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Abstract
Random fiber laser based on Raman gain and random distributed feedback has drawn great attention in recent years. One of the most widely-studied fields is to improve the optical efficiency and the output power. However, the power scaling of a random fiber laser is instinctively restricted by the high order Stokes generation. In this manuscript, we propose a simple yet effective method, which employs a homemade all-fiber Lyot filter to manipulate the polarization dependent Raman gain, thus increasing the threshold of the 2nd-order Stokes wave and enhancing the maximum output power of the linearly polarized random fiber laser. Through reliable theoretical analysis, we optimize the design of the wavelength dependent Lyot filter. Moreover, the performance of the filter and the power scaling capability of the linearly polarized random fiber laser are investigated in detail. A proof-of-principle experiment is carried out by inserting the homemade Lyot filter into a half-opened random fiber laser. The experimental results indicate that the 2nd-order Stokes wave can be effectively suppressed, and the maximum output power of the 1st-order Stokes wave is significantly increased with a range of ~50% (from 43.6 to 63.2 W).
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past few years, random fiber laser (RFL) based on Raman gain and random distributed feedback (RDFB) has attracted great attention due to its advantages such as easy implementation, low background spontaneous emission, small quantum defects and no photodarkening effect [1–4]. Recent advances of RFL include power scaling and efficiency improving [5–7], pulse operating [8–11], linewidth narrowing [12,13], spectral tuning and expanding [14–18]. The emerging applications of RFL cover the fields such as remote sensing and telecommunication [19,20], frequency conversion in second-harmonic generation [21], speckle free imaging [22], optical pumping in mid-infrared laser and optical parametric oscillator [4,23–25], supercontinuum source generation [26], and serving as the stable seed for power amplification [27–29].
Particularly, enhancing the maximum output power is one of the most significant research topics of RFL, and one direct approach is increasing the available pump power. However, the output power of the 1st-order random lasing will soon reach a maximum and start to roll over, owing to the generation of high order Stokes wave, whose threshold is believed to be inversely correlated to the fiber length. Therefore, reducing the fiber length could increase the threshold of high order Stokes wave as well as the maximum output power of the RFL. Intensive researches have proved the feasibility of the so-called short-cavity-method in theory and experiment [5,7,30,31]. Consequently, 193.5 W random polarized and 86.3 W linearly polarized RFLs are obtained through 120-m-long passive single mode fiber (SMF) and 157-m-long polarization maintaining (PM) passive fiber, respectively [5,30]. However, when further reducing the length of the passive SMF, one may encounter a number of obstacles such as much weaker distributed feedback, higher generation threshold, and more sensitivity to the parasitic feedback of the end facets. One way to further enhance the output power is replacing the most commonly used SMF with the tapered fiber [32] or large mode area (LMA) fiber [6]. Zhang et al. demonstrated a 1-km-long tapered fiber based RFL with an output power of 26.5 W, and they experimentally and theoretically proved that tapered fiber based RFL can suppress the nonlinear effect and increase the maximum output power compared with the equal length of SMF based RFL [32]. Very recently, a piece of 130-m-long LMA fiber based RFL with a record power of more than 400 W has been reported, proving that the LMA fiber based RFL can suppress the high order Stokes wave and achieve a higher output power as well [6]. Besides replacing the passive fiber, employing novel pump source with high temporal stability, rather than the commonly used rare-earth-doped fiber lasers or Raman fiber lasers, may also make it possible to further increase the maximum output power of RFLs. Xu et al. have presented a hundred-watt-level linearly polarized RFL pumped by a stable amplified spontaneous emission (ASE) source [7].
In this manuscript, we propose a simple yet effective approach, which employs a homemade all-fiber Lyot filter to manipulate the polarization dependent Raman gain, thus increasing the threshold of the 2nd-order Stokes wave, and eventually achieving the enhancement of the maximum output power of the linearly polarized RFL. Since the first proposal of the all-fiber Lyot filter, it has been widely applied in fiber lasers and sensors, as well as the suppression of high order Stokes wave in Raman fiber laser [33–36]. Here we first employ the all-fiber Lyot filter in an RFL to suppress the high order Stokes wave and enhance the maximum output power of the linearly polarized RFL. The performance of the filter and the power scaling capability of the RFL are investigated in detail. A proof-of-principle experiment is carried out by inserting the homemade Lyot filter into a half-opened RFL, indicating that the maximum output power of the 1st-order Stokes wave can be boosted from 43.6 to 63.2 W. The proposed all-fiber Lyot filter has the advantages of relatively simple implementation, high flexibility and robust operation, and can be applied to achieve a linearly polarized RFL with higher maximum output power.
