We define a complex refractive-index profile for the pumped erbium-doped fiber that depends on radial distance, pump and signal powers, and erbium-doping profile to obtain a modal gain and loss of the propagating signal and pump power by Rayleigh–Ritz variational analysis. This profile provides a novel way of looking at the gain characteristics of erbium-doped fiber amplifiers. The advantage of this approach is that it gives the actual modal gain and also eliminates the need to approximate the modal fields and can easily take into account any dopant and index profile.
© 1999 Optical Society of America
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