Improved Q2 shooting algorithm using answer ranges definition to design doped optical fiber laser Maryam Karimi, Amir Hossein Farahbod Q1 La Q3 ser and Optics Research School, AEOI, P.O. Box 14399-51113, Tehran, Iran article info Article history: Received 14 September 2013 Received in revised form 1 March 2014 Accepted 4 March 2014 Keywords: Optical fiber Laser Shooting method Optimum length abstract 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. & 2014 Published by Elsevier B.V. 1. Introduction Doped optical fibers have a potential to be used as a laser components and have many applications such as communications [1], industrial processing [2], sensors [3], medical applications [4,5] and so on. Erbium doped fibers (EDFs) are a suitable source for L and C band communication systems [1]. These amplifiers have high gain, wide optical bandwidth, high output saturation, low noise figure, polarization independent gain, no crosstalk and low insertion loss [6]. The Nd and Yb doped fiber lasers (NDFL, YDFL) were developed for use in high power and double clad fiber laser in industry [7]. Fiber lasers have many advantages over bulk glass lasers, such as low cost, broad gain bandwidth, high efficiency, good beam quality and small quantum defects [8]. Modeling (simulation and analytical results) is important which investigates static and dynamic characteristics of lasers and amplifiers for parameters of practical systems optimization [9]. The dynamic analysis of energy level populations in laser media are often modeled using a system of rate equations [10]. Several authors have studied high power fiber lasers (HPFLs) theoretically and got many significant achievements [5,7,11]. In strongly pumped fiber lasers, the population density of the upper lasing level N 2 is assumed to be much smaller than dopant concentration N 0 , so the analytical simulations can lead to the right results in such highly pumped fiber lasers [7–10,12,13]. But, analytical expressions had a large relative error comparing with the exact numerical simulation for conventional pump power and high reflectivity of the output mirror [11]. For the forward pumped amplifiers, the rate equations can simply have a numerical solu- tion with Runge–Kutta or other methods [14,15]. These kinds of problems have an initial value for pump and signal, and classified as initial value problems (IVPs). The conventional fiber lasers and bi-directional pump on doped amplifiers are classified as two point boundary value problems (BVPs) [16,17], which are much more difficult to be solved than the IVPs. There are several numerical algorithms for solving BVPs, such as shooting method (S-method), relaxation method (R-method) and finite difference method (FD-method) [17], or use of genetic algorithm (GA) [18]. Using the FD method is a time consuming technique [19]. Both S and R-methods reduce a BVP to the initial value problem. The accuracy of the R-method has high accuracy for small values of N 0 , and L, where N 0 and L are dopant concentration and fiber laser length respectively [20]. However, the S-method is commonly used for solving fiber laser problems such as spatial counter propagation and bi-directional multi pump Raman fiber laser. The S-method has faster computational speed than GA [18]. In the shooting method, the process starts with 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optcom Optics Communications http://dx.doi.org/10.1016/j.optcom.2014.03.013 0030-4018/& 2014 Published by Elsevier B.V. E-mail address: mykarimi@aeoi.org.ir (M. Karimi). Please cite this article as: M. Karimi, A.H. Farahbod, Optics Communications (2014), http://dx.doi.org/10.1016/j.optcom.2014.03.013i Optics Communications ∎ (∎∎∎∎) ∎∎∎–∎∎∎