## 2 Amplifier Configuration
The second half of the CWDM signal wavelengths within Sub-band 2 (e.g., 1,350 nm to 1430 nm) generate idlers that are at wavelengths lower than the pump wavelength and fall within Sub-band 1 (e.g., 1256 nm-1336 nm). In each arm of the OPA section of the HROPA, the parametric pump must be filtered out by an appropriate DWDM filter (e.g., 25 GHz DWDM fiber Bragg grating (FBG) filter [9]). The two sub-bands are then recombined using a WDM multiplexer (MUX) [10]. Note that since the idlers generated at each sub-band fall outside the pass band of the associated WDM MUX port, the idler wavelengths are suppressed. The amplified CWDM PON channels are separated by a CWDM filter, as is required in any CWDM PONs. Each port of the CWDM DEMUX has a filter transfer function with a bandwidth of 23 nm at -30 dB [11]. Finally, each wavelength is routed to the desired ONU through the appropriate optical path [4]. In the above description, we did not provide any specifics on the pump wavelength and power selection to achieve low ripple wide bandwidth amplification. To address the wide band amplification, a pump wavelength at 1340.2 nm is required for the OPA process. Furthermore, in order to achieve a ripple of \(<\)5 dB, the Raman pump must be placed at \(\sim\)1270 nm. However, a 1270-nm Raman pump overlaps with the 1270-nm signal (first channel band) of the US traffic. Hence, in this case, a WDM coupler cannot be used as in Figure 1 to couple the Raman pump to the HNLF. To overcome this limitation, a potential solution is the use of an optical circulator, which can couple the Raman pump in the HNLF and, through counter-propagation through the HNLF, achieve the desired signal amplification (Figure 2). In Figure 2a, we show only the modified Raman stage. The OPA stage is the same as the one described earlier (Figure 1) and is not shown. Nevertheless, due to the high optical power (e.g., \(\sim\)1 W) of the Raman pump and the non-ideal circulator isolation performance (e.g., 55 dB), a portion of the original Raman pump leaks through the circulator port (Port 1 to Port 3 leakage) and co-propagates with the CDWM signals (Figure 2). Since the pump optical power is \(\sim\)1 W, the leaked optical power through the circulator is at similar or even higher optical power levels as the first CWDM signal at 1270 nm (Figure 2b). Thus, the leaked Raman pump causes significant crosstalk issues at the receiver and significantly deteriorates the signal performance. Using a single pump at a lower or higher wavelength than 1270 nm is not an effective and viable solution either, because although it overcomes the crosstalk issue, it generates a very high ripple (e.g., \(>\)7 dB) that can be detrimental to the signal performance. To overcome both the crosstalk issue, as well as the high ripple performance, an alternative and viable approach is to use two Raman pumps as shown in Figure 3a. The first one (P\({}_{\text{R1}}\)) is at 1260 nm, and the second one (P\({}_{\text{R2}}\)) is at 1280 nm, with powers of 1.1 W and 0.63 W, respectively. Since these two pumps are 10 nm apart from the first two CWDM channels, 1270 nm and 1290 nm, crosstalk at the receivers is not an issue, as it is suppressed significantly through the optical filters used in the HROPA for the recombination and splitting of bands and/or channels. The WDM MUX/DEMUX filter transfer function used in the HROPA is shown in Figure 3b, and it is typical in WDM network designs. The use of two Raman pump wavelengths at 1260 nm and 1280 nm, is equivalent to a single Raman pump at 1270 nm at higher optical power. To model the HROPA, we used the well-known Raman and parametric equations with the goal of achieving a bandwidth of 170 nm with a minimum ripple. We separate the HROPA model into two sets of equations. The first one describes the Raman pump process, which takes place in HNLF1. For a multiple pump scheme, variations in the \(i\)-th Raman pump (\(P_{Ri}\)) and signal (\(P_{s}\)) powers along the amplifier length can be described by the following wave equations [12,13].