Noise figure and gain temperature dependent of praseodymium-doped fiber amplifier by using rate equations

A theoretical study of the temperature dependent noise effects of praseodymium-doped fiber amplifiers (PEDFAs) has been examined. The Pr³⁺-doped ZBLAN fiber amplifier pumped at 1017 nm and Pr³⁺-doped GeGa-sulfied fiber amplifier pumped at 1028 nm are chosen. The temperature-dependent rate and propagation equation related to four-level system consideration which is based on the population difference among amplification levels has been used. The population difference depends on pump and signal powers, Boltzman factor K_B, cross-sections, noise figure (NF) and Pr³⁺ concentration. The numerical results obtained over the temperature range from −20 °C to + 60 °C are used to present an analytical expression for the signal gain and noise figure effects in PDFAs length and noise figure with input pump power. The amplified spontaneous emission (ASE) has been taken into account.