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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 3525–3530
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Dual-wavelength domain wall solitons in a fiber ring laser

Han Zhang, Dingyuan Tang, Luming Zhao, and Xuan Wu  »View Author Affiliations


Optics Express, Vol. 19, Issue 4, pp. 3525-3530 (2011)
http://dx.doi.org/10.1364/OE.19.003525


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Abstract

We report on the first experimental observation of dual wavelength domain wall type of dark solitons in a fiber laser made of all normal group velocity dispersion fibers. It was shown that this solitary wave is formed due to the cross coupling between two different wavelength laser beams and consists of localized dip structures separating the two different wavelength laser emissions.

© 2011 OSA

1. Introduction

Soliton formation in single mode fibers (SMFs) is a well-known effect and has been extensively investigated. It is now well recognized that the dynamics of the formed solitons is governed by the nonlinear Schrödinger equation (NLSE), and bright solitons are formed in the anomalous group velocity dispersion (GVD) fibers, while dark solitons are formed in the normal GVD fibers [1

1. P. Emplit, J. P. Hamaide, F. Reynaud, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987). [CrossRef]

3

3. Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18(5), 337–339 (1993). [CrossRef] [PubMed]

]. A fiber laser is mainly made of SMFs. It is natural to anticipate that under appropriate conditions solitary waves could be formed in the single mode fiber lasers. Indeed, both the bright and dark NLSE solitons have been experimentally observed in fiber lasers [4

4. I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991). [CrossRef] [PubMed]

,5

5. T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002). [CrossRef]

]. Recently, we also observed a train of dark soliton pulses in an all-normal dispersion fiber laser [6

6. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

]. Different from reference [5

5. T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002). [CrossRef]

] that reported the first demonstration of high repetition rate (10 GHz) dark soliton pulses, reference [6

6. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

] investigated a low repetition rate dark soliton pulse train which could be visualized by a commercial oscilloscope other than an auto-correlator.

In addition to the NLSE solitons, recently a new type of optical solitary waves known as the polarization domain wall solitons (PDWSs) was also experimentally revealed in fiber lasers [7

7. H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010). [CrossRef] [PubMed]

]. Formation of PDWSs was first theoretically predicted by Haelterman and Sheppard [8

8. M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19(2), 96–98 (1994). [CrossRef] [PubMed]

]. It was shown that the cross coupling between the two orthogonal polarization components of light propagating in a dispersive Kerr medium could lead to the formation of a stable localized structure that separates domains of the two orthogonal polarization fields. Cross coupling between waves is a common phenomenon in a wide range of nonlinear physical systems. The experimental confirmation of PDWSs suggests that similar domain wall solitons could also be observed in other nonlinear wave coupling systems [9

9. B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994). [CrossRef] [PubMed]

,10

10. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998). [CrossRef]

]. Later, Haelterman and Badolo further found that the mutual interaction of two different wavelength optical waves (but the same polarization) could also lead to formation of domain wall solitons, known as dual-wavelength DWSs [11

11. M. Haelterman and M. Badolo, “Dual-frequency wall solitary waves for nonreturn-to-zero signal transmission in W-type single-mode fibers,” Opt. Lett. 20(22), 2285–2287 (1995). [CrossRef] [PubMed]

]. In this paper, to the best of our knowledge, we report on the first experimental evidence of a dual-wavelength optical DWS in a fiber ring laser made of all-normal GVD fibers. We show both experimentally and numerically that strong coupling between two different wavelength beams in the fiber laser can result in the formation of DWSs, representing as a stable dark intensity pulse separating the two different wavelength laser emissions.

