IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 27, NO. 3, FEBRUARY 1, 2015
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Low-Threshold, High-Efficiency Random Fiber Laser With Linear Output Mengqiu Fan, Zinan Wang, Han Wu, Wei Sun, and Li Zhang
Abstract— In this letter, we numerically study and experimentally achieve a low-threshold, high-efficiency random fiber laser, featuring a linear output as well. The lasing cavity incorporates a section of standard single-mode fiber and a band-selective point reflector placed at the far end of the fiber. The numerical result indicates that most energy is further pushed toward the pump side comparing with the open cavity scheme, producing a high-efficiency output. Then, we analyze the dependence of threshold and slope efficiency on cavity length and pumping wavelength. Most importantly, shorter cavity length would yield higher efficiency, and for different pumping wavelengths, there will be different cavity lengths corresponding to the lowest lasing threshold. Finally, we deliberately choose the parameters and experimentally achieve an 1145-nm random fiber laser with 7.13-W output and >90% slope efficiency (with 10-W pump), while the slope efficiency is almost constant above the 2-W lasing threshold. This letter provides a comprehensive guideline for designing such random fiber lasers with tailored performance. Index Terms— Random media, Raman scattering, Rayleigh scattering, optical fiber lasers.
I. I NTRODUCTION
T
HE random fiber laser (RFL) has attracted lots of interests since the first demonstration reported by Turitsyn et al [1]. The RFL is a new type of laser since the feedback of the lasing light solely depends on the random distributed Rayleigh scattering along the fiber, rather than reflective point-mirrors as in conventional fiber lasers. The fiber itself provides both optical amplification and distributed feedback. RFL shows the properties of “modeless” spectrum [1], long-distance signal delivery ability [2], stable output with little thermal sensitivity [3] and singletransverse-mode profile. Due to these advantages, attentions have been paid to their applications in fiber-optic sensing and communication [3]–[5]. Also, various aspects of RFL have been studied: RFL has been designed to be narrow bandwidth [6], multiwavelength [7], [8] wavelength-tunable [9],
Manuscript received September 3, 2014; revised October 16, 2014; accepted November 10, 2014. Date of publication November 13, 2014; date of current version January 19, 2015. This work was supported in part by the Research Fund for the Doctoral Program of Higher Education of China under Grant 20120185120003, in part by the Program for Changjiang Scholars and Innovative Research Team University under Grant IRT1218, in part by the 111 Project under Grant B14039, in part by the National Natural Science Foundation of China under Grant 61205048 and Grant 61290312, and in part by the Fundamental Research Funds for the Central Universities under Grant ZYGX2012J002. (Corresponding author: Zinan Wang.) The authors are with the Key Laboratory of Optical Fiber Sensing and Communications, University of Electronic Science and Technology of China, Chengdu 610051, China (e-mail:
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2014.2370644
high power [10]–[12] and generating high order Stokes waves [13], [14]. Besides, the concept of RFL can be further developed by using Brillouin gain instead of Raman gain [15]. Most of the previous RFL studies focus on the long fiber cavity with a length of tens of kilometers; however, RFL with short cavity has a unique advantage to generate high power mode-less Stokes wave, because of the very high thresholds of higher order Stokes waves, but this subject is yet to be fully explored. For short-cavity RFL the lasing threshold of the 1st-order Stoke wave is also very high, therefore the cavity design and the fiber selection are essential in order to make it operational. Recently, some achievements about high power RFL were reported [10]–[12]. In Reference [10], near the 5.5W lasing threshold, more than 2W of output power is generated from only 0.5W of pump power excess over the threshold, and finally they obtained 7.3W output with 11W pump source, while the input-output curve is nonlinear. However, a linear output is generally preferred in most applications. In Reference [11], 73.7W output power with 74.7% optical efficiency is obtained. But it should be noted that the output power is a sum of forward power and backward power rather than the power from the same output port. Also, in both of the two achievements, the purpose of high power output is at the expense of the relatively high lasing threshold. In Reference [8], linear input-output dependence with backward pumping is demonstrated, also in the recent review [16], brief numerical results are given, while leaving space for further study, particularly for simultaneously realizing lowthreshold and high-efficiency in such RFLs. In this letter, we present the detailed analysis for the key factors of forming a low-threshold, high-efficiency random fiber laser with linear output. The cavity incorporates a short section of single mode fiber (SMF) and a point reflector placed at the far end of the fiber. With the numerical calculations, we elaborately analyze the optimal cavity length and operating wavelength for the purpose of achieving low-threshold and generating high-power random lasing. As the verification, we experimentally demonstrate a high power (7.13W output), highly efficient (more than 90% slope efficiency) RFL at 1145nm using 10W 1090nm pump and 5km standard SMF, with a threshold of only 2W. The experimental results coincide with the theoretical model well, and this work provides a comprehensive guideline for the design of such RFLs. II. T HEORETICAL A NALYSIS The schematic setup for the low-threshold, high-power random fiber laser is shown in Fig.1. Without loss of generality,
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Fig. 1.
IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 27, NO. 3, FEBRUARY 1, 2015
Schematic setup. TABLE I F IBER PARAMETERS FOR N UMERICAL C ALCULATIONS
the pump wavelength is at first set to 1090nm and the corresponding 1st-order Stokes wavelength is 1145nm for cavity made with standard SMF. At the far-end of the SMF, a fiber loop mirror (FLM) is attached to the selected port of a wavelength division multiplexer in order to reflect the 1st-order Stokes light only. To make a comprehensive theoretical analysis on power optimization, we use the steady-state model as the following equations [14]: d P0± f0 = ∓α0 P0± ∓ g1 P0± P1+ + P1− + 1 ± ε0 P0∓ (1) dz f1 d P1± = ∓α1 P1± ± g1 P1± + 0.51 P1+ + P1− ± ε1 P1∓ (2) dz 1 i = 4h f i f i 1 + (3) exp h( fi−1 − f i )/(K B T ) − 1 where lower indexes ‘0’ and ‘1’ correspond to the pump, the 1st-order lasing, respectively. Lower indexes ‘+’ and ‘−’ denotes the forward and backward waves, respectively. P0,1 denotes the optical power, f0,1 is the wave frequency. i denotes the population of phonon, where f1 = 0.25THz is the lasing bandwidth, T (= 298K) is the absolute temperature and KB is the Boltzmann’s constant, h is the Plank’s constant, α0,1 is the fiber loss, g1 is the Raman gain coefficient, ε0,1 is the Rayleigh backscattering coefficient. The parameters used are summarized in Table I. The boundary conditions are P0+ (0) = Pin , P1+ (0) = R L1 P1− (0) and P1− (L) = R R1 P1+ (L) where Pin denotes the pump power, the reflectivity of the FLM, R R1 , is set to 0.6 [14]. The model can be solved numerically through the shooting method. Firstly, we analyze the lasing power distribution along the fiber to evaluate the possibility of generating high-power output with high-efficiency. The result is shown in Fig. 2. Comparing Fig. 2(a) and (b), for the case with the proposed half-open cavity, the forward power along the fiber is significantly restrained since most energy moves towards the pump side. Based on the result, we deduce the output efficiency with our scheme can be higher than the case with open cavity.
Fig. 2. Power distributions of the 1st-order random lasing. (a) Lasing power distributions with open cavity (10W pump power). (b) Lasing power distributions with half-open cavity (10W pump power).
In order to evaluate the effect of the possible parasitic reflection at the near pump side, we also perform the simulation with the assumed R L1 = 5 × 10−5 . Because the anglepolished connectors usually have no less than 10−6 reflectivity, the assumption of the value of R L1 is practical [16]. As we can see in Fig. 2(b), in the proposed scheme, the major power of the 1st-order Stokes wave is located in the first 1km of the fiber, and the backward power is much (more than 100 times) higher than the forward power, because of the far-end reflector. Moreover, taking account of the parasitic reflection near the pump will not affect the power distribution significantly, for both the forward and the backward waves. On the other hand, in the scheme with open cavity, forward power increases significantly after the first 1.5km of the fiber. The maximum values of the forward power along the fiber reach to 1.9W and 1.4W in the scheme with and without the parasitic reflection, respectively. This result means that the half-open cavity is able to weaken the effects from the parasitic reflection. Therefore, we could achieve the desired laser performances without worrying parasitic reflection in experiments. Secondly, we calculate the lasing thresholds and the slope efficiencies with different cavity lengths with 1455nm, 1365nm and 1090nm pumping, respectively. The aim is to study how the backscattering coefficient and Raman gain coefficient affect the performance of such RFLs, as well as to optimize the fiber length with different pump wavelengths for different applications. We follow the simulation model
FAN et al.: LOW-THRESHOLD, HIGH-EFFICIENCY RANDOM FIBER LASER
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TABLE II F IBER PARAMETERS FOR N UMERICAL C ALCULATIONS
Fig. 5.
Fig. 3. Lasing thresholds vs. fiber cavity lengths with different pump wavelengths.
Fig. 4. Slope efficiencies vs. fiber cavity lengths with different pump wavelengths.
mentioned in previous context and the parameters of the fiber are summarized in Table II. The numerical results for lasing threshold are shown in Fig. 3. From the insert in Fig. 3, we can see all the three lasing threshold curves have the similar variation trend on the whole. If the fiber length is long enough, the gap between the two curves of 1365nm pumping and 1455nm pumping vanishes gradually, and the thresholds turn to be constant values. It should be noted that, with 1090nm pumping, the lasing threshold over the cavity length converges to a constant value much faster than the other two cases. Particularly, the threshold with 1090nm pumping is lowest among all the three cases, if the fiber length is less than 9km. It can be understood that both Rayleigh scattering coefficient and Raman gain coefficient are larger at shorter wavelength, therefore it leads to lower threshold with short fiber cavity; however, as the cavity length increases, large loss at short wavelength will be the dominant factor, thus the threshold will rise faster than the cases operating at longer wavelengths. The slope efficiency curves in Fig. 4 show that as the fiber length is shorter, the slope efficiency is higher. The differences between the three curves with different pumping wavelengths are not obvious with short fiber cavity; however, it turns to be
Output power vs. pump power with the proposed half-open cavity.
