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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2839–2844
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Multiwavelength generation in a random distributed feedback fiber laser using an all fiber Lyot filter

S. Sugavanam, Z. Yan, V. Kamynin, A. S. Kurkov, L. Zhang, and D. V. Churkin  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2839-2844 (2014)
http://dx.doi.org/10.1364/OE.22.002839


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Abstract

Multiwavelength lasing in the random distributed feedback fiber laser is demonstrated by employing an all fiber Lyot filter. Stable multiwavelength generation is obtained, with each line exhibiting sub-nanometer line-widths. A flat power distribution over multiple lines is obtained, which indicates that the power between lines is redistributed in nonlinear mixing processes. The multiwavelength generation is observed both in first and second Stokes waves.

© 2014 Optical Society of America

1. Introduction

Multiwavelength fiber lasers are of significant interest to the scientific community due to their application diversity. Multiwavelength fiber lasers find applications in DWDM systems, optical fiber sensors, spectroscopy, etc. They can be broadly classified in terms of the gain medium used, and/or the procedure used to generate the multiple wavelengths. Multiwavelength fiber lasers have been demonstrated using lasers employing erbium doped fiber [1

1. A. Bellemare, M. Karasek, M. Rochette, S. LaRochelle, and M. Têtu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU frequency grid,” J. Lightwave Technol. 18(6), 825–831 (2000). [CrossRef]

], stimulated Raman scattering (SRS) [2

2. Y. G. Han, C. S. Kim, J. U. Kang, and U. C. Paek, “Multiwavelength raman fiber-ring laser based on tunable cascaded long-period fiber gratings,” IEEE Photonics Technol. Lett. 15(3), 383–385 (2003). [CrossRef]

,3

3. X. Dong, P. Shum, N. Q. Ngo, and C. C. Chan, “Multiwavelength Raman fiber laser with a continuously-tunable spacing,” Opt. Express 14(8), 3288–3293 (2006). [CrossRef] [PubMed]

], stimulated Brillouin scattering (SBS) [4

4. M. R. Shirazi, N. S. Shahabuddin, S. N. Aziz, K. Thambiratnam, S. W. Harun, and H. Ahmad, “A linear cavity Brillouin fiber laser with multiple wavelengths output,” Laser Phys. Lett. 5(5), 361–363 (2008). [CrossRef]

], or a hybrid of the above [5

5. G. Cowle and D. Stepanov, “Multiple wavelength generation with Brillouin/erbium fiber lasers,” IEEE Photonics Technol. Lett. 8(11), 1465–1467 (1996). [CrossRef]

]. The procedure used to generate the multiple wavelengths can be either passive or active. For example, passive elements such as fiber Bragg gratings (FBGs) [6

6. Z. Wang, Y. Cui, B. Yun, and C. Lu, “Multiwavelength generation in a Raman fiber laser with sampled Bragg grating,” IEEE Photonics Technol. Lett. 17(10), 2044–2046 (2005). [CrossRef]

], Fabry-Perot filters (FFPs) [7

7. S. Pan, C. Lou, and Y. Gao, “Multiwavelength erbium-doped fiber laser based on inhomogeneous loss mechanism by use of a highly nonlinear fiber and a Fabry-Perot filter,” Opt. Express 14(3), 1113–1118 (2006). [CrossRef] [PubMed]

], Sagnac loop mirrors [8

8. C. Kim, R. M. Sova, and J. U. Kang, “Tunable multi-wavelength all-fiber Raman source using fiber Sagnac loop filter,” Opt. Commun. 218(4-6), 291–295 (2003). [CrossRef]

], and Lyot filters [9

9. C.-S. Kim and J. U. Kang, “Multiwavelength switching of Raman fiber ring laser incorporating composite polarization-maintaining fiber Lyot-Sagnac filter,” Appl. Opt. 43(15), 3151–3157 (2004). [CrossRef] [PubMed]

] have been used. Examples of ‘active’ nonlinear processes are SBS, nonlinear polarization rotation [10

10. X. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express 14(18), 8205–8210 (2006). [CrossRef] [PubMed]

], or four wave mixing [11

11. Y.-G. Han, T. V. A. Tran, and S. B. Lee, “Wavelength-spacing tunable multiwavelength erbium-doped fiber laser based on four-wave mixing of dispersion-shifted fiber,” Opt. Lett. 31(6), 697–699 (2006). [CrossRef] [PubMed]

]. For a passive element based multiwavelength fiber lasers, the individual wavelengths and their inter-spacings are solely determined by the specifications of the incorporated device. Thus tunability (wavelengths and/or the free spectral range) can be achieved in such multiwavelength fiber lasers [2

2. Y. G. Han, C. S. Kim, J. U. Kang, and U. C. Paek, “Multiwavelength raman fiber-ring laser based on tunable cascaded long-period fiber gratings,” IEEE Photonics Technol. Lett. 15(3), 383–385 (2003). [CrossRef]

,12

12. Y.-G. Han, J. H. Lee, S. B. Lee, L. Poti, and A. Bogoni, “Novel multiwavelength erbium-doped fiber and Raman fiber ring lasers with continuous wavelength spacing tunability at room temperature,” J. Lightwave Technol. 25(8), 2219–2225 (2007). [CrossRef]

].

