English title

In the fiber amplifiers, the initial values of pump and signal powers are specified. so; Solving rate equation in the fiber amplifiers includes initial value problems. In the fiber lasers, the initial value of the pump is known but signal (laser) power must be determined. Hence; solving the rate equation in the fiber lasers is the part of the boundary problems. Different methods are presented for solving boundary value problems. In this paper, using the shooting method, a proper region introduced as answer range and solutions for rate equations of fiber laser and amplifier have been found. The advantage of this method is that to start calculation, we do not need the accurate initial guesses. With the proposed method, different forward, backward and bidirectional pump schema in Ytterbium doped fiber laser is verified. The parametric optimum length is introduced in high pump power with simplification in rate equations. In this paper we introduced a new definition of optimum length in conventional pump power fiber lasers and effects of background loss verified in the optimum length.