Abstract

We report a high-efficiency (25%) Brillouin random fiber laser (BRFL) with Brillouin gain medium of 2-km polarization maintaining fiber (PMF) as well as distributed Rayleigh scattering feedback from 500-m PMF. The characteristics of lasing efficiency and relative intensity noise (RIN) have been comprehensively studied comparing with the BRFLs with half-open ring cavity and bidirectional pumping linear open configuration. The enhanced lasing efficiency using PMF-BRFL with half-open ring cavity enables sub-kHz linewidth, lower phase fluctuation and frequency jitter comparing with phase locked pump laser, thanks to the polarization-matched efficient Brillouin gain in PMFs. The RIN and frequency instability of the proposed PMF-BRFL induced from external disturbance, e.g., mechanical and thermal noise, have been effectively suppressed with respect to conventional SMF-based BRFL.

© 2017 Optical Society of America

1. Introduction

In past few years, random fiber lasers (RFLs) has been widely demonstrated by incorporating one-dimensional random feedback of distributed Rayleigh scattering from refractive index inhomogeneity in silica fiber instead of conventional mirror [1]. Such new breed of the laser with unique spectral dynamic and noise properties has shown immense potentials in underlying fundamental research [2, 3] as well as practical applications such as distributed amplification for fiber optics communication [4–8]. Attempts have been made in various gain mechanisms such as Raman scattering [9–11], rare-earth-doped fiber amplification [12–14], and Brillouin scattering [15–17] with distributed Rayleigh scattering naturally presented in optical fiber or random fiber gratings with artificially disordered random feedback [18, 19].

One important approach to generate random fiber laser is the utilization of stimulated Brillouin scattering (SBS) amplification and distributed Rayleigh feedback in ultra-long fibers, providing significant extension of the light coherence for narrow linewidth lasing emission [16, 20]. Brillouin random fiber laser (BRFL) has been attractive for promising applications in high-precision metrology [21, 22], microwave generation [23] and truly random number generator [24]. In early literatures, Brillouin-based random lasing emission was achieved in linear open cavity [15, 20] and half-open ring configuration [16]. Afterwards, attentions have been extensively paid to improve laser characteristics. For instance, bidirectional pump injection has been proposed to enhance the lasing efficiency of BRFL with the linear open cavity [17] while intensity noise of BRFL can be suppressed by the assistance of random fiber gratings [25]. To stabilize the frequency of BRFL, a high finesse narrow-band Fabry-Perot interferometer was incorporated to lock the random lasing frequency at the cost of complex laser design and lasing efficiency [26]. Nevertheless, all these BRFLs based on ultra-long single mode fiber (SMF) random cavity still suffer from high intensity fluctuation and frequency instability due to strong gain competition under polarization-sensitive Brillouin gain. The evolution of the polarization state of both pump and Stokes at each location of the ultra-long SMFs is strongly influenced by external disturbances, leading to the deterioration of the laser characteristics. More recently, a linearly polarized BRFL with bidirectional pumping (bi-pump) scheme was demonstrated in the linear open cavity consisting of polarization maintaining fibers (PMFs) as both Brillouin gain medium and double distributed Rayleigh feedback fibers [27]. Polarization-matched SBS between linearly polarized pump and Stokes along PMFs supported a stable laser emission with 20-dB intensity noise suppression. However, weak feedback strength of doubly Rayleigh “mirrors” in linear open cavity basically limited the lasing efficiency (~8%) and Q-factor of the random cavity with lower coherence for a moderate linewidth (~2 kHz). To date, BRFL with balanced performance in terms of lasing efficiency, intensity noise and frequency stability has not been well discussed yet.

In this paper, we demonstrated a high-efficiency PMF-based Brillouin random fiber laser (PMF-BRFL) with half-open ring configuration by the combination of the Brillouin gain in 2-km PMF and random feedback from distributed Rayleigh scatting along 500m-PMF. Compared to bi-pump PMF-BRFL, the proposed laser with half-open ring configuration reduced cavity loss and hence delivered a lasing efficiency of 25.4% for a random lasing radiation with sub-kHz linewidth. A prominent suppression of random mode density by the selection of polarization-matched Brillouin gain and the immunity to external disturbances in PMFs contribute to optimized RIN suppression and frequency stabilization compared to that of SMF-based BRFL. Additionally, the random lasing emission was comprehensively characterized considering the temporal dynamics, polarization properties and phase fluctuation.

2. Experimental setup

Figure 1 illustrates the PMF-BRFL configuration and measuring setups for characterizing the random lasing radiation. A fiber laser (Rock Module, NP Photonics) was amplified by an Erbium doped fiber amplifier (EDFA) and its polarization can be adjusted by a polarization controller (PC) to align into the slow axis of a polarization beam splitter (PBS). Then, the generated linearly polarized pump light was launched into the all-PMF random laser cavity through a PM circulator (PM-CIR1). The Brillouin gain medium is a 2-km Panda-type PMFs with fiber loss of 0.296 dB/km and a mode field diameter of 6.48 μm at the wavelength of 1550 nm. Another 500-m same type PMF was utilized to provide randomly distributed Rayleigh feedback which was injected back to the fiber cavity through a second PM circulator (PM-CIR2). As one increased the pump power, sufficient feedback of Rayleigh scattered Stokes wave was then amplified by the SBS to compensate the round trip loss for lasing oscillation. Finally, the laser emitted after a PM isolator which was placed at the end of 500-m PMF for blocking the Fresnel reflection from the fiber connectors.

 

Fig. 1 Experimental setup of the PMF-BRFL for the measurements of (a) power/spectrum, (b) polarization extinction ratio, (c) intensity noise, (d) linewidth and (e) phase fluctuation.