The choice of gain media is a factor determining the stability of the generated lines. Inhomogeneous gain media are the primary choice for making multiwavelength fiber lasers, as they provide more stability, in comparison to homogenous media. In this regard, gain obtained via the stimulated Raman scattering process is very attractive. While the Raman gain coefficient is small, this is compensated by its THz order bandwidth and the availability of ultra-low loss, ultra-long gain spans made available in the form of conventional telecommunication fibers. Multiwavelength generation employing the Raman gain mechanism has been demonstrated in many configurations [3

3. X. Dong, P. Shum, N. Q. Ngo, and C. C. Chan, “Multiwavelength Raman fiber laser with a continuously-tunable spacing,” Opt. Express 14(8), 3288–3293 (2006). [CrossRef] [PubMed]

,6

6. Z. Wang, Y. Cui, B. Yun, and C. Lu, “Multiwavelength generation in a Raman fiber laser with sampled Bragg grating,” IEEE Photonics Technol. Lett. 17(10), 2044–2046 (2005). [CrossRef]

,12

12. Y.-G. Han, J. H. Lee, S. B. Lee, L. Poti, and A. Bogoni, “Novel multiwavelength erbium-doped fiber and Raman fiber ring lasers with continuous wavelength spacing tunability at room temperature,” J. Lightwave Technol. 25(8), 2219–2225 (2007). [CrossRef]

].

Recently, a random distributed feedback (DFB) fiber laser operating via Raman gain and random feedback owing to the Rayleigh backscattering is demonstrated [13

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

]. While the threshold of this laser is relatively high, the efficiency was noted to be quite comparable to existing CW lasers [13

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

,14

14. I. D. Vatnik, D. V. Churkin, and S. A. Babin, “Power optimization of random distributed feedback fiber lasers,” Opt. Express 20(27), 28033–28038 (2012). [CrossRef] [PubMed]

]. A number of different random DFB fiber laser configurations are realized up to date [13

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

34

34. Z. Wang, H. Wu, M. Fan, Y. Li, Y. Gong, and Y. Rao, “Broadband flat-amplitude multiwavelength Brillouin-Raman fiber laser with spectral reshaping by Rayleigh scattering,” Opt. Express 21(24), 29358–29363 (2013). [CrossRef]

]. It can be tunable [21

21. 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]

,22

22. A. Sarmani, R. Zamiri, and M. Bakar, “Tunable Raman fiber laser induced by Rayleigh backscattering in an ultra-long cavity,” J. Eur. Opt. Soc. Rapid Publ. 6, 11043 (2011).

], operate in different spectral bands [23

23. 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]

,24

24. R. Teng, Y. Ding, and L. Chen, “Random fiber laser operating at 1,115 nm,” Appl. Phys. B 111(2), 169–172 (2013).

], provide cascaded operation at higher Stokes components [23

23. 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]

,25

25. W. L. Zhang, Y. J. Rao, J. M. Zhu, Z. X. Yang, Z. N. Wang, and X. H. Jia, “Low threshold 2nd-order random lasing of a fiber laser with a half-opened cavity,” Opt. Express 20(13), 14400–14405 (2012). [CrossRef] [PubMed]

] and made narrow-band [26

26. S. Sugavanam, N. Tarasov, X. Shu, and D. V. Churkin, “Narrow-band generation in random distributed feedback fiber laser,” Opt. Express 21(14), 16466–16472 (2013). [CrossRef] [PubMed]

]. Different ways to generate multiple wavelength simultaneously in random DFB fiber laser has been also demonstrated: for example by using a set of FBGs [18

18. 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]

,19

19. A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett. 36(2), 130–132 (2011). [CrossRef] [PubMed]

], or by using fiber loop mirror made of photonic crystal fiber [20

20. A. M. R. Pinto, O. Frazão, J. L. Santos, and M. Lopez-Amo, “Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering,” Appl. Phys. B 99(3), 391–395 (2010). [CrossRef]

]. Tunable, multiwavelength generation is obtained in the scheme with long period FBGs and microstructured fibers [32

32. Y. Zhu, W. Zhang, and Y. Jiang, “Tunable multi-wavelength fiber laser based on random Rayleigh back-scattering,” IEEE Photonics Technol. Lett. 25(16), 1559–1561 (2013). [CrossRef]

]. Co-operative Brillouin-Rayleigh interactions could results in a generation of frequency comb over a wide span (<40 nm) [33

33. H. Wu, Z. Wang, X. Jia, P. Li, M. Fan, Y. Li, and Y. Zhu, “Flat amplitude multiwavelength Brillouin–Raman random fiber laser with a half-open cavity,” Appl. Phys. B 112, 467–471 (2013).

,34

34. Z. Wang, H. Wu, M. Fan, Y. Li, Y. Gong, and Y. Rao, “Broadband flat-amplitude multiwavelength Brillouin-Raman fiber laser with spectral reshaping by Rayleigh scattering,” Opt. Express 21(24), 29358–29363 (2013). [CrossRef]

].

