  A comparative study of the gain achievement is performed in a waveguide
optical amplifier whose active layer is constituted by a silica matrix
containing silicon nanograins acting as sensitizer of either neodymium ions (Nd
3+) or erbium ions (Er 3+). Due to the large difference between population
levels characteristic times (ms) and finite-difference time step (10 --17 s),
the conventional auxiliary differential equation and finite-difference
time-domain (ADE-FDTD) method is not appropriate to treat such systems.
Consequently, a new two loops algorithm based on ADE-FDTD method is presented
in order to model this waveguide optical amplifier. We investigate the steady
states regime of both rare earth ions and silicon nanograins levels populations
as well as the electromagnetic field for different pumping powers ranging from
1 to 10 4 mW.mm-2. Furthermore, the three dimensional distribution of
achievable gain per unit length has been estimated in this pumping range. The
Nd 3+ doped waveguide shows a higher gross gain per unit length at 1064 nm (up
to 30 dB.cm-1) than the one with Er 3+ doped active layer at 1532 nm (up to 2
dB.cm-1). Considering the experimental background losses found on those
waveguides we demonstrate that a significant positive net gain can only be
achieved with the Nd 3+ doped waveguide. The developed algorithm is stable and
applicable to optical gain materials with emitters having a wide range of
characteristic lifetimes.
