Improved shooting algorithm using answer ranges definition to design doped optical fiber laser

Shooting method is a simple and powerful method to solve boundary value problems. By using shooting method and appropriate definition of comparative function with a proper guess for the initial value of pump and signal the computation process has short time and quick converge to correct answers. In this paper by definition of the answer ranges and proper comparative function, the requirement of proper initial guesses for forward signal and backward pump to solve rate equation is resolved. By putting initial and end of answer ranges as two set guesses, the signal and pump initial values were achieved fast and easily using the second method. In other words using answer ranges, the shooting algorithm was equipped with a process of response screening. This computational procedure, without requirement of experimental lookout can be used for fiber lasers and amplifiers. We also show that the former optimum length definition in strongly pumped power lasers cannot be used in lasers with conventional pump power and must be replaced with suitable one. Forward, backward and bi-directional pump scheme have been investigated using the proposed calculation procedure. An effect of background loss on optimum fiber laser length is also verified and the effects of input and output mirrors reflectivity, dopant concentration and fiber length in laser output power is investigated.