Theoretical Study of High Power Mode Instabilities in 2μm Thulium-Doped Fiber Amplifiers

We studied the high power mode instabilities (MI) in 2μm thulium-doped fiber amplifier theoretically. The MI threshold powers of two kinds of thulium-doped fiber are studied. It revealed that the threshold power of thulium-doped fiber with core/inner cladding diameter being 20/400 is about 1.3kW while that of 25/400 thulium-doped fiber is about 610W, which means that the power level of 2μm thulium-doped fiber amplifiers is about to running into MI issues. Keywords—mode instabilities, thulium-doped fiber, high power fiber amplifier Due to the impressive development of high brightness diode pump technology and large mode area double clad fiber craft in recent years, fiber laser systems have rapidly evolved into laser sources able to deliver output powers beyond myriadwatt level with diffraction-limited beam quality [1]. However, with the current technological limitations, large mode areas inevitably results in multimode operation, which in conjunction with high average powers has led to the onset of a new effect: mode instabilities (MI) [2]. The onset of MI currently limits the further power scaling of ytterbium-doped fiber laser systems with diffraction-limited beam quality. Thulium fiber lasers, which emits in the 1.9-2.1 μm wavelength range and has many useful applications, have undergone rapid development in power without MI phenomenon reported [3, 4]. Thulium fiber lasers suffers severer quantum defect [5], heat load of which is thought to be the main cause of MI [2]. Although the MI in 2μm thulium fiber amplifier, has not been reported, it is only natural that, with average powers growing increasingly fast, even this kind of fiber amplifiers run into MI issues sooner or later, the study of which has not been reported. In this manuscript, the theoretical study of MI in 2μm thulium fiber amplifier is presented for the first time. It is known that 2μm thulium fiber amplifier is pumped around 793nm and via a cross relaxation, the quantum defect of which can be expressed as (vp-2vs)/2vs. Therefore, the heat power density Q in the semi-analytic model, which is developed by K. R. Hansen et al.[6], should be modified as       , 1 , 2 s p Q t g I t             r r r (1) Then the quantum-noise-induced MI threshold powers, which is thought to be the ultimate limitation on power scaling of fiber amplifier imposed by MI [6], of two thulium fiber amplifier (thulium-doped fibers with core/inner cladding diameter being 20/400 and 25/400, respectively) are calculated and the results are shown in Fig. 1, which shows the high order mode content as a function of output laser power. Some of the parameters, such as injected seed power, wavelength of the signal and pump laser, core NA of the active fiber, are taken the same as that in Refs. [5] and [6], respectively. It is shown that the threshold power of 20/400 and 25/400 thulium fiber amplifier is 1.3kW and 610W, respectively, which reveals that the power level of 2μm thulium-doped fiber amplifiers is about to encountering MI limitation [5, 6]. Fig.1 High order mode content versus output laser power.