1. Introduction

Fiber lasers have earned its solid reputation due to their good beam quality and remarkable power scalability, and been widely used in medical treatment, material processing, additive manufacturing and other fields [1,2]. However, further power scaling of fiber lasers is limited by the well-known stimulated Raman scattering (SRS) [3–5] and transverse mode instability (TMI) [6–8]. They all show threshold characteristics. When the output power reaches a certain threshold, the SRS effect will transfer the desired signal power to a longer wavelength exponentially, while the beam quality will be degraded when the TMI threshold is reached. These two phenomena are usually considered to be independent, just like the two ends of the balance, until a new phenomenon named SRS-induced beam distortion was found in 2017, which manifest itself as the simultaneous occurrence of TMI and SRS [9], and a fluctuation on a scale of seconds [10]. That phenomenon is quite different from the traditional dynamic mode instability with a kHz energy fluctuation [11], and become another factor limiting the power scaling of near-single-mode fiber lasers [12]. However, the origin of SRS-induced beam quality distortion under TMI threshold is still under debate.

One possible origin is due to the heat accumulation in the process of Stokes frequency shift, which changes the distribution of the refractive index in the fiber core through the thermo-optical effect, resulting in the generation of higher-order modes (HOMs) based on coupled mode theory [13]. According to this explanation, the same amounts of heat accumulation in the fiber core will lead to the the same degree of beam quality degradation for a specific fiber laser.

The other is related to nonlinear effect. W. Liu, et al., [12] theoretically derive that the inter mode mixing (IM-WM) effect caused by SRS can lead to mode distortion. While the recent experimental results of R. Tao’s research team demonstrated that the Raman light mainly exists in FM after the onset of SRS-induced mode distortion, which rules out the aforementioned IM-WM origin [14]. They believe that the real reason for beam quality degradation is the core-pumped SRS effect [10,14], and propose a theoretical model based on the hypothesis utilizing the mode decomposition technique [15]. That hypothesis holds that, the signal power is mainly concentrated in the fundamental mode (FM) and presents a Gaussian distribution before the onset of SRS, while after the SRS occurs, the Stokes preferentially weakens the center region of the signal, so that the Gaussian beam degenerates into a super Gaussian one, and even a hole appears in the center, which leads to the increase of HOMs. According to this hypothesis, the origin of beam quality degradation does not involve heat, and the same Stokes intensity should result in the same degree of beam quality degradation.

However, in a CW-pumped laser system, the Stokes intensity and the heat accumulation in the process of Stokes frequency shift always ebb and flow synchronously. Thus, it is difficult to distinguish whether the final beam quality degradation is determined by one of these factors or both. QCW fiber laser provides a possibility, which can generate millisecond square pulses by direct pump modulation. During the pulse duration, the signal has the same properties as a CW laser, but the heat accumulation in the fiber core is much lower due to the periodic off output. For example, when the duty cycle (DC) of the QCW laser is set to 5%, the heat accumulation in the process of Stokes frequency shift is only 1/20 of that of the CW laser at the same peak power, or even less. In this way, we have the opportunity to distinguish the effects of these two factors on beam quality degradation.

2. Experimental setup

The experimental setup is shown in Fig. 1. A co-pumped oscillator regime is adopted for lower SRS threshold [1], and all the core/cladding diameter of the components are 20∼20.5/400 µm with a core numerical aperture (NA) of 0.065. The pump power is provided by 981 nm LDs, and injects into the gain fiber via a (6 + 1) × 1 combiner. All the LDs can work continuously (CW mode) or be modulated by square wave (QCW mode). The gain fiber is 25 m long to provide a total absorption of 10 dB at 981 nm and coiled in a racetrack groove with a diameter of 11.5-17.5 cm on the water-cooled plate. The central wavelength, reflectivity, and -3 dB bandwidth of the high reflection fiber bragg grating (HR FBG) are 1080.06 nm, 99.9%, and 1.99 nm, respectively, and that of the output coupled fiber bragg grating (OC FBG) are 1079.97 nm, 10.9%, and 0.98 nm, respectively. The backward output port of the oscillator is cleaved with an angle of 7.9° to reduce the feedback coefficient [3]. A section of homemade cladding power stripper (CPS) is performed on the tail of the quartz blockhead (QBH) to strip the residual pump and high-order signal mode propagating in the fiber cladding. According to the fiber waveguide theory, the laser is a typical few mode fiber, whose fiber core can supports three LP modes at 1080 nm, namely LP01, LP11 and LP21, corresponding to the maximum core diameter of 20.5 µm.

