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Abstract
An all-fiberized linearly polarized nanosecond master oscillator power amplifier based on polarization-maintaining large-mode-area Yb-doped tapered double cladding fiber (T-DCF) is comprehensively investigated. Firstly, excellent performance of the Yb-doped T-DCF for suppressing nonlinear effects, including stimulated Brillouin scattering (SBS) effect and spectral broadening effects, is experimentally demonstrated and qualitatively analyzed. An SBS-free average output power of 8.8 W is obtained under pulse duration of 3.8 ns and repetition frequency of 80 kHz, with peak power of ∼30 kW, pulse energy of 110 µJ and nearly transform-limited linewidth of < 283.8 MHz respectively. The polarization extinction ratio is > 16 dB and near-diffraction-limited beam quality with M2 factor of 1.2 is maintained at the maximal output power. Moreover, the discussion on the optimization of the system for further power scaling is carried out based a nonlinear dynamic model that is capable of simultaneously evaluating the time-domain and frequency-domain evolution properties of the narrow-linewidth linearly-polarized pulsed laser, and meaningful conclusion is obtained.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The pulsed fiber lasers, with more tunable parameters and higher peak power compared with their continuous wave (CW) counterparts, have found tremendous applications in various fields with their rapid development in recent years [1]. However, besides higher peak power, narrower linewidth and higher coherence are radically required in some special situations, such as deep-space communication [2], coherent lidar [3,4], terahertz source generation [5,6], narrow linewidth frequency doubling [7,8] and so on. Among all kinds of pulsed laser, the fiber laser with nanosecond (ns) duration is almost irreplaceable candidate for narrow-linewidth output due to relatively long pulse duration and more diverse pulsing regimes in comparison to the mode-locked ones of which the spectral linewidth is generally broadened due to the existence of extremely multiple longitudinal modes and thus strong nonlinear effects during power amplification.
Generally, there are mainly three kinds of ways to generate ns narrow-linewidth pulsed seed laser. One way is to internally switch a linear-cavity resonator, mainly including gain-switched laser diode/fiber-based oscillator [9–12] and Q-switched single-frequency fiber laser through the piezoelectric ceramic [13–15]. Another way is to externally modulate a CW single frequency laser by the electrical-optical intensity modulator (EOIM) or the acoustic-optical modulator (AOM) [16–18]. Besides, the mode-locked pulse laser based on well-designed fiber ring-cavity with nonlinear loop mirror (NOLM) is also capable of realizing narrow-linewidth output [19,20]. In general, the spectral linewidth of the gain-switched LD and the mode-locked pulsed laser is relatively wide compared with other schemes. The Q-switched single-frequency pulsed laser via the piezoelectric ceramic has long pulse duration and low repetition frequency due to the response speed limitation of the piezoelectric ceramic, while the pulse duration would vary nonlinearly with the repetition frequency changed [6]. By contrast, the external modulation method provides wider controllable tuning range of both the pulse duration and the repletion frequency while maintaining narrow spectral linewidth. Besides, it is compatible with the pulse shaping techniques based on single or cascaded EOIM/AOM [21,22] to realize arbitrary pulse shape. Once narrow-linewidth pulsed seed laser is available, high power output becomes achievable based on the master oscillator power amplification (MOPA) configuration, especially for the Yb-doped MOPA that has low quantum deficit and ultra-high efficiency [23,24].
However, during the power scaling process, the detrimental nonlinear effects must be carefully addressed, especially the SBS effect which is regarded as the main factor limiting the power scaling [25] and the spectral broadening effects which decline the laser coherence [26]. Generally, employing active fiber with large mode area is the most common way to synchronously suppress SBS and spectral broadening effects, such as large-mode-area (LMA) step-index fiber [24,27] or photonics crystal fiber (PCF) [12,28]. If combined with appropriate doping profile or anti-waveguide acoustic structure in the fiber core, the capability of the LMA fiber in suppressing nonlinear effects could be further enhanced [29–31]. However, for the LMA fiber, too large mode area may make it quite challenging to handle the beam quality with the output power increasing. Besides, the utilization of PCF generally means a bulk-optical configuration that may sacrifice the compactness of the system and increasing the risk of facet damage. Broadening the linewidth of seed laser to some degree by phase modulation is also a feasible way for SBS suppression [32,33], but it is at the cost of impairing laser coherence and thus hampering some practical applications. Fortunately, some passive methods not against maintaining narrow linewidth and good beam quality have been proven effective, such as applying the stress gradient [34,35] or temperature gradient [36,37] to gain fiber, changing the doping concentration of the gain fiber [38], adopting the backward pumping scheme [39,40], and so on.
