Abstract

We demonstrate a novel random laser based on a single fiber Bragg grating. A long fiber Bragg grating fabrication technique allows the insertion of a large number of randomly distributed phase errors in the structure of the grating which induces light localization. By writing such a grating in a polarisation maintaining Er-doped fiber, a random laser is demonstrated by pumping the fiber with 976 and 1480 nm pump lasers. The number of emitted modes is observed to be a function of the length of the grating and of the pump power and single-mode operation is shown to be possible. The random fiber laser shows low-threshold (~3 mW) and measured ~0.5 pm emission linewidth at a wavelength of around 1534 nm.

©2009 Optical Society of America

1. Introduction

A considerable amount of research has been dedicated in the last few years to a new breed of cavity-less lasers, since the first demonstrations of a random laser [1, 2]. These random lasers (RL) are based on the phenomenon of light localization which provides the feedback that is usually obtained in conventional lasers by Fabry-Perot or DFB cavity. Interest in RLs is motivated by unusual properties such as low pump power threshold, relatively simple technology, high efficiency, low coherence, narrow linewidth emission, and irregular electric field distribution inside the gain medium [36]. Various applications in investigating the unusual properties of cancer tissue through diffuse scattering or exploiting their unique emission spectrum for photonic encoding [7, 8] are also possible.

The localization of light has attracted attention by itself in recent years [9, 10]. This is the optical equivalent of Anderson localization in solids which describes the behavior of electrons in a random medium [11]. Light localization is typically characterized by an exponential decay of the transmission through the length of the medium.

Various types of RLs have been demonstrated: semiconductor and rare earth powders [2, 12, 13], organic films [14], liquid crystals [15] and colloidal suspensions in dye solution [1]. All these RLs share the lack of directionality of the emission by having a 2D or 3D geometry. This lack of directionality caused by random scattering also limits the depth at which the pump light can penetrate the gain medium. This in turn causes the lasing threshold to be larger than what could be expected from such a medium.

The low threshold behavior can be explained from the spontaneous emission factor β which is the fraction of spontaneous emission that seeds the laser process [16]. In the case of a conventional laser relying on a cavity, the β factor is obtained from geometric parameters and from the spectral overlap between the spontaneous emission and the discrete cavity modes. RLs differ from conventional lasers by having a β factor being only dependant on the spectral dependence of the gain which can be related to the localization properties of the medium. The result is that RLs can achieve significantly higher values of β than conventional lasers.

Some attempts have been made to obtain purely 1D random lasing. The first was reported by Milner et al. [17] and uses a stack of microscope cover slides of random thickness with interspersed dye films. The RL obtained by pumping this medium with a CW Argon-ion laser showed a low-threshold and narrow line width. As the light is not guided, this scheme is considered one dimensional as it is limited to short lengths of the scattering medium. Another scheme proposed by de Matos et al. uses a hollow-core photonic crystal fiber filled with a solution of rhodamine 6G with TiO2 particles in suspension [18]. The fiber is pumped transversely with a 532 nm Nd: YAG laser, allowing a uniform gain profile to be obtained but limiting the maximum length of the component to 4 mm. The use of a waveguide allows the efficiency of this scheme to be two orders of magnitude superior to similar RLs in bulk format.

In 2005, Shapira et al. [9] demonstrated experimentally that a randomly spaced identical fiber Bragg grating array could give rise to light localization and they suggested that this could be use to obtain random lasing. It was noted that in the asymptotic limit where the number of gratings is high, the transmission of a random array of grating can be obtained from the multiplication of the single gratings transmission. This implies that multiple reflections are cancelled in such an array.

More recently, Lizárraga et al. [19] used this scheme in a Er-doped fiber and effectively demonstrated random fiber lasers (RFLs). The use of a 976 nm pump which is not affected by the Bragg gratings allows the gain to be spatially uniform contrary to most other RL schemes. The result is a lower threshold noted to be around 10 mW. This scheme is also relatively simple to realize as Bragg gratings in rare-earth doped fibers are possible in hydrogenated fibers. It was noted that the addition of more gratings to the array lowered the measured threshold but raised the number of modes that were lasing. It was also found out that relative power of each mode and the overall power output fluctuate significantly.