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Instead of SMF, the utilization of PMF offers several advantages for establishing Brillouin random lasing: (1) PMF provides a higher Brillouin gain coefficient due to a smaller effective mode field diameter of 6.48μm than that of SMF (10.4μm); (2) polarization-matched SBS between identical linearly polarized pump and Stokes could enhance the Brillouin gain by a factor of 2; (3) two-dimensional stress from Baron-doped-silica rods in PMF naturally introduces additional transverse non-uniformity in fiber core to enhance Rayleigh scattering for efficient distributed random feedback; (4) stress-induced birefringence in PMF makes linearly polarized light immune against external perturbations during its propagation in one principal axis of the PMF. However, BRFL with linear open cavity employing double Rayleigh mirror at both ends of the gain fibers introduces significant cavity loss for the roundtrip of the recaptured photons and thus limits the lasing efficiency as well as linewidth reduction. On the other hand, random lasing mode density in linear cavity could be roughly twice than that of the ring cavity for the same fiber length, which induces higher intensity noise. Consequently, the PMF-based BRFL with half-open ring cavity would exhibit an optimal performance in terms of the lasing efficiency, intensity fluctuation and frequency stabilization compared to the conventional SMF-BRFL and PMF-based BRFL with open linear cavity.

3. Laser characteristics

In Fig. 1(a), the laser power and spectrum were monitored by a power meter and an optical spectrum analyzer (OSA) (AP2043B, Apex), respectively. Figure 2(a) shows that the laser emission appeared as the input pump power surpassed the threshold power of 14.60 mW, exhibiting a lasing efficiency of 25.4%. The laser wavelength was measured as 1550.182 nm which corresponds to the Brillouin shift of 0.082 nm from the pump light. Note that, the Stokes laser power was around 40-dB higher than that of the Rayleigh scattered pump as the input pump power was well beyond the laser threshold. In the bi-pump BRFL, however, the residual pump light were comparable with the Stokes laser emission and thus a narrowband filter (< 10 GHz) was basically required for a pure Stokes laser radiation [27].

 

Fig. 2 (a) Laser output power and spectrum of the PMF-BRFL with half-open ring cavity; (b) PER of PMF-BRFL under different pump powers. (Inset: normalized transmission versus the rotation angle of the polarizer.)

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The linear polarization of the pump and the laser radiation were validated through rotating a polarizer and detecting the transmission power by a polarimeter (IPM5300, Thorlabs), as depicted in Fig. 1(b). Maximum transmission power (Pmax) was achieved at rotation angles of 0 ̊/180 ̊ of the polarizer which aligns with the slow axis of the PMF while the transmitting power dropped to a minimum level (Pmin) at rotation angles of 90 ̊/270 ̊. The polarization extinction ratio (PER) is defined by PER = 10log(Pmax/Pmin). In Fig. 2(b), the PER of the laser output grew up to ~25 dB as the pump power was well beyond the threshold. A slight PER reduction of PMF-BRFL with ring cavity was found comparing to PMF-BRFL with bi-pump scheme in which identical linearly polarized pump light provided highly selective polarization-dependent Brillouin amplification of Stokes lasing resonance. The linear polarization of the laser output could be further validated by the transmission power with respect to the rotation degree of the polarizer. In the inset of Fig. 2(b), the transmission of both input pump and laser was observed with a well fit of the function I = I0cos2θ, which is consistent with Malus’ law.

To investigate the intensity dynamics and the statistical feature of random lasing emission, the temporal trace of the laser output at the pump power of 35.10 mW was recorded through a photodetector (PDB130C, Thorlabs) and an oscilloscope (DS081204B, Agilent). For comparison, SBS emission under the same pump power was also measured without random Rayleigh feedback. In Fig. 3(a-1), stochastic intensity fluctuation without random feedback corresponding typical SBS process in optical fiber was observed, attributing to thermal noise-dominated emission by the SBS process [28–30]. However, the intensity fluctuation was significantly modified as random lasing oscillation occurred under the feedback from distributed Rayleigh scattering. Instead of an asymmetric probability distribution without random feedback, the intensity statistics of the random laser emission exhibits a Gaussian distribution on the intensity probability. The phase portrait was reconstructed by a two-dimensional intensity plot of IN versus IN + 1 (N = 1, 2 …) with a delay of one step intervals, which can evidently exhibit the temporal evolution of the trajectory. As illustrated in Figs. 3(a-3) and 3(b-3), the random Rayleigh feedback enables the random lasing emission with confined cycle signature while SBS emission exhibits a chaotic behavior in phase portrait [28].

 

Fig. 3 Intensity dynamics of (a) SBS (without random Rayleigh feedback) and (b) Brillouin random lasing (with random Rayleigh feedback): (1) temporal trace; (2) power density distribution; (3) phase portrait.

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A delayed self-heterodyne (DSH) technique consisting of a Mach-Zehnder interferometer was utilized to characterize the linewidth of the PMF-BRFL, as shown in Fig. 1(d). The optical beat signal was converted by a photodetector (PDB130C, Thorlabs) and measured by an electrical spectrum analyzer (ESA) (E4446A, Agilent). By using the delay fiber of 200-km SMF, the 20-dB linewidth of the proposed PMF-BRFL was measured as 13.6 kHz with a contrast of 50 dB, as shown in Fig. 4(a). In comparison, the 20-dB linewidth of pump laser was also characterized as 66.7 kHz. Hence, the corresponding 3-dB linewidth of the PMF-BRFL and the pump laser at 3-dB were calculated as 0.7 kHz and 3.4 kHz, respectively. Moreover, delay fibers with different lengths from 0 to 200 km were tested for linewidth measurement. Figure 4(b) shows that the measured 3-dB linewidth of both the pump laser and PMF-BRFL increased with delay fiber length. Particularly, the measured linewidth of the pump laser saturated at 3.4 kHz as the delay fiber length was longer than 50 km. Due to narrowing effect of Brillouin lasing [31], the measured linewidth of the proposed PMF-BRFL reached 0.7 kHz at 200-km delay fiber. Compared with PMF-BRFL with bi-pump configuration [27], an enhanced lasing efficiency as well as reduced cavity loss of the PMF-BRFL in ring cavity can eventually improve the Q-factor, resulting in ~3 times linewidth reduction.