The tapered double cladding fiber (T-DCF), a newly-proposed fiber with nonuniform longitudinal geometry, has been demonstrated to be intrinsically effective for SBS suppression owing to its dependence of SBS frequency shift on the core diameter [41]. Besides, with the parameters of T-DCF well optimized, excellent beam quality could also be maintained owing to its mode selection effect in spite of large core diameter [42,43]. So, the suppression on nonlinear effects could be additionally enhanced by employing large mode area [44–46]. All of these advantages make T-DCF an attractive candidate for high power pulsed laser with excellent beam quality and narrow linewidth. Up to now, several representative high-peak-power pulsed lasers of picosecond regime have been demonstrated [47–52], and the development of ns fiber lasers with narrower linewidth has also made great progress [12,22,53–56]. However, most of the reported work possessed spectral linewidth of near gigahertz or far more than ten GHz. In some special application situations like coherent detection, narrower linewidth would be extremely required. By far, the Yb-doped T-DCF-based pulsed laser with both nearly-transform-limited linewidth and high peak power is still absent, let alone a linear-polarization one facing stronger SBS effect compared with its random-polarization counterpart [57]. Furthermore, the theoretical analysis on the LMA T-DCF-based narrow-linewidth ns pulsed laser is also lacked up to date.
In this paper, we demonstrate a linear-polarization high-peak power ns pulsed laser with near-transform-limited linewidth based on a compact all-fiber MOPA configuration. The power amplification chain is capable of simultaneously realizing narrow linewidth and high output power owing to the utilization of a short polarization maintaining (PM) Yb-doped T-DCF with high concentration and large mode area in the main amplifier to suppress SBS and spectral broadening effects. As a result, a peak power of ∼30 kW with near-transform-limited linewidth of 283.8 MHz and pulse energy of 110 µJ is realized. Excellent polarization extinction ratio (PER) of ∼16 dB and nearly-diffraction-limited beam quality are also ensured. Furthermore, the approaches to optimizing present system for further power scaling is discussed based on a nonlinear model capable of evaluating the power scaling and spectral evolution process of narrow-linewidth linearly-polarized pulsed laser.
2. Experimental setup
The experimental setup is depicted in Fig. 1. The MOPA configuration consists of a ns pulsed seed laser, three-stages pre-amplifiers and a main amplifier.
Fig. 1. Experimental setup. CW: continuous wave, ISO: isolator, AFG: arbitrary function generator, EOIM: electric-optical intensity modulator, AOM: acoustic-optical modulator, LD: laser diode, LMA: large mode area, PM: polarization maintaining, T-DCF: tapered double cladding fiber.
2.1 Nanosecond pulsed seed laser
The ns pulsed seed laser is generated by externally modulating a 1064 nm PM continuous-wave (CW) single-frequency fiber laser via two cascaded EOIMs. The two cascaded EOIMs are integrated together and triggered by a common arbitrary function generator to fully control the pulse shape. As a result, the modulated pulsed seed laser features steep rise/fall edges and thus a nearly rectangular shape in temporal domain. To achieve high-peak-power output, the modulation frequency is fixed at a low level of 80 kHz, while the pulse duration is tunable with a minimum value of 4 ns. A boost amplifier utilizing single-mode PM Yb-doped fiber with core diameter of 6 µm is firstly employed to boost the power of seed laser, to provide sufficient injection power for the following cascaded pre-amplifiers. Then, an acoustic-optical modulator (AOM) is used to remove the amplified spontaneous emission (ASE) and residual CW component, to ensure the purity of the pulsed seed laser [21]. The 5% port of the 95:5 coupler is used to monitor the property of the boosted seed laser. As shown in Fig. 2 is the pulse profile of the seed laser under different pulse durations captured by the high-speed oscilloscope, indicating that the boosted seed laser still possesses nearly rectangular pulse shape.
2.2 Three pre-amplifiers
Three pre-amplifiers are arranged to provide sufficient injection power for the main amplifier. The 1st and 2nd pre-amplifiers are both based on PM single-mode Yb-doped fiber as used in the boost amplifier, while the 3rd pre-amplifier adopts a PM double cladding Yb-doped fiber with core/inner cladding diameters of 10/125 µm. Between adjacent stages of the three pre-amplifiers, a PM bandpass filter (BPF) is employed to remove ASE and a PM isolator is inserted to block the backward power from the following amplifier. As a result, the average power of ns pulsed laser is boosted to ∼300 mW level. Then, a PM circulator is used to monitor the backward propagation light stemming from the main amplifier. Finally, the pre-amplified ns pulsed laser is injected into the main amplifier via a signal/pump combiner. The output port of the combiner is 0.89 m-long and has core/inner cladding diameters of 25/250 µm.
