# Comparison of Basic Notch Filters for Semiconductor Optical Amplifier Pattern Effect Mitigation
## 5 ODI vs. MRR Comparison: Results and Discussion
Then, it is possible to determine: (i) the input power dynamic range (IPDR) [53]; (ii) the permissible variation from the specified detuning; and (iii) the maximum signal transmission distance in standard single-mode fiber (SSMF) without dispersion compensation. The signal powers involved in the above definitions can be found through simulation run at 10 Gb/s. This bit rate is in line with data rates of modern applications that exploit SOAs as linear amplification elements [2; 8] and falls in the range within which significant bit pattern distortions are caused on signals directly amplified by typical SOAs [54]. The input to the SOA is a pseudo random binary sequence (PRBS) of 127 bits in length, which allows one to fully capture and investigate the detrimental impact of the SOA pattern effect [55]. This data stream contains Gaussian-shaped RZ pulses of such duty cycle and peak power that together saturate heavily the SOA and provoke a strong pattern effect at its output [31]. The default parameters values used in the simulation are those reported in [31; 33]. The simulation procedure involves [15; 33] numerically calculating the SOA integrated gain temporal response, substituting the outcome in the electric field (normalized so that its squared modulus represents power [26]) of the optical signal at the SOA output, applying fast Fourier transform (FFT) to pass it into the frequency domain, convolving it with the OOI or MRR spectral response given from (4) and finally converting the convolution product back into the time domain using inverse FFT (IFFT). The FFT and IFFT operations are available and executed in MATLAB software. The calculation of the \(Q^{2}\)-factor is done according to the method described in [15]. The integrals involved in the definition of \(XC\) are numerically calculated in MATLAB using Simpson's rule. Figures 7-11 show the simulation results obtained for each notch filter. To facilitate comparison, the waveforms and curves have been placed in the same figure with differently colored lines, i.e., red for the ODI and green for the MRR. From these graphical and numerical results, the following concise comments can be made with regard to each performance metric and accordingly to the SOA pattern effect suppression capability of the ODI and MRR:  
(a) _AM_: Both filters can improve this metric and render it acceptable even between the '1' that follows after the longest string of repeated '0's, i.e., six in our case [56], and the '1' that appears just before this run, but also after the same number of consecutive '1's (Figure 7a). In fact, the _AM_ between the target marks is reduced from 1.15 dB after the SOA (Figure 7b) to 0.22 dB by the ODI (Figure 7c) and to 0.34 dB by the MRR (Figure 7d), which therefore indicates that this demanding situation can equally be confronted with success. The stronger suppression of the _AM_ achieved by the ODI is justified by the fact that, for the specified detuning values, the notch lies closer to the reference optical wavelength than for the MRR. Consequently, the ODI filters a greater portion of the broadened spectrum of the amplified signal, as indicated in Figure 5 by the red-colored oblique-line zone versus the yellow-colored zone for the MRR. This enhances the amplitude equalization of the spectral components that have asymmetrically been shifted to the longer sideband, but as explained in the following, this enhancement is compromised by the higher _AR_ and the accompanying performance implications. Although the difference in the reduction of the _AM_ seems to be small between the two filters, it is not insignificant. In fact, it may become important when cascading several SOAs [12; 57], where the peak amplitude differences between amplified pulses should be prevented from being accumulated from stage to stage so that they do not become detrimental for the optical transmission performance.