In this paper we report the experimental demonstration of an Er-doped fiber random laser with a threshold of 3 mW, which is significantly lower than the previous scheme [19], and with ~0.5 pm linewidth, This is achieved by replacing the random array of gratings by a continuous grating with randomly distributed phase errors. This in turn allows the number of scatterers and the randomness to be significantly raised without the need of longer component, which would otherwise raise mode competition further. Single mode operation is obtained for a certain pump power range. The fabrication technique allows easy wavelength tunability of the Bragg wavelength which is close to the lasing wavelength. This paper also demonstrates random lasing with two different pump wavelengths of 976nm and 1480nm.

2. Fiber Bragg grating fabrication technique

The fabrication technique presented in this section is a variation of a custom fiber Bragg grating fabrication technique based on push/pull phase shifting interferometry, which we published recently [20]. This scheme uses electro-optical phase modulators placed in each arm of a Talbot interferometer to create a continuously moving fringe pattern, which can be synchronized with a moving fiber. This is made possible by applying a high voltage ramp signal to the modulators. In this scheme, the grating period can be controlled by changing the ramp signal frequency. Phase shifts can also be simply inserted along the grating by purely electrical means. Figure 1 shows a schematic of the fabrication setup.

 figure: Fig. 1

Fig. 1 Schematic of the interferometer. SL: spherical lens; PM: phase mask; EOPM: electro-optical phase modulators.

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The fiber is moved by pulling it from a stable mount with an Aerotech rotary motor stage. The fiber is placed in vacuum v-grooves so that it can be moved freely by pulling it and still be stable with respect to the writing beams. It was noted that friction between the fiber and the mount causes irregularities in the grating spectrum that could be reduced by lowering the air flow from the vacuum. These irregularities could be seen as small phase errors that were randomly but continuously distributed along the grating profile. By keeping the vacuum at a maximum level, the friction created between the fiber and the mount ensures that the number of phase errors in the grating is high and random. The grating that is formed in the process can be seen as a succession of a great number of short length gratings of different lengths and random phase shifts between them.

Localization behavior from such a grating is expected to be observed since it is a limiting case of the randomly spaced array of equal length gratings that was reported [9, 19]. Figure 2 shows the reflection spectrum while Fig. 3 shows the transmission spectrum of a 30 cm long grating made from a CorActive Er-doped polarization maintaining fiber which was used as a gain medium for RFLs. This fiber exhibits peak absorption of 28 dB/m at 1530 nm. The measurements were obtained with a JDS Uniphase OMNI swept wavelength system.

 figure: Fig. 2

Fig. 2 Reflection spectrum of a 30 cm long grating made from hydrogenated Er-doped PM fiber.

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 figure: Fig. 3

Fig. 3 Transmission spectrum of a 30 cm long grating made from hydrogenated Er-doped PM fiber.

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The general shape of the reflection spectrum corresponds to what is predicted from numerical simulation as a reflection spectrum for an array of a large number of gratings (>>1000) by Shapira et al. [9]. The envelope matches the reflection spectrum of a much shorter grating with 8 nm separation of the first zeros. The bandwidth of an individual peak is observed to be around 0.01 nm. The resolution of the JDSU system is 3 pm, which is sufficient to observe the small ripples in the transmission and reflection spectra of the un-pumped laser. The narrow bandwidth of the individual peaks can be attributed to the large number of phase shifts distributed along the grating.

The transmission spectrum is shifted from the reflection spectrum by 1 nm due to the time delay between the two measurements, as the reflection spectrum was taken immediately after the writing process and the transmission spectrum was taken weeks after. As the hydrogen leaks away from the fiber after the grating inscription, the Bragg wavelength shifts to the blue. The somewhat large bandwidth of the transmission spectra can be attributed to the polarization maintaining properties of the fiber which normally leads to two separate Bragg wavelengths separated by approximately 1 nm in a uniform grating.

