An Analytical Model for Rare Earth Doped Fiber Lasers Consisting of High Reflectivity Mirrors

The present article is concerned with an analytical solution for some parts of rare earth doped fiber laser equations. The presented model is valid for both four and three-level fiber lasers consisting high reflectivity mirrors. A typical method to obtain initial value in the numerical solutions of fiber laser equations is shooting method, which is based on an iteration process. Whereas this standard method needs to repeat computational loops to correct an initial guess value in order to satisfy the boundary conditions, which is a time consuming task. The model and its analytical solution, presented in this article, and the accuracy of the obtained values reveals that the method significantly reduces the time computation. The proposed method has been used for an erbium doped fiber laser and it shows that when the reflectivity of mirrors is more than 0.6 (60%), the calculated results are in agreement with the results of standard numerical methods and the error is less than 10 percent.