Abstract

In this paper, we reported the realization of 2nd-order random lasing in a half-opened fiber cavity, which is formed by a FBG with central wavelength at the 1st–order Raman Stokes wavelength and a single-mode fiber (SMF) performing as a random distributed feedback mirror. Using this proposed method, the threshold of 1st-order (2nd-order) random lasing is reduced to 0.7 (2.0) W, which is nearly 2 times lower than that observed in a completely-opened cavity.

©2012 Optical Society of America

1. Introduction

Random lasers are disordered optical structures of stimulated emission in which light waves are both multiply scattered and amplified [1]. Hence, the feedback is provided by light scattering in a gain medium rather than a cavity, as in conventional lasers [27].

To overcome the problem of irregular and undirectional output characteristics of random lasers, low-dimensional random structures were proposed [3, 7, 8]. Recently, an important breakthrough in this research area was reported by Turitsyn et. al. [9]. They realized a stable continue-wave (CW) random lasing in a standard single-mode fiber (SMF) based on Raman amplified distributed Rayleigh scattering (RS) feedback. The SMF itself performs as the disorder medium, where RS captured by the fiber waveguide provides positive feedback and the pump-induced Raman gain provides light amplification. Compared with traditional random lasers, the random fiber laser (RFL) shows relative stable output, single-transverse-mode profile, long-distance emission and wide wavelength tunability, which are of great interest in optical communication and optical sensing [10, 11].

Based on similar principle, dual-wavelength random lasing was realized in a 200 km fiber span, wherein the RS performs as random distributed mirrors forming a cavity together with a FBG at each end of the fiber [12]. A tunable RFL with broad wavelength range was proposed [13]. Thanks to the ultra-long laser cavity, a RFL was also used in optical sensing to increase the transmission distance [14, 15]. Churkin et al. studied the output characteristics of RFLs under different operation regimes, wherein a half-opened cavity formed by a fiber Bragg grating (FBG) and a SMF can help reducing the laser threshold to about half, compared with a completely-opened cavity [16]. However, this studied only focused on the 1st-order random lasing.

Recently, Vatnik et al. [17] reported firstly cascaded (2nd-order) random lasing of optical fiber pumped by an ytterbium fiber laser. Due to the completely-opened cavity structure (i.e., the laser cavity is formed only by a span of optical fiber), 2nd-order random lasing needs a pump power of more than 6 W. In this paper, we proposed 2nd-order random lasing at a much lower threshold using a half-opened fiber cavity, wherein a FBG with central wavelength at the 1st-order Raman Stokes wavelength is placed at the pump side and a SMF performs as the gain medium as well as the distributed feedback mirrors [18].

2. Experimental results

The schematic diagram of the half-opened cavity random fiber laser (HOCRFL) is given in Fig. 1 . A Raman fiber laser with central wavelength of 1366 nm is used as the pump. The pump is launched into the fiber spool through a 1365/1461 nm wavelength division multiplexer (WDM). A FBG with central wavelength of 1454 nm and reflectivity of 0.979 is spliced between the common port of the WDW and the spool of 50 km SMF. The right tip of the SMF was angle-cleaved to avoid end reflection. The lasing characteristics are monitored at the right end of the SMF.

 figure: Fig. 1

Fig. 1 The schematic setup of the HOCRFL. WDM: wavelength division multiplexer. OSA: optical spectrum analyser; OPM: optical power meter.

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With the increase of pump power, 1st-order Stokes light generates. The generated light is feedback forwardly and backwardly in the SMF due to distributed RS. At the left end of the SMF, the backscattered light is selectively reflected by the FBG. This forms a multitude of resonant modes with random frequencies. However, since the reflection from the FBG is dominant, only the resonant modes within the refection spectrum of the FBG reach their threshold (when the Raman amplification overcomes the fiber loss) and begin to radiate first. For the 2nd-order Stokes light, resonant modes are formed only by distributed RS feedback, thus, those modes having the largest gain begin to radiate first.

