Abstract
We present a rigorous theoretical and experimental analysis of signal
propagation along a long-period fiber grating (LPFG) made in an Erbium-doped
amplifying fiber (EDF). First, numerous effects that influence amplifying
process in Erbium-doped fibers were considered. These are clustering of Er
ions and subsequent upconversion and change of fiber refractive index due
to the optical pumping. Subsequently, LPFG-assisted interaction between the
amplified fiber core mode and a cladding mode is described combining rate
equations that describe propagation through the EDF and coupled-mode equations
that describe propagation through the LPFG. While this implementation is relatively
straightforward for the signal and pump, it requires particular attention
when dealing with spontaneous emission and amplified spontaneous emission
(ASE) that are incoherent (described purely by amplitude), but have to diffract
on the LPFG (that is amplitude and phase sensitive). This issue is carefully
addressed here. As a result, we were able to rigorously describe the propagation
of pump, signal, and ASE through the LPFG-amplifying diffractive structure
considering effects such as pump depletion, shift of the coupling wavelength
due to the pump power, and ASE formation along the structure. Forward pumping
(pump copropagating with the signal) and backward pumping (pump counterpropagating
to the signal) were both considered. The theoretical analysis was fully verified
by carried-out experiments.
© 2009 IEEE
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