The localization length can be calculated from the expression [17]:

T(L)~exp(L/2ξ)
where L is the length of the random medium and ξ is the localization length (and is misquoted in Ref. 19). ξ is found to be approximately 5 cm for the peak wavelengths of the grating shown in of Fig. 3. In comparison, Lizárraga et al. [19] observed a localization length corresponding to 6 individual gratings distributed over approximately 6 cm. The difference in the different gratings spectra lies in the greater bandwidth of the gratings presented here and the higher frequency of the ripples both of which can be attributed to the high degree of randomness in our grating. Also, the general shape of the reflection spectra observed by Lizárraga et al. [19] do not match the general sinc shape of a uniform grating which is attributed to the asymptotic behavior of light localization with the addition of a large number of scatterers [9]. The respective strength of the gratings is similar in both cases. It is still uncertain if the large bandwidth which presents strong reflections could be reduced or if it is an unavoidable characteristic of the fabrication process, and is presently under investigation.

3. Characterization of random fiber lasers

The fibers Bragg gratings presented in the previous section are used with a gain medium to obtain random fiber lasers. The characterization setup is fairly simple: a fiber pigtailed 976 nm, or 1480 nm pump laser is connected to the RFL in different experiments, and which is then connected to an Ando AQ6317B optical spectrum analyzer. An Exfo SA confocal Fabry-Perot interferometer (FPI) spectrum analyzer with a 27 MHz resolution and 8 GHz free spectral range was also used to characterize the linewidth of the RFL.

Three random fiber lasers grating samples of different lengths, obtained using identical fabrication parameters were fabricated. The first one is a 6 cm long grating having a similar localization length to the other gratings. No laser emission was measured from this medium even at high pump power (~120 mW). This is in accordance with what was observed by Milner et al. [17], who noted that lasing could be detected at a medium length just larger than the localization length.

The other two samples that were used as a gain medium were 20 cm and 30 cm long gratings, as indicated in the previous section. Figure 4 shows the maximum measured emitted power from one end of the RFL as a function of the incident pump power for the 20 cm long RFL for both pump laser wavelength. These results should not be used for a calculation of the actual efficiency of the laser as the fusion splice between the Corning SMF28 fiber and Er-doped fiber was found out to exhibits losses. The absorption of pump power in the doped fiber was measured to be 3 dB for the 976 nm laser and 2 dB for the 1480 nm laser. The efficiency should not be expected to be high since the reflectivity of the grating is high, leading to a high intra-cavity flux. The threshold using a 976 nm pump laser is measured to be around 3 mW, which is lower than what was previously reported by Lizárraga et al. [19]. The length of the gain medium does not seem to influence the threshold to any great extent.

 figure: Fig. 4

Fig. 4 Laser power as a function of the pump power for a 20 cm grating with 976 and 1480 nm pump lasers.

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The emission spectrum contains a number of peaks which are a function of the length of the gain medium and the pump power. The emission spectrum of the 20 cm RFL at a pump power of 120 mW is shown in Fig. 5 . The power distribution between the two modes of the 20 cm RFL typically oscillates from one mode to the other over a period of a few seconds. Whilst the number of modes one can observe at one time can change from measurement to measurement, the number of modes for the 20 cm RFL was typically limited to two, while it can reach 7 modes for the 30 cm RFL at higher pump power as shown at Fig. 6 . The relative power distribution between the modes is also much more stable in the case of the 20 cm RFL.

 figure: Fig. 5

Fig. 5 Laser emission spectra of the 20 cm RFL for a 120 mW pump power at 1480 nm measured a few seconds apart.

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 figure: Fig. 6

Fig. 6 Laser emission spectrum of the 30 cm RFL for a 120 mW pump power at 976 nm.