 

Fig. 1. Schematic diagram of experimental setup.

Download Full Size | PDF

3. Experiment results and discussion

3.1 Output properties of CW-pumped scheme

Firstly, we need to confirm the position of SRS-induced heat accumulation, and rule out the interference of TMI to the experiment. The output characteristics of Configuration I is investigated under the CW-pumped scheme. When the pump power reaches 2265 W, the output power is 1756 W, with a SRS intensity -36 dB lower than the signal, as shown in Fig. 2(a) and 2(b). In order to enhance the strength of the Stokes light outside the cavity, a 16 m long 20/400 µm Ge-doped fiber (GDF) with a core numerical aperture (NA) of 0.064 is added between OC FBG and QBH (Configuration II) . According to the fiber waveguide theory, the newly added GDF can not support the LP21 mode when the transmitted wavelength is greater than 1050 nm. When the pump reaches the same 2265 W, the output power is 1626 W, with a SRS intensity -12 dB lower than the signal, as shown in Fig. 2(a) and 2(b). The optical-to-optical conversion efficiency decreased from 77.5% to 71.8%, mainly for two reasons, the welding loss and the filtering out of the possible LP21 mode of signal by the newly added GDF. Therefore, the Stokes components in the output spectrum of Configuration II mainly come from the amplification of Stokes by GDF outside the cavity. There are two main sources of heat accumulation in GDF, the quantum defect in Stokes frequency shift process and the background loss of laser transmission. The latter source is small and can be ignored, thus the heat accumulation in GDF is mainly the quantum defect induced by SRS process. The following discussion and further QCW-pumped experiments are carried out under Configuration II.

 

Fig. 2. Output properties of CW-pumped scheme. Output power and efficiency (a), and spectra (b) at pump power 2265W in two configurations. (c) The evolution of beam quality (blue markers) and SRS energy ratio (SER, purple markers) as a function of pump power in Configuration II. (d) The temporal dynamical and its FFT at the highest output power in Configuration II.

Download Full Size | PDF

The illustration in Fig. 2(b) show the normalized linear values of the spectra. Since the energy of signal light and Stokes light is mainly concentrated in the range of 1050 ∼1110 nm and 1120∼1150 nm respectively, the energy proportion of signal and Stokes light in the output spectra can be calculated through spectral integration. The SRS energy ratio (SER) is defined as the proportion of the spectral envelope energy of 1120∼1150 nm in the full spectral envelope energy, to characterize the Stokes intensity in the laser. The evolution of beam quality M² and SRS energy ratio as a function of pump power are studied as shown in Fig. 2(c), implying that there is a srong relationship between the beam quality degradation and Stokes light enhancement. There are no characteristic spikes of kHz level in the FFT transformation of time-domain signals when the output power exceed 1600 W as shown in Fig. 2(d), implying that the TMI threshold of the system is greater than 1600 W (pump 2300 W). As QCW-pumped scheme is conducive to improving the TMI threshold of the system [16,17], the TMI threshold in the QCW-pumped scheme is no less than 1600 W (pump 2300W). In the QCW-pumped operations next section, the maximum average pump power and the average output power did not exceed this threshold, so the TMI can be ruled out in this process, and the beam quality distortion occurs under TMI threshold.