In the present work, multiwavelength lasing in the random distributed feedback fiber laser is demonstrated by employing an all fiber Lyot filter [35

35. Z. Yan, C. Mou, H. Wang, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “All-fiber polarization interference filters based on 45°-tilted fiber gratings,” Opt. Lett. 37(3), 353–355 (2012). [CrossRef] [PubMed]

]. The all fiber Lyot filter operates on the principle of fiber birefringence and polarization interferometry – thus providing a transmission comb of well-defined frequency spacing. Being an all-fiber based architecture, it provides distinct advantages over fiber based Fabry-Perot filters and FBGs in terms of form factor and power handling. A properly designed filter does away the need of using multiple Bragg gratings. Stable multiwavelength generation is obtained with the use of the all fiber Lyot filter, with each line exhibiting sub-nanometer linewidth.

2. Experimental methods

The all fiber Lyot filter is a type of polarization filter, which comprises of two in-fiber linear polarizers based on 45° tilted FBG that was inscribed into a polarization maintaining (PM) fiber along its principle axis [35

35. Z. Yan, C. Mou, H. Wang, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “All-fiber polarization interference filters based on 45°-tilted fiber gratings,” Opt. Lett. 37(3), 353–355 (2012). [CrossRef] [PubMed]

,36

36. Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett. 37(18), 3819–3821 (2012). [CrossRef] [PubMed]

] and a PM fiber as cavity, as shown in Fig. 1(a)
Fig. 1 (a) Schematic representation of the all fiber Lyot filter. (b) Experimental configuration of the random DFB fiber laser based on all fiber Lyot filter.
. The filter has both filtering and polarizing functions, and its bandwidth and free spectra range (FSR) could be adjusted by changing the length of the PM fiber. See [35

35. Z. Yan, C. Mou, H. Wang, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “All-fiber polarization interference filters based on 45°-tilted fiber gratings,” Opt. Lett. 37(3), 353–355 (2012). [CrossRef] [PubMed]

,36

36. Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett. 37(18), 3819–3821 (2012). [CrossRef] [PubMed]

] for detailed description of the all fiber Lyot filter. Here we use a filter having 20 m long PM fiber cavity (birefringence of PM fiber is around 3.47 × 10−4) which results in a bandwidth of 0.2 nm and a FSR of 0.4 nm. The insertion loss of the filter is approximately 6 dB for unpolarized light.

The all fiber Lyot filter is incorporated in the random DFB fiber laser cavity as shown in Fig. 1(b). Two spans of 40 km standard Corning SMF 28 fiber are pumped from the central point by two Raman fiber lasers (RFLs) at 1450 nm. The all fiber Lyot filter is inserted between at the point where the generation power is very low because of specific distribution of the longitudinal power in the random DFB fiber laser [37

37. D. V. Churkin, A. E. El-Taher, I. D. Vatnik, J. D. Ania-Castañón, P. Harper, E. V. Podivilov, S. A. Babin, and S. K. Turitsyn, “Experimental and theoretical study of longitudinal power distribution in a random DFB fiber laser,” Opt. Express 20(10), 11178–11188 (2012). [CrossRef] [PubMed]

,38

38. S. V. Smirnov and D. V. Churkin, “Modeling of spectral and statistical properties of a random distributed feedback fiber laser,” Opt. Express 21(18), 21236–21241 (2013). [CrossRef] [PubMed]

].

3. Results and discussions

The power transfer curve of the system exhibits a well-defined lasing threshold, Fig. 2
Fig. 2 Output power of the multiwavelength random DFB fiber laser based on Lyot filter.
. The stable quasi-CW multiwavelength generation is obtained above the power 1.3 W. Below this point, the generation is unstable because of influence of SBS [13

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

]. The laser generates multiple wavelengths simultaneously in the whole range of the Raman gain spectral profile, Fig. 3(a)
Fig. 3 (a) Generation spectra for two different pump powers. (b) Spectrum of the first Stokes wave at pump power 1.5 W and the all fiber Lyot filter transmission profile.
. The position of each individual wavelength coincides with the passbands of the Lyot filter, Fig. 3(b). Because of the double-peak nature of the Raman gain, the multiwavelength generation is observed both near 1555 nm and 1565 nm.

The number of generated lines as well as overall generation spectrum shape depends on the generation power, Fig. 3(a). The generated power in each line is of order of 10 mW. Lines have a typical spectral width within 0.08-0.14 nm range. The spectral lines located near the center of the comb are wider than lines located at the side of the comb. However, the each line is narrower than the spectral width of the all fiber Lyot filter transmission peak of 0.2 nm. At higher pump power, the second Stokes wave is generated being also multiwavelength, Fig. 4(b)
Fig. 4 Generation spectra in random lasers in different configurations: upper row – without any filter, middle row – with Lyot filter placed at the laser output, bottom row – with a Lyot filter placed in the middle of fiber span. (a) first Stokes wave (b) second Stokes wave.
(bottom row). The spectrum width at second Stokes wavelength is about 0.2 nm.

Near the Raman gain peak, the power distribution of generated lines is exceptionally flat, with only about 0.5 dB of variation over a 4 nm, Fig. 3(b). The higher the pump power, the flatter is the power distribution and more lines are generated within 3 dB intensity difference.