Figure 2(a) and 2(b) give the output spectra of the HOCRFL for pump power at 0.701 and 0.911 W, respectively. In Fig. 2(a), the pump power is slightly beyond the threshold of the 1st-order random lasing. Numerous narrowband wavelength components are found in the output spectrum. These narrowband components change stochastically due to cascade Brillouin scattering effect. This is similar to the near-threshold operation regime of a RFL with a completely-opened cavity [9, 12]. However, because of the wavelength-selective reflection from the FBG, the bandwidth of random lasing is less than 0.3 nm in our case. When pump power increases, complex nonlinear interactions (i.e., four-wave mixing and phase modulation) take effect. As a result, the stochastic narrowband components are broadened and superposed, generating a uniform spectrum. This also suppresses Brillouin scattering dynamics, leading to stable CW random lasing as shown in Fig. 2(b).

 figure: Fig. 2

Fig. 2 Output spectra of the HOCRFL. In (a) and (b) the pump power is 0.701 and 0.911 W, respectively. Δλ: bandwidth; λc: the central wavelength.

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With further increase of pump power, the spectrum of the 1st-order random lasing broadens. Its output power increases. For pump power beyond a critical value, the 2nd-order Stokes light also begins to emit. Figure 3 shows the output spectrum of the HOCRFL pumped at 2.265 W. In this case, that the 2nd-order random lasing is in the near-threshold regime, i.e., irregular dynamics and narrowband wavelength components appear in the spectrum, seeing Fig. 3(b). Figure 3(a) indicates that the 1st-order random lasing also exhibits similar output characteristics correspondingly. The 2nd-order random lasing has a relative broad spectrum that is determined by the gain profile, because the feedback is only provided by RS. This is the same to random lasing in a completely-opened fiber cavity.

 figure: Fig. 3

Fig. 3 Output spectra of the random fiber laser for pump at 2.265 W. (a) and (b) correspond to the 1st-order and 2nd-order lasing, respectively.

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Figure 4 shows the spectra of the HOCRFL pumped at 2.944 W. In this case, both the 1st and 2nd -order random lasing are stable. In Fig. 4(a), the 1st-order random lasing has a spectrum bandwidth of ~0.898 nm which is three times larger than the bandwidth of FBG. It is supposed that both the nonlinear effect and the 2nd-order random lasing contribute to the spectrum broadening. In Fig. 4(b), there are two peaks localized nearby the Raman gain maxima. The one at the shorter wavelength (1.55nm) with a bandwidth of ~1.183 nm is much more pronounced, which is similar to the results reported in reference [9].

 figure: Fig. 4

Fig. 4 Output spectra of the random fiber laser for pump at 2.944 W. (a) and (b) correspond to the 1st-order and 2nd-order lasing, respectively. Δλ: bandwidth; λc: the central wavelength.

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Figure 5(a) shows the output power of the HOCRFL as a function of pump power. The dot and the triangle correspond to the 1st and the 2nd -order random lasing, respectively. The threshold pump power for 1st (2nd) -order random lasing is found to be ~0.7 W (~2 W). Obviously, the threshold of 1st and 2nd –order random lasing is much smaller for the HOCRFL than for a RFL with a completely-opened cavity [17]. It is also observed that the power of 2nd-order random lasing exceeds that of the 1st-order when pump power is larger than ~2.4 W.

 figure: Fig. 5

Fig. 5 Output power as a function of the pump power. (a) with a half-opened cavity; (b) with a completely-opened cavity.

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For comparison, we also studied the output power of a RFL with a completely-opened cavity. The RFL has a same structure as described in Fig. 1, except that the FBG is removed. Figure 5(b) indicates that the threshold of 1st-order random lasing is ~1.4 W, and no obvious 2nd-order random lasing is observed for pump increased to 3.5 W. Hence, the use of a FBG at one side of the laser cavity can help to reduce the lasing threshold greatly, while keeping random lasing characteristics of the laser.

3. Theoretical analysis

The lasing characteristics of the HOCRFL can be analyzed theoretically using the steady-state light propagation equations [9, 12, 19].

dP0±dz=α0P0±g1f0f1P0±(P1++P1+Γ1)±ε0P0
dP1±dz=α1P1±±g1(P1±+0.5Γ1)(P0++P0)g2f1f2P1±(P2++P2+Γ2)±ε1P1
dP2±dz=α2P2±±g2[P2±+0.5Γ2](P1++P1)±ε2P2
Γi=4hfiΔfi{1+1exp[h(fi1fi)/(KBT)]1}
where subscripts ‘0’, ‘1’ and ‘2’ correspond to the pump, 1st-order lasing, and 2nd-order lasing waves, respectively. Superscripts ‘ + ’ and ‘-’ denotes the forward and backward waves, respectively. P0,1,2 denotes the optical power, z denotes the coordinate of the wave propagation direction, a0,1,2 ( = 0.306, 0.24, 0.193 dB⋅km−1) is the fiber loss, g1,2 ( = 0.54, 0.44 W−1km−1, respectively) is the Raman gain index, ε0,1,2 ( = 1 × 10−4, 6 × 10−5, 4.5 × 10−5 km−1, respectively) is the Rayleigh backscattering coefficient, f0,1,2 ( = c/λ0,1,2, c is the vacuum light speed and λ0,1,2 is the wavelength) is the wave frequency. The symbol Γ1,2 denotes the population of phonon, where Δf1,2 ( = 0.05, 0.17 THz, respectively) is the lasing bandwidth, h is the Plank’s constant, KB is the Boltzmann’s constant and T ( = 298 K) is the absolute temperature of the laser.