2.3 Main amplifier
In the main amplifier, a piece of high-concentration Yb-doped PM T-DCF with total length of ∼1.27 m is adopted. Different from the traditional T-DCF that has absolutely gradually-changed diameter along the whole fiber, only the middle part of the PM T-DCF used here is tapered, namely both sides have uniform core diameter to make it easily matched with the fiber-based devices to build a robust all-fiber structure. The longitudinal profile of the PM T-YDF has been described in Ref. [58]. The core /inner cladding numerical apertures are 0.064 and 0.5, respectively. The tapered zone is ∼ 0.74 m-long with nearly linearly-changed diameter, and the lengths of the uniform parts at the small end and the large end are ∼0.33 m and ∼0.2 m, respectively. The core diameters of the small end and the large end are ∼36 µm and ∼58 µm respectively, corresponding to a taper ratio of 1.61. The cladding pump absorption coefficient is 12.1 dB/m at 975 nm. It is worth mentioning that, the splicing quality of the point located at the injection of the main amplifier is well handled to avoid the excitation of the higher-order modes to the utmost and thus ensure good beam quality as much as possible. An endcap is spliced at the end to avoid facet damage and possible parasitic lasing. The output beam is collimated by a free-space collimator and then its overall properties are evaluated. The residual pump light is stripped by the dichroic mirror before all the measurements.
It is necessary to state that, the co-pumping regime is really adequate for efficient pump absorption due to high enough cladding pump absorption coefficient of the PM T-DCF here, although the counter-pumping regime could sometimes be optionally employed to improve pump absorption especially when low-brightness pump LD are used [59,60]. The counter-pumping regime may help to suppress nonlinear effects, but it seems not the exclusive superiority of the T-DCF, as also demonstrated in conventional fiber-based amplifiers [61–63]. Moreover, counter-pumping regime means a bulk-optical structure absolutely and thus may impair the robustness of the system to some degree. At present, the commercial combiner compatible with the large end of the PM T-DCF is still absent. So, the co-pumping regime from the small end is a feasible choice to simultaneously ensure a robust all-fiber structure and exploit the advantage of the LMA T-TCF in suppressing nonlinear effects and maintaining good beam quality, as has been demonstrated in Ref. [45,58,64].
3. Results and discussion
3.1 Output power property
The power property of the main amplifier is firstly demonstrated and analyzed. Figure 3(a) shows the dependence of the average output power and backward power on the pump power in the main amplifier when the pulse duration is set as 4 ns. The slope efficiency of the average output power is ∼53.3% and the maximal output power reaches 9.5 W. It is noted that the backward power tends to burst due to the occurrence of SBS effect, and the same phenomenon is also observed under other pulse durations, as shown in Fig. 3(b).
Fig. 3. (a) Dependence of the average output power and backward power on the pump power under pulse duration of 4 ns; (b) Evolution of the backward power with output power increasing under varied pulse durations.
Here, we define SBS threshold as the output power to which the increasing ratio of the backward power exceeds 0.5mW/W. Based on such definition, corresponding SBS thresholds characterized by average power for varied pulse durations are shown in Fig. 4. In addition, SBS thresholds in the form of peak output power are also displayed in Fig. 4, which are calculated by the integration method as below [65]:
Form Fig. 4, it is found that SBS threshold increases with the pulse duration decreasing. This is mainly related to the changing effective fiber length and spectral linewidth when the pulse duration is tuned. Theoretically, for a CW linear-polarization single-frequency single-mode laser propagating in the uniform passive fiber, the SBS threshold could be estimated by the formula [57]:
where gB is SBS peak gain coefficient, Leff is effective fiber length, and Aeff is acoustic-optical interaction area which is approximately equal to the effective mode area of signal laser. However, for the pulsed laser, Leff should be modified as Loverlap, which characterizes the interaction length of the signal light and the acoustic field [66]:Fig. 5. (a) The value of Loverlap under different pulse durations; (b) 3dB spectral linewidth of the pulsed laser from the 3rd pre-amplifiers.
Theoretically, the SBS-free output power can be continuously increased by reducing the pulse duration. However, this approach will intrinsically broaden the spectral linewidth. On the other hand, the enhancement of the output peak power will in turn aggravate the spectral broadening due to the nonlinear effects such as SPM effect and cross-phase modulation (XPM) effect. Out of question, sometimes it is necessary to balance the output peak power and spectral linewidth.