Note, that demonstrated power distribution among different lines is much flatter when compared to the spectral profile of the Raman gain or that of a random DFB fiber laser without any filtering elements. Indeed, in Fig. 4 we compare spectral properties of different configuration of random lasers at power 3.5 W. Without any spectral elements, the generation spectrum is smooth for both first at second Stokes waves, Fig. 4(upper row). The spectral width at 0.5 dB level is only 0.8 nm for first Stokes wave being much less than total bandwidth in the multi-wavelength regime of 4 nm, Fig. 3(b). If the Lyot filter is placed at the laser output, the envelope of generated spectrum repeats in general the generation spectrum of the random DFB fiber laser without any filters, Fig. 4 (middle row). The spectral width of individual line repeats the spectral width of the Lyot filter transmission peak being equal to 0.2 nm. So in this case the Lyot filter is just a passive filter which filters out the output laser radiation but does not affect the generation properties. However, if the Lyot filter is placed inside the resonator, the resulting generation spectrum is very different being significantly flatter for both first and second Stokes waves, Fig. 4 (bottom row). This proves that the Lyot filter placed inside the cavity does not just filter the radiation, but acts as a real intra-cavity filtering element despite random feedback. Note that at the power level of 3.5 W, the additional flattening for the first Stokes wave is resulted from the cascaded pumping for the second Stokes wave. The flatness could be potentially increased further by opting for a multiple pump configuration, or by nonlinear broadening of pump linewidth [19

19. A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett. 36(2), 130–132 (2011). [CrossRef] [PubMed]

].

The demonstrated flatness and narrow linewidth suggests that nonlinear processes play an important role in the formation of generation in multiwavelength random DFB fiber laser and different lines could interact nonlinearly with each other. In particular, each generation line could have its own longitudinal distribution of the power along the power thus decreasing the competition of the different lines for the same pump [19

19. A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett. 36(2), 130–132 (2011). [CrossRef] [PubMed]

]. This effect, however, does not account directly for the observed line narrowing when compared with a configuration where the Lyot filter passively filters the generated radiation, Fig. 4 (middle row). Note that existence of possible mode correlations in the random DFB fiber laser has been reported recently in [38

38. S. V. Smirnov and D. V. Churkin, “Modeling of spectral and statistical properties of a random distributed feedback fiber laser,” Opt. Express 21(18), 21236–21241 (2013). [CrossRef] [PubMed]

] that resulted in non-Gaussian intensity statistics similarly to the statistics of conventional RFLs [39

39. D. V. Churkin, S. V. Smirnov, and E. V. Podivilov, “Statistical properties of partially coherent cw fiber lasers,” Opt. Lett. 35(19), 3288–3290 (2010). [CrossRef] [PubMed]

43

43. D. V. Churkin and S. V. Smirnov, “Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers,” Opt. Commun. 285(8), 2154–2160 (2012). [CrossRef]

] as well as in Ytterbium-doped fiber lasers [44

44. A. E. Bednyakova, O. A. Gorbunov, M. O. Politko, S. I. Kablukov, S. V. Smirnov, D. V. Churkin, M. P. Fedoruk, and S. A. Babin, “Generation dynamics of the narrowband Yb-doped fiber laser,” Opt. Express 21(7), 8177–8182 (2013). [CrossRef] [PubMed]

]. Moreover, dark and grey solitons can be generated in normal dispersion quasi-CW RFL [45

45. E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013). [CrossRef]

]. The origin of these correlations is unknown. The multi-wavelength random DFB fiber laser could be used as a test bed for experimental investigation of possible nonlinear interaction and correlations as spectral width of individual line (0.08-0.14 nm being equal to 10-18 GHz) is within the electrical bandwidth of real time oscilloscopes. Simultaneous measurements of the intensity dynamics in different lines could be of interest as it could reveal directly spectral correlations.

One can control the properties of the generated radiation by managing the all fiber Lyot filter properties: spacing between the generated lines can be controlled by adjusting the length of the PM fiber in the filter. Linewidth of the individual lines can be controlled by employing a cascade of such Lyot filters. This is a significant advantage over existing Brillouin-Raman fiber lasers, where there is a minimal control over the width of the individual lines [33

33. H. Wu, Z. Wang, X. Jia, P. Li, M. Fan, Y. Li, and Y. Zhu, “Flat amplitude multiwavelength Brillouin–Raman random fiber laser with a half-open cavity,” Appl. Phys. B 112, 467–471 (2013).

,34

34. Z. Wang, H. Wu, M. Fan, Y. Li, Y. Gong, and Y. Rao, “Broadband flat-amplitude multiwavelength Brillouin-Raman fiber laser with spectral reshaping by Rayleigh scattering,” Opt. Express 21(24), 29358–29363 (2013). [CrossRef]

]. Previously, the random DFB fiber laser has been demonstrated to sustain picometer order linewidth [26

26. S. Sugavanam, N. Tarasov, X. Shu, and D. V. Churkin, “Narrow-band generation in random distributed feedback fiber laser,” Opt. Express 21(14), 16466–16472 (2013). [CrossRef] [PubMed]

], hence the above Lyot based system can be potentially used to obtain narrow-linewidth multiwavelength generation. It is also possible to control generation properties in a different way, as the PM fiber in the Lyot filter can be replaced by any suitable birefringent device, allowing room for possibility of wavelength and spacing tuning.

