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In this paper, we thoroughly analyze the role of the point reflector’s reflectivity in the performance of forward-pumped random fiber laser, in both the long- and short-cavity cases. The results show that the power performance is sensitive to the small reflection added on the pump side of the fiber end, whereas both the power distribution and threshold tend to be stable when the reflectivity reaches a relatively high level (>0.4). Moreover, for the short cavity case (e.g. 500m), the maximum achievable 1st-oder random lasing output can even increase when the reflectivity decreases from 0.9 to 0.01, due to the different lasing power distributions with different reflectivity values. This work reveals a new and unique property of random fiber lasers and provides insights into their design for the applications such as distributed amplification and high power sources.
© 2015 Optical Society of America
1. Introduction
Random laser (RL) refers to a new kind of lasers where the feedback is provided by randomly distributed scattering centers in a gain medium [1]. As an important type of RLs, random fiber laser (RFL) via Raman gain and Rayleigh scattering in fiber as the randomly distributed feedback has been demonstrated in 2010 [2]. RFLs have attracted a lot of attention due to their unique advantages, such as ultra-long-distance cavity, stable output, simplicity and high lasing efficiency, etc [3–6]. Valuable work has been carried out to study RFLs, and various physical features have been reported. RFLs have been tailored to be multi-wavelength [7,8], wavelength-tunable [9,10], narrow bandwidth [11,12], high output power [4,5,13,14] and cascaded operation to generate high order Stokes waves [15].The RFL-based distributed fiber-optic amplification could offer low-noise and stable amplification for long-distance transmission [16,17], making it attractive for telecom and sensing applications.
Specifically, forward-pumped RFL [6,7,15], which has a point reflector at the pump side of the fiber span, is proposed for the purpose of reducing the threshold first. Furthermore, the random lasing amplification based on the forward-pumped RFL has been utilized to significantly extend the sensing range of BOTDA and Φ-OTDR systems due to its specific power distribution and advantageous noise specification [18,19]. Also, forward-pumped RFL with short fiber length has been demonstrated to have the superb ability to generate high power lasing output, creating a new direction for high-power optical sources [4,5,13]. In previous works, intuitively the preferred reflectors should have high reflectivity [7,15], similar to the cases in conventional Raman fiber lasers.
However, different types of the reflectors such as narrow-band FBG, chirped FBG and fiber loop mirror (FLM) etc., are required for diverse demands for laser properties [20], and the reflectivity values vary among different reflectors. In this paper, we thoroughly investigate the effect of point reflector’s reflectivity on the characteristics of forward-pumped RFLs with long (e.g. 50km) and short (e.g. 500m) fiber length respectively, and we also discuss the corresponding influences in the applications of distributed amplification and high power generation. The results reveal that with the increase of the reflectivity, the threshold change drastically in the case of relatively low reflectivity (<0.1), but it would change just slightly when the reflectivity is increased to a relatively high value (>0.4). Also, for the short fiber length (500m), the maximum 1st-oder random lasing output power can even increase (from 41W to 45.7W) when the reflectivity decreases(from 0.9 to 0.01), due to the different lasing power distribution with different reflectivity value. These results also contribute insights into the recently vibrant research on high-power RFLs [5].
2. Forward-pumped RFL with long fiber length
We study the RFL with half-open configuration and unidirectional forward-pumping (forward-pumped RFL) [15,21].Without loss of generality, the pump wavelength is set to 1365nm and the corresponding 1st-order Stokes wavelength is 1455nm in SMF.A 50km SMF is performed as both the Raman gain medium and random distributed mirrors. A point reflector is placed at the pump side of the fiber to reflect the 1st-order Stokes light only, and we change the reflectivity of the point reflector in the simulation. Forward-pumped RFL with long fiber length can be used for distributed amplification and the lasing power distribution and the threshold are the main concerns in such systems [18,19].
We apply the steady-state model [15,21] for a detailed analysis of the performance of the laser. The parameters used are summarized in Table 1.
Table 1. Parameters for numerical calculation
First, we calculate the power distribution of the 1st-order random lasing with different reflectivity of point-feedback (with 2W pump) (see Fig. 1). Without any point-feedback on the fiber end (R = 0), the majority of lasing power flows toward the pump side of the fiber span. Adding the point reflector at the pump side of the fiber, the power distribution of the 1st-order lasing changes dramatically. Due to the extremely small Rayleigh backscattering coefficient, the integral Rayleigh backscattering coefficient is as weak as ~5 × 10−4. Therefore, even with the point reflector with reflectivity as low as 0.01, most of the lasing power is re-distributed towards the far end of the fiber cavity. With higher reflectivity, the forward power becomes more dominant, and the position of power maximum shifts towards the pump side of the fiber. Moreover, this tendency is more significant in the range of relatively low reflectivity, whereas the power distribution is just slightly changed when the reflectivity is increased to a high level (>0.4).
