Holey fibers (HF) with their peculiar properties have been used in fabrication of Erbium doped holey fiber amplifiers (EDHFA) for third optical communication window. In this paper, by using scalar effective index method, the analyses are presented to investigate the effects of HF geometrical parameters on the gain performance of the EDHFAs. The hierarchical variations of the parameters, including the air-hole sizes (AHS), propagating modes of the core and cladding, mode field diameter of the signal and pump, would cause alterations in the maximum gain and the optimum lengths of the EDHFAs. By determining the normalized frequency of the HF in wide range variations of the air-hole diameter, air-hole spacing, and air-filling factor (AFF), the single-mode regions for signal and pump wavelengths are obtained, where the maximum gain and the optimum lengths are evaluated. In addition, the influence of pump power and the dopant concentration in terms of the AFF are investigated. It is shown that by using suitable AHS and AFF, one can obtain a higher gain for a shorter optimum length in the EDHFAs. The obtained results can be a useful tool for design of HF-based optical amplifiers with lesser effects of amplified spontaneous emission and nonlinearities because of shorter optimized length.
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