3. Summary

Here we have demonstrated a robust multiwavelength random DFB fiber laser based on Lyot all-fiber filter. The laser generates multiple lines both in first and second Stokes waves. The separation between lines is defined by the transmission profile of Lyot filter. However, the individual linewidth of the generated lines is found to be less than the spectral width of Lyot filter transmission profile. Nonlinear interaction between different lines could play an important role in formation of multiwavelength random DFB fiber laser generation properties.

Acknowledgments

Authors thank Mr. N. Tarasov and Dr. A. El-Taher for valuable inputs & the support of the ERC, EPSRC, Grant of Ministry of Education and Science of the Russian Federation (agreement No. 14.B25.31.0003).

References and links

1.

A. Bellemare, M. Karasek, M. Rochette, S. LaRochelle, and M. Têtu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU frequency grid,” J. Lightwave Technol. 18(6), 825–831 (2000). [CrossRef]

2.

Y. G. Han, C. S. Kim, J. U. Kang, and U. C. Paek, “Multiwavelength raman fiber-ring laser based on tunable cascaded long-period fiber gratings,” IEEE Photonics Technol. Lett. 15(3), 383–385 (2003). [CrossRef]

3.

X. Dong, P. Shum, N. Q. Ngo, and C. C. Chan, “Multiwavelength Raman fiber laser with a continuously-tunable spacing,” Opt. Express 14(8), 3288–3293 (2006). [CrossRef] [PubMed]

4.

M. R. Shirazi, N. S. Shahabuddin, S. N. Aziz, K. Thambiratnam, S. W. Harun, and H. Ahmad, “A linear cavity Brillouin fiber laser with multiple wavelengths output,” Laser Phys. Lett. 5(5), 361–363 (2008). [CrossRef]

5.

G. Cowle and D. Stepanov, “Multiple wavelength generation with Brillouin/erbium fiber lasers,” IEEE Photonics Technol. Lett. 8(11), 1465–1467 (1996). [CrossRef]

6.

Z. Wang, Y. Cui, B. Yun, and C. Lu, “Multiwavelength generation in a Raman fiber laser with sampled Bragg grating,” IEEE Photonics Technol. Lett. 17(10), 2044–2046 (2005). [CrossRef]

7.

S. Pan, C. Lou, and Y. Gao, “Multiwavelength erbium-doped fiber laser based on inhomogeneous loss mechanism by use of a highly nonlinear fiber and a Fabry-Perot filter,” Opt. Express 14(3), 1113–1118 (2006). [CrossRef] [PubMed]

8.

C. Kim, R. M. Sova, and J. U. Kang, “Tunable multi-wavelength all-fiber Raman source using fiber Sagnac loop filter,” Opt. Commun. 218(4-6), 291–295 (2003). [CrossRef]

9.

C.-S. Kim and J. U. Kang, “Multiwavelength switching of Raman fiber ring laser incorporating composite polarization-maintaining fiber Lyot-Sagnac filter,” Appl. Opt. 43(15), 3151–3157 (2004). [CrossRef] [PubMed]

10.

X. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express 14(18), 8205–8210 (2006). [CrossRef] [PubMed]

11.

Y.-G. Han, T. V. A. Tran, and S. B. Lee, “Wavelength-spacing tunable multiwavelength erbium-doped fiber laser based on four-wave mixing of dispersion-shifted fiber,” Opt. Lett. 31(6), 697–699 (2006). [CrossRef] [PubMed]

12.

Y.-G. Han, J. H. Lee, S. B. Lee, L. Poti, and A. Bogoni, “Novel multiwavelength erbium-doped fiber and Raman fiber ring lasers with continuous wavelength spacing tunability at room temperature,” J. Lightwave Technol. 25(8), 2219–2225 (2007). [CrossRef]

13.

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

14.

I. D. Vatnik, D. V. Churkin, and S. A. Babin, “Power optimization of random distributed feedback fiber lasers,” Opt. Express 20(27), 28033–28038 (2012). [CrossRef] [PubMed]

15.

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

16.

W. L. Zhang, Y. Y. Zhu, Y. J. Rao, Z. N. Wang, X. H. Jia, and H. Wu, “Random fiber laser formed by mixing dispersion compensated fiber and single mode fiber,” Opt. Express 21(7), 8544–8549 (2013). [CrossRef] [PubMed]

17.

A. R. Sarmani, M. H. Abu Bakar, A. A. A. Bakar, F. R. M. Adikan, and M. A. Mahdi, “Spectral variations of the output spectrum in a random distributed feedback Raman fiber laser,” Opt. Express 19(15), 14152–14159 (2011). [CrossRef] [PubMed]

18.

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]

19.

A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett. 36(2), 130–132 (2011). [CrossRef] [PubMed]

20.

A. M. R. Pinto, O. Frazão, J. L. Santos, and M. Lopez-Amo, “Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering,” Appl. Phys. B 99(3), 391–395 (2010). [CrossRef]

21.

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]

22.

A. Sarmani, R. Zamiri, and M. Bakar, “Tunable Raman fiber laser induced by Rayleigh backscattering in an ultra-long cavity,” J. Eur. Opt. Soc. Rapid Publ. 6, 11043 (2011).

23.

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]

24.

R. Teng, Y. Ding, and L. Chen, “Random fiber laser operating at 1,115 nm,” Appl. Phys. B 111(2), 169–172 (2013).

25.