3.2 Temporal property
The temporal intensity of the ns pulsed laser along the whole chain is collaboratively measured by a high-speed photo-diode (response frequency=5 GHz) and a digital oscilloscope (maximal analog response frequency of 1 GHz and sampling rate of 5 GS/s. As shown in Fig. 6(a), the output pulses with set pulse duration of 4 ns are stable at the maximal SBS-free output power of 8.8 W. Due to the gain saturation effect, the rising edge of the amplified pulses is reshaped and becomes steeper and steeper than the falling edge with the output power increasing [21]. As a result, the pulse shape deviates from that of the seed laser. For example, when the pulse duration of seed laser is set as 4 ns, the pulse duration after the amplification is narrowed to be ∼3.8 ns, as depicted in Fig. 6(b). As a result, this reshaping effect contributes to the enhancement of pulse peak power, as illustrated in Fig. 4(b). It was reported that the pre-shaped pulsed seed laser can help to maintain a Gaussian-like pulse shape and thus benefit impairing SBS effect [54]. This method could be introduced in our work if programmable arbitrary waveform generator is available in the future.
Fig. 6. (a) The oscillogram of the pulse trains at the maximal SBS-free output power of 8.8 W; (b) The pulse profiles of the seed laser and the main amplifier at different output powers.
3.3 Output spectrum and 3dB spectral linewidth
The output spectrum of the amplified pulse laser with varied pulse duration is monitored by a spectrum analyzer. When the pulse duration of seed laser is set as 4 ns to realize highest output power in present condition, the measured spectrum indicates that there is no residual pump light and ASE at the maximal output power of 9.5 W (as shown in Fig. 7(a)), despite the fact that operating at low repletion frequency is generally prone to ASE. This result demonstrates the ability of the system to obtain high-peak power narrow-linewidth pulsed laser with pure spectrum. The 3 dB spectral linewidths of the amplified pulses are shown in Fig. 7(b). For all the pulse durations, the spectral linewidths are not obviously broadened throughout the power scaling process compared with the injected laser from the 3rd pre-amplifier, illustrating that the large mode area and short length of the PM Yb-doped T-DCF succeed in suppressing spectral broadening effects in high peak power situation [67,68]. Nonetheless, compared with the seed laser, the spectral linewidth is broadened a little as shown in Table 1, which is mainly induced by the nonlinear effects in the pre-amplifiers due to their small core diameter. It is noted that, with the pulse duration reduced, the spectral broadening factor generally shows a trend to be larger gradually, due to the increase of the pulse peak power.
Fig. 7. (a) Output spectrum at the maximal output power; (b) Evolution of 3 dB spectral linewidth under varied pulse durations.
Table 1. The comparison of the spectral linewidth of the seed laser and the main amplifier at SBS threshold level
For the 4 ns seed pulse, the 3 dB spectral linewidth is measured to be 283.8 MHz at the maximal SBS-free output power (pulse duration is narrowed to be 3.8 ns after the amplification, as mentioned above). Corresponding spectral detail is shown in Fig. 8(a). It is known that, when the product of 3 dB pulse width and 3 dB spectral linewidth of a unchirped Gaussian-like pulse is near 0.441, it can be considered as transform-limited pulse. For a high-order super Gaussian-like pulse with nearly rectangular shape and pulse duration of 3.8 ns, its theoretical product of pulse width and spectral linewidth reaches 0.88, as shown in Fig. 8(b). By calculation, the product of 3 dB pulse width and 3 dB spectral linewidth of the nearly rectangular pulse in our experiment is 1.078 at the maximum output power. So, it is rational to consider that the amplified pulse possesses nearly transform-limited linewidth. To the best of our knowledge, this represents the narrowest linewidth of the linearly polarized ns pulsed laser with peak power of such level based on a monolithic step-index fiber-based MOPA up to now. In Ref. [12], a Gaussian-like seed pulse with pulse duration of <2 ns and spectral linewidth of 1 GHz (Δt·Δν≈2) has been boosted to 180 kW with energy of 220 uJ. Although the product of pulse width and spectral linewidth of the seed pulse was close to transform limitation to some degree, the spectral linewidth after the amplification was not clearly given and it may be broadened to some degree in fact.
Fig. 8. (a) Spectral detail at the maximum output power when seeded with the pulse of 4 ns; (b) Theoretical pulse shape and corresponding spectrum (inset) of the rectangular pulse.
