# Comparison of Basic Notch Filters for Semiconductor Optical Amplifier Pattern Effect Mitigation
## 5 ODI vs. MRR Comparison: Results and Discussion
By calculating the maximum chirp variation, which occurs in the transition between the last '0' in a run of spaces and the '1' that immediately follows, we can extract the chirp parameter at the filters' output similarly to the numerical procedure described in [66]. The value of this parameter is positive and is larger for the ODI than for the MRR. In the presence of anomalous chromatic dispersion, this fact subsequently affects the pulse width of the chirped signal at the filters' output [52]. Thus, after a short distance zone of pulse compression, pulse broadening occurs, which is more significant for the ODI than for the MRR. This is reflected in the \(Q^{2}\)-factor, which is smaller for the ODI and becomes worsened after propagation in a shorter SSMF length (which is also smaller than that calculated from [64] (cf. Equation (1)) for the chirped-free signal case). The obtained results are further supported by the so-called pseudo-eye diagrams (PEDs) [67], which are displayed at different points of the \(Q^{2}\)-factor curves. Thus, both MRR and ODI restore the form of the PED, which has severely been degenerated into asymmetric sub-envelopes at the SOA output. This improvement is further quantified by the degree of eye opening (EOP) [68], which is higher for the MRR than for the ODI, i.e., 91% vs. 87%, respectively, for transmission in the same fiber length of 12 km. Figure 11: \(Q^{2}\)-factor vs. standard single-mode fiber (SSMF) distance for ODI (red color) and MRR (green color). The horizontal dotted line denotes the lower limit set for the \(Q^{2}\)-factor. Figure 10: \(Q^{2}\)-factor for different detuning offset values for ODI (red color) and MRR (green color). The zero detuning refers to the case that the notch of the filters is located away from the data carrier by so many spectral units as defined in Figure 5.  
The above improvements can be attributed to the different shape of the MRR and ODI transfer functions [69]. This difference affects the efficiency of the frequency-to-amplitude conversion mechanism, which is essential for suppressing the SOA pattern effect [44] and thus makes the MRR and ODI perform differently when employed as notch filters. Moreover, the comparatively better performance of the MRR can be justified from a qualitative standpoint by noting that the MRR exhibits higher wavelength sensitivity than the ODI. In fact, for the MRR, this quantity is determined, and hence enhanced, by the finesse [70], which is a function of the coupling coefficient and internal loss [27] and accordingly can be flexibly adjusted. In contrast, the finesse of the ODI is very small, i.e., it equals only two [52], and therefore is fixed so that the design freedom is very limited. Physically, this happens due to the different operating nature of the ODI and MRR, since in the former, only two constituents of the input field interfere to produce an output, whilst in the MRR, the field experiences multiple circulations before it leaves the resonant cavity [71]. Since in the first case, the interfering paths are feeding forward, while in the second case there is a recirculating, feedback delay path, this difference, which is reflected on the polynomial form of the respective transfer functions, can also be expressed in signal processing terms. Accordingly, the ODI and MRR can be used not only as notch filters, but in general as finite impulse response (FIR) and infinite impulse response (IIR) filters, respectively [72]. FIR filters that exploit MRRs are also possible if sophisticated designs based on the combination of multiple such elements are adopted [73]. The values obtained for the employed performance metrics have been gathered in Table 1.