W. L. Zhang, Y. J. Rao, J. M. Zhu, Z. X. Yang, Z. N. Wang, and X. H. Jia, “Low threshold 2nd-order random lasing of a fiber laser with a half-opened cavity,” Opt. Express 20(13), 14400–14405 (2012). [CrossRef] [PubMed]

26.

S. Sugavanam, N. Tarasov, X. Shu, and D. V. Churkin, “Narrow-band generation in random distributed feedback fiber laser,” Opt. Express 21(14), 16466–16472 (2013). [CrossRef] [PubMed]

27.

A. M. R. Pinto, M. Lopez-Amo, J. Kobelke, and K. Schuster, “Temperature fiber laser sensor based on a hybrid cavity and a random mirror,” J. Lightwave Technol. 30(8), 1168–1172 (2012). [CrossRef]

28.

Z. N. Wang, Y. J. Rao, H. Wu, P. Y. Li, Y. Jiang, X. H. Jia, and W. L. Zhang, “Long-distance fiber-optic point-sensing systems based on random fiber lasers,” Opt. Express 20(16), 17695–17700 (2012). [CrossRef] [PubMed]

29.

X.-H. Jia, Y.-J. Rao, Z.-N. Wang, W.-L. Zhang, Y. Jiang, J.-M. Zhu, and Z.-X. Yang, “Towards fully distributed amplification and high-performance long-range distributed sensing based on random fiber laser,” Proc. SPIE 8421, 842127 (2012). [CrossRef]

30.

J. Nuño, M. Alcon-Camas, and J. D. Ania-Castañón, “RIN transfer in random distributed feedback fiber lasers,” Opt. Express 20(24), 27376–27381 (2012). [CrossRef] [PubMed]

31.

X.-H. Jia, Y.-J. Rao, F. Peng, Z.-N. Wang, W.-L. Zhang, H.-J. Wu, and Y. Jiang, “Random-lasing-based distributed fiber-optic amplification,” Opt. Express 21(5), 6572–6577 (2013). [CrossRef] [PubMed]

32.

Y. Zhu, W. Zhang, and Y. Jiang, “Tunable multi-wavelength fiber laser based on random Rayleigh back-scattering,” IEEE Photonics Technol. Lett. 25(16), 1559–1561 (2013). [CrossRef]

33.

H. Wu, Z. Wang, X. Jia, P. Li, M. Fan, Y. Li, and Y. Zhu, “Flat amplitude multiwavelength Brillouin–Raman random fiber laser with a half-open cavity,” Appl. Phys. B 112, 467–471 (2013).

34.

Z. Wang, H. Wu, M. Fan, Y. Li, Y. Gong, and Y. Rao, “Broadband flat-amplitude multiwavelength Brillouin-Raman fiber laser with spectral reshaping by Rayleigh scattering,” Opt. Express 21(24), 29358–29363 (2013). [CrossRef]

35.

Z. Yan, C. Mou, H. Wang, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “All-fiber polarization interference filters based on 45°-tilted fiber gratings,” Opt. Lett. 37(3), 353–355 (2012). [CrossRef] [PubMed]

36.

Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett. 37(18), 3819–3821 (2012). [CrossRef] [PubMed]

37.

D. V. Churkin, A. E. El-Taher, I. D. Vatnik, J. D. Ania-Castañón, P. Harper, E. V. Podivilov, S. A. Babin, and S. K. Turitsyn, “Experimental and theoretical study of longitudinal power distribution in a random DFB fiber laser,” Opt. Express 20(10), 11178–11188 (2012). [CrossRef] [PubMed]

38.

S. V. Smirnov and D. V. Churkin, “Modeling of spectral and statistical properties of a random distributed feedback fiber laser,” Opt. Express 21(18), 21236–21241 (2013). [CrossRef] [PubMed]

39.

D. V. Churkin, S. V. Smirnov, and E. V. Podivilov, “Statistical properties of partially coherent cw fiber lasers,” Opt. Lett. 35(19), 3288–3290 (2010). [CrossRef] [PubMed]

40.

S. Randoux, N. Dalloz, and P. Suret, “Intracavity changes in the field statistics of Raman fiber lasers,” Opt. Lett. 36(6), 790–792 (2011). [CrossRef] [PubMed]

41.

D. V. Churkin, O. A. Gorbunov, and S. V. Smirnov, “Extreme value statistics in Raman fiber lasers,” Opt. Lett. 36(18), 3617–3619 (2011). [CrossRef] [PubMed]

42.

S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in Raman fiber lasers,” Opt. Lett. 37(4), 500–502 (2012). [CrossRef] [PubMed]

43.

D. V. Churkin and S. V. Smirnov, “Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers,” Opt. Commun. 285(8), 2154–2160 (2012). [CrossRef]

44.

