Impact of cavity loss on the performance of a single-mode Yb:silica MOFPA array
Introduction
Intense activities have been devoted to characterize rare-earth-doped DC fiber lasers [1], [2], [3], cladding pumped photonic crystal fibers [4], [5], long period gratings (LPGs) [6], [7], and optical switching based on fiber gratings [8], [9], [10] during the recent years. Owing to their compactness, superb beam quality and high pump efficiency, the fiber lasers exhibit to be important light sources in the medicine and modern telecommunications. Those are vastly employed in industry for the purpose of cutting, drilling, welding, marking, lithography and micromachining utilizing high-power domain. The elemental identification of oil well structure is investigated during drilling using high power Yb:silica MOFPA lasers [11]. There are the applications such as information transmission, free-space communication and printers that high beam quality is needed. In this case, a low loss SM core fiber is essential. High-power SM lasers are required to pump erbium (Er)-doped fibers and Raman laser amplifiers [12]. An efficient coupling of a high-power pump source into the fiber core is necessary in order to attain high powers. One possible strategy is to employ DC fibers in which the strong pumping source is efficiently coupled into the multimode cladding, where it is much larger than a typical SM core [13]. After the invention of the DC fibers, the output powers of the doped structures have been lifted by several orders of magnitude, afterwards immense activities have been devoted to the relevant topics. In general, the DC fiber lasers demonstrate several inherent features including [14] non-uniformly distributed population inversion due to end-pumping, single-pass high-gain and large ratio of gain length to cross-sectional area, however the losses are distributed along the fiber length. Furthermore, Yb doping is attractive for high-power cladding-pumped fiber lasers, particularly high pump absorption gives rise the ultimate efficiency [14], [15]. In the same time, Yb-doped fiber lasers are getting renown and popular to be an alternative high power sources with narrow linewidth.
Presently, the rate equations are still taken into account as the most powerful tools to analyze the laser characteristics along the fiber [16], [17]. The previous papers concerning numerical loss calculation, mainly explain the solution of rate equations for the configurations without considering the distributed component’s loss and ASE effect [13], [16], [18], [19], [20]. It is worthwhile to mention that the pump coupling, end-face cleaving and splicing losses are not negligible in a factual laser system. Imperfections in splicing include core non-concentricity, lateral and angular misalignments, difference in core diameters, numerical apertures and cladding shape of two fiber end separation casualties [21]. Those articles focused mostly on scattering coefficients for the laser radiation (αs) and the background loss (αp) of the pump wave in the fiber lasers [13], [14], [18], [19], [22], [23], [24]. Hence, several errors come up during calculation of high power lasers.
Inspecting the similar numerical analysis in the literatures, the modified model given here has some features regarding the dominant effect of numerous cavity losses mainly due to the optical components and ASE power. The reforming configuration represents better insight respect to the common schemes that do not include losses.
While the characteristics of a home-made SM Yb:silica MOFPA array were measured in our previous work [25], an extensive numerical analysis was carried out too. A set of coupled steady-state rate equations is introduced by making use of the relevant parameters. The dynamics of Yb3+-doped silica fibers is brought by solving iteratively appropriate modified numerical rate equations of a homogeneous gain media according to the dopant atomic structure. Using the fourth-order Runge–Kutta method with the shooting technique for initial conditions, the effect of component losses are considered to assess the laser efficiency as well as the contribution of ASE and gain on the amplifier performance.
Second, simulation results demonstrate the evolution of the upper state population, pump and signal as well as forward and backward ASE powers at different fiber locations. The correlations of fiber length and dopant concentration with the output performance are investigated as well. The results have shown that the lasing threshold, slope efficiency and the optimum length are strongly dependent on losses. Furthermore, the rigorous numerical solutions are in good agreement to the empirical data to emphasize the accuracy of the analysis. Despite, clustering and quenching in Er-doped fibers are known to be significant factors, however the model ignores polarization effects and interactions between neighboring ions for Yb-doped fibers as expected. Eventually, there are no significant nonlinear optical effects such as stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) as well as thermal damages up to 50W-CW SM pump powers [14]. Hence, those events demonstrate negligible effects in this work.
Section snippets
Experimental setup
An all-fiber monomode narrow-linewidth laser array is arranged as shown in Fig. 1 which operates at CW regime. The alignment of the system is implemented by fusion splicing of all optical components. The conceptual design for the SM DC fiber laser is depicted in Fig. 1(a). It contains the Yb-doped gain fiber pumped by a diode laser, a 7×1 end-pumped combiner and a pair of FBGs. A fiber-coupled laser diode (105/125 μm, 0.15 NA delivery fiber) is employed to provide the output power up to 4 W at 976
Laser oscillator rate equations
The local rate equations describe the dynamics of the emission and absorption processes of the rare-earth ions within its host material by making use of its spectroscopic properties [28]. Fig. 3 demonstrates a model for the Yb3+ energy level structure, consisting of two manifolds; the ground state 2F7/2 (with four Stark levels labeled L0, L1, L2 and L3) and a well-separated excited state 2F5/2 (with three Stark levels labeled U0, U1 and U2), which is seated ~10,000 cm−1 above the ground level.
Results and discussion
The impact of component losses are investigated along the optimum length, coupling efficiency and laser output power, as well as undesired ASE effect on the fiber amplifier performance. In comparison, the numerical solution for an ideal system is obtained assuming negligible loss coefficients. A CW SM Yb3+-doped silica MOFPA configuration is chosen for the simulation which emits a signal beam at 1082.5 nm involving forward pumping at 976 nm transition. The corresponding parameters are tabulated
Conclusion
This work is a continuation of our previous investigations on various gain media [51], [52], [53], [54], that particularly focuses on the performance of Yb:silica MOFPA arrays [25], [30], [31], [34], [55], [56], [57], [58], [59].
Here, a modified numerical method is introduced to determine the losses that burden by the fiber laser amplifiers. A linear cavity CW SM Yb-doped DC MOFPA configuration is modeled regarding the solution of rate equations enhanced by ASE parasitic noises as well as the
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