It is worth mentioning that the value of a0,1,2 are experimentally tested, while g1,2 and ε0,1,2 are fitting parameters based on typical experimental values [16, 17, 19, 20]. To better fit our experimental results, values of g1,2 are chosen slightly larger (the increase is less than 5%) than that given in the references, and a 0.8 dB insertion loss (experimentally tested value) at the output end is considered. The boundary conditions areP0+(0)=Pin and P1+(0)=R1P1(0), where Pin denotes the pump power, and R1 is the reflectivity of the FBG. Taking these conditions into consideration, the model can be solved numerically through the shooting method. In the simulation, Eqs. (1)(3) are integrated along the z direction to get the power distribution of the forward (backward) propagating waves, P1,2,3+(z)[P1,2,3(z)], using guessed value of P1,2,3(z)[P1,2,3+(z)] as the know condition. Then the guessed power distributions are replaced by the integration results, and a next integration of Eqs. (1)(3) is done to renew the values of P1,2,3±(z). This procedure is repeated untilled the difference of results between the last two integrations are less than 10−5.

The solid and doted curves in Fig. 5 correspond to the numerically calculated output power of the 1st-order and 2nd-order random lasing, respectively. It is seen that the numerical results are in accordance with the experimental results. The small mismatch might arise from the ignoring of spectrum characteristic and nonlinear effect in the theoretical model.

Using the same numerical method, the power distribution of the RFL along the fiber length is simulated in Fig. 6 . The pump power is chosen at 1.8 W. The solid and dotted curves correspond to the forward and backward propagating light, respectively. For the completely-opened cavity (see Fig. 6(b)), the backward propagating light is relative strong at the pump side. For the half-opened cavity (see Fig. 6(a)), the FBG feedback most of the backward propagating light which re-enters the SMF and is re-amplified by the pump, changing the power distribution and reducing the laser threshold considerably.

 figure: Fig. 6

Fig. 6 Power distribution of the lasers pumped at 1.8 W. (a) with a half-opened cavity, (b) with a completely-opened cavity.

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4. Conclusions

In summary, we have studied the 2nd-order random lasing in a half-opened fiber cavity. Due to the wavelength-selective feedback of FBG, the threshold of 1st-order and 2nd-order random lasing are reduced to 0.7 and 2.0 W, respectively, which is much smaller than that of a completely-opened cavity. For the 1st-order random lasing, the laser cavity is half-opened (i.e., the central wavelength of the FBG is at the 1st Raman stokes wavelength), so the lasing does not correspond to a certain cavity resonance. It has random lasing characteristics with spectrum tailored by the FBG. For the 2nd-order random lasing, the cavity can be thought of as completely-opened, so the spectrum of random lasing is determined by the Raman gain.

In fact, the central wavelength of the FBG can be changed intentionally to control the wavelength of the 1st and 2nd -order random lasing. Besides, there also exists a relative wide range of pump power, where the 1st and 2nd -order random lasing coexist. These characteristics provide a flexible method to generate high-order or mixed-order random emission, which may found its applications in optical communication as well as optical sensing.

Acknowledgment

The authors would like to thank Dr. X. F. Chen and Prof. L. Zhang in Aston University for providing the 1454nm FBG. This work is supported by the National Natural Science Foundation of China under Grant 61106045 and the Fundamental Research Funds for the Central Universities under Grant 2011J001.

References and links

1. V. S. Letokhov, “Generation of light a scattering medium with negative resonance absorption,” Sov. Phys 26, 835–840 (1968).

2. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]  

3. E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006). [CrossRef]  

4. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007). [CrossRef]  

5. C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007). [CrossRef]   [PubMed]  

6. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008). [CrossRef]   [PubMed]  

7. M. A. Noginov, “Random lasers resonance control,” Nat. Photonics 2(7), 397–398 (2008). [CrossRef]  

8. H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011). [CrossRef]  

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

10. D. D. Sampson, “Staying coherent after Kent: from optical communication to biomedical optics,” Photon. Sens. 1(4), 323–350 (2011). [CrossRef]  

11. Y. J. Rao, “Study on fiber-optic low-coherence interferometric and fiber Bragg grating sensors,” Photon. Sens. 1(4), 382–400 (2011). [CrossRef]  

12. A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010). [CrossRef]   [PubMed]  

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

14. Z. N. Wang, X. H. Jia, Y. J. Rao, Y. Jiang, and W. L. Zhang, “Novel long-distance fiber-optic sensing systems based on random fiber lasers,” APOS 2012, Proc. SPIE 8351, 835142, 835142-4 (2012). [CrossRef]  

15. X. H. Jia, Y. J. Rao, Z. N. Wang, W. L. Zhang, Z. L. Ran, K. Deng, and Z. X. Yang, “Detailed theoretical investigation on improved quasi-lossless transmission using third-order Raman amplification based on ultra-long fiber lasers,” J. Opt. Soc. Am. B 29(4), 847–854 (2012). [CrossRef]  

16. D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010). [CrossRef]  

17. I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express 19(19), 18486–18494 (2011). [CrossRef]   [PubMed]  

18. W. L. Zhang, Y. J. Rao, Z. X. Yang, Z. N. Wang, and X. H. Jia, “Low threshold fiber laser formed by FBG & single-mode fiber,” Presented at International Conference on Optical Communication Systems-OPTICS 2012, Roma, Italy, 24–27 July 2012.

19. S. Martin-Lopez, M. Alcon-Camas, F. Rodriguez, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Brillouin optical time-domain analysis assisted by second-order Raman amplification,” Opt. Express 18(18), 18769–18778 (2010). [CrossRef]   [PubMed]  

20. J. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express 12(19), 4372–4377 (2004). [CrossRef]   [PubMed]  

References

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  1. V. S. Letokhov, “Generation of light a scattering medium with negative resonance absorption,” Sov. Phys 26, 835–840 (1968).
  2. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
    [Crossref]
  3. E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006).
    [Crossref]
  4. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
    [Crossref]
  5. C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
    [Crossref] [PubMed]
  6. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
    [Crossref] [PubMed]
  7. M. A. Noginov, “Random lasers resonance control,” Nat. Photonics 2(7), 397–398 (2008).
    [Crossref]
  8. H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
    [Crossref]
  9. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fiber laser,” Nat. Photonics 4(4), 231–235 (2010).
    [Crossref]
  10. D. D. Sampson, “Staying coherent after Kent: from optical communication to biomedical optics,” Photon. Sens. 1(4), 323–350 (2011).
    [Crossref]
  11. Y. J. Rao, “Study on fiber-optic low-coherence interferometric and fiber Bragg grating sensors,” Photon. Sens. 1(4), 382–400 (2011).
    [Crossref]
  12. A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
    [Crossref] [PubMed]
  13. S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011).
    [Crossref]
  14. Z. N. Wang, X. H. Jia, Y. J. Rao, Y. Jiang, and W. L. Zhang, “Novel long-distance fiber-optic sensing systems based on random fiber lasers,” APOS 2012, Proc. SPIE 8351, 835142, 835142-4 (2012).
    [Crossref]
  15. X. H. Jia, Y. J. Rao, Z. N. Wang, W. L. Zhang, Z. L. Ran, K. Deng, and Z. X. Yang, “Detailed theoretical investigation on improved quasi-lossless transmission using third-order Raman amplification based on ultra-long fiber lasers,” J. Opt. Soc. Am. B 29(4), 847–854 (2012).
    [Crossref]
  16. D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
    [Crossref]
  17. I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express 19(19), 18486–18494 (2011).
    [Crossref] [PubMed]
  18. W. L. Zhang, Y. J. Rao, Z. X. Yang, Z. N. Wang, and X. H. Jia, “Low threshold fiber laser formed by FBG & single-mode fiber,” Presented at International Conference on Optical Communication Systems-OPTICS 2012, Roma, Italy, 24–27 July 2012.
  19. S. Martin-Lopez, M. Alcon-Camas, F. Rodriguez, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Brillouin optical time-domain analysis assisted by second-order Raman amplification,” Opt. Express 18(18), 18769–18778 (2010).
    [Crossref] [PubMed]
  20. J. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express 12(19), 4372–4377 (2004).
    [Crossref] [PubMed]