A. E. Bednyakova, O. A. Gorbunov, M. O. Politko, S. I. Kablukov, S. V. Smirnov, D. V. Churkin, M. P. Fedoruk, and S. A. Babin, “Generation dynamics of the narrowband Yb-doped fiber laser,” Opt. Express 21(7), 8177–8182 (2013). [CrossRef] [PubMed]

45.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013). [CrossRef]

OCIS Codes
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3550) Lasers and laser optics : Lasers, Raman
(290.5870) Scattering : Scattering, Rayleigh
(290.5910) Scattering : Scattering, stimulated Raman

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: October 8, 2013
Revised Manuscript: December 13, 2013
Manuscript Accepted: January 2, 2014
Published: January 31, 2014

Citation
S. Sugavanam, Z. Yan, V. Kamynin, A. S. Kurkov, L. Zhang, and D. V. Churkin, "Multiwavelength generation in a random distributed feedback fiber laser using an all fiber Lyot filter," Opt. Express 22, 2839-2844 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2839


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References

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  2. Y. G. Han, C. S. Kim, J. U. Kang, and U. C. Paek, “Multiwavelength raman fiber-ring laser based on tunable cascaded long-period fiber gratings,” IEEE Photonics Technol. Lett.15(3), 383–385 (2003). [CrossRef]
  3. X. Dong, P. Shum, N. Q. Ngo, and C. C. Chan, “Multiwavelength Raman fiber laser with a continuously-tunable spacing,” Opt. Express14(8), 3288–3293 (2006). [CrossRef] [PubMed]
  4. M. R. Shirazi, N. S. Shahabuddin, S. N. Aziz, K. Thambiratnam, S. W. Harun, and H. Ahmad, “A linear cavity Brillouin fiber laser with multiple wavelengths output,” Laser Phys. Lett.5(5), 361–363 (2008). [CrossRef]
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  6. Z. Wang, Y. Cui, B. Yun, and C. Lu, “Multiwavelength generation in a Raman fiber laser with sampled Bragg grating,” IEEE Photonics Technol. Lett.17(10), 2044–2046 (2005). [CrossRef]
  7. S. Pan, C. Lou, and Y. Gao, “Multiwavelength erbium-doped fiber laser based on inhomogeneous loss mechanism by use of a highly nonlinear fiber and a Fabry-Perot filter,” Opt. Express14(3), 1113–1118 (2006). [CrossRef] [PubMed]
  8. C. Kim, R. M. Sova, and J. U. Kang, “Tunable multi-wavelength all-fiber Raman source using fiber Sagnac loop filter,” Opt. Commun.218(4-6), 291–295 (2003). [CrossRef]
  9. C.-S. Kim and J. U. Kang, “Multiwavelength switching of Raman fiber ring laser incorporating composite polarization-maintaining fiber Lyot-Sagnac filter,” Appl. Opt.43(15), 3151–3157 (2004). [CrossRef] [PubMed]
  10. X. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express14(18), 8205–8210 (2006). [CrossRef] [PubMed]
  11. Y.-G. Han, T. V. A. Tran, and S. B. Lee, “Wavelength-spacing tunable multiwavelength erbium-doped fiber laser based on four-wave mixing of dispersion-shifted fiber,” Opt. Lett.31(6), 697–699 (2006). [CrossRef] [PubMed]
  12. Y.-G. Han, J. H. Lee, S. B. Lee, L. Poti, and A. Bogoni, “Novel multiwavelength erbium-doped fiber and Raman fiber ring lasers with continuous wavelength spacing tunability at room temperature,” J. Lightwave Technol.25(8), 2219–2225 (2007). [CrossRef]
  13. S. Turitsyn, S. A. Babin, A. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics4(4), 231–235 (2010). [CrossRef]
  14. I. D. Vatnik, D. V. Churkin, and S. A. Babin, “Power optimization of random distributed feedback fiber lasers,” Opt. Express20(27), 28033–28038 (2012). [CrossRef] [PubMed]
  15. D. Churkin, S. A. Babin, A. El-Taher, P. Harper, S. Kablukov, V. Karalekas, J. Ania-Castañón, E. Podivilov, and S. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A82(3), 033828 (2010). [CrossRef]
  16. W. L. Zhang, Y. Y. Zhu, Y. J. Rao, Z. N. Wang, X. H. Jia, and H. Wu, “Random fiber laser formed by mixing dispersion compensated fiber and single mode fiber,” Opt. Express21(7), 8544–8549 (2013). [CrossRef] [PubMed]
  17. A. R. Sarmani, M. H. Abu Bakar, A. A. A. Bakar, F. R. M. Adikan, and M. A. Mahdi, “Spectral variations of the output spectrum in a random distributed feedback Raman fiber laser,” Opt. Express19(15), 14152–14159 (2011). [CrossRef] [PubMed]
  18. 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]
  19. A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett.36(2), 130–132 (2011). [CrossRef] [PubMed]
  20. A. M. R. Pinto, O. Frazão, J. L. Santos, and M. Lopez-Amo, “Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering,” Appl. Phys. B99(3), 391–395 (2010). [CrossRef]
  21. S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A84(2), 021805 (2011). [CrossRef]