2. Experimental setup

We used a fiber laser with similar configuration as shown in Fig. 1
Fig. 1 Schematics of the fiber laser. WDM: wavelength division multiplexer. EDF: erbium doped fiber. PDI: polarization dependent isolator. PCs: polarization controllers.
. Briefly, the cavity is made of ~5.0 m Erbium-doped fiber (EDF) with a GVD parameter of –32 (ps/nm)/km, ~6.1 m dispersion shifted fiber (DSF) with a GVD parameter of –2 (ps/nm)/km. A polarization sensitive isolator was employed in the cavity to force the unidirectional operation of the ring cavity, and an in-line polarization controller (PC) was used to fine-tune the linear cavity birefringence. The laser was pumped by a high power Fiber Raman Laser source of wavelength 1480 nm. A 10% fiber coupler was used to output the signal, and the laser output was monitored with a 2 GHz photo-detector and displayed on a multi-channeled oscilloscope.

3. Experimental results

A major difference of the current laser to that of [6

6. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

] is that in setting up the laser we have intentionally imposed large birefringence into the cavity. Consequently, the birefringence induced multi-pass filter effect becomes very strong and can no longer be ignored for the laser. Under the combined action of the laser gain and the birefringent filter, the laser is forced to operate in a dual wavelength CW emission mode. Figure 2(a)
Fig. 2 (a) Spectrum; (b) a magnified figure of the dual-wavelength DWS emission of the laser ; (c) full oscilloscope trace of dual wavelength DWS;(d) FWHM duration and total output power versus pump power.
shows a typical spectrum of the laser under dual-wavelength emission. Figure 2(b) and Fig. 2(c) show a typical case of the dark pulse emission of the laser. The dark pulse repeated with the cavity roundtrip time. Depending on the laser operation conditions multiple dark pulses could be formed in the cavity. Figure 2(d) shows the measured total output power versus the input pump power of the laser operation. The laser had a threshold pump power of about 90 mW and the laser emission increased almost linearly with the pump power. Under relatively low pumping the laser emission displayed a constant intensity on the oscilloscope trace. However, as the pump power increased to about 260 mW, it was observed that a dark intensity pulse appeared on the laser output. The stronger the pump power, the narrower became the dark pulse, as depicted in Fig. 2(d).

Under even stronger pumping (~450 mW), a new type of dark pulses could also suddenly appear [6

6. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

]. These new dark pulses moved with respect to the DWS. Limited by the resolution of our detection system we cannot measure the actual pulse width of the new dark pulses [13

13. S. Coen and T. Sylvestre, “Comment on ‘Dark pulse emission of a fiber laser’,” Phys. Rev. A 82(4), 047801 (2010). [CrossRef]

], but in contrast with the domain wall type dark pulses, they have different darkness and appeared randomly in the cavity. We had studied previously the NLSE dark solitons in a fiber laser [6

6. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

]. The observed features of the new dark pulses suggest that they could be the NLSE dark solitons. In our experiment we could control the strength of the laser emission of either wavelength through shifting the filter frequencies. In this way we can suppress the appearance of the NLSE dark solitons on either of the two wavelength laser emissions. Figure 4
Fig. 4 (a) Spectra and (b) oscilloscope traces of the laser emission with the NLSE dark solitons appeared on emission at one of the wavelengths, measured under higher pump power ~450 mW. The upper (lower) trace corresponds to the spectrum whose longer (shorter) wavelength line is broadened.
shows a comparison on the laser emissions where one of the two-wavelength laser emissions is beyond the NLSE soliton threshold. Figure 4(a) shows the laser emission spectra. The upper (lower) oscilloscope trace shown in Fig. 4(b) corresponds to the spectrum whose longer (shorter) wavelength spectral line has become broadened. Associated with the appearance of the NLSE dark solitons the corresponding laser emission spectrum became further broadened.