3.4 PER and beam quality
When seeded with the pulse of 4 ns, the PER over power scaling is measured by collaboratively using a l/2 waveplate and a polarization beam splitter (PBS). It is found that, the PER is above 16 dB even at the maximal output power (Fig. 9(b)), demonstrating good polarization maintaining ability of the PM T-DCF. Besides, at the maximum output power, the M2 factor is measured to be 1.2 by a beam quality monitor (PRIMES) (as shown in Fig. 10), indicating nearly diffraction-limited beam quality.
Fig. 9. (a) The PER measurement devices; (b) Evolution of PER during power scaling process when seeded with the pulse of 4 ns.
4. Analyses on further optimization of the system
To deeply understand the potential of the LMA Yb-doped T-DCF-based linearly-polarized narrow-linewidth ns fiber amplifier, a nonlinear dynamic model which can simultaneously evaluate the time-domain and the frequency-domain properties of pulsed fiber laser is introduced. Then, the optimization approaches aiming at present experimental configuration is discussed.
4.1 Theoretical model and simulation condition
The nonlinear dynamic model is based on the SBS three-coupled amplitude equations and the power equilibrium equations. Besides, the SPM effect as well as XPM effect that mainly causes spectral broadening are all taken into account. The equations of the model are expressed as below [32]:
The values of the various parameters in the model are listed as in Table 2.
Table 2. Parameters and corresponding values in the theoretical model
It is worth emphasizing that, different from the conventional PM LMA fiber, Aao and νA of the PM T-DCF are varied parameters rather than constants. This difference is a key factor that should be considered in the simulation. Aao and νA are calculated by the formula, respectively [41,57]:
In the theoretical model, the complex amplitude of the signal laser is a key initial input which has direct influence on both the time-domain and the frequency-domain properties of output laser. To make the simulation condition consistent with the real experimental situation to the utmost, we choose the real experimental pulse injected into the main amplifier as the input of the theoretical model, which is captured by a high-speed digital oscilloscope with maximum sampling rate of 5 Gs/s (corresponding to the minimum time interval of 0.2 ns). To improve the calculation precision, the pulse profile is further interpolated in the simulation. Here, we take the pulse with set pulse duration of 4 ns as example. As shown in Fig. 12 is the captured real pulse profile after interpolation process. All the following simulations take this pulse as input.
Fig. 12. The profile of the real pulse injected into the main amplifier after the interpolation process
4.2 Simulation results and discussion
For the time being, suitable backward pump/signal combiner that can be compatible with the large end of the PM LMA T-DCF used in present amplifier is not available to achieve an all-fiber structure. Anyway, it is still significant to theoretically analyze the feasibility of employing backward pumping regime to enhance the performance of the PM T-DCF-based narrow-linewidth fiber laser. In our simulation, we firstly focus on this issue. Then, the optimization on the design of the T-DCF is further discussed.
4.2.1 Potential of employing the backward pumping regime
Firstly, SBS-free power property is concerned. In the simulation, SBS threshold is defined as the output power to which the ratio of the backward-propagation SBS Stokes power reaches 0.01%. Generally, this definition method is consistent with the way that recognizes the turn-point of nonlinear increase of the backward-propagation power in the experiment. The simulation results are shown in Fig. 13(a). For the forward pumping regime, the simulated SBS threshold peak power is 30.93 kW and agrees well with the experimental result of 29.97 kW. Under the backward pumping regime, SBS threshold is increased to 53.16 kW that is 1.72 times as high as under the forward pumping regime, revealing efficient suppression on SBS effect by the backward pumping regime.
Fig. 13. (a) The peak output power and backward peak Stokes power under the forward pumping regime (black mark) and the backward pumping regime (blue mark) respectively; (b) The evolution of the 3 dB spectral linewidth under the forward pumping regime and the backward pumping regime respectively, compared with the experimental result.
Moreover, the evolution of the spectral linewidth is also investigated. Both the simulated results and the experimental result are comparatively shown in Fig. 13(b). It is revealed that, for both the forward pumping regime and the backward pumping regime, the spectral linewidth is well maintained during the power scaling process and keeps consistent trend with the experimental data. By contrast, the spectral broadening effect under the backward pumping regime is better suppressed than under the forward pumping regime. For the forward pumping regime, there is a little gap between the simulated and experimental result, which may be attributed to the accuracy difference in the simulation condition and the experimental measurement. In the experiment, the accuracy of measured data is limited by the utmost frequency resolution of FP scanning interferometer (with nominal value of 7.5 MHz). However, in the simulation, the frequency resolution is as high as 2 kHz, which is capable of better reflecting the real spectral linewidth of the output laser. Typically, the spectral profiles and corresponding linewidths at SBS threshold are illustrated in Fig. 14. It is noted that the experimental result has similar profile with the simulated results, revealing the veracity of the measurement.