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The 30 cm RFL is single-mode up to a pump power of 10 mW (at 980 nm) whilst the 20 cm RFL shows such features up to a pump power of 40 mW. While the relative power distribution and the overall emitted power are both fluctuating in time, the wavelengths of the different lasing modes remain constant. The number of modes could probably be reduced by exploiting the polarization maintaining properties of the fiber by adding a polarization controller before the grating.

The FWHM linewidth was measured with the scanning FPI to be around 0.5 pm. These individual peaks are stable over several tens of scans of the scanning FP etalon and are therefore not considered to be noise bursts. This linewidth is also significantly lower than what has been previously obtained for a random array of gratings (~20 pm) [19]. This should be expected from the grating’s spectra as it has a much smaller ripple period. The effective cavity quality factor Q = λ/Δλ is estimated to be of the order of 3 × 106. The processes behind this narrow linewidth are under investigation.

In Figs. 5 and 6 it is interesting to note the high isolation between the maximum emitted intensity and background amplified spontaneous emission. No photoluminescence could effectively be measured at low pump intensities. This is in contrast to the results reported by Lizárraga et al. [19] in which the isolation between the laser emission at threshold (10 mW) and the photoluminescence maximum is approximately 3 dB. This should be expected from a lower threshold, hence higher β factor scheme in which a greater fraction of spontaneous emission seeds the laser process. The actual value of β could not be calculated as a precise measurement of the total emitted power and absorbed pump power is needed and will be reported in a subsequent publication along with further experiments results.

Since the two configurations have supposedly similar localization lengths, one could expect similar characteristics. The explanation of the difference between respective threshold levels, smaller linewidth and fewer lasing modes may lie in the high degree of randomness obtained within our scheme (i.e. single longitudinal-mode at higher power). This is supported by the noted fine structure in the grating’s spectra, which will force more energy into a dominant mode. By having a greater number of scatterers, the field intensity variation should also be smoother along the gain medium and the light localization behavior should match the asymptotic limit. Lizárraga et al. [19] noted the presence of “hot spots” of high field intensity in simulations opposed to regions that do not contribute significantly to the lasing process. Hot-spots should not appear in a medium that exhibits ideal light localization behavior. In this regard, the proposed scheme appears to be a truly random laser. Ideal localization should lead to coherence enhancement forcing energy into a dominant mode [21], forcing single frequency operation, whereas in the coherence collapsed regime [22], as would be the case of a long laser, the lasing tendency is in the multimode regime. Measurements of our random laser with a high resolution FP etalon have confirmed single frequency operation.

As mentioned earlier, the fabrication technique proposed in this article can be used to add additional phase shifts along the grating. This could be used to further add to the randomness of the grating. Several exposures of the fiber to the UV beams could also be used to raise the randomness. The precise influence of the writing parameters over the grating and the RFL’s characteristics is still to be determined. It is speculated that a narrow line-width and higher power single-mode regime could be obtained by designing a highly random grating with a carefully chosen ratio of grating length and localization length.

4. Conclusion

We have presented an original fabrication technique allowing the insertion of a large number of phase errors in long fiber Bragg gratings. These fiber Bragg gratings exhibits a typical light localization behavior which have allowed the fabrication of 1D random fiber lasers. The high degree of randomness obtained with this scheme allows the RFLs to exhibit the lowest threshold (~3 mW) and linewidth (~0.5 pm) compared to any previously reported schemes. Depending on the length and on the pump power, the random lasers show both single and multimode operation. Overall, relative power fluctuation between the modes was observed, characteristic of RLs.

Acknowledgments

The authors acknowledge the support from Canadian Institute for Photonics Innovation (CIPI)’s BP5 Project: ‘Biopsy’ and RK also acknowledges support from the Govt. of Canada’s Canada Research Chairs Program. The authors are also grateful to the Dr. Stephen Mihailov and Mr. Joe Seregelyi of the Communication Research Center, Canada for providing the hydrogenated fiber.