2. Theoretical analysis
It’s well known that the Raman gain coefficient is closely relied on the polarization direction correlation of the pump and the Stokes wave. As depicted in Fig. 1(a), the blue solid curve represents the normalized Raman gain for fused silica when the pump and the Stokes wave are polarized parallelly to each other, while the red dotted curve shows the orthogonally polarized case [37,38]. And it’s found that the Raman gain of the orthogonally polarized situation is much lower than that of the co-polarized case. This interesting feature naturally provides us a distinctive way to increase the threshold of the 2nd-order Stokes wave in linearly polarized RFL. In practice, in order to use this typical feature, one can manage to make the 1st-order Stokes wave and the 2nd-order Stokes wave be orthogonally polarized, and meanwhile make the pump and the 1st-order Stokes wave be co-polarized, as seen in Fig. 1(b). In such conditions, the Raman gain from the 1st-order Stokes wave to the 2nd-order Stokes wave will be much lower, thus the 2nd-order Stokes wave and the maximum output power of the linearly polarized RFL can be suppressed and boosted, respectively.
Fig. 1 (a) Normalized Raman gain for fused silica. (b) Schematic diagram of the polarization orientations.
The key of this approach is to realize the polarization-orientation-rotation of the 2nd-order Stokes wave with an angle of 90°, and meanwhile guarantee the maintenance of the polarization orientations of the pump and the 1st-order Stokes wave. Fortunately, this process can be realized using an artificial all-fiber Lyot filter, which is based on the birefringence and dispersion of a short length of PM fiber [33,34]. As plotted in Fig. 2(a), the axes of the PM fiber segments are spliced with a dislocation angle of 45°, thereby coupling the light into both axes. The accumulated phase difference between the fast and slow axes is given by Δφ = (2π/λ)LΔn, where λ is the wavelength of the light, L is the length of the PM fiber, and Δn = nslow-nfast represents the birefringence [33]. The combination of two polarization beam splitters (PBSs) with a supercontinuum (SC) source is assumed to measure the transmission spectrum of the artificial Lyot filter. As depicted in Fig. 2(b), a broad and flat spectrum can be yielded by the SC source, and the 1st PBS is used as a polarizer. The PM fiber segment with 45° cross-splicing at both ends acts as the birefringent plate, and the 2nd PBS serves as the analyzer. Then the normalized transmittance of the artificial Lyot filter is given by T = cos2(πLΔn/λ) [34], which is quasi-periodic in wavelength, showing a peak-to-peak filtering bandwidth of Δλ~λ2/LΔn. Thus, by changing the length of the PM fiber segment, the filtering bandwidth can be tailored [33]. Moreover, the birefringence Δn is temperature-dependent, so that one can precisely tune the transmission spectrum of the artificial Lyot filter through a temperature control system.
Fig. 2 (a) Schematic diagram of the 45° cross-spliced PM fiber based Lyot filter. (b) Supposed experimental setup to measure the polarization dependent transmission spectrum.
We calculate the theoretical transmission spectrum of the all-fiber Lyot filter, in which the birefringence Δn is set to 2.9 × 10−4, and the temperature sensitivity d(Δn)/dT is estimated to be −2.51 × 10−7/°C [39]. Figure 3(a) shows the transmission spectra for the PM fiber length of 80 cm, 40 cm and 20 cm, indicating that the shorter the fiber length, the wider the filtering bandwidth. The peak-to-peak filtering bandwidth for the fiber length of 80 cm is ~5.5 nm (@1120 nm), which reaches 21 nm for the 20-cm-long PM fiber segment. At the same time, raising the temperature can result in the blue-shift of the transmission spectrum with a rate of about −1 nm/°C, as seen in Fig. 3(b). In fact, the transmission spectrum shows the polarization state of different wavelength. The peaks of the filtering spectrum indicate that the polarization orientations keep still after the Lyot filter, while the valleys imply that the polarization orientations have rotated to the perpendicular direction. Therefore, in order to achieve the goal mentioned above, we should optimize the length of the PM fiber segment and precisely control the temperature, to guarantee that the pump and the 1st-order Stokes wave locate at the peaks, and that the 2nd-order Stokes wave falls in the valley of the transmission spectrum, just as the schematic diagram charted in Fig. 3(c). In this condition, the 2nd-order Stokes wave is orthogonally polarized to the 1st-order Stokes wave, and thus the 2nd-order Stokes wave will experience a much lower Raman gain and its suppression can be realized theoretically.