Fig. 14. The spectral profiles and corresponding linewidths at SBS thresholds: (a) experimental result under the forward pumping regime, (b) simulated result under the forward pumping regime and (c) simulated result under the backward pumping regime.
To sum up, above theoretical results show a promising perspective of employing the backward pumping regime to enhance the output power of linearly polarized near-transform-limited ns fiber laser based on the PM LMA T-DCF. In the future, with development of the backward pumping combiner, further power enhancement of linearly polarized near-transform-limited ns fiber laser can be expected.
4.2.2 Discussion on optimizing the tapered ratio of the PM T-DCF
Apart from employing the backward pumping regime to enhance the performance of the LMA T-DCF-based pulsed amplifier, optimizing the design of the LMA T-DCF itself may be a radical way to maximize its ability of suppressing SBS effect. It is out of question that further enlarging the core diameter along the whole fiber length can strengthen the suppression on SBS effect. However, overlarge diameter may deteriorate the beam quality and decline the buckling resistance property of the fiber, which may not meet the requirement of practical applications.
The tapered ratio, defined as the ratio of the diameter at the large end (d2) to the narrow end (d1), i.e. T = d2/d1, is a key parameter that maybe have an effect on the function of the LMA T-DCF in suppressing nonlinear effects. The equivalent diameter of the LMA T-DCF in present experimental is calculated to be 46.3 µm, based on the formula:
Then, we propose three theoretical designs in which the equivalent diameter deff is maintained to be same as the T-DCF used in present experiment while the tapered ratio is changed. The specified parameters of three theoretical designs as well as the T-DCF used in present amplifier are listed in Table 3. For the three theoretical designs, the core diameter of the small end is smaller than that of the T-DCF used in present amplifier, selected as 15.7 µm, 20.8 µm and 31 µm respectively to benefit achieving good beam quality while be compatible with mature commercial fiber devices such as LMA combiner, mode field adapter and so on. Correspondingly, the core diameter of the large end is 95.4 µm, 86.1 µm and 67.2 µm respectively, larger than that of the T-DCF used in present amplifier. It is noted that when the core diameter of the small end shrinks, the diameter of the large end expands inversely to keep the equivalent diameter deff as constant. The longitudinal profiles of the core diameter of these four T-DCFs are illustrated in Fig. 15.
Table 3. Comparison of the parameters of the four T-DCFs and the simulated SBS thresholds of the amplifiers employing them respectively
By calculation, SBS thresholds of the amplifiers employing present T-DCF and three theoretical designs are also listed in Table 3. It is found that SBS threshold decreases with the core diameter of the small end reducing under forward pumping regime. The 15.7-95.4 µm T-DCF-based amplifier has lowest SBS threshold of 1.98 W under pump power of 2.8 W. To seek the reason of this result, the peak power distributions of SBS Stokes light and the signal laser along the four T-DCFs at the pump power of 2.8 W are contrastively given in Fig. 16. It is indicated that, the diameter expansion of the rear part of the T-DCF helps to suppress SBS effect effectively. However, in the front part, the diameter shrink of the T-DCF remarkably enhances SBS effect, although the power of the signal laser is still low in this region (as shown in Fig. 16(b)). In other words, the diameter expansion of the small end contributes to suppressing SBS effect under forward pumping regime. This is a result of the fact that SBS Stokes light has maximal nonlinear gain along contrary propagation direction to the signal laser and that the SBS gain is inversely proportional to the core crosse-section area. It is noted in Fig. 16(b) that, the power of signal laser in 15.7-95.4 µm-based amplifier rises fastest at the front part of the fiber. The bigger the core diameter of the small end is, the slower the signal laser power rises. This is because the shrink of the diameter condenses the signal laser intensity and thus enhance its ability to extract active gain in the fiber core. In contrary, the power of the signal laser tends to decline at the rear part of the T-DCF. The bigger the core diameter of the large end is, the faster the signal laser power declines. It is because the pump power is too low to provide enough active gain along the whole fiber in the face of core attenuation. Meanwhile, the re-absorption of the signal laser by the active ions in this region can not be neglected. The bigger the core diameter of the large end is, the higher the core attenuation and the re-absorption of the signal laser are. Besides, for 15.7-95.4 µm T-DCF-based amplifier, the occurrence of SBS effect aggravates the consumption of the signal laser.
Fig. 16. The peak power distribution of (a) SBS Stokes light and (b) the signal laser along the T-DCFs with different tapered ratios under forward pumping regime.
