# Comparison of Basic Notch Filters for Semiconductor Optical Amplifier Pattern Effect Mitigation
## 6 ODI vs. MRR Qualitative Comparison  
The key characteristics that the ODI- and MRR-based notch filters must exhibit in order to mitigate the SOA pattern effect can be further assessed in a qualitative manner by considering the following functional and technological issues:  
1. [label=()]
2. FSR:
3. The FSR of both filters can conveniently lie within the SOA wide gain spectrum enabled through suitable adjustment of the SOA active layer material composition [1]. For the ODI, the FSR can be adjusted either statically, by fixing the path length imbalance, which can be of the order of um, between the ODI upper and lower arms, or dynamically, by using an optical delay line [32]. In the first case, a precise construction is required, but which is compensated by the reduction in footprint [74], while in the second case, a wide range of relative delays can be offered with fine resolution at the expense of a more bulky configuration [29]. For the MRR, the FSR can be readily set by choosing the MRR radius, which can be down to the micrometer scale using high index contrast waveguide materials [40; 75]. This offers the comparative benefit of ultra-compact total size at the expense of resorting to elaborate and delicate microelectronic fabrication processes, which detracts from the global use of the specific scheme. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **ODI** & **MRR** \\ \hline \(AM\) (dB) & 0.22 & 0.34 \\ \(AR\) (dB) & 3 & 2.78 \\ Net gain (dB) & 8.91 \({}^{*}\) & 12.13 \\ \(XC\) (\%) & 93 & 97 \\ \(\Delta P\) (dB) & 14 & 14 \\ \(\Delta Q^{2}\) (dB) & 1 & 2.87 \\ (negative) Detuning & 0.05 & 0.12 \\ offset (nm) & & \\ SSMF distance (km) & & \\ w/o dispersion & 12 & 15 \\ compensation & & \\ EOP at 12 km (\%) & 87 & 91 \\ \hline \multicolumn{3}{c}{\({}^{*}\) 3 dB insertion losses included.} \\ \end{tabular}
\end{table} 
Table 1: Values of employed performance metrics. Detuning:  
The position of the notches relative to the input data carrier wavelength can be practically adjusted by exploiting effects such as thermo-optic. For this purpose, either active phase shifters are used to control the phase bias in the ODI [58] or electrical heaters in the direct vicinity of the MRR to spectrally shift its resonance [75]. This method is particularly efficient for materials of large positive thermo-optic coefficients, such as silicon, since the required amount of detuning across the FSR can be achieved with a power supply of the order of mWs for both filters. On the other hand, the need for precise detuning is inherently more demanding for the ODI than for the MRR. This happens due to the different way by which the amount of phase shift required for efficiently suppressing the SOA pattern effect is obtained. Thus, for the ODI, this amount is acquired through one-way interference of a pair of delayed signal copies, while for the MRR through periodic round-trips and resonant enhancement. Accordingly, the ODI operation is more sensitive to deviations from the condition of destructive interference, which must be tightly satisfied at its cross-wise output port [30], thus requiring special design [76; 77]. PNCR:  
For the ODI the optimum PNCR can be achieved by adjusting the power splitting ratios of the optical couplers that form its two branches to be as symmetric as possible, i.e., as close as possible to 3 dB [78]. In practice, in order to ensure a PNCR over 20 dB, the deviation from the perfect 3-dB splitting ratio must be kept within 10% [29]. This tolerance is satisfiable with the coupling technology employed both in the fiber [79] and the waveguide [80] versions of the ODI. Similarly, for the MRR, it is necessary to satisfy the condition of critical coupling, where the MRR field transmission coefficient, \(r\), and amplitude attenuation factor, \(l\), are equal while tending to unity [40]. In effect, the PNCR exceeds 20 dB even if this matching is less than 3% perfect [81].