 

Fig. 4 Linewidth measurement (a) beat signal with 200km delay fiber; (b) 3-dB linewidth with varied delay fiber lengths. (ESA resolution bandwidth, 510 Hz; sweep time, 100 ms; average times, 20)

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The phase fluctuation of the PMF-BRFL was characterized by an imbalanced Michelson interferometer based on a symmetric 3×3 optical coupler with 4-km delay fiber in one arm, as shown in Fig. 1(e). The temporal phase fluctuation of the laser emission can be demodulated within the time window of 0.1 s. As shown in Fig. 5, the stimulated PMF-BRFL represents phase shift within ±0.5×10−6 rad which is about 1/3 of the phase locked pump laser due to the combined influence of acoustic damping and weak feedback, which has been predicted by theoretical analysis of Brillouin fiber laser in [32].

 

Fig. 5 Phase fluctuations of pump laser and PMF-BRFL.

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4. Comparison and discussions

4.1 Laser efficiency

The PMF can improve the lasing efficiency and reduce the laser threshold over the SMF-BRFL, as shown in Figs. 6(a) and 6(b). In linear-cavity BRFL with the bi-pump scheme, the lasing efficiency is mainly limited by the strength of distributed random feedback along the gain fiber span itself. Thus, longer-length gain fiber provides a higher lasing efficiency in SMF-BRFL with the bi-pump scheme. However, BRFL with ring configuration shows a much higher lasing efficiency and lower threshold than that of bi-pump BRFL with linear cavity due to reduced cavity loss in ring cavity with single Rayleigh “mirror”. Consistently, PMF-BRFL with ring cavity also exhibits a three times higher lasing efficiency than that of bi-pumping PMF-BRFL with linear cavity. On the other hand, the lasing efficiency of SMF-BRFL with ring cavity decreases due to strong gain saturation in long-length gain fibers [33]. The lasing efficiency of 25.4% is highest efficiency in BRFLs, to the best of our knowledge.

 

Fig. 6 Comparison of (a) lasing efficiency and (b) threshold power with different gain fiber lengths. The lasing efficiency is calculated by η = ΔPlaserPpump.

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4.2 Relative intensity noise

For the characterization of the relative intensity noise (RIN), the temporal intensity fluctuation of the PMF-BRFL with ring cavity was recorded by a photodetector (PDB130C, Thorlabs) and an oscilloscope (DS081204B, Agilent). For comparison, RINs of the bi-pump PMF-BRFL based on the open linear cavity of the 2-km PMF and the SMF-BRFL with half-open ring cavity using the gain fiber of 25-km SMF and Rayleigh fibers of 5-km non-uniform fibers were illustrated in Fig. 7 using the same pump laser: both of SMF-BRFL and PMF BRFL with distributed Rayleigh feedback exhibited a high RIN than the pump laser in which the RIN was suppressed by feedback control mechanism. In the Fourier frequency domain of 10 Hz ~1 kHz, the RIN of PMF-BRFL with ring cavity shows a 20-dB suppression with respect to that of SMF-BRFL with ring cavity, attributing to a high random lasing efficiency as well as a significant alleviation of low-frequency external thermal and mechanical disturbances in all-PMF configuration. Compared to bi-pumping PMF-BEFL with bidirectional distributed Rayleigh mirrors, the RIN of the ring-cavity PMF-BRFL with single distributed Rayleigh mirror was reduced by 10 dB in low frequency domain (<1 kHz). Since polarization-dependent Brillouin gain of the linearly polarized pump efficiently diluted unmatched random modes density and alleviated gain competition during the lasing oscillation, the PMF-BRFL with both bi-pump and ring configurations were observed with highly suppressed discrete peaks in high frequency domain of >2 kHz.

4.3 Frequency stability

The frequency stability of the random laser was characterized through the frequency shift of beat signals between two independent random laser emissions, as shown in Fig. 8. Here, the dynamics of the two uncorrelated random laser emissions were guaranteed by three aspects: 1) The utilization of 100-km delay fiber (larger than the ~60-km coherent length of pump laser) decorrelated mutual coherence between two pump lights. 2) Two pump lights were separated by 40MHz frequency shift from an acousto-optic modulator (AOM), and the two Stokes waves were also separated by the same frequency difference, which is well beyond of the bandwidth of each Brillouin gain, and hence the gain competition between two wavelengths can be neglected in lasing process. 3) The shared random laser cavity would deliver the similar laser dynamics. Then, the beat signal of two random laser emissions was converted by the PD and then mixed down to 5 MHz. The data was acquired by an oscilloscope and then analyzed through Fourier transform. Consequently, the central frequency shift of the beat signal represents the optical frequency variation of the random laser emission.

 

Fig. 8 Frequency jitter measurement setup for (1) SMF- BRFL, (2) PMF-BRFL and (3) the pump laser.

