in short: the correct terms - Amplified Spontaneous Emission or  Stimulated Emission, they are, in principle, synonyms. The term Amplified Stimulated Emission is nonsense since "stimulated" already means amplification process and otherwise. 

Wiki gives:

"Amplified spontaneous emission (ASE) or superluminescence is light, produced by spontaneous emission, that has been optically amplified by the process of stimulated emission in a gain medium"

Thanks a lot for clarification Sergii. I agree with you.

I was thinking like you, but when I see Amplified Stimulated Emission as a project title I confused. Therefore, I asked this question under this project.

 yes, Ibrahim, i totally agree. But research project always assumes some new horizonts. May be in this project it will be discovered something which doesnt fit to standard definitions ))