  Here a detailed formalism to achieve an analytical solution of a lossy high
power Yb-doped silica fiber laser is introduced. The solutions for the lossless
fiber laser is initially attained in detail. Next, the solution for the lossy
fiber laser is obtained based on the lossless fiber laser solution. To examine
the solutions for both lossless and lossy fiber laser two sets of values are
compared with the exact numerical solutions and the results are in a good
agreement. Furthermore, steps and procedures for achieving the final solutions
are explained clearly and precisely.
