We aim to amplify a signal in a strip loaded waveguide composed by an active silica layer co-doped with silicon nanograins and rare-earth ions deposited on a silica cladding layer and topped by a silica strip. The signal wavelength corresponds to the transition wavelength between two energy levels of a rare earth ions. To achieve an efficient population inversion, the rare earth ions benefit from the indirect excitation via silicon nanograins which show an absorption cross section fourfold higher than the one of rare earth ions. In order to study the influence of the type of rare earth on the optical gain, we consider two rare earth ions : neodymium ions (Nd3+) for a signal wavelength at 1060 nm and erbium ions (Er3+) for a signal wavelength at 1540 nm. The optical gain is simulated using a modified two loops auxiliary-differential equation and finite-difference time-domain (ADE-FDTD) algorithm. Within this new scheme we can compute the steady state levels populations as well as the spatial distribution of the guided field in the waveguide whatever the populations levels lifetime considered. We also calculate the gross gain as well as the net gain by taking into account the experimental background losses. We demonstrate that a significant positive net gain can only be achieved with the Nd3+ doped waveguide up to 30 dB/cm for a pump power density of 10^4 mW/mm².