Fig. 3 (a) Transmission spectrum of the PM fiber based Lyot filter with different lengths. (b) Temperature dependence of the transmission spectrum (with 80-cm-long PM fiber). (c) Schematic diagram of the pump, the 1st-order Stokes wave and the 2nd-order Stokes wave in the transmission spectrum.
3. Experimental results and discussion
3.1 Experimental setup
The setup of the proof-of-principle experiment is schematically presented in Fig. 4. A linearly polarized ytterbium-doped fiber laser centered at 1069.5 nm is employed as the pump source, which can yield a maximum output power of ~100 W. The pump light is injected through the 1070-nm-port of a PM wavelength division multiplexer (WDM), whose common port is connected with two pieces of PM fiber with lengths of 160 m and 300 m. The two pieces of PM fiber are spliced with a short PM fiber segment of the same model at an angle of 45°, acting as an artificial all-fiber Lyot filter. It should be noted that the lengths of these two pieces of PM passive fiber are not intentionally selected, and in fact, they are just available in our laboratory. The core and cladding diameter of the PM fiber are 10 and 125 μm, respectively. The 1120-nm-port of the PM WDM is spliced with a fiber Bragg grating (FBG) (1120 nm central wavelength, 0.46 nm reflection bandwidth), to provide point feedback and construct a classical half-opened RFL. In addition, all the free end facets are cleaved at an angle of 8° to suppress the undesired backward reflection.
3.2 Operation without the Lyot filter
Firstly, we investigated the spectral and power performance without employing the homemade all-fiber Loyt filter. The output spectra with different pump power are plotted in Fig. 5(a). At lower pump power (<50 W), only the pump wave at 1069.5 nm and the 1st-order Stokes emission at 1120 nm can be observed. With further increment of pump power, the 2nd-order Stokes wave can be measured. And the 2nd-order Stokes wave shows a profile with dual peaks centered at 1178 and 1184 nm, respectively, corresponding to the two nearly equal peaks of the Raman gain at ~13.2 and ~14.7 THz. In the beginning, the subcomponent of 1178 nm dominates as the Raman gain was slightly larger (by about 1%) for that peak [37]. However, with increasing pump power, the peak at 1178 nm can pump the peak at 1184 nm through the Raman-amplification process. Thus, the effective Raman gain for the 14.7-THz peak becomes higher, making the subcomponent of 1184 nm dominate in the output spectrum under higher pump power [40].
Fig. 5 (a) Evolution of the output spectra. (b) Output powers dependence on the pump power without applying the homemade Lyot filter.
At the same time, by measuring the total output power and doing numerical integration based on the spectral data at different pump power, we can obtain the power evolutions of the residual pump wave, the 1st-order Stokes wave and the 2nd-order Stokes wave with the pump power, as seen in Fig. 5(b). The threshold of the 1st-order Stokes wave is measured to be ~19 W, while that of the 2nd-order Stokes wave is ~55 W. The maximum output power of the 1st order Stokes wave reaches about 43.55 W with 61.42 W pump power, corresponding to an optical conversion efficiency of ~70.9%. And before the appearance of the 2nd-order Stokes wave, the slope efficiency is up to ~75.3%. However, with boosting the pump power, the slope efficiency drops sharply due to the increased heat loss at high power situation. The higher loss of the WDM for the 2nd-order Stokes wave is also responsible for the decrease of slope efficiency.
