# Investigation of 2D-WH/TS OCDMA Code Stability in Systems with SOA-Based Device
## 1 Introduction  
Incoherent optical code-division multiple access (OCDMA) is a promising multiplexing technique known for its soft blocking capabilities that allows a trade-off between the system bit-error-rate (BER) and number of users [1]. To ensure the optimal operation of an OCDMA system, it is necessary to maintain the integrity and fidelity of optical codes during system operation. For instance, the use of two-dimensional (2D) wavelength-hopping time-spreading (WH/TS) incoherent OCDMA with implemented carrier-hopping prime code (CHPC) [2] (a class of 2D asynchronous codes that support wavelength hopping within time spreading over the Galois field of prime numbers with zero autocorrelation side-lobes and periodic cross correlation functions of at most one) will ensure minimal multiple-access interference. The code offers good cardinality and supports a large number of simultaneous users. To further improve the code scalability, 2D-WH/TS coding uses a set of wavelengths as the code carries with a temporal duration of a few picoseconds [3].  
In past decades, semiconductor optical amplifiers (SOAs) were developed and demonstrated to support different tasks and functionalities in optical systems, networks, and applications including data centres [4; 5; 6; 7]. A great deal of switching architectures utilizing SOAs in different configurations such as \(2\times 2\) multi-cascaded switch fabrics, cross-point matrices, for broadcast and select, wavelength selection [8], and DeMux operation [9] have already been successfully demonstrated.  
The severity of gain recovery time on 2D-WH/TS OCDMA systems using SOAs is evident even at low data rates [10]. This is because of the nature of the code carriers' time-spreading. The code carriers are spread with different time delays when forming a unique code signature for each user. The SOA's response time to incoming code is related to carrier lifetime, which in turn determines the SOA gain recovery [11]. A slow SOA gain recovery time poses a stringent limitation on the choices of the 2D-WH/TS code spreading, thus limiting the overall system scalability, including the number of simultaneous users. For the sake of illustration, even a 2.5 Gbit/s OCDMA system, if using a temporal code carriers' separation of 25 ps (i.e., 40 OCDMA GHz/s chip rate), will experience the equivalent SOA limitations of a 40 Gbit/s on-off keying (OOK) system.  
Many techniques have been developed and demonstrated to address and improve the gain recovery time of SOAs [11; 12] and these techniques fall into three categories. In the first category, a continuous wave beam is utilized to saturate the SOA at the operating wavelength, which lies in the SOA's spectral gain region or near the transparency point. The second method comprises the use of quantum wells or quantum dots semiconductors [11]. The third technique utilizes the SOA's amplified spontaneous emission (ASE) when driving the SOA with a high bias current into saturation. In [12], this method was used to reduce the gain recovery time from 200 ps down to 10 ps with the caveat that signal quality margins were somewhat sacrificed in situations where the SOA was followed by spectral slicing [13]. As the 2D-WH/TS systems can deploy both SOAs and spectral slicing, more investigations are required.  
The paper is organized as follows. In Section 2, the impact of SOA-induced redshift on multi wavelength picosecond code carriers under different bias conditions is investigated, experimentally demonstrated, and then confirmed by simulations. In Section 3, the impact of the SOA operating under high bias current/gain conditions is demonstrated on the 2D-WH/TS OCDMA code integrity. The overall performance (the probability of error and the maximum number of simultaneous users) of two different 2D-WH/TS OCDMA systems deploying the SOA is calculated. The results obtained are discussed in Section 4 and then summarized in the Conclusion.