Optimization of strongly pumped Yb-doped double-clad fiber lasers using a wide-scope approximate analytical model Ziad Mohammed n , Hossein Saghafifar Department of Physics, Malek-ashtar University of Technology, Shahin-shahr, P.O. Box 83145/115, Islamic Republic of Iran article info Article history: Received 20 November 2012 Received in revised form 24 May 2013 Accepted 10 June 2013 Keywords: Fiber laser Double-clad fiber Analytical model abstract An analytical model based on the rate equations of strongly pumped Yb-doped double-clad fiber laser (DCFLs) is presented. The output power and the distributed laser along the whole fiber have been found. In this paper, most parameters affecting the laser performance have been considered. The influences of scattering losses, pump reflection, output reflectivity, doping concentration and fiber length have been studied. It is shown that for wide ranges of the previous parameters and large variations of the input powers for all types of pumping (forward, backward and two-end), the maximum relative error of the output power would be less than 2.72% when the results are compared with the numerical model. Depending on our analytical model, a simple optimization method has been illustrated for high-power laser oscillators. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction High efficiency, high power, good beam quality and compact- ness are interesting features of double-clad fiber lasers (DCFLs) over the other lasers. These attractive features led to applications of DCFLs in diverse fields such as industry, military, medicine and telecommunications. In recent years, an output power of 1.36 kW and an efficiency of 83%, was obtained from a single fiber with no amplifying stages [1]. There are some analytical approximations for predicting the output parameters of fiber lasers which have different levels of complexity. In an attempt the scattering losses were considered, but it has a large relative error when compared to numerical results and it increases with the increase of the output reflectivity. The relative error is 6.4% for an output reflectivity of 0.2 [2]. Other approximations showed that the relative error increases with the decrease of the output reflectivity and it is 6% for a typical resonator (high feedback reflectivity of about 0.98 and low output reflectivity of about 0.04) [3]. In a new model, the relative error has been improved to about 2.4%, but this model works only for short fibers (15 m for a typical resonator), also this model has not been tested for a wide range of reflectivities that the mentioned error has been obtained after testing only three reflectivities′ values [4]. Furthermore the men- tioned articles [2], [3,4], never consider the pump reflection. In this paper, the set of rate equations (REs) for linear Yb +3 -doped DCFLs are solved analytically using two steps, the first step is done by applying rough approximations to obtain the preliminary values of unknowns. The second step uses only one main approximation regarding the backward signal power, to develop an explicit analytical model whose inputs are the preliminary values calculated in the first step. Our analytical model considers most influencing parameters on the fiber laser performance. The analytical results are in good agreement with the numerical ones that the maximum relative error between both results remains below 2.72%, even though wide ranges of these- parameters values and different pumping types are investigated. Finally, a simple method is presented to optimize high-power fiber lasers. The numerical analysis is based on the fourth-order Runge– Kutta method to solve the fiber′s REs while the binary chopping method is used as a shooting method to correct the successive initial values until reaching the desired precision. 2. Rate equations Our linear cavity is composed of Yb-doped DCFL of length L and four fiber Bragg gratings (FBGs) with reflectivities of R 1p , R 2p at the pump wavelength λ p , and R 1s , R 2s at laser wavelength λ s . The back FBGs serve as feedback mirrors for both laser and backward pump radiations in the backward pumping case. The output FBGs have reflectivities of R 2p at λ p and R 2s at λ s . They are used as an output coupler for laser and as a feedback mirror for forward pump radiation in the forward pumping case. Fig. 1. shows schematic illustration of the laser oscillator. CW operation with the strong pumping case is assumed, therefore the gain is well saturated and the spontaneous emission Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/optlastec Optics & Laser Technology 0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.06.010 n Corresponding author. Tel.: +98 9395444150; fax: +98 3125225096. E-mail address: ziademohammed@yahoo.com (Z. Mohammed). Optics & Laser Technology 55 (2014) 50–57