  22. A. Sarmani, R. Zamiri, and M. Bakar, “Tunable Raman fiber laser induced by Rayleigh backscattering in an ultra-long cavity,” J. Eur. Opt. Soc. Rapid Publ.6, 11043 (2011).
  23. 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. Express19(19), 18486–18494 (2011). [CrossRef] [PubMed]
  24. R. Teng, Y. Ding, and L. Chen, “Random fiber laser operating at 1,115 nm,” Appl. Phys. B111(2), 169–172 (2013).
  25. W. L. Zhang, Y. J. Rao, J. M. Zhu, Z. X. Yang, Z. N. Wang, and X. H. Jia, “Low threshold 2nd-order random lasing of a fiber laser with a half-opened cavity,” Opt. Express20(13), 14400–14405 (2012). [CrossRef] [PubMed]
  26. S. Sugavanam, N. Tarasov, X. Shu, and D. V. Churkin, “Narrow-band generation in random distributed feedback fiber laser,” Opt. Express21(14), 16466–16472 (2013). [CrossRef] [PubMed]
  27. A. M. R. Pinto, M. Lopez-Amo, J. Kobelke, and K. Schuster, “Temperature fiber laser sensor based on a hybrid cavity and a random mirror,” J. Lightwave Technol.30(8), 1168–1172 (2012). [CrossRef]
  28. Z. N. Wang, Y. J. Rao, H. Wu, P. Y. Li, Y. Jiang, X. H. Jia, and W. L. Zhang, “Long-distance fiber-optic point-sensing systems based on random fiber lasers,” Opt. Express20(16), 17695–17700 (2012). [CrossRef] [PubMed]
  29. X.-H. Jia, Y.-J. Rao, Z.-N. Wang, W.-L. Zhang, Y. Jiang, J.-M. Zhu, and Z.-X. Yang, “Towards fully distributed amplification and high-performance long-range distributed sensing based on random fiber laser,” Proc. SPIE8421, 842127 (2012). [CrossRef]
  30. J. Nuño, M. Alcon-Camas, and J. D. Ania-Castañón, “RIN transfer in random distributed feedback fiber lasers,” Opt. Express20(24), 27376–27381 (2012). [CrossRef] [PubMed]
  31. X.-H. Jia, Y.-J. Rao, F. Peng, Z.-N. Wang, W.-L. Zhang, H.-J. Wu, and Y. Jiang, “Random-lasing-based distributed fiber-optic amplification,” Opt. Express21(5), 6572–6577 (2013). [CrossRef] [PubMed]
  32. Y. Zhu, W. Zhang, and Y. Jiang, “Tunable multi-wavelength fiber laser based on random Rayleigh back-scattering,” IEEE Photonics Technol. Lett.25(16), 1559–1561 (2013). [CrossRef]
  33. H. Wu, Z. Wang, X. Jia, P. Li, M. Fan, Y. Li, and Y. Zhu, “Flat amplitude multiwavelength Brillouin–Raman random fiber laser with a half-open cavity,” Appl. Phys. B112, 467–471 (2013).
  34. Z. Wang, H. Wu, M. Fan, Y. Li, Y. Gong, and Y. Rao, “Broadband flat-amplitude multiwavelength Brillouin-Raman fiber laser with spectral reshaping by Rayleigh scattering,” Opt. Express21(24), 29358–29363 (2013). [CrossRef]
  35. Z. Yan, C. Mou, H. Wang, K. Zhou, Y. Wang, W. Zhao, and L. Zhang, “All-fiber polarization interference filters based on 45°-tilted fiber gratings,” Opt. Lett.37(3), 353–355 (2012). [CrossRef] [PubMed]
  36. Z. Yan, K. Zhou, and L. Zhang, “In-fiber linear polarizer based on UV-inscribed 45° tilted grating in polarization maintaining fiber,” Opt. Lett.37(18), 3819–3821 (2012). [CrossRef] [PubMed]
  37. D. V. Churkin, A. E. El-Taher, I. D. Vatnik, J. D. Ania-Castañón, P. Harper, E. V. Podivilov, S. A. Babin, and S. K. Turitsyn, “Experimental and theoretical study of longitudinal power distribution in a random DFB fiber laser,” Opt. Express20(10), 11178–11188 (2012). [CrossRef] [PubMed]
  38. S. V. Smirnov and D. V. Churkin, “Modeling of spectral and statistical properties of a random distributed feedback fiber laser,” Opt. Express21(18), 21236–21241 (2013). [CrossRef] [PubMed]
  39. D. V. Churkin, S. V. Smirnov, and E. V. Podivilov, “Statistical properties of partially coherent cw fiber lasers,” Opt. Lett.35(19), 3288–3290 (2010). [CrossRef] [PubMed]
  40. S. Randoux, N. Dalloz, and P. Suret, “Intracavity changes in the field statistics of Raman fiber lasers,” Opt. Lett.36(6), 790–792 (2011). [CrossRef] [PubMed]
  41. D. V. Churkin, O. A. Gorbunov, and S. V. Smirnov, “Extreme value statistics in Raman fiber lasers,” Opt. Lett.36(18), 3617–3619 (2011). [CrossRef] [PubMed]
  42. S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in Raman fiber lasers,” Opt. Lett.37(4), 500–502 (2012). [CrossRef] [PubMed]
  43. D. V. Churkin and S. V. Smirnov, “Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers,” Opt. Commun.285(8), 2154–2160 (2012). [CrossRef]
  44. A. E. Bednyakova, O. A. Gorbunov, M. O. Politko, S. I. Kablukov, S. V. Smirnov, D. V. Churkin, M. P. Fedoruk, and S. A. Babin, “Generation dynamics of the narrowband Yb-doped fiber laser,” Opt. Express21(7), 8177–8182 (2013). [CrossRef] [PubMed]
  45. E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminar–turbulent transition in a fibre laser,” Nat. Photonics7(10), 783–786 (2013). [CrossRef]

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