References and links

1. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994). [CrossRef]  

2. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus,“Genration of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10(12), 2358–2363 (1993). [CrossRef]  

3. H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003). [CrossRef]  

4. O. Zaitsev, L. Deych, and V. Shuvayev, “Statistical properties of one-dimensional random lasers,” Phys. Rev. Lett. 102(4), 043906 (2009). [CrossRef]   [PubMed]  

5. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005). [CrossRef]  

6. R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003). [CrossRef]  

7. R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289 (2004). [CrossRef]  

8. N. M. Lawandy, “Paint-on lasers’ light the way for new technologies,” Photon. Spectra , 119–127 (1994).

9. O. Shapira and B. Fischer, “Localization of light in a random-grating array in a single-mode fiber,” J. Opt. Soc. Am. B 22(12), 2542–2552 (2005). [CrossRef]  

10. V. D. Freilikher, and S. A. Gredeskul, “Localization of waves in media with one-dimensional disorder,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), V. XXX, pp. 137–203.

11. P. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958). [CrossRef]  

12. 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]  

13. G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002). [CrossRef]  

14. R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001). [CrossRef]  

15. S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004). [CrossRef]  

16. G. van Soest and A. Lajendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002). [CrossRef]   [PubMed]  

17. V. Milner and A. Genack, “Photon localization laser,” Phys. Rev. Lett. 94, 073901 (2005). [CrossRef]   [PubMed]  

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

19. N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, “Single-mode Er-doped fiber random laser with distributed Bragg grating feedback,” Opt. Express 17(2), 395–404 (2009). [CrossRef]   [PubMed]  

20. M. Gagné, L. Bojor, R. Maciejko, and R. Kashyap, “Novel custom fiber Bragg grating fabrication technique based on push-pull phase shifting interferometry,” Opt. Express 16(26), 21550–21557 (2008). [CrossRef]   [PubMed]  

21. I. A. Kostko and R. Kashyap, “Dynamics of ultimate spectral narrowing in a semiconductor fiber-grating laser with an intra-cavity saturable absorber,” Opt. Express 14(7), 2706–2714 (2006). [CrossRef]   [PubMed]  

22. F. N. Timofeev and R. Kashyap, “High-power, ultra-stable, single-frequency operation of a long, doped-fiber external-cavity, grating-semiconductor laser,” Opt. Express 6, 515–520 (2003). [CrossRef]  

References

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  1. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
    [Crossref]
  2. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus,“Genration of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10(12), 2358–2363 (1993).
    [Crossref]
  3. H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
    [Crossref]
  4. O. Zaitsev, L. Deych, and V. Shuvayev, “Statistical properties of one-dimensional random lasers,” Phys. Rev. Lett. 102(4), 043906 (2009).
    [Crossref] [PubMed]
  5. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005).
    [Crossref]
  6. R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003).
    [Crossref]
  7. R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289 (2004).
    [Crossref]
  8. N. M. Lawandy, “Paint-on lasers’ light the way for new technologies,” Photon. Spectra, 119–127 (1994).
  9. O. Shapira and B. Fischer, “Localization of light in a random-grating array in a single-mode fiber,” J. Opt. Soc. Am. B 22(12), 2542–2552 (2005).
    [Crossref]
  10. V. D. Freilikher, and S. A. Gredeskul, “Localization of waves in media with one-dimensional disorder,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), V. XXX, pp. 137–203.
  11. P. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
    [Crossref]
  12. 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]
  13. G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
    [Crossref]
  14. R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001).
    [Crossref]
  15. S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
    [Crossref]
  16. G. van Soest and A. Lajendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002).
    [Crossref] [PubMed]
  17. V. Milner and A. Genack, “Photon localization laser,” Phys. Rev. Lett. 94, 073901 (2005).
    [Crossref] [PubMed]
  18. C. J. S. de Matos, L. de S Menezes, A. M. Brito-Silva, M. A. Martinez Gámez, A. S. Gomes, and C. B. de Araújo, “Random fiber laser,” Phys. Rev. Lett. 99(15), 153903 (2007).
    [Crossref] [PubMed]
  19. N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, “Single-mode Er-doped fiber random laser with distributed Bragg grating feedback,” Opt. Express 17(2), 395–404 (2009).
    [Crossref] [PubMed]
  20. M. Gagné, L. Bojor, R. Maciejko, and R. Kashyap, “Novel custom fiber Bragg grating fabrication technique based on push-pull phase shifting interferometry,” Opt. Express 16(26), 21550–21557 (2008).
    [Crossref] [PubMed]
  21. I. A. Kostko and R. Kashyap, “Dynamics of ultimate spectral narrowing in a semiconductor fiber-grating laser with an intra-cavity saturable absorber,” Opt. Express 14(7), 2706–2714 (2006).
    [Crossref] [PubMed]
  22. F. N. Timofeev and R. Kashyap, “High-power, ultra-stable, single-frequency operation of a long, doped-fiber external-cavity, grating-semiconductor laser,” Opt. Express 6, 515–520 (2003).
    [Crossref]

