Owing to the increasing demand on the telecommunication bandwidth and the advent of the OH--free dry fiber developed by Lucent Technology, a new transmission bandwidth for the fiber optical communication which is centered around 1400 nm has been created in recent years. However, the corresponding light sources, optical amplifiers and other devices needed in the new transmission window are still under development. This thesis is to dissert with respect to the Cr4+:YAG crystal fiber based ASE (amplified spontaneous emission) light sources which emit light with broadband wavelengths from around 1200 nm to 1600 nm. Our previous study showed that side-pumping configuration can achieve a maximum ASE power of 0.65 mW with a pump power of 11 W at 980 nm in wavelength, whereas the end-pumping configuration successfully generated an optimum ASE power of 2.45 mW with a pump power of 11 W using a 1064-nm Yb fiber laser. This thesis reviewed the Cr4+:YAG material and studied on the single and double-pumping configuration of ASE light source, numerical simulations of the L-I curve of both configurations, and of the emission and the gain spectrum of the material, plus the introductions of the experiments needed for the simulations will be reported.