N-fold symmetric gratings as gain-flattening filters

We present N-fold symmetric gratings as gain-flattening filters, since they are polarization insensitive and capable of exhibiting low back reflection. These gratings consist of N superimposed identical tilted gratings which are evenly distributed azimuthally. The coupling interactions between the forward propagating core mode and the backward propagating cladding modes are analyzed, including the limit when N→∞ which is a rotationally symmetric grating. The fiber grating parameters are optimized to equalize the gain profile of a typical erbium doped fiber amplifier to within 0.07 dB. Finally, we examine how the performance of the gain-flattening filter depends on the blaze angle and the effect of an uneven azimuthal distribution of the grating.