  We present a comparative study of the gain achievement in a waveguide whose
active layer is constituted by a silica matrix containing silicon nanograins
acting as sensitizer of either neodymium ions (Nd3+) or erbium ions (Er3+). By
means of an auxiliary differential equation and finite difference time domain
(ADE-FDTD) approach that we developed, we investigate the steady states regime
of both rare earths ions and silicon nanograins levels populations as well as
the electromagnetic field for different pumping powers ranging from 1 to 104
mW/mm2. Moreover, the achievable gain has been estimated in this pumping range.
The Nd3+ doped waveguide shows a higher gross gain per unit length at 1064 nm
(up to 30 dB/cm) than the one with Er3+ doped active layer at 1532 nm (up to 2
dB/cm). Taking into account the experimental background losses we demonstrate
that a significant positive net gain can only be achieved with the Nd3+ doped
waveguide.
