# Comparison of Basic Notch Filters for Semiconductor Optical Amplifier Pattern Effect Mitigation
## 5 ODI vs. MRR Comparison: Results and Discussion
(d) \(Q^{2}\)-factor and associated metrics: (i) both filters enhance the IPDR and extend the SOA error- and distortion-free operation from the low saturation region (A in Figure 9) to the deep saturation region (C in Figure 9), in which the SOA gain is decreased by more than 3 dB and 6 dB, respectively. This fact allows one to passively relax the stringent management [60; 61] of the input power levels going into the SOA and hence of the degree of SOA gain saturation, which otherwise is required in order to allow SOAs to deliver unimpaired linear amplification functionality. This improvement is realized for both filters, as quantified by the increase of the peak input data power (\(P_{peak}\)) by \(\Delta P=14\) dB (assuming a maximum power of 10 dBm going into the SOA). Furthermore, at \(P_{peak}\simeq 6.6\) dBm, which heavily saturates the SOA [31], the \(Q^{2}\)-factor is over its critical limit, which for the SOA alone fell short by \(\Delta Q^{2}=4.3\) dB. This is better achieved for the MRR than for the ODI, i.e., \(\Delta Q^{2}=2.87\) dB and \(\Delta Q^{2}=1\) dB, respectively. (ii) The MRR exhibits better tolerance to detuning offset than the ODI, which is an important feature as it obviates the need for resorting to electronic equalization [44]. In fact, Figure 10 shows that the (negative) detuning of the MRR can be varied within 0.12 nm or equivalently by 50% further for the data pulses wavelength modulation bandwidth [52] in the C-band and still keep the \(Q^{2}\)-factor acceptable. The corresponding variation for the ODI is comparatively reduced by more than 50%, i.e., 0.05 nm, and hence is narrower, which may impose tighter requirements with regard to wavelength locking [62]. (iii) The MRR allows the amplified signal to propagate over a longer distance of SSMF without dispersion compensation than the ODI. This is shown in Figure 11, which has been obtained by modeling the SSMF of typical attenuation coefficient 0.2 dB/km and dispersion parameter 17 ps/nm/km by its low-pass equivalent field transfer function [63]. From this figure, it can be seen first that subject to chromatic dispersion, the maximum SSMF length is reduced to around 20 km, as calculated from [64] (cf. Equation (1)) for intensity-modulated data pulses of a 100-ps repetition period and 27% duty cycle. Then, looking for the transmission range for which the \(Q^{2}\)-factor is acceptable, we observe that the amplified signal can travel up to 12 km with the ODI, while this span is extended to 15 km with the MRR. This length difference may seem small, but nevertheless, it corresponds to the reach of real short-haul fiber interconnection links and networks [65]. Moreover, the \(Q^{2}\)-factor is well over its lower permissible bound for the MRR, while it is much closer to the borderline for the ODI, across the SSMF distance over which this metric remains acceptable for both filters. These observations can be interpreted by referring to the instantaneous frequency deviation, i.e., chirp, which inevitably accompanies a signal when directly amplified in an  
Figure 9: \(Q^{2}\)-factor as a function of different peak input data powers for SOA alone (black color) and with the connection of ODI (red color) and MRR (green color). The horizontal dotted line denotes the lower limit set for the \(Q^{2}\)-factor. The vertical dashed lines define the different saturation regions: A, low; B, medium; C, deep. SOA [26]. More specifically, suppressing the SOA pattern effect by means of optical notch filtering relies on compensating for the chirp components, which are induced due to the irregular SOA gain variation by the optical excitation, and converting them into amplitude changes that counteract those after the SOA ([27], cf. Figure 4.18). Still, it is not possible to fully eliminate the SPM-induced negative-magnitude chirp components, which are directly associated with the SOA pattern effect, but only reduce the variations of their uneven peaks [31].