However, for the backward pumping regime, it is interesting to find that the diameter expansion of the large end does not always helps to suppress SBS effect. As listed in Table 3, among four kinds of situations, the 20.8-86.1 µm T-DCF-based amplifier has the highest SBS threshold of 106.03 kW under the pump power of 32 W, about 2 times as high as that of 36-58 µm T-DCF-based amplifier (53.16 kW). Meanwhile, SBS threshold of the 15.7-95.4 µm T-DCF-based amplifier is lower than that of the 20.8-86.1 µm T-DCF-based and 31-67.2 µm T-DCF-based amplifiers, even if it has largest diameter at the large end. The peak power distributions of SBS Stokes light and the signal laser along the four T-DCFs at the pump power of 32 W are contrastively given in Fig. 17. It is indicated that when the core diameter of the large end is enlarged to reach certain value, the shrink of core diameter at the small end will turn around to strengthen SBS effect, although SBS effect is well suppressed due to enlarged core diameter in the rear part of the fiber and the power of the signal laser is relatively lower in the front part of the fiber. In other words, it implies that SBS threshold goes through a rising trend and then a decline trend by enlarging the core diameter of the small end, under backward pumping regime. As for the power distribution of the signal laser, there is no significant difference for the four situations because the pump power is high enough to provide sufficient active gain, regardless of the influence of SBS effect and core attenuation.
Fig. 17. The peak power distribution of (a) SBS Stokes light and (b) the signal laser power along the T-DCFs with different tapered ratios under backward pumping regime.
In summary, it is revealed that enlarging the core diameter of the small end of the T-DCF while maintaining the tapered ratio can steadily increase SBS threshold under the forward pumping regime. Whereas, there exists an optimal core diameter of the small end under the backward pumping regime. If feasible way to perform the backward pumping regime is available, the output power of the narrow-linewidth linearly-polarized ns fiber laser could be hugely promoted in prospect by introducing the optimal design.
4.2.3 Discussion on optimizing the length of the PM T-DCF
In Ref. [70], some special features of the tapered fibers with backward pumping regime were demonstrated in this paper. Typically, the stimulated Raman scattering (SRS) threshold could be enhanced with the length of the tapered fiber increased. The reason was explained to be the fact that the signal laser almost obtains no gain in the front part of the tapered fiber but huge gain in the rear part under backward pumping regime. In order to investigate on whether similar phenomenon happens to SBS effect, we conduct extended simulation based on our theoretical model. In the extended simulation, we maintain the core diameter of both the small end and the large end, and lengthen the total length of the tapered fiber by extending the uniform part at the large end. As a result, two additional theoretical configurations are involved, as listed in Table 4.
Table 4. SBS threshold of the 36-58 µm T-DCF-based main amplifier with different length under the backward pumping regime.a
It is surprising to find that, no matter how we extend the length of the uniform part at the large end (equivalent to extend the total length), SBS threshold does not show increasing trend. It is quite different from the SRS-related result in Ref. [70]. In analysis, this difference is tightly related to the distributions of the signal laser and SBS Stokes light. As shown in Fig. 18 are the distributions of the signal laser and the SBS Stokes light at the pump power of 26 W. It is found that, although the fiber length is changed, it has weak effect on the output of the signal laser and SBS Stokes light. As a result, SBS threshold is changed little. As for the deeper reason, it is thought to be attributed to the difference in the longitudinal profile of the core diameter and the pump absorption coefficient, compared with the tapered fiber used in Ref. [70]. Firstly, the tapered fiber used in Ref. [70] had ultrahigh pump absorption coefficient of 24 dB/m at 976 nm, which was about two times as large as that of the T-DCF (12.1 dB/m at 975 nm) used in our experiment. Ultrahigh pump absorption coefficient made the pump power mainly absorbed near the thick part under backward pumping regime and thus the signal laser was mainly amplified in this region. And then, the ultrahigh mode area near the thick part helped to reduce the density of the signal laser and thus suppress SRS effect. For the T-DCF used in our work, the pump absorption coefficient is far smaller so that higher ratio of pump power is absorbed in the thin part of the fiber and thus the amplified signal laser contributes more to the amplification of the counter-propagation SBS Stokes light, for the reason that SBS Stokes light is amplified during the process of backward propagation and the thin part of the T-DCF plays primary role in its amplification. This is quite different from SRS effect. Secondly, the T-DCF used in our work has smaller tapered ratio (∼1.61) than that (∼4.6) of the tapered fiber used in Ref. [70]. Smaller tapered ratio means the length of the thick part has weaker effect on the amplification of SBS Stokes light. Thirdly, similarly, the tapered fiber in Ref. [70] has gradually-increased diameter in the tapered region, so the lengthening of the tapered fiber is accompanied with extra increasement of the mode area to benefit suppressing SRS effect. However, the T-DCF used in our work has uniform core diameter at the large end so that it has no extra expansion of the mode area by lengthening the fiber length to suppress SBS effect.
