LIL and LMJ are two French high power lasers dedicated to fusion and plasma experiments. One of the main issues of these lasers is the beam amplification that is achieved by large glass slabs (Nd doped phosphate glass). We have determined several fundamental parameters of this laser glass. In order to avoid non-linear effects during beam propagation, the spectrum of the pulse is broadened. When the spectrum is not amplified symmetrically, temporal modulation appears in the pulse. As we need to accurately center the wavelength of the laser pulse in the amplifier material gain curve, we have achieved precise measurements of its fluorescence spectrum. To predict the behaviour of the laser glass for short pulses, we have determined the sublevels structure of the laser transitions. We have also made a Judd-Offelt analysis to calculate the emission cross-section of Nd3+ in this glass. Finally, we have developed an experimental setup to measure the fluorescence decay which is related to glass manufacturing. We obtained an accuracy close to 1 μs (for the fluorescence lifetime at 1/e).