# A Comprehensive Study on EDFA Characteristics: Temperature Impact
## 1 Introduction  
In early days, communication systems suffered from many limiting factors concerning the permitted transmission distances due to the absorption mechanisms inside the fiber [1]. The first applied solution to avoid absorption loss was the use of electrical repeaters to enhance the signal while being transmitted [2]. The main drawback was the need to use optoelectronic (O/E) and electrooptical (E/O) energy converters, which caused the system to be more complicated. Additionally, cost is increased and slow rates are gained [1, 2]. Optical amplifiers were developed in the early 1980s, but were used commercially in the 1990s [1]. They represented the solution thanks to introducing a fully optical system [3]. The common types of optical amplifiers are: semiconductor optical amplifier (SOA) [4, 5, 6], Raman amplifier (RA) [6, 7] and rare-earth doped fiber amplifier (DFA) [4, 6]. Rare-earth DFAs have some advantages over SOAs due to their lower noise and higher gain, while they are also advantageous compared to RAs for their lower cost and higher pump power utilization. Also, amplification using DFAs can cover a wide range of wavelengths of input signals. The range could be from visible to infrared depending on the rare-earth material used as a dopant [2, 8]. The most frequently used rare-earth material is the erbium (E\({}_{\rm r}^{+3}\)) [2, 3]. This is due to its capability of operating in the broad range of the third transmission window at 1550 nm, which is characterized by its minimum attenuation [9]. The amplifier in this case is called an erbium-doped fiber amplifier(EDFA). Other rare-earth elements are also used in several applications such as: lanthanum (La) in the improvement of the microstructure and mechanical properties of some aluminum alloys [10], and ytterbium (Yb) in signal amplification in the 975-1200 nm range [11; 12]. An EDFA pumping laser wavelength should be 980 nm or 1480 nm [3; 13]. However, the 1480 nm has also some advantages over the 980 nm pumping wavelength. It is less affected by the so-called excited state absorption (ESA) that results from various transitions to upper energy levels in case of strong pumping schemes [14; 15], and affects the pump absorption along the fiber [16]. In addition, according to [PERSON] et al. [14], although the 980-nm pumping affords a weaker dependence of the performance of EDFA on temperature than that for 1480-nm pumping, a more effective performance of EDFA at the pumping wavelength of 1480 nm as compared to the 980 nm is obtained for a wide range of temperature and high-pump powers. Other pumping wavelengths are also available such as: 510 nm, 532 nm, 665 nm, and 810 nm. However, these wavelengths suffer from the ESA. Different pumping configurations can be used such as forward, backward, or even bi-directional configuration [17]. Modeling EDFA gain and its characteristics has been studied in the literature, in addition to gain temperature dependency. However, the main concern was only dedicated to the gain variation with temperature [12; 18; 19; 20]. Another drawback is the use of complicated methods in some of these studies [20; 21]. Also, the EDFA gain dependency on temperature has been used in some sensing applications [22]. Despite this, to the best of our knowledge, no complete and comprehensive investigation has been driven regarding the EDFA characteristics' dependency on temperature. The aim of this work is to present a simple analytical model to follow and use to fully study the temperature impact on EDFA gain in case of 1480-nm pumping schema. The temperature range under study is \(-40\)\({}^{\circ}\)C to \(+80\)\({}^{\circ}\)C. Here, the solutions are calculated numerically, and summations replace the integrals of the previous work [14; 23]. In addition, previous work has focused on gain temperature dependency. In our work, the investigation of temperature effect is extended to include the effect of more EDFA parameters such as the maximum peak gain, optimum fiber length, saturation output signal power, and saturation pump power.