2012 (2)

2011 (5)

I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express 19(19), 18486–18494 (2011).
[Crossref] [PubMed]

D. D. Sampson, “Staying coherent after Kent: from optical communication to biomedical optics,” Photon. Sens. 1(4), 323–350 (2011).
[Crossref]

Y. J. Rao, “Study on fiber-optic low-coherence interferometric and fiber Bragg grating sensors,” Photon. Sens. 1(4), 382–400 (2011).
[Crossref]

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

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

2010 (4)

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

A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
[Crossref] [PubMed]

S. Martin-Lopez, M. Alcon-Camas, F. Rodriguez, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Brillouin optical time-domain analysis assisted by second-order Raman amplification,” Opt. Express 18(18), 18769–18778 (2010).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

2008 (2)

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[Crossref] [PubMed]

M. A. Noginov, “Random lasers resonance control,” Nat. Photonics 2(7), 397–398 (2008).
[Crossref]

2007 (2)

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

2006 (1)

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006).
[Crossref]

2004 (1)

1999 (1)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

1968 (1)

V. S. Letokhov, “Generation of light a scattering medium with negative resonance absorption,” Sov. Phys 26, 835–840 (1968).

Alcon-Camas, M.

Ania-Castañon, J. D.

Ania-Castañón, J.

Ania-Castañón, J. D.

A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Babin, S. A.

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

I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express 19(19), 18486–18494 (2011).
[Crossref] [PubMed]

A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Brito-Silva, A.

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

Cao, H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Chang, R. P. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Churkin, D. V.

I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express 19(19), 18486–18494 (2011).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Corredera, P.

de Araújo, C.

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

de Matos, C.

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

de S. Menezes, L.

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

Deng, K.

El-Taher, A. E.

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

A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Ge, L.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[Crossref] [PubMed]

Gomes, A.

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

Gonzalez-Herraez, M.

Harper, P.

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

A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Ho, S. T.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Jia, X. H.

Jiang, Y.

Z. N. Wang, X. H. Jia, Y. J. Rao, Y. Jiang, and W. L. Zhang, “Novel long-distance fiber-optic sensing systems based on random fiber lasers,” APOS 2012, Proc. SPIE 8351, 835142, 835142-4 (2012).
[Crossref]

Kablukov, S. I.

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

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

Karalekas, V.

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Lau, S. P.

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006).
[Crossref]

Leong, E. S. P.

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006).
[Crossref]

Letokhov, V. S.

V. S. Letokhov, “Generation of light a scattering medium with negative resonance absorption,” Sov. Phys 26, 835–840 (1968).

Li, X. F.

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

Liang, H. K.

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

Ma, S. Z.

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

Martinez Gámez, M.

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

Martin-Lopez, S.

Mujumdar, S.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Noginov, M. A.

M. A. Noginov, “Random lasers resonance control,” Nat. Photonics 2(7), 397–398 (2008).
[Crossref]

Podivilov, E. V.

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

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Ran, Z. L.

Rao, Y. J.

X. H. Jia, Y. J. Rao, Z. N. Wang, W. L. Zhang, Z. L. Ran, K. Deng, and Z. X. Yang, “Detailed theoretical investigation on improved quasi-lossless transmission using third-order Raman amplification based on ultra-long fiber lasers,” J. Opt. Soc. Am. B 29(4), 847–854 (2012).
[Crossref]

Z. N. Wang, X. H. Jia, Y. J. Rao, Y. Jiang, and W. L. Zhang, “Novel long-distance fiber-optic sensing systems based on random fiber lasers,” APOS 2012, Proc. SPIE 8351, 835142, 835142-4 (2012).
[Crossref]

Y. J. Rao, “Study on fiber-optic low-coherence interferometric and fiber Bragg grating sensors,” Photon. Sens. 1(4), 382–400 (2011).
[Crossref]

Rodriguez, F.

Rotter, S.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[Crossref] [PubMed]

Sampson, D. D.

D. D. Sampson, “Staying coherent after Kent: from optical communication to biomedical optics,” Photon. Sens. 1(4), 323–350 (2011).
[Crossref]

Seelig, E. W.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Stone, A. D.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[Crossref] [PubMed]

Thévenaz, L.

Torre, R.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Türck, V.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Türeci, H. E.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[Crossref] [PubMed]

Turitsyn, S. K.

