Theoretical and Experimental Analysis of Long-Period Fiber Gratings Made Directly Into Er-Doped Active Fibers

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.