4. Numerical simulation

To better understand the dual-wavelength DWS formation in our laser, we have further numerically simulated the operation of our laser under two wavelength emissions. The following coupled Ginzburg-Landau equations were used to describe the light propagation in the fibers [14

14. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). [CrossRef] [PubMed]

]:
u1z=iβu1ik22u1t2+k63u1t3+iγ(|u1|2+2|u2|2)u+g2u1+g2Ωg22u1t2u2z=iβu2ik''22u2t2+k'''63u2t3+iγ(|u2|2+2|u1|2)u2+g2u2+g2Ωg22u2t2
(1)
where u1 and u2 are the normalized envelopes of the optical pulses along the same polarization in the optical fiber but having different central wavelengths λ1 and λ2. β = 2πΔn/(λ1 + λ2) is the wave-number difference between the two optical waves. Δn=n1n27.16*109 is the refractive index difference between these two waves. k″ is the second order dispersion coefficient, k′′′ is the third order dispersion coefficient and γ represents the nonlinearity of the fiber. g is the saturable gain coefficient of the fiber and Ωg is the bandwidth of the laser gain. For undoped fibers g = 0; for erbium doped fiber, we considered its gain saturation as
g=Gexp[(|u1|2+|u2|2)dtPsat]
(2)
Where G is the small signal gain and Psat is the gain saturation energy. Obviously, gain competition between the waves exists. Moreover, we considered the cavity feedback effect by circulating the light in the cavity [14

14. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). [CrossRef] [PubMed]

]. We have assumed that the two wavelength beams have the same group velocity and used the following parameters: γ = 3 W–1km–1, Ωg = 16 nm, k″DSF = 2.6 ps2/km, k″EDF = 41.6 ps2/km, k′′′ = –0.13 ps3/km, Psat = 500 pJ, cavity length L = 11.1 m, and G = 120 km–1.

A weak dual-wavelength beam with ~2.6 nm wavelength separation and an intensity switching between the two wavelengths was used as the initial condition. We let the light circulate in the cavity until a stable state is obtained. The CGLEs were solved using the split-step method. We found numerically that a stable DWS separating the laser emissions of different wavelengths could indeed be formed in our laser, as shown in Fig. 5
Fig. 5 Dual-wavelength DWS numerically calculated. (a) Domain wall profiles and DWS at a particular roundtrip (b) The corresponding spectrum. Evolution of the dual wavelength domain wall with the cavity roundtrips: (c) one wavelength (shorter wavelength) (d) Another wavelength (longer wavelength).
. Figure 5(a) shows the domain walls and the corresponding dark DWS calculated. Figure 5(b) shows the optical spectrum of the laser emission. Stable evolution of dual wavelength domain wall could also be identified in Fig. 5(c) and Fig. 5(d).

We have also numerically simulated dual-wavelength DWS formation under various laser parameters. Independent of the concrete laser cavity parameters DWSs could always be obtained. We note that third order dispersion (TOD) impacts dark solitons in the near zero dispersion regime and it could even induce continuum generation by dark solitons [15

15. C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34(14), 2096–2098 (2009). [CrossRef] [PubMed]

]. To study the TOD effect, we also deliberately varied the TOD parameter in our simulations and found that the DWS could become temporally asymmetric and even unstable if the TOD was too large. However, since the total cavity dispersion of our laser is far away from the zero dispersion, it only plays a minor role in our experiment. Based on our numerical simulations, we noticed that for the formation of the DWS an initial intensity alternation between the two wavelengths is crucial. Antiphase dynamics between two different wavelength laser emissions was previously experimentally observed in an erbium-doped fiber laser [12

12. P. L. Boudec, C. Jaouen, P. L. François, J.-F. Bayon, F. Sanchez, P. Besnard, and G. Stéphan, “Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers,” Opt. Lett. 18(22), 1890–1892 (1993). [CrossRef] [PubMed]

]. The numerical result suggests that the gain competition caused antiphase dynamics could also have played a role on the formation of the DWSs in our laser.