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The frequency instability of the BRFL arises from mechanical and thermal noise which shifts the Brillouin gain at different location along the gain fibers and induces the fluctuation. The bandwidth of these technical noise sources are of the order of 100 Hz, which is responsible for the slow drift of the frequency. Here, the frequency drift of every 1 millisecond within time window of 2 second was collected through Fourier transform of beat signal recorded by the high-speed oscilloscope. The SMF-BRFL with gain fiber of 25 km SMF and Rayleigh fibers of 5 km non-uniform fibers was also measured for comparison. In Fig. 9(a), the frequency of the SMF-BRFL fluctuated within the ~10MHz Brillouin gain bandwidth in the SMF since the mode hopping effect was aggravated by external disturbance. However, the BRFL of all-PMF configuration offers frequency drift of 0.9 MHz, which is one order of magnitude smaller than that of the SMF-BRFL. The minimum frequency jitter of the PMF-BRFL is imposed by the pump source in a range of ~60 kHz, shown by the statistical probability in Fig. 9(b). Note that, SMF-BRFL shows two probability peaks of around ±2.5 MHz is induced by the gain saturation of 25km SMF due to hole burning [34], while the probability peak of 0 Hz was found in PMF-BRFL and pump laser.

 

Fig. 9 (a) Frequency jitter and (b) statistical probability in 2 s. (Inset is the zooming of the PMF-BRFL and pump laser).

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5. Conclusion

In summary, we reported a high-efficiency stable BRFL based on all-PMF half-open ring configuration. Compared to bidirectional pumping linear open cavity configuration, the proposed laser improved the lasing efficiency at 25.4% and suppressed intensity noise by reducing random lasing mode density. Sub-kHz linewidth of the random laser radiation was characterized using self-delay heterodyne interferometer. The PMF-BRFL exhibits significant frequency stability with respect to SMF-BRFL, paving the way for applications in the fields of communication, high-precision metrology, sensing and spectroscopy.

Funding

Natural Sciences and Engineering Research Council of Canada (NSERC) (06071/FGPIN/2015); Canada Research Chair Program (CRC in Fiber Optics and Photonics).

Acknowledgments

The Authors thank Yangtze Optical Fibre & Cable Joint Stock Co., Ltd., for providing the 2 km PMF fiber.

References and links

1. S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014). [CrossRef]  

2. D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015). [CrossRef]   [PubMed]  

3. A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016). [CrossRef]  

4. D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015). [CrossRef]  

5. S. Papernyi, V. Karpov, and W. Clements, “Third-order cascaded Raman amplification,” in Optical Fiber Communication Conference (OFC 2002), paper FB4–FB4.

6. V. Karpov, S. Papernyi, V. Ivanov, W. Clements, T. Araki, and Y. Koyano, “Cascaded pump delivery for remotely pumped erbium doped fiber amplifiers,” in Proceedings of Suboptic Conference (2004), paper We 8.8.

7. S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Six-order cascaded Raman amplification,” in Optical Fiber Communication Conference (OFC, 2005), paper OThF4.

8. M. Schneiders, S. Vorbeck, R. Leppla, E. Lach, M. Schmidt, S. B. Papernyi, and K. Sanapi, “Field transmission of 8/spl times/170 gb/s over high-loss SSMF link using third-order distributed Raman amplification,” J. Lightwave Technol. 24(1), 175–182 (2006). [CrossRef]  

9. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

10. Z. Wang, H. Wu, M. Fan, Y. Rao, X. Jia, and W. Zhang, “Third-order random lasing via Raman gain and Rayleigh feedback within a half-open cavity,” Opt. Express 21(17), 20090–20095 (2013). [CrossRef]   [PubMed]  

11. S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011). [CrossRef]  

12. G. Yin, B. Saxena, and X. Bao, “Tunable Er-doped fiber ring laser with single longitudinal mode operation based on Rayleigh backscattering in single mode fiber,” Opt. Express 19(27), 25981–25989 (2011). [CrossRef]   [PubMed]  

13. T. Zhu, X. Bao, and L. Chen, “A single longitudinal-mode tunable fiber ring laser based on stimulated Rayleigh Scattering in a nonuniform optical fiber,” J. Lightwave Technol. 29(12), 1802–1807 (2011). [CrossRef]  

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22. S. Gao, L. Zhang, Y. Xu, P. Lu, L. Chen, and X. Bao, “Tapered fiber based Brillouin random fiber laser and its application for linewidth measurement,” Opt. Express 24(25), 28353–28360 (2016). [CrossRef]   [PubMed]  

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34. A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002). [CrossRef]   [PubMed]  

