# Comparison of Basic Notch Filters for Semiconductor Optical Amplifier Pattern Effect Mitigation
## 1 Introduction  
Optical amplifiers (OAs) are key elements for the development, implementation and evolution of fiber-based transportation, distribution and access networks [1; 2]. Their traditional functions include (Figure 1[3]) enhancing the signal power before being launched into an optical link (boosters), compensating for signal losses incurred either by the fiber medium, components along the propagation path or optical splitters, branches and taps (in-line reach extenders) and increasing the level of the received signal before photodetection (preamplifiers). Figure 1: SOA direct amplification applications. In this manner, they decisively contribute to achieving high global capacities, long transmission spans, multipoint-to-multipoint connectivity and ubiquitous information availability. These are critical requirements for efficiently coping with the growing data volumes and the diverse users' needs that govern the changeable broadband environment. Especially OAs that exploit semiconductor materials in the form of 'SOA' devices have been enjoying continuous preference by the optical communications research [4] and commercial (see indicatively [5]) sectors. The reason for this fact stems from SOAs' potential for signal amplification and multi-functionality entirely in the optical domain, within a broad wavelength range, with low power consumption, in a tiny volume at reasonable cost. Despite SOAs attractive features, the employment of these elements for the aforementioned linear amplification purposes in diverse applications, such as optical transmission [6], radio over fiber [7], passive optical networks [8], optical wireless communications [9], optical data interconnects [10], converged metro-access networks with heterogeneous services [11] and burst information handling [12], has been compromised by SOAs carrier lifetime, which is finite [3]. When this physical parameter is comparable to the repetition period of the SOA driving data, as is often the case, it dominates the time scale of the SOA gain dynamics. Thus, if the combination of the power and duration of the input data signal is such that the SOA is deeply saturated, then the SOA gain is not perturbed and recovered in the same way for all excitation pulses (Figure 2). As a consequence, the SOA operation becomes pattern dependent so that the amplification received by a given bit does not depend solely on this input, but also on the history of the SOA response to previous bits. This undesirable situation is referred to as the 'pattern effect' (PE) [13] and is more pronounced for data pulses that occupy a fraction of the assigned bit slot, i.e., of return-to-zero (RZ) data format, and hence, impose a heavy strain on the SOA gain dynamics [14]. Due to the PE, the profile of the pulses at the SOA output is not uniform, since pulses are distorted by peak-to-peak amplitude fluctuations, and therefore is far from ideally being an amplified replica of the input signal (Figure 3). Figure 2: Evolution of semiconductor optical amplifier (SOA) gain in response to data train input of repetition period, \(T_{period}\), such that pulses arrive faster than the interval available for SOA carrier replenishment, \(T_{recovery}\). In order to allow conventional SOAs to fulfil their classical role, it is necessary to combat the PE and its deleterious consequences. For RZ pulses, this requires lowering their power well below the SOA strong saturation regime, as well as substantially shortening their width [15]. These actions are not sufficient since the first one results in a poor optical signal-to-noise ratio (OSNR), reduced maximum output power, closer amplifier spacings and narrower input power dynamic range (IPDR) [16], while the second one requires applying intricate ultrafast pulse generation approaches [17] and dealing with practical related issues, such as nonlinear effects [18] and intraband phenomena [19].