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

I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express 19(19), 18486–18494 (2011).
[Crossref] [PubMed]

A. E. El-Taher, M. Alcon-Camas, S. A. Babin, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback,” Opt. Lett. 35(7), 1100–1102 (2010).
[Crossref] [PubMed]

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

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

Vatnik, I. D.

Wang, Q. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Wang, Z. N.

Wiersma, D. S.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Yang, H. Y.

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

Yang, Z. X.

Yu, S. F.

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006).
[Crossref]

Zhang, W. L.

Zhao, Y. G.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

APOS 2012, Proc. SPIE (1)

Z. N. Wang, X. H. Jia, Y. J. Rao, Y. Jiang, and W. L. Zhang, “Novel long-distance fiber-optic sensing systems based on random fiber lasers,” APOS 2012, Proc. SPIE 8351, 835142, 835142-4 (2012).
[Crossref]

Appl. Phys. Lett. (1)

E. S. P. Leong, S. F. Yu, and S. P. Lau, “Directional edge-emitting UV random laser diodes,” Appl. Phys. Lett. 89(22), 221109 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (1)

H. K. Liang, S. F. Yu, X. F. Li, S. Z. Ma, and H. Y. Yang, “An index-guided ZnO random laser array,” IEEE Photon. Technol. Lett. 23(8), 522–524 (2011).
[Crossref]

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

Nat. Photonics (2)

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

M. A. Noginov, “Random lasers resonance control,” Nat. Photonics 2(7), 397–398 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Photon. Sens. (2)

D. D. Sampson, “Staying coherent after Kent: from optical communication to biomedical optics,” Photon. Sens. 1(4), 323–350 (2011).
[Crossref]

Y. J. Rao, “Study on fiber-optic low-coherence interferometric and fiber Bragg grating sensors,” Photon. Sens. 1(4), 382–400 (2011).
[Crossref]

Phys. Rev. A (3)

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

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

D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castañón, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A 82(3), 033828 (2010).
[Crossref]

Phys. Rev. Lett. (2)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

C. de Matos, L. de S. Menezes, A. Brito-Silva, M. Martinez Gámez, A. Gomes, and C. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
[Crossref] [PubMed]

Science (1)

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[Crossref] [PubMed]

Sov. Phys (1)

V. S. Letokhov, “Generation of light a scattering medium with negative resonance absorption,” Sov. Phys 26, 835–840 (1968).

Other (1)

W. L. Zhang, Y. J. Rao, Z. X. Yang, Z. N. Wang, and X. H. Jia, “Low threshold fiber laser formed by FBG & single-mode fiber,” Presented at International Conference on Optical Communication Systems-OPTICS 2012, Roma, Italy, 24–27 July 2012.

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Figures (6)

Fig. 1
Fig. 1 The schematic setup of the HOCRFL. WDM: wavelength division multiplexer. OSA: optical spectrum analyser; OPM: optical power meter.
Fig. 2
Fig. 2 Output spectra of the HOCRFL. In (a) and (b) the pump power is 0.701 and 0.911 W, respectively. Δλ: bandwidth; λc: the central wavelength.
Fig. 3
Fig. 3 Output spectra of the random fiber laser for pump at 2.265 W. (a) and (b) correspond to the 1st-order and 2nd-order lasing, respectively.
Fig. 4
Fig. 4 Output spectra of the random fiber laser for pump at 2.944 W. (a) and (b) correspond to the 1st-order and 2nd-order lasing, respectively. Δλ: bandwidth; λc: the central wavelength.
Fig. 5
Fig. 5 Output power as a function of the pump power. (a) with a half-opened cavity; (b) with a completely-opened cavity.
Fig. 6
Fig. 6 Power distribution of the lasers pumped at 1.8 W. (a) with a half-opened cavity, (b) with a completely-opened cavity.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

d P 0 ± dz = α 0 P 0 ± g 1 f 0 f 1 P 0 ± ( P 1 + + P 1 + Γ 1 )± ε 0 P 0
d P 1 ± dz = α 1 P 1 ± ± g 1 ( P 1 ± +0.5 Γ 1 )( P 0 + + P 0 ) g 2 f 1 f 2 P 1 ± ( P 2 + + P 2 + Γ 2 )± ε 1 P 1
d P 2 ± dz = α 2 P 2 ± ± g 2 [ P 2 ± +0.5 Γ 2 ]( P 1 + + P 1 )± ε 2 P 2
Γ i =4h f i Δ f i { 1+ 1 exp[ h( f i1 f i )/( K B T) ]1 }

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