2009 (2)

2008 (1)

2007 (1)

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

2006 (1)

2005 (3)

V. Milner and A. Genack, “Photon localization laser,” Phys. Rev. Lett. 94, 073901 (2005).
[Crossref] [PubMed]

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005).
[Crossref]

O. Shapira and B. Fischer, “Localization of light in a random-grating array in a single-mode fiber,” J. Opt. Soc. Am. B 22(12), 2542–2552 (2005).
[Crossref]

2004 (2)

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289 (2004).
[Crossref]

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
[Crossref]

2003 (3)

H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
[Crossref]

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003).
[Crossref]

F. N. Timofeev and R. Kashyap, “High-power, ultra-stable, single-frequency operation of a long, doped-fiber external-cavity, grating-semiconductor laser,” Opt. Express 6, 515–520 (2003).
[Crossref]

2002 (2)

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[Crossref]

G. van Soest and A. Lajendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002).
[Crossref] [PubMed]

2001 (1)

R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001).
[Crossref]

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]

1994 (2)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[Crossref]

N. M. Lawandy, “Paint-on lasers’ light the way for new technologies,” Photon. Spectra, 119–127 (1994).

1993 (1)

1958 (1)

P. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Anderson, P.

P. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Auzel, F.

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[Crossref]

Bayram, S. B.

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[Crossref]

Bojor, L.

Brito-Silva, A. M.

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

Cao, H.

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005).
[Crossref]

H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
[Crossref]

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]

Cavalieri, S.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
[Crossref]

Chaikina, E. I.

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]

Chipouline, A.

R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001).
[Crossref]

de Araújo, C. B.

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

de Matos, C. J. S.

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

de S Menezes, L.

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

Deych, L.

O. Zaitsev, L. Deych, and V. Shuvayev, “Statistical properties of one-dimensional random lasers,” Phys. Rev. Lett. 102(4), 043906 (2009).
[Crossref] [PubMed]

Fischer, B.

Gagné, M.

Genack, A.

V. Milner and A. Genack, “Photon localization laser,” Phys. Rev. Lett. 94, 073901 (2005).
[Crossref] [PubMed]

Gomes, A. S.

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

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[Crossref]

Gottardo, S.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
[Crossref]

Gouedard, C.

Hinklin, T.

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[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]

Husson, D.

Kashyap, R.

Kostko, I. A.

Laine, R. M.

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[Crossref]

Lajendijk, A.

G. van Soest and A. Lajendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002).
[Crossref] [PubMed]

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[Crossref]

N. M. Lawandy, “Paint-on lasers’ light the way for new technologies,” Photon. Spectra, 119–127 (1994).

Leskova, T. A.

Lizárraga, N.

Maciejko, R.

Martinez Gámez, M. A.

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

Méndez, E. R.

Migus, A.

Milner, V.