References

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  1. S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
    [Crossref]
  2. D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
    [Crossref] [PubMed]
  3. A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
    [Crossref]
  4. D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
    [Crossref]
  5. S. Papernyi, V. Karpov, and W. Clements, “Third-order cascaded Raman amplification,” in Optical Fiber Communication Conference (OFC 2002), paper FB4–FB4.
  6. V. Karpov, S. Papernyi, V. Ivanov, W. Clements, T. Araki, and Y. Koyano, “Cascaded pump delivery for remotely pumped erbium doped fiber amplifiers,” in Proceedings of Suboptic Conference (2004), paper We 8.8.
  7. S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Six-order cascaded Raman amplification,” in Optical Fiber Communication Conference (OFC, 2005), paper OThF4.
  8. M. Schneiders, S. Vorbeck, R. Leppla, E. Lach, M. Schmidt, S. B. Papernyi, and K. Sanapi, “Field transmission of 8/spl times/170 gb/s over high-loss SSMF link using third-order distributed Raman amplification,” J. Lightwave Technol. 24(1), 175–182 (2006).
    [Crossref]
  9. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).
  10. Z. Wang, H. Wu, M. Fan, Y. Rao, X. Jia, and W. Zhang, “Third-order random lasing via Raman gain and Rayleigh feedback within a half-open cavity,” Opt. Express 21(17), 20090–20095 (2013).
    [Crossref] [PubMed]
  11. S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
    [Crossref]
  12. G. Yin, B. Saxena, and X. Bao, “Tunable Er-doped fiber ring laser with single longitudinal mode operation based on Rayleigh backscattering in single mode fiber,” Opt. Express 19(27), 25981–25989 (2011).
    [Crossref] [PubMed]
  13. T. Zhu, X. Bao, and L. Chen, “A single longitudinal-mode tunable fiber ring laser based on stimulated Rayleigh Scattering in a nonuniform optical fiber,” J. Lightwave Technol. 29(12), 1802–1807 (2011).
    [Crossref]
  14. B. Saxena, X. Bao, and L. Chen, “Suppression of thermal frequency noise in erbium-doped fiber random lasers,” Opt. Lett. 39(4), 1038–1041 (2014).
    [Crossref] [PubMed]
  15. M. Pang, S. Xie, X. Bao, D. P. Zhou, Y. Lu, and L. Chen, “Rayleigh scattering-assisted narrow linewidth Brillouin lasing in cascaded fiber,” Opt. Lett. 37(15), 3129–3131 (2012).
    [Crossref] [PubMed]
  16. M. Pang, X. Bao, and L. Chen, “Observation of narrow linewidth spikes in the coherent Brillouin random fiber laser,” Opt. Lett. 38(11), 1866–1868 (2013).
    [Crossref] [PubMed]
  17. B. Saxena, Z. Ou, X. Bao, and L. Chen, “Low frequency-noise random fiber laser with bidirectional SBS and Rayleigh feedback,” IEEE Photonics Technol. Lett. 27(5), 490–493 (2015).
    [Crossref]
  18. M. Gagné and R. Kashyap, “Random fiber Bragg grating Raman fiber laser,” Opt. Lett. 39(9), 2755–2758 (2014).
    [Crossref] [PubMed]
  19. Y. Li, P. Lu, X. Bao, and Z. Ou, “Random spaced index modulation for a narrow linewidth tunable fiber laser with low intensity noise,” Opt. Lett. 39(8), 2294–2297 (2014).
    [Crossref] [PubMed]
  20. A. A. Fotiadi and R. V. Kiyan, “Cooperative stimulated Brillouin and Rayleigh backscattering process in optical fiber,” Opt. Lett. 23(23), 1805–1807 (1998).
    [Crossref] [PubMed]
  21. Y. Xu, D. Xiang, Z. Ou, P. Lu, and X. Bao, “Random Fabry-Perot resonator-based sub-kHz Brillouin fiber laser to improve spectral resolution in linewidth measurement,” Opt. Lett. 40(9), 1920–1923 (2015).
    [Crossref] [PubMed]
  22. S. Gao, L. Zhang, Y. Xu, P. Lu, L. Chen, and X. Bao, “Tapered fiber based Brillouin random fiber laser and its application for linewidth measurement,” Opt. Express 24(25), 28353–28360 (2016).
    [Crossref] [PubMed]
  23. D. Xiang, P. Lu, Y. Xu, L. Chen, and X. Bao, “Random Brillouin fiber laser for tunable ultra-narrow linewidth microwave generation,” Opt. Lett. 41(20), 4839–4842 (2016).
    [Crossref] [PubMed]
  24. D. Xiang, P. Lu, Y. Xu, S. Gao, L. Chen, and X. Bao, “Truly random bit generation based on a novel random Brillouin fiber laser,” Opt. Lett. 40(22), 5415–5418 (2015).
    [Crossref] [PubMed]
  25. Y. Xu, S. Gao, P. Lu, S. Mihailov, L. Chen, and X. Bao, “Low-noise Brillouin random fiber laser with a random grating-based resonator,” Opt. Lett. 41(14), 3197–3200 (2016).
    [Crossref] [PubMed]
  26. M. Pang, X. Bao, L. Chen, Z. Qin, Y. Lu, and P. Lu, “Frequency stabilized coherent Brillouin random fiber laser: theory and experiments,” Opt. Express 21(22), 27155–27168 (2013).
    [Crossref] [PubMed]
  27. L. Zhang, Y. Xu, S. Gao, B. Saxena, L. Chen, and X. Bao, “Linearly polarized low-noise Brillouin random fiber laser,” Opt. Lett. 42(4), 739–742 (2017).
    [Crossref] [PubMed]
  28. R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
    [Crossref] [PubMed]
  29. A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44(5), 3205–3209 (1991).
    [Crossref] [PubMed]
  30. M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
    [Crossref] [PubMed]
  31. A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 18(4), 556–567 (2001).
    [Crossref]
  32. A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000).
    [Crossref]
  33. L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
    [Crossref]
  34. A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
    [Crossref] [PubMed]

2017 (1)

2016 (4)

2015 (5)

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

B. Saxena, Z. Ou, X. Bao, and L. Chen, “Low frequency-noise random fiber laser with bidirectional SBS and Rayleigh feedback,” IEEE Photonics Technol. Lett. 27(5), 490–493 (2015).
[Crossref]

D. Xiang, P. Lu, Y. Xu, S. Gao, L. Chen, and X. Bao, “Truly random bit generation based on a novel random Brillouin fiber laser,” Opt. Lett. 40(22), 5415–5418 (2015).
[Crossref] [PubMed]

Y. Xu, D. Xiang, Z. Ou, P. Lu, and X. Bao, “Random Fabry-Perot resonator-based sub-kHz Brillouin fiber laser to improve spectral resolution in linewidth measurement,” Opt. Lett. 40(9), 1920–1923 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (3)

2012 (1)

2011 (3)

2010 (1)

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

2008 (1)

L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
[Crossref]

2006 (1)

2002 (1)

2001 (1)

2000 (1)

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000).
[Crossref]

1998 (1)

1993 (1)

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
[Crossref] [PubMed]

1991 (1)

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44(5), 3205–3209 (1991).
[Crossref] [PubMed]

1990 (1)

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
[Crossref] [PubMed]

Ania-Castanon, J. D.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Babin, S.

