# Comparison of Basic Notch Filters for Semiconductor Optical Amplifier Pattern Effect Mitigation
## 5 ODI vs. MRR Comparison: Results and Discussion
(b) _AR_: Although the ODI filters more spectral components, as explained in (a), this also means that a greater portion of useful information contained in these components is inevitably lost. As a by-product, the data sequence receives less amplification than after the SOA alone, which is translated into an analogous difference between the _AR_ of the two filters, i.e., 3 dB for the ODI and 2.78 dB for the MRR. This in turn affects the net gain of the SOA-notch filter system, which is further lowered by the losses inserted by each type of filter [15]. Although the loss per length unit of the MRR and the ODI is comparable [58; 59], taking into account the significantly longer propagation length of the ODI, which is required in order to create the necessary length imbalance between its two arms, it can be deduced that the total losses exceed by a magnitude order of 3 dB those of the MRR, which are extremely low owing to the much smaller size of the latter. Thus, for the ODI, it is necessary to compensate for its increased losses by adjusting the SOA to provide more gain, which, as explained in [15], is an action that does not impair the capability of this notch filter to suppress the _AM_. This extra gain can be offered by supplying more carriers via a higher bias current [8], but at the inevitable expense of  
Figure 7: Simulated temporal waveforms that contain maximum strings of ‘1’s and ‘0’s. (**a**) SOA input, (**b**) SOA output, (**c**) ODI output and (**d**) MRR output. The vertical arrows indicate the amplitude modulation (_AM_). increased power consumption. Accordingly, if insertion losses (IL) are included, the MRR allows the SOA-filter system to exhibit a higher net gain [15], i.e., 12.13 dB vs. 8.91 dB for the ODI. (c) \(X\)C: The numerically-obtained values, 97% for the MRR and 93% for the ODI, indicate that in both cases, the filtered pulse temporal waveform deviates only by 3% and 7%, respectively, from that at the SOA input. This degree of matching implies that the Gaussian-like power profile of the input data pulses is strongly preserved at the filters' output. This is visually confirmed in Figure 8a, which shows that the envelope of an isolated data pulse maintains its original form. However, the time-bandwidth product at the output of both filters is over the minimum defined for Gaussian-shaped pulses [52], which means that the filtered pulses become chirped. The profile of this chirp, which is shown in Figure 8b, reflects the qualitative differences in the data pulse profiles of Figure 8a. More specifically, in the pulse rising part (region of 10-35 ps), the chirp declines to negative values, i.e., red chirp, but this drop is more dominant for the ODI than for the MRR. This partly explains why the AMattained with the former notch filter is lower than that achieved with the latter. As the pulse continues to temporally evolve, the chirp is decreased more strongly for the ODI until we reach the pulse center, where its absolute magnitude becomes maximum. From this point onwards the situation is reversed and the chirp begins to incline with a slope that is sharper for the ODI than for the MRR. Consequently, and as explained in detail below, the chirp parameter is larger for the ODI, which has a negative impact on the transmission performance of this notch filter in the presence of fiber dispersion. Finally, as we move off the pulse center and approach the pulse falling part (region of 65-80 ps), the chirp changes sign and becomes positive, i.e., blue chirp, which, nevertheless, because of its different cause and time scale over its red chirp counterpart, is not of major concern with regard to the SOA pattern effect suppression [31]. Figure 8: (a) Profile of isolated data pulse at ODI (red color) and MRR (green color) output in comparison to SOA input (black color). (b) Corresponding chirp profile at ODI (red color) and MRR (green color).