3.3 Performance of the Lyot filter
According to the experiment above, the all-fiber Lyot filter has been developed and the length of the PM fiber segment has been optimized. It is known that the transmittance of the Lyot filter is quasi-periodic in wavelength and the peak-to-peak filtering bandwidth is given by Δλ~λ2/LΔn. In fact, the transmission spectrum is totally periodic in the frequency domain, in which the peak-to-peak filtering bandwidth is transformed into Δυ~c/LΔn (c is the velocity of light in the vacuum). On the basis of the experimental results above, the frequency shift from the 1069.5 nm pump wave to the 1120 nm 1st-order Stokes wave (ΔΩ1), is calculated to be 12.639 THz, while that from the 1st-order Stokes wave to the 1184.2 nm 2nd-order Stokes wave (ΔΩ2), reaches about 14.511 THz. To guarantee that the pump and the 1st-order Stokes wave can locate at the peaks, and the 2nd-order Stokes wave can lie in the valley of the transmission spectrum, the frequency shifts ΔΩ1 and ΔΩ2 must satisfy ΔΩ1 = M × Δυ and ΔΩ2 = (N + 1/2) × Δυ, in which M and N are integers and N≥M. Therefore, according to the measured frequency shifts, the integers M and N are chosen to be 10 and 11, respectively. In this case, the filtering bandwidth Δυ is calculated to be ~1.264 THz. Then the corresponding fiber length of the artificial Lyot filter L~c/ΔυΔn is estimated as ~81.8 cm.
We experimentally measured the transmission spectrum of the homemade all-fiber Lyot filter utilizing the setup displayed in Fig. 2(b). The top picture in Fig. 6(a) shows the emission spectrum of the homemade SC source and the filtering spectrum after the homemade Lyot filter at room temperature, in which the terrace near 1064 nm stands for the residual pump of the SC source. Then the transmission spectrum is given by the filtering spectrum minus the SC source emission spectrum, as depicted in the bottom picture of Fig. 6(a). It can be seen that the valleys of the transmission spectrum are ~20 dB lower than the peaks, which implies that the potential Raman suppression ratio with this homemade Lyot filter may be as high as 20 dB. However, the transmission spectrum at room temperature cannot exactly meet our requirement, it must be fine-tuned by adjusting the temperature. Therefore, a water cooling system is utilized for precisely controlling the temperature of the filter. As a result, when adjusting the temperature to 19.5 °C, the transmission spectrum can meet the requirement well, as shown in Fig. 6(b). In this condition, the pump and the 1st-order Stokes wave locate at the peaks, and the 2nd-order Stokes wave lies in the valley.
Fig. 6 (a) Measured transmission spectrum of the homemade all-fiber Lyot filter at room temperature. (b) Transmission spectrum at 19.5 °C and the locations of the pump, the 1st-order Stokes wave and the 2nd-order Stokes wave.
3.4 Power scaling with the Lyot filter
Finally, we studied the spectral and power performance of the RFL by inserting the homemade Lyot filter after the 160-m-long PM fiber, as illustrated in Fig. 4. The evolution of the output spectra with the pump power is shown in Fig. 7(a). Owing to the filtering of the homemade Lyot filter, the 2nd-order Stokes wave shows a multi-peak structure, including the subcomponents at 1169, 1176, 1184 and 1193 nm, wherein the subcomponent at 1184 nm donates the original highest peak, and the others correspond to the nearby peaks of the filtering spectrum. The results also show that the 2nd-order Stokes wave has been effectively suppressed, and the intensity of the highest peak at 1176 nm is ~14 dB lower than that of the 1st-order Stokes wave at 1120 nm with the pump power of 99.7 W. Moreover, the peak at 1184 nm shows a higher suppression ratio of ~17 dB.
Fig. 7 (a) Evolution of the output spectra with employing the homemade Lyot filter. (b) Output powers dependence on the pump power.