Fig. 18. The power distributions of (a) SBS Stokes light and (a) the signal laser of the 36-58 µm T-DCF-based main amplifier with different length under backward pumping regime.
Nonetheless, as demonstrated in Section 4.2.2, it is inspiring that by enlarging the tapered ratio to a certain value with the equivalent core diameter (deff) unchanged, SBS threshold can be enhanced under backward pumping regime. It is inferred that, if the tapered ratio has a proper value, the effect of lengthening the fiber length on SBS threshold may be revealed. So, we carry out extended simulation aiming at the 20.8-86.1 µm T-DCF-based main amplifier which has been demonstrated to have highest SBS threshold under backward pumping regime, with the fiber length maintained. It is worth noting that it has similar tapered ratio (4.14) to the tapered fiber (4.6) used in Ref. [70]. SBS threshold of the main amplifier based on the 20.8-86.1 µm T-DCFs with different length is shown in Table 5 and Fig. 19. It is really interesting to find that SBS threshold can be enhanced by lengthening the fiber length to some degree. With the fiber length lengthened to around 1.4 m, SBS threshold peak power can be increased to ∼128 kW. In analysis, this phenomenon is also tightly related to the distributions of the signal laser and SBS Stokes light along the fiber, which are comparatively shown in Fig. 20 under the pump power of the 48 W. It is noted that, with the fiber length increased, the amplification of SBS Stokes light within the thin part of the fiber is well suppressed and thus SBS threshold is increased correspondingly. With the fiber length increased further, this effect does not work gradually. Even so, further increasement of the fiber length does not induce the decline of SBS threshold either, because of ultra-large mode area in the thick part. As for the evident decline of the signal output power with the fiber length increased, it is due to the increasement of the length-dependent attenuation and the reduction of the core-diameter-dependent pump absorption efficiency.
Fig. 20. The power distributions of (a) SBS Stokes light and (b) the signal laser of the 20.8-86.1 µm T-DCF-based main amplifier with different length under backward pumping regime.
Table 5. SBS threshold of the 20.8-86.1 µm T-DCF-based main amplifier with different length under the backward pumping regime.a
In summary, it is theoretically revealed that SBS threshold can be enhanced to some degree under the backward pumping regime by lengthening the fiber length on the condition of high tapered ratio. It is inferred that if the thick part of the 20.8-86.1 µm T-DCF has gradually-increased diameter, as the tapered fiber used in Ref. [70], the effect of lengthening fiber length on increasing SBS threshold can be better made use. So, it can be concluded that, if one wants to exploit the backward pumping regime to suppress SBS effect to the utmost, it is really important to carefully design the core diameter, tapered ratio and length of the tapered fiber.
5. Conclusion
In conclusion, we demonstrate an all-fiber high-peak power and narrow-linewidth linearly polarized ns MOPA based on a piece of Yb-doped PM LMA T-DCF with high concentration and large mode area to suppress nonlinear effects. As the result, maximal average output power of 8.8 W is obtained under forward pumping regime with pulse duration of 3.8 ns and repetition frequency of 80 kHz, corresponding to a peak power of ∼30 kW and a pulse energy of 110 uJ. Nearly transform-limited linewidth of ∼283.8 MHz and nearly-diffraction-limited beam quality are realized at the maximal SBS-free output power. This result is known as a record peak power of all-fiberized linearly polarized ns fiber laser with nearly-transform-limited linewidth and simultaneously nearly-diffraction-limited beam quality, to the best of our knowledge. The feasible optimization approaches of present system, including changing pumping regime and the fiber’s geometry, are further analyzed based on a nonlinear dynamic model. This work directs a promising route to obtaining high power linear-polarization narrow-linewidth pulsed laser source for various frontier technologies.
Funding
Natural Science Foundation of Hunan Province (2019JJ10005); Guangdong Key Research and Development Program (2018B090904001); National Natural Science Foundation of China (61705264); National Key Research and Development Program of China (2017YFF0104600).
Acknowledgments
The authors also would like to thank Dr. Tao Rumao and Dr. Shi Chen for their supports in theoretical analysis.
Disclosures
The authors declare no conflicts of interest.
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