectral width of the RSOA-FCL is determined by the optical bandpass filter, which has a 3 dB bandwidth of 200 GHz. Gradually, the spectrum narrows down to less than 75 GHz bandwidth. As lasing sets in, a large number of longitudinal modes compete and only a fraction of the modes dominates the lasing process. The resulting narrow spectrum makes the RSOA-FCL more robust against dispersion compared to an ASE spectrum-sliced scheme. Figure 6b,c show sample spectra before and after the spectrum settles. Additional simulated and measured spectral widths for longer cavities are discussed in [21]. In the same manner we have simulated and plotted the optical power evolution as a function of the round trips in Figure 7a. It is clearly visible that the power requires three to five round trips to reach a steady state for different bias currents [31,32]. Initially, only filtered ASE is emitted when the RSOA bias current is turned on. On the second round trip, the RSOA amplifies and re-emits the reflected light (after passing through the cavity). This step repeats continuously and the power builds up until it reaches a steady state when the RSOA gain saturates. Figure 6: Spectral width evolution of an RSOA-FCL. The insets show the simulated spectra before and after the spectrum settles. We also followed the change in the RIN as a function of the cavity round trip times, as shown in Figure 7b. For practical reasons we do not plot the RIN as a function of the frequency but give the RIN as an average RIN within a spectral window up to 2.5 GHz. Figure 7b indicates the RIN evolution with the round trip and shows that the RIN follows a similar time scale as the output power to reach steady state. Initially, the RIN is very high as the cavity just emits spectrum-sliced ASE. The dashed lines depict the initial high RIN for 50, 100 and 200 GHz OBPFs. As the power in the cavity builds up, the RIN also goes down. This can be explained by the same concept used in the nonlinear suppression of amplitude modulation in Figure 3b,c. In the same manner, as the optical power of the RSOA-FCL builds up, the RSOA is driven into the nonlinear region and amplitude noise of the seeding ASE is suppressed. This results in a reduction of RIN with each round trip, as is shown in Figure 7b. Figure 7b also shows that, for wider filter bandwidths, we get lower RINs [33]. This could be accredited to two effects. First, a wider bandwidth means a lower filtering loss of power, and thus the RSOA is driven into the nonlinear region more quickly and leads to stronger noise suppression. Another explanation is related to the mode partition noise of multimode lasers.