remarkable as the fiber length increases. If the fiber cavity exceeds 15km, the slope efficiency with 1090nm pumping will worsen significantly, because the pump and the Stokes experience much more attenuation than the other two cases. The curve under 1090nm pump behaves differently from the other two curves, and it can be seen as a complicated interplay among Raman gain, Rayleigh back-scattering and the loss. Therefore, through the numerical analysis, we can conclude that in order to achieve certain combination of low lasing threshold and high slope efficiency, the used fiber length can be optimized. It can be concluded that the optimal fiber length would be between 5km to 10km. Based on the above results, one can get the optimal combination of fiber cavity length and operation wavelength in different occasions. For example, if certain slope efficiency is required, from Fig. 4 one can know the longest fiber cavity that can be used, for each of the pumping wavelength; afterwards, based on the limited range of cavity length and the selected wavelength, one can know the requirement for pump power. III. E XPERIMENTAL R ESULTS Based on the aforementioned theoretical analysis, we experimentally demonstrate the proposed RFL using the design shown in Fig. 1. From Fig. 4 it can be known that shorter fiber length is required to yield high-efficiency, then from Fig. 3 it can be seen that pumping at 1090nm will have lowest lasing threshold; also, powerful source at 1090nm is easier to obtain, which is an important condition for generating high power random lasing. Therefore, a 1090nm Ytterbium-doped fiber laser is used as the pump source. The pump is launched into the fiber spool via an isolator and a wavelength division multiplexer (WDM). A 5km standard SMF performs as the Raman gain medium and random distributed feedback mirrors. A fiber loop mirror (FLM) connected with the 1145nm port of the WDM at the far-end of the cavity, providing a high reflectivity for the 1st-order random lasing at the far end, and the isolation of 1220nm light via the 1145nm port is >20dB. The lasing characteristics are monitored at the two ports of the optical coupler (OC) connected with the 1145nm port of the WDM at the pump side. The 99% port is used to monitor the output power. The measured output power of the 1st-order random lasing versus pump power is shown in Fig. 5. The lasing threshold is ∼2W. As expected, the lasing power increases linearly with the pump power beyond the threshold. The slope efficiency
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 27, NO. 3, FEBRUARY 1, 2015
Output power vs. pump power with the open cavity.
fiber laser. At first, we analyze the power distribution along the fiber with point reflector placed at the far end of the fiber cavity. Based on the results, we reveal the mechanism of generation high-efficiency random lasing with the proposed scheme. Second, we calculate the lasing thresholds and the slope efficiencies with different pump wavelengths and different cavity lengths. The results show that the cavity length is very crucial for the laser’s threshold and maximum efficiency, and the lowest lasing threshold is highly relevant on the operating wavelength; from another perspective, the results provide the basis for optimizing a laser’s parameters for various applications. We cross-reference the two key factors and select 5km as the SMF cavity length and 1090nm as the pump wavelength, in order to demonstrate an example with optimized overall performance. As a result, a low-threshold (2W), high-power (7.13W output at 10W pump), high-efficiency (more than 90% slope efficiency) random fiber laser with linear output at 1145nm is achieved, and the experimental data fits the numerical results well. R EFERENCES
Fig. 7.
The RF spectrum of the laser output and receptor noise.
is more than 90%, and the maximum 7.13W of 1145nm random lasing is obtained with 10W pump power, which corresponds to 71.3% optical conversion efficiency (75.2% quantum efficiency). Considering the parasitic reflection at the pump side, here we assume R L1 = 5 × 10−5 . The solid red line corresponds to the calculated output power with parasitic reflection at the pump side, while the dotted blue line corresponds to the calculated output power without parasitic reflection. The experimental results fit the numerical results well. The inserted figure shows the lasing spectra evolution. As a comparison, we measure the output power of the 1st-order random lasing versus pump power with open cavity (FLM removed). As shown in Fig. 6, the threshold is 3.4W, which is higher than the scheme with the half-open cavity, and the slope efficiency is about 83%, which is lower than the halfopen cavity as well. Also, the optical conversion efficiency is only 52%. It is worth noting that in the numerical simulation there is an obvious difference between results with and without parasitic reflection at the far end. We set the parasitic reflection at the far end as R R1 = 1.5 × 10−4 , and then the data matches the experimental results well. With the parasitic reflection, the threshold is slightly lower than the case without the parasitic reflection, while the output power of each case is about the same with the 10W pump power. To validate the random lasing behavior, we also measure the radio frequency (RF) spectrum of the output lasing with 8W pump power, as depicted in Fig. 7. The resolution of the spectrum is 200Hz and the signal power level is about −15dBm. It can be found that there is no longitudinal mode beating corresponding to c/2nl ≈ 20k H z spacing. IV. C ONCLUSIONS In this letter, we thoroughly study the approach to form a low-threshold, high-efficiency and linear output random
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