S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
[Crossref]

Babin, S. A.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Bao, X.

L. Zhang, Y. Xu, S. Gao, B. Saxena, L. Chen, and X. Bao, “Linearly polarized low-noise Brillouin random fiber laser,” Opt. Lett. 42(4), 739–742 (2017).
[Crossref] [PubMed]

Y. Xu, S. Gao, P. Lu, S. Mihailov, L. Chen, and X. Bao, “Low-noise Brillouin random fiber laser with a random grating-based resonator,” Opt. Lett. 41(14), 3197–3200 (2016).
[Crossref] [PubMed]

S. Gao, L. Zhang, Y. Xu, P. Lu, L. Chen, and X. Bao, “Tapered fiber based Brillouin random fiber laser and its application for linewidth measurement,” Opt. Express 24(25), 28353–28360 (2016).
[Crossref] [PubMed]

D. Xiang, P. Lu, Y. Xu, L. Chen, and X. Bao, “Random Brillouin fiber laser for tunable ultra-narrow linewidth microwave generation,” Opt. Lett. 41(20), 4839–4842 (2016).
[Crossref] [PubMed]

Y. Xu, D. Xiang, Z. Ou, P. Lu, and X. Bao, “Random Fabry-Perot resonator-based sub-kHz Brillouin fiber laser to improve spectral resolution in linewidth measurement,” Opt. Lett. 40(9), 1920–1923 (2015).
[Crossref] [PubMed]

B. Saxena, Z. Ou, X. Bao, and L. Chen, “Low frequency-noise random fiber laser with bidirectional SBS and Rayleigh feedback,” IEEE Photonics Technol. Lett. 27(5), 490–493 (2015).
[Crossref]

D. Xiang, P. Lu, Y. Xu, S. Gao, L. Chen, and X. Bao, “Truly random bit generation based on a novel random Brillouin fiber laser,” Opt. Lett. 40(22), 5415–5418 (2015).
[Crossref] [PubMed]

Y. Li, P. Lu, X. Bao, and Z. Ou, “Random spaced index modulation for a narrow linewidth tunable fiber laser with low intensity noise,” Opt. Lett. 39(8), 2294–2297 (2014).
[Crossref] [PubMed]

B. Saxena, X. Bao, and L. Chen, “Suppression of thermal frequency noise in erbium-doped fiber random lasers,” Opt. Lett. 39(4), 1038–1041 (2014).
[Crossref] [PubMed]

M. Pang, X. Bao, and L. Chen, “Observation of narrow linewidth spikes in the coherent Brillouin random fiber laser,” Opt. Lett. 38(11), 1866–1868 (2013).
[Crossref] [PubMed]

M. Pang, X. Bao, L. Chen, Z. Qin, Y. Lu, and P. Lu, “Frequency stabilized coherent Brillouin random fiber laser: theory and experiments,” Opt. Express 21(22), 27155–27168 (2013).
[Crossref] [PubMed]

M. Pang, S. Xie, X. Bao, D. P. Zhou, Y. Lu, and L. Chen, “Rayleigh scattering-assisted narrow linewidth Brillouin lasing in cascaded fiber,” Opt. Lett. 37(15), 3129–3131 (2012).
[Crossref] [PubMed]

T. Zhu, X. Bao, and L. Chen, “A single longitudinal-mode tunable fiber ring laser based on stimulated Rayleigh Scattering in a nonuniform optical fiber,” J. Lightwave Technol. 29(12), 1802–1807 (2011).
[Crossref]

G. Yin, B. Saxena, and X. Bao, “Tunable Er-doped fiber ring laser with single longitudinal mode operation based on Rayleigh backscattering in single mode fiber,” Opt. Express 19(27), 25981–25989 (2011).
[Crossref] [PubMed]

Blondel, M.

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44(5), 3205–3209 (1991).
[Crossref] [PubMed]

Chen, L.

L. Zhang, Y. Xu, S. Gao, B. Saxena, L. Chen, and X. Bao, “Linearly polarized low-noise Brillouin random fiber laser,” Opt. Lett. 42(4), 739–742 (2017).
[Crossref] [PubMed]

Y. Xu, S. Gao, P. Lu, S. Mihailov, L. Chen, and X. Bao, “Low-noise Brillouin random fiber laser with a random grating-based resonator,” Opt. Lett. 41(14), 3197–3200 (2016).
[Crossref] [PubMed]

S. Gao, L. Zhang, Y. Xu, P. Lu, L. Chen, and X. Bao, “Tapered fiber based Brillouin random fiber laser and its application for linewidth measurement,” Opt. Express 24(25), 28353–28360 (2016).
[Crossref] [PubMed]

D. Xiang, P. Lu, Y. Xu, L. Chen, and X. Bao, “Random Brillouin fiber laser for tunable ultra-narrow linewidth microwave generation,” Opt. Lett. 41(20), 4839–4842 (2016).
[Crossref] [PubMed]

B. Saxena, Z. Ou, X. Bao, and L. Chen, “Low frequency-noise random fiber laser with bidirectional SBS and Rayleigh feedback,” IEEE Photonics Technol. Lett. 27(5), 490–493 (2015).
[Crossref]

D. Xiang, P. Lu, Y. Xu, S. Gao, L. Chen, and X. Bao, “Truly random bit generation based on a novel random Brillouin fiber laser,” Opt. Lett. 40(22), 5415–5418 (2015).
[Crossref] [PubMed]

B. Saxena, X. Bao, and L. Chen, “Suppression of thermal frequency noise in erbium-doped fiber random lasers,” Opt. Lett. 39(4), 1038–1041 (2014).
[Crossref] [PubMed]