Meanwhile, by measuring the total output power and doing numerical integration based on the spectral data at different pump powers, we can obtain the powers of the residual pump wave, the 1st-order Stokes wave and the 2nd-order Stokes wave as functions of the pump power, as plotted in Fig. 7(b). The threshold of the 1st-order Stokes wave is ~32 W, which is a little higher than the case of no filter. The increase of the threshold could be explained as follows: the pump wave at 1069.5 nm and the 1st-order Stokes wave at 1120 nm are not precisely co-polarized due to the filtering of the Lyot filter, resulting in the decrease of the effective Raman gain from the pump to the 1st-order Stokes wave. The threshold of the 2nd-order Stokes wave is increased to ~82 W, and the maximum output power of the 1st-order Stokes wave reaches more than 65 W under the pump power of 95.3 W, which is 49.7% higher than the case of no filter. The optical conversion efficiency of the 1st-order Stokes wave is calculated to be 68.4% at the maximum output power. And the slope efficiency before the appearance of the 2nd-order Stokes wave reaches as high as 74.8%, which is nearly the same as the former value, proving that the artificial all-fiber Lyot filter has the advantages of robust operation and nearly no loss on the output power.
What’s more, the bandwidth of the 2nd-order Stokes wave is rather broad when comparing to the filter period. Thus, instead of being entirely suppressed, the 2nd-order Stokes wave is divided into several parts, in which only the wavelengths near the valleys of the filtering transmission spectrum can be suppressed. This process, in some extent, is equal to decrease the overall Raman gain of the 2nd-order Stokes wave. In other words, the wavelengths corresponding to the peaks of the filtering transmission spectrum obtain the highest Raman gain, while the other wavelengths deviating from the peaks obtain lower Raman gain, and the wavelengths corresponding to the valleys of the filtering transmission spectrum only obtain the lowest orthogonally polarized Raman gain. Therefore, considering the 2nd-order Stokes wave as a whole, the effective Raman gain is significantly decreased by utilizing the artificial Lyot filter. Consequently, the threshold of the 2nd-order Stokes wave is increased, and the enhancement of the maximum output power of the linearly polarized RFL with relatively low threshold can be realized.
However, since the bandwidth of the 2nd-order Stokes wave is rather broad as compared with the filter period, the decrease of the effective Raman gain of the 2nd-order Stokes wave is relatively limited, which has led to a relatively limited suppression effect. It seems that the suppression effect would be better if the 2nd-order Stokes component is totally covered by the filter period. As previously mentioned, the filter period is determined by the frequency shifts through the conditions ΔΩ1 = M × Δυ and ΔΩ2 = (N + 1/2) × Δυ, and the greater the difference between ΔΩ1 and ΔΩ2, the broader the filter period Δυ. Thus, the operating wavelength of the 1st-order Stokes wave has to be controlled to deviate from the peak of the Raman gain. However, the deviation is limited due to the effective Raman gain range. Besides, the deviation from the gain peak, in some extent, could also cause the increase of the generation threshold and the decrease of the optical efficiency. In other words, the difference between ΔΩ1 and ΔΩ2 is also relatively limited, which makes it difficult to realize a much broader filter period. In this case, we employed a Lyot filter with relatively narrow filter period in the proof-of-principle experiment, and achieving a relatively limited power enhancement of the 1st-order Stokes wave. Appropriate further decrease of the frequency shift ΔΩ1 (such as utilizing a shorter wavelength FBG) and improvement of the filter period may lead to a relatively better power enhancement effect.
4. Conclusion
In conclusion, based on the birefringence and dispersion of the PM fiber, we developed a homemade all-fiber Lyot filter to manipulate the polarization dependent Raman gain, and applied it to reduce the effective Raman gain of the 2nd-order Stokes wave and increase its threshold, thus hopefully enhancing the maximum output power of the linearly polarized RFL. With the theoretical analysis, the proposed method is proved to be feasible, and the fiber length of the filter is optimized to ~81.8 cm. The results of the proof-of-principle experiment show that the maximum output power of the 1st-order Stokes wave can be improved by ~50% while maintaining a relatively low threshold. This approach has the advantages of simple implementation, robust operation and almost no loss, and may introduce new possibilities for the further power scaling of the high power linearly polarized RFL.
Funding
National Natural Science Foundation of China (NSFC) (61635005); Huo Yingdong Education Foundation of China (151062); Natural Science Foundation of Hunan Province, China (2018JJ3588).
Acknowledgments
We thank Prof. Jing Hou’s group for providing the homemade supercontinuum source.
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