5. Conclusion

In conclusion, we have experimentally observed a new type of dark soliton in an erbium-doped fiber laser made of all-normal GVD fibers. It is shown that the formation of the dark soliton is a result of the mutual nonlinear coupling between two different wavelength laser beams and the formed soliton has the characteristic of separating the two different wavelength laser emissions. The features of the soliton suggest that it is a dual wavelength domain wall soliton.

Acknowledgement

This project is supported by the National Research Foundation Singapore under the contract NRF-G-CRP 2007-01. Authors wish to acknowledge the Institute for Infocomm Research (I2R), Singapore for providing the L-band tunable filter. Han Zhang is indebted to Professor Marc Haelterman and Pascal Kockaert for useful discussions and acknowledges support by the Belgian Science Policy Office (BELSPO) Interuniversity Attraction Pole (IAP) programme under grant no. IAP-6/10.

References and links

1.

P. Emplit, J. P. Hamaide, F. Reynaud, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987). [CrossRef]

2.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988). [CrossRef] [PubMed]

3.

Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18(5), 337–339 (1993). [CrossRef] [PubMed]

4.

I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991). [CrossRef] [PubMed]

5.

T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002). [CrossRef]

6.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

7.

H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010). [CrossRef] [PubMed]

8.

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19(2), 96–98 (1994). [CrossRef] [PubMed]

9.

B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994). [CrossRef] [PubMed]

10.

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998). [CrossRef]

11.

M. Haelterman and M. Badolo, “Dual-frequency wall solitary waves for nonreturn-to-zero signal transmission in W-type single-mode fibers,” Opt. Lett. 20(22), 2285–2287 (1995). [CrossRef] [PubMed]

12.

P. L. Boudec, C. Jaouen, P. L. François, J.-F. Bayon, F. Sanchez, P. Besnard, and G. Stéphan, “Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers,” Opt. Lett. 18(22), 1890–1892 (1993). [CrossRef] [PubMed]

13.

S. Coen and T. Sylvestre, “Comment on ‘Dark pulse emission of a fiber laser’,” Phys. Rev. A 82(4), 047801 (2010). [CrossRef]

14.

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). [CrossRef] [PubMed]

15.

C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34(14), 2096–2098 (2009). [CrossRef] [PubMed]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.3510) Lasers and laser optics : Lasers, fiber

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 13, 2010
Revised Manuscript: January 27, 2011
Manuscript Accepted: January 27, 2011
Published: February 8, 2011

Citation
Han Zhang, Dingyuan Tang, Luming Zhao, and Xuan Wu, "Dual-wavelength domain wall solitons in a fiber ring laser," Opt. Express 19, 3525-3530 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3525


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References

  1. P. Emplit, J. P. Hamaide, F. Reynaud, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987). [CrossRef]
  2. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988). [CrossRef] [PubMed]
  3. Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18(5), 337–339 (1993). [CrossRef] [PubMed]
  4. I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991). [CrossRef] [PubMed]
  5. T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002). [CrossRef]
  6. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]
  7. H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010). [CrossRef] [PubMed]
  8. M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19(2), 96–98 (1994). [CrossRef] [PubMed]
  9. B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994). [CrossRef] [PubMed]
  10. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998). [CrossRef]
  11. M. Haelterman and M. Badolo, “Dual-frequency wall solitary waves for nonreturn-to-zero signal transmission in W-type single-mode fibers,” Opt. Lett. 20(22), 2285–2287 (1995). [CrossRef] [PubMed]
  12. P. L. Boudec, C. Jaouen, P. L. François, J.-F. Bayon, F. Sanchez, P. Besnard, and G. Stéphan, “Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers,” Opt. Lett. 18(22), 1890–1892 (1993). [CrossRef] [PubMed]
  13. S. Coen and T. Sylvestre, “Comment on ‘Dark pulse emission of a fiber laser’,” Phys. Rev. A 82(4), 047801 (2010). [CrossRef]
  14. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). [CrossRef] [PubMed]
  15. C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34(14), 2096–2098 (2009). [CrossRef] [PubMed]

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