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Summary1-IntroductionThe operational properties of erbium-doped fiber amplifiers (EDFAs), which have an important role in optical fiber communication systems operating at the 1.55 μm window, directly depend on the pump and signal characteristics. It is well-known that an erbium-doped fiber amplifier demonstrates the property of two-level amplification system when it is pumped at 1480 nm wavelength [1]. Particularly, the distribution of Er3+-ions within the metastable level (4I13/2) changes continuously with temperature according to Boltzmann’s distribution law, owing to the closeness of the pump and signal rates within this level. Thus, the population of metastable level shows a highly temperature sensitive signal gain for 1480 nm pumping regime [2, 3]. In this study, we analyzed theoretically the signal gain performance of EDFAs pumped at 1480 nm pump wavelength by using the temperature-sensitive rate equation model in the practical temperature range of - 20 to 60 °C. 2-Modified Rate Equation ModelThe solution of the two-level amplification system can be carried out by using the modified rate equations in terms of the pump absorption and emission rates (R1-22 and R22-1, respectively), the signal absorption and emission rates (S1-21 and S21-1, respectively) and the amplified spontaneous emission rate γsp. Then, an expression for the relative populations in the metastable level, N2 / N, at steady state conditions is found as where vp and vs are the pump and signal frequencies, respectively; h is Planck’s constant; τ is the lifetime of metastable level; Γp and Γs are the pump and signal overlap factors, respectively; Aeff is the effective core area. The relevant parameters used in Eq.(1) are as bellows: σ1-22 and σ22-1 are the stimulated absorption and emission cross sections for the pump wavelength, while σ1-21 and σ21-1 are for the signal wavelength; η = σ21-1/σ1-21 (from McCumber’s theory). Pp and Ps are the pump and signal powers, respectively. The parameter β in Eq.(1) is characterized by the Boltzmann’s distribution of Er3+-ions within the 4I13 / 2 energy state and given by β = N22/N21 = exp(-ΔE2/kBT). kB is the Boltzmann’s constant, ΔE2 = E22 - E21 is the energy difference between the sublevels N22 and N21 and its value is nearly 200 cm-1 at temperature range of-20 to 60 oC. The gain parameter G(λs) is defined by G(λs) = eγ.L, where γ = σ1-21(ν2 -N1)Γ, γ is small-signal gain coefficient and L is the doped fiber length. Results and DiscussionsUsing EDFA parameters given in Table 1, we have plotted the dependence of gain on the launched pump powers at temperature values of-20°C, 20°C and 60°C in Fig.1. Table 1.EDFA parameters used for the calculations.
The value ofσ21-1/σ1-21 at room temperature (20°C) for 1550 nm signal wavelength is obtained as 1.76, because there is a relationship between signal emission and absorption cross sections in the form of η = exp [hc/kBT(1/λ0-1/λs)] according to McCumber’s theory. The wavelength λ0 depends on the electronic structure of the ground and the excited state of the Er3+-ion and its value is calculated as 1522, 7 nm. Thus, the values of η at – 20 and 60°C are 1.93 and 1.65 and also the values of β at – 20, 20 and 60°C are calculated as 0.33, 0.38, 0.43, respectively. Fig. 1 shows in 50 μW signal power regime that, the gain values increase an amount of 3-5 dB when the temperature is decreased from 60 °C to -20 °C. Thus, it is seen from the gain analysis that the performance of EDFAs pumped at 1480 nm pump wavelength is affected by the temperature. In addition, it is seen from the modified rate equation (Eq.1) that the smaller signal powers are more efficient than the higher signal powers. Moreover, this model which involves β and η is more accurate to describe the signal gain for a wide range of temperatures for EDFAs pumped at 1480 nm pump wavelength. AcknowledgmentThis study is supported by Scientific Research Projects Council (SRPC) of Erciyes University under Grant No FBA-04-01. ReferencesE. Desurvire,
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