V. Milner and A. Genack, “Photon localization laser,” Phys. Rev. Lett. 94, 073901 (2005).
[Crossref] [PubMed]

Polson, R. C.

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289 (2004).
[Crossref]

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003).
[Crossref]

R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001).
[Crossref]

Puente, N. P.

Raikh, M. E.

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003).
[Crossref]

Rand, S. C.

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[Crossref]

Sauteret, C.

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[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]

Shapira, O.

Shuvayev, V.

O. Zaitsev, L. Deych, and V. Shuvayev, “Statistical properties of one-dimensional random lasers,” Phys. Rev. Lett. 102(4), 043906 (2009).
[Crossref] [PubMed]

Timofeev, F. N.

F. N. Timofeev and R. Kashyap, “High-power, ultra-stable, single-frequency operation of a long, doped-fiber external-cavity, grating-semiconductor laser,” Opt. Express 6, 515–520 (2003).
[Crossref]

van Soest, G.

G. van Soest and A. Lajendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002).
[Crossref] [PubMed]

Vardeny, Z.

R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001).
[Crossref]

Vardeny, Z. V.

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289 (2004).
[Crossref]

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003).
[Crossref]

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]

Wiersma, D. S.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
[Crossref]

Williams, G. R.

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[Crossref]

Yaroshchuk, O.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
[Crossref]

Zaitsev, O.

O. Zaitsev, L. Deych, and V. Shuvayev, “Statistical properties of one-dimensional random lasers,” Phys. Rev. Lett. 102(4), 043906 (2009).
[Crossref] [PubMed]

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]

Adv. Mater. (1)

R. C. Polson, A. Chipouline, and Z. Vardeny, “Random lasing in π−conjugated films and infiltrated opals,” Adv. Mater. 13(10), 760–764 (2001).
[Crossref]

Appl. Phys. Lett. (1)

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, “Universal properties of random lasers,” IEEE J. Sel. Top. Quantum Electron. 9(1), 120–123 (2003).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. Math. Gen. (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005).
[Crossref]

Nature (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain,“Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[Crossref]

Opt. Express (4)

Photon. Spectra (1)

N. M. Lawandy, “Paint-on lasers’ light the way for new technologies,” Photon. Spectra, 119–127 (1994).

Phys. Rev. (1)

P. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Phys. Rev. A (1)

G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65(1), 013807 (2002).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

G. van Soest and A. Lajendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

V. Milner and A. Genack, “Photon localization laser,” Phys. Rev. Lett. 94, 073901 (2005).
[Crossref] [PubMed]

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

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma,“Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004).
[Crossref]

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]

O. Zaitsev, L. Deych, and V. Shuvayev, “Statistical properties of one-dimensional random lasers,” Phys. Rev. Lett. 102(4), 043906 (2009).
[Crossref] [PubMed]

Waves Random Media (1)

H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
[Crossref]

Other (1)

V. D. Freilikher, and S. A. Gredeskul, “Localization of waves in media with one-dimensional disorder,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), V. XXX, pp. 137–203.

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Figures (6)

Fig. 1
Fig. 1 Schematic of the interferometer. SL: spherical lens; PM: phase mask; EOPM: electro-optical phase modulators.
Fig. 2
Fig. 2 Reflection spectrum of a 30 cm long grating made from hydrogenated Er-doped PM fiber.
Fig. 3
Fig. 3 Transmission spectrum of a 30 cm long grating made from hydrogenated Er-doped PM fiber.
Fig. 4
Fig. 4 Laser power as a function of the pump power for a 20 cm grating with 976 and 1480 nm pump lasers.
Fig. 5
Fig. 5 Laser emission spectra of the 20 cm RFL for a 120 mW pump power at 1480 nm measured a few seconds apart.
Fig. 6
Fig. 6 Laser emission spectrum of the 30 cm RFL for a 120 mW pump power at 976 nm.

Equations (1)

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T(L)~exp(L/2ξ)

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