M. Pang, X. Bao, L. Chen, Z. Qin, Y. Lu, and P. Lu, “Frequency stabilized coherent Brillouin random fiber laser: theory and experiments,” Opt. Express 21(22), 27155–27168 (2013).
[Crossref] [PubMed]

M. Pang, X. Bao, and L. Chen, “Observation of narrow linewidth spikes in the coherent Brillouin random fiber laser,” Opt. Lett. 38(11), 1866–1868 (2013).
[Crossref] [PubMed]

M. Pang, S. Xie, X. Bao, D. P. Zhou, Y. Lu, and L. Chen, “Rayleigh scattering-assisted narrow linewidth Brillouin lasing in cascaded fiber,” Opt. Lett. 37(15), 3129–3131 (2012).
[Crossref] [PubMed]

T. Zhu, X. Bao, and L. Chen, “A single longitudinal-mode tunable fiber ring laser based on stimulated Rayleigh Scattering in a nonuniform optical fiber,” J. Lightwave Technol. 29(12), 1802–1807 (2011).
[Crossref]

Churkin, D. V.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Dämmig, M.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
[Crossref] [PubMed]

de Araújo, C. B.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

Debut, A.

A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 18(4), 556–567 (2001).
[Crossref]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000).
[Crossref]

Deparis, O.

El-Taher, A.

S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
[Crossref]

El-Taher, A. E.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Falkovich, G.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Fan, M.

Fotiadi, A. A.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44(5), 3205–3209 (1991).
[Crossref] [PubMed]

Gagné, M.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

M. Gagné and R. Kashyap, “Random fiber Bragg grating Raman fiber laser,” Opt. Lett. 39(9), 2755–2758 (2014).
[Crossref] [PubMed]

Gao, S.

Gomes, A. S.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

Harper, P.

S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
[Crossref]

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Harrison, R. G.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
[Crossref] [PubMed]

Jia, X.

Johnstone, A.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
[Crossref] [PubMed]

Kablukov, S. I.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Karalekas, V.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Kashyap, R.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

M. Gagné and R. Kashyap, “Random fiber Bragg grating Raman fiber laser,” Opt. Lett. 39(9), 2755–2758 (2014).
[Crossref] [PubMed]

Kiyan, R.

Kiyan, R. V.

Kolokolov, I. V.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Lach, E.

Lebedev, V. V.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Leppla, R.

Li, Y.

Lima, B. C.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

Lu, P.

Lu, Y.

Luo, S.

L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
[Crossref]

Mégret, P.

Mihailov, S.

Mitschke, F.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
[Crossref] [PubMed]

Moloney, J. V.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
[Crossref] [PubMed]

Moura, A. L.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

Nikulin, M.

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

Nikulin, M. A.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Ou, Z.

Pang, M.

Papernyi, S. B.

Pincheira, P. I.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

Podivilov, E.

S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
[Crossref]

Podivilov, E. V.

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Qin, Z.

Randoux, S.

A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 18(4), 556–567 (2001).
[Crossref]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000).
[Crossref]

Rao, Y.

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

Z. Wang, H. Wu, M. Fan, Y. Rao, X. Jia, and W. Zhang, “Third-order random lasing via Raman gain and Rayleigh feedback within a half-open cavity,” Opt. Express 21(17), 20090–20095 (2013).
[Crossref] [PubMed]

Raposo, E. P.

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

Sanapi, K.

Saxena, B.

Schmidt, M.

Schneiders, M.

Sugavanam, S.

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

Terekhov, I. S.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Turitsyn, S.

S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
[Crossref]

Turitsyn, S. K.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Uppal, J. S.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
[Crossref] [PubMed]

Vatnik, I. D.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

Vergeles, S. S.

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Vorbeck, S.

Wang, Z.

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

Z. Wang, H. Wu, M. Fan, Y. Rao, X. Jia, and W. Zhang, “Third-order random lasing via Raman gain and Rayleigh feedback within a half-open cavity,” Opt. Express 21(17), 20090–20095 (2013).
[Crossref] [PubMed]

Welling, H.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
[Crossref] [PubMed]

Wu, H.

Xia, Y.

L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
[Crossref]

Xiang, D.

Xie, S.

Xing, L.

L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
[Crossref]

Xu, Y.

Yin, G.

Zemmouri, J.

A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 18(4), 556–567 (2001).
[Crossref]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000).
[Crossref]

Zhan, L.

L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
[Crossref]

Zhang, L.

Zhang, W.

Zhou, D. P.

Zhu, T.

Zinner, G.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

D. V. Churkin, S. Sugavanam, I. D. Vatnik, Z. Wang, E. V. Podivilov, S. A. Babin, Y. Rao, and S. K. Turitsyn, “Recent advances in fundamentals and applications of random fiber lasers,” Adv. Opt. Photonics 7(3), 516–569 (2015).
[Crossref]

IEEE J. Quantum Electron. (1)

L. Xing, L. Zhan, S. Luo, and Y. Xia, “High-power low-noise fiber Brillouin amplifier for tunable slow-light delay buffer,” IEEE J. Quantum Electron. 44(12), 1133–1138 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (1)

B. Saxena, Z. Ou, X. Bao, and L. Chen, “Low frequency-noise random fiber laser with bidirectional SBS and Rayleigh feedback,” IEEE Photonics Technol. Lett. 27(5), 490–493 (2015).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

D. V. Churkin, I. V. Kolokolov, E. V. Podivilov, I. D. Vatnik, M. A. Nikulin, S. S. Vergeles, I. S. Terekhov, V. V. Lebedev, G. Falkovich, S. A. Babin, and S. K. Turitsyn, “Wave kinetics of random fibre lasers,” Nat. Commun. 2, 6214 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castanon, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010).