Fig. 1 Calculated power distribution of lasers with different reflectivity of point reflector pumped at 2W.
Figure 2 shows the calculated generation threshold with different reflectivity. The insert is the enlarged view of the threshold with low reflectivity (<0.1). With the open cavity, the threshold is as high as 1.5W. When the point reflector is added at the pump side of the fiber, the threshold drops sharply at first, and then the slope of reduction slows down with the increase of reflectivity. The calculated results show the threshold decreases by 0.5W when the reflectivity increases from 0 to 0.1. However, when the reflectivity increases from 0.4 to 0.9, the threshold only decreases by less than 0.1W.
In order to validate the numerical results, we experimentally investigate the influence of reflector’s reflectivity on the laser characteristics. The experimental setup is shown in Fig. 3. A 1365nm Raman fiber laser is used as the pump laser. A fiber loop mirror (FLM) is connected to the 1455nm port of the WDM to form the half-open cavity for the 1st-order random lasing, assisting by the randomly distributed Rayleigh feedback along the 50km G.652 fiber. The FLM is formed by a wide-band 50:50 coupler and a variable optical attenuator (VOA). The reflectivity of the FLM can be tuned by setting different attenuations of the VOA. We can calculate the actual reflectivity by comparing the 1455nm lasing power between Port 2 and Port 4 of the 1:99 coupler, with the excess loss of the coupler taken into account. Due to the wide-band reflection of the FLM, the reflectivity can be treated as an invariant as the pump power grows. The far-end of the SMF is angle-cleaved to avoid end reflection, and it is used to monitor the lasing characteristics.
Fig. 3 Experimental setup for investigating the influence of reflectivity on the laser characteristics.
Figure 4 shows the measured output power of the first-order random lasing power versus pump power under different reflectivity values. For the maximum achievable reflectivity (0.72) using FLM, the threshold (0.81W) is the lowest. The trend of the experimental data is the same as the theoretical results: the threshold for the 1st-order lasing is only increased by 0.1W when the reflectivity drops from 0.72 to 0.35. By further decreasing the reflectivity, the generation threshold increases more sharply. Comparing with the cases with 0.35reflectivity, the 1st-oder lasing threshold has increased by 0.2W in the case of the 0.06 reflectivity. All the measured thresholds coincide with the numerical simulated results well. The insert in Fig. 4 shows the random laser spectrum with 1W pump power in the cases with 0.72 reflectivity and 0.35 reflectivity. The spectra are stable and the laser outputs are CW in both cases. The random lasing has a relatively wide spectrum with two peaks located at 1455nm and 1463nm, respectively. The two spectra have the nearly same shape, showing that the spectrum also varies little when the reflectivity reaches to a high enough level.
Fig. 4 Experimental measured output power of the first-order random lasing power vs. pump power with different reflectivity values. Insert: The measured random laser spectra with different reflectivity values.
For the reflectors, wide-bandwidth and high-reflectivity are usually difficult to achieve simultaneously. For the RFL-based distributed amplification, since lasing power distribution and threshold are slightly changed when reflectivity is higher than 0.4, a wide-band reflector with relatively lower reflectivity can be helpful to widen and flatten the gain profile.
3. Forward-pumped RFL with short fiber length
Forward-pumped RFL with short fiber length has the ability to generate high power, high efficiency random lasing at far end of the fiber [4,5,13]. We make a numerical simulation and the schematic setup is similar to the long fiber length case, except that the pump wavelength is 1090nm and the corresponding 1st-order Stokes wavelength is 1145nm in SMF (the SMF length is only 500m). The lasing output is at the far end of the fiber. The parameters used are as the same as [13].
First, we calculate the threshold of the 1st-order and the 2nd-order random lasing, respectively. The threshold of the 1st-order random lasing drops from 20.3W to 17.3W when the reflectivity increase from 0.01 to 0.1; and the threshold variation is only 1W (from 15.4W to 14.4W) in the range of 0.4 to 0.9 reflectivity. Also, for the 2nd-order random lasing threshold, it drops from 56W to 50W when the reflectivity increase from 0.01 to 0.1; and the threshold decreases only 1.5W (from 47.5W to 46W) in the range of 0.4 to 0.9 reflectivity.