3.2 Output properties of CW-pumped scheme and discussion

The experiment of QCW-pumped scheme is carried out based on Configuration II. The LDs are modulated simultaneously to provide pump power with a repetition rate (PRF) of 1kHz, and duty cycle (DC) of 10%. The modulation current peak of each LD do not exceed the rated working current of the CW-pumped scheme to ensure the safety and the stability of the pump output. The beam quality M² as a function of the SER is shown in Fig. 3(a). The same SER implys the same spectral morphology and the same Stokes intensity in the output laser as shown in Fig. 3(b),while a larger M² value represents an increase of HOMs components. Figure 3(a) shows that, when the SER is very small,for example, less than 1% (Stokes intensity about -20 dB lower than the signal), the beam quality change little for both CW-pumped and QCW-pumped schemes. But with the increase of SRS energy ratio, the distortion of M² in QCW-pumped scheme is much smaller than that of CW-pumped scheme at the same Stokes intensity. That is inconsistent with the inference of the core-pumped Raman effect theory, indicating that the theory is not applicable to explain the experimental phenomena here. The 5% DC experiment that will be discussed below illustrates this more intuitively.

 

Fig. 3. Experimental results of different pumping schemes. (a) The beam quality as a function of SRS energy ratio in two cases: CW-pumped scheme (red dot) and QCW-pumped scheme (blue square). (b) Spectra in two cases when the SRS energy ratio are about 6%.

Download Full Size | PDF

In further experiments, we set the PRF to 1 kHz, and measured the evolution of beam quality with Stokes intensity at different DCs in detail. The results are shown in Fig. 4. It can be seen from Fig. 4(a) that, with the increase of DC, the distortion of M² becomes faster and faster, approaching the CW-pumped scheme. On the contrary, when the DC is reduced to 5%, the beam quality distortion is almost independent with the SRS energy ratio. Even though Stokes energy accounts for 20% of the total energy (- 5 dB lower than signal in the spectrum), M² only increases by 0.02, and signal far-field intensity profile remains Gaussian as shown in Fig. 4(b). These phenomena conflict with the core pumped Raman effect theory proposed in [14,15]. According to that theory, whether in the CW-pumped scheme or QCW-pumped scheme, the mode degradation degree should be the same under the same SRS energy ratio, which is obviously inconsistent with the experimental phenomena.

 

Fig. 4. Experimental results of different DC where PRF is 1 kHz. (a) The beam quality as a function of SRS energy ratio. (b) Spectra and signal far-field intensity profile at DC = 5%.

Download Full Size | PDF

The amount of heat induced by quantum defect can be approximately calculated by the formula,

It can be seen from Fig. 5 that the degradation curve of M² with quantum defect is highly consistent at different duty cycles, which indicates that the origin for beam quality degradation is heat accumulation. According to this explanation, the strategies to suppress the degradation of beam quality should be to reduce the energy density of the laser output, such as using long tapered fiber as an output [18]. Or to reduce the heat accumulation of quantum defects, such as using the QCW-pumed scheme, accelerating heat dissipation, and so on.

 

Fig. 5. The curve of beam quality versus quantum defect under different duty cycle.

Download Full Size | PDF

4. Conclusion

With the favor of QCW fiber laser oscillator, we separate thermal and Stokes intensity in our research, and intuitively proved the origin of SRS-induced beam quality distortion under the TMI threshold for the first time. We analyzed the evolution of the beam quality M² with the SRS energy ratio under different duty cycles, and found that when the duty cycle gradually increasing to approach 100% (CW-pumped scheme), the beam quality distortion became faster and faster with the increase of Raman ratio, while when the duty cycle is reduced to 5%, the beam quality M² distortion is almost independent with the SRS energy ratio. On the other hand, the degradation curve of M² with quantum defect is highly consistent at different duty cycles, which indicates that the origin for beam quality degradation is heat accumulation rather than core-pumped Raman effect theory [14]. Thus, the strategies to suppress the degradation of beam quality should be to reduce the energy density of the laser output to reduce the heat accumulation of quantum defects.