Opt. Express (4)

Opt. Lett. (12)

D. Xiang, P. Lu, Y. Xu, L. Chen, and X. Bao, “Random Brillouin fiber laser for tunable ultra-narrow linewidth microwave generation,” Opt. Lett. 41(20), 4839–4842 (2016).
[Crossref] [PubMed]

D. Xiang, P. Lu, Y. Xu, S. Gao, L. Chen, and X. Bao, “Truly random bit generation based on a novel random Brillouin fiber laser,” Opt. Lett. 40(22), 5415–5418 (2015).
[Crossref] [PubMed]

Y. Xu, S. Gao, P. Lu, S. Mihailov, L. Chen, and X. Bao, “Low-noise Brillouin random fiber laser with a random grating-based resonator,” Opt. Lett. 41(14), 3197–3200 (2016).
[Crossref] [PubMed]

M. Gagné and R. Kashyap, “Random fiber Bragg grating Raman fiber laser,” Opt. Lett. 39(9), 2755–2758 (2014).
[Crossref] [PubMed]

Y. Li, P. Lu, X. Bao, and Z. Ou, “Random spaced index modulation for a narrow linewidth tunable fiber laser with low intensity noise,” Opt. Lett. 39(8), 2294–2297 (2014).
[Crossref] [PubMed]

A. A. Fotiadi and R. V. Kiyan, “Cooperative stimulated Brillouin and Rayleigh backscattering process in optical fiber,” Opt. Lett. 23(23), 1805–1807 (1998).
[Crossref] [PubMed]

Y. Xu, D. Xiang, Z. Ou, P. Lu, and X. Bao, “Random Fabry-Perot resonator-based sub-kHz Brillouin fiber laser to improve spectral resolution in linewidth measurement,” Opt. Lett. 40(9), 1920–1923 (2015).
[Crossref] [PubMed]

L. Zhang, Y. Xu, S. Gao, B. Saxena, L. Chen, and X. Bao, “Linearly polarized low-noise Brillouin random fiber laser,” Opt. Lett. 42(4), 739–742 (2017).
[Crossref] [PubMed]

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27(2), 83–85 (2002).
[Crossref] [PubMed]

B. Saxena, X. Bao, and L. Chen, “Suppression of thermal frequency noise in erbium-doped fiber random lasers,” Opt. Lett. 39(4), 1038–1041 (2014).
[Crossref] [PubMed]

M. Pang, S. Xie, X. Bao, D. P. Zhou, Y. Lu, and L. Chen, “Rayleigh scattering-assisted narrow linewidth Brillouin lasing in cascaded fiber,” Opt. Lett. 37(15), 3129–3131 (2012).
[Crossref] [PubMed]

M. Pang, X. Bao, and L. Chen, “Observation of narrow linewidth spikes in the coherent Brillouin random fiber laser,” Opt. Lett. 38(11), 1866–1868 (2013).
[Crossref] [PubMed]

Phys. Rep. (1)

S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014).
[Crossref]

Phys. Rev. A (5)

A. S. Gomes, B. C. Lima, P. I. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. de Araújo, and R. Kashyap, “Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser,” Phys. Rev. A 94(1), 011801 (2016).
[Crossref]

S. Babin, A. El-Taher, P. Harper, E. Podivilov, and S. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
[Crossref]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: Theoretical analysis,” Phys. Rev. A 62(2), 023803 (2000).
[Crossref]

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44(5), 3205–3209 (1991).
[Crossref] [PubMed]

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, “Stimulated Brillouin scattering in fibers with and without external feedback,” Phys. Rev. A 48(4), 3301–3309 (1993).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65(2), 167–170 (1990).
[Crossref] [PubMed]

Other (3)

S. Papernyi, V. Karpov, and W. Clements, “Third-order cascaded Raman amplification,” in Optical Fiber Communication Conference (OFC 2002), paper FB4–FB4.

V. Karpov, S. Papernyi, V. Ivanov, W. Clements, T. Araki, and Y. Koyano, “Cascaded pump delivery for remotely pumped erbium doped fiber amplifiers,” in Proceedings of Suboptic Conference (2004), paper We 8.8.

S. Papernyi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Six-order cascaded Raman amplification,” in Optical Fiber Communication Conference (OFC, 2005), paper OThF4.

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Figures (9)

Fig. 1
Fig. 1 Experimental setup of the PMF-BRFL for the measurements of (a) power/spectrum, (b) polarization extinction ratio, (c) intensity noise, (d) linewidth and (e) phase fluctuation.
Fig. 2
Fig. 2 (a) Laser output power and spectrum of the PMF-BRFL with half-open ring cavity; (b) PER of PMF-BRFL under different pump powers. (Inset: normalized transmission versus the rotation angle of the polarizer.)
Fig. 3
Fig. 3 Intensity dynamics of (a) SBS (without random Rayleigh feedback) and (b) Brillouin random lasing (with random Rayleigh feedback): (1) temporal trace; (2) power density distribution; (3) phase portrait.
Fig. 4
Fig. 4 Linewidth measurement (a) beat signal with 200km delay fiber; (b) 3-dB linewidth with varied delay fiber lengths. (ESA resolution bandwidth, 510 Hz; sweep time, 100 ms; average times, 20)
Fig. 5
Fig. 5 Phase fluctuations of pump laser and PMF-BRFL.
Fig. 6
Fig. 6 Comparison of (a) lasing efficiency and (b) threshold power with different gain fiber lengths. The lasing efficiency is calculated by η = ΔPlaserPpump.
Fig. 7
Fig. 7 RIN comparison.
Fig. 8
Fig. 8 Frequency jitter measurement setup for (1) SMF- BRFL, (2) PMF-BRFL and (3) the pump laser.
Fig. 9
Fig. 9 (a) Frequency jitter and (b) statistical probability in 2 s. (Inset is the zooming of the PMF-BRFL and pump laser).

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