Figure 5(a) shows the calculated output power of the first-order random lasing power versus pump power under different reflectivity values. Even though the reflectivity is as low as 0.01, the half-open cavity has the ability of generating highly efficient, high power 1st-order random lasing at the output end of the fiber. In all cases with different reflectivity values, the lasing power increases rapidly after the pump power across the threshold. The slope efficiency is defined as , and the insert of Fig. 5(a) shows the slope efficiency variation with the increase of the pump power. The slope efficiency can be as high as ~570% near the threshold when the reflectivity is 0.9, and the value can be even above 600% in the cases with 0.1 reflectivity or 0.01 reflectivity. When the pump power further increase, the slope efficiency gradually falls down and finally is stabilized at a constant value. The constant values are 88.5%, 86% and 80% for 0.9 reflectivity, 0.1 reflectivity and 0.01reflectivity, respectively. Moreover, in the case of lower reflectivity, the threshold for 2nd-order random lasing is higher, and the achievable 1st-order random lasing output power is also higher. We calculate the maximum output power and optical conversion efficiency of 1st-order random lasing as a function of reflectivity, which are depicted in Fig. 5(b). When the reflectivity decreases from 0.9 to 0.01, even though the total optical conversion efficiency drops from 88% to 81%, the maximum 1st-oder random lasing output power increases from 41W to 45.7W. Also, the variations of output power and optical conversion efficiency are more significant in the range of relatively low reflectivity (<0.1).
Fig. 5 (a) Calculated output power of the first-order random lasing power vs. pump power with different reflectivity values. Insert: The slope efficiency variation with the increase of the pump power. (b) Calculated maximum output power and optical conversion efficiency of 1st-order random lasing as a function of reflectivity.
The above-mentioned output characteristics can be attributed to the different lasing power distribution with different reflectivity values of the point reflector. Figure 6 shows the calculated lasing power distributions with the same output power at the end of the fiber, in the case of different reflectivity values. With a shorter fiber length, the integral Rayleigh backscattering coefficient is weaker. Therefore, for a point reflector with 0.01 reflectivity, the lasing power can be mainly distributed towards the far-end of the fiber span, enabling the high power, high efficiency output. In our scheme, the completely open cavity is used for the 2nd-order random lasing, so the threshold for 2nd-order random lasing is determined by the 1st-order lasing power distribution. From Fig. 6(a), in the cases with the same output power (40W), with the higher reflectivity, the rising edge of the forward lasing power is much closer to the pump side of the fiber. Therefore, it can be easily seen that the 1st-order lasing power distribution of the higher reflectivity is more beneficial to generate the 2nd-order random lasing. Therefore, the maximum 1st-order lasing output power can be higher with lower reflectivity, because the 2nd-order lasing is more constrained in that case. Figure 6(b) shows that the backward lasing power is more significant in the case with relatively low reflectivity, which will decrease the total optical conversion efficiency of far-end output.
Fig. 6 The calculated lasing power distributions with the same output power at the end of the fiber in the case of different reflectivity values: (a) Forward direction; (b) Backward direction.
These calculations also have the important practical meanings. For applications to generate high power lasing, the specific FBG or FLM providing high reflectivity for the 1st Stokes wave is actually not always necessary. A mirror with low reflectivity is more preferable in order to achieve higher output power, and even with a flat fiber end, which has ~4% broadband reflection, could be sufficient. Therefore, the half-open cavity can be easier to construct for various lasing wavelength, and the configuration is much simpler, making the forward-pumped high power RFL very attractive.
4. Conclusions
In this paper, we study the influence of point reflector’s reflectivity on the characteristics of the forward-pumped RFL. With the increase of reflectivity, the lasing threshold drops rapidly in the range of low reflectivity (<0.1); by further increasing the reflectivity to a high enough level (>0.4), the laser’s power distribution and threshold tend to be relatively stable over the change of reflectivity. Furthermore, for the short fiber length (e.g. 500m), though at the expense of lower optical conversion efficiency, the maximum 1st-oder random lasing output power can increase from 41W to 45.7W when the reflectivity decreases from 0.9 to 0.01, due to the different lasing power distributions with different reflectivity values. These results are useful for the design of random fiber lasers for various applications such as distributed amplification and high power laser source.
Acknowledgments
This work is supported by Natural Science Foundation of China (61205048, 61290312, 61106045), Research Fund for the Doctoral Program of Higher Education of China (20120185120003), and PCSIRT (IRT1218), and the 111 Project (B14039).
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