OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 19 — Sep. 12, 2011
  • pp: 18495–18500
« Show journal navigation

Evidence of dissipative solitons in Yb3+:CaYAlO4

W. D. Tan, D. Y. Tang, C. W. Xu, J. Zhang, X. D. Xu, D. Z. Li, and J. Xu  »View Author Affiliations


Optics Express, Vol. 19, Issue 19, pp. 18495-18500 (2011)
http://dx.doi.org/10.1364/OE.19.018495


View Full Text Article

Acrobat PDF (876 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Operation of an end-pumped Yb3+: CaYAlO4 laser operating in the positive dispersion regime is experimentally investigated. The laser emitted strongly chirped pulses with extremely steep spectral edges, resembling the characteristics of dissipative solitons observed in fiber lasers. The results show that dissipative soliton emission constitutes another operating regime for mode locked Yb3+-doped solid state lasers, which can be explored for the generation of stable large energy femtosecond pulses.

© 2011 OSA

1. Introduction

Femtosecond solid-state lasers are usually designed to operate in the negative dispersion regime in which the interplay between self-phase modulation (SPM) and negative cavity dispersion results in mode-locked pulses to be shaped into nonlinear Schrödinger equation (NLSE) type solitons [1

1. F. X. Kärtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers–­-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998). [CrossRef]

]. This type of pulse shaping stabilizes the mode-locking and reduces the pulse width to the femtosecond regime [2

2. W. De Tan, D. Y. Tang, X. D. Xu, J. Zhang, C. W. Xu, F. Xu, L. H. Zheng, L. B. Su, and J. Xu, “Passive femtosecond mode-locking and cw laser performance of Yb3+: Sc2SiO5.,” Opt. Express 18(16), 16739–16744 (2010). [CrossRef] [PubMed]

4

4. Y. Zaouter, J. Didierjean, F. Balembois, G. Lucas Leclin, F. Druon, P. Georges, J. Petit, P. Goldner, and B. Viana, “47-fs diode-pumped Yb3+:CaGdAlO4 laser,” Opt. Lett. 31(1), 119–121 (2006). [CrossRef] [PubMed]

]. However, a drawback to this type of pulse shaping exists. Limited by the soliton area theorem the achievable pulse energy is small. As the net cavity dispersion reduces, the pulse energy reduces correspondingly. Proctor et al. [5

5. B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18(19), 1654–1656 (1993). [CrossRef] [PubMed]

] first studied the operation of a Kerr-lens mode-locked Ti: Al2O3 laser in the positive group-velocity dispersion regime. In order to generate mode-locked pulses with larger energies, Cho et al. [6

6. S. H. Cho, F. X. Kärtner, U. Morgner, E. P. Ippen, J. G. Fujimoto, J. E. Cunningham, and W. H. Knox, “Generation of 90-nJ pulses with 4-MHz repetition-rate Kerr-lens mode-locked Ti: Al2O3 laser operating with net positive and negative intracavity dispersion,” Opt. Lett. 26(8), 560–562 (2001). [CrossRef] [PubMed]

] also operated a mode locked Ti: Al2O3 laser in the positive cavity dispersion and showed that chirped pulses with higher pulse energy could be obtained. Fernandez et al. [7

7. A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett. 29(12), 1366–1368 (2004). [CrossRef] [PubMed]

] demonstrated a positive dispersion Ti: Al2O3 chipped pulse oscillator (CPO) and generated stable chirped pulses with record high pulse energy of 220 nJ.

Recently, Zhao et al. [8

8. L. M. Zhao, D. Y. Tang, and J. Wu, “Gain-guided soliton in a positive group-dispersion fiber laser,” Opt. Lett. 31(12), 1788–1790 (2006). [CrossRef] [PubMed]

] and Chong et al. [9

9. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006). [CrossRef] [PubMed]

] independently demonstrated the existence of dissipative solitons (DSs) in an all-normal Er3+ and Yb3+ doped fiber laser, respectively. It was shown that soliton pulses could even be formed in net positive cavity dispersion fiber lasers where no NLSE solitons are possible. They showed that the soliton formation in positive dispersion cavity lasers is a result of the mutual nonlinear interaction among the positive cavity dispersion, SPM, gain saturation and effective gain bandwidth filtering. DSs have a number of distinctive features compared to NLSE solitons. They are strongly chirped pulses whose spectra have characteristic steep spectral edges. Moreover, DSs have significantly larger pulse energy when compared to NLSE solitons. The dynamics of DSs and their relation to the operation of passively mode-locked fiber lasers were theoretically investigated by Akhmediev et al. [10

10. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5 Pt 2), 056602 (2001). [CrossRef] [PubMed]

12

12. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372(17), 3124–3128 (2008). [CrossRef]

]. Kalashinikov and Apolonski showed that the chirped pulses obtained in CPOs are chirped solitons [13

13. V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: a unified standpoint,” Phys. Rev. A 79(4), 043829 (2009). [CrossRef]

] and in essence DSs. Nevertheless, the DS operation of solid state lasers is less experimentally studied, particularly in Yb3+-doped solid state lasers. In this paper, the authors demonstrate experimental evidence of DS operation of a diode pumped Yb3+: CaYAlO4 (Yb: CYA) laser by mode-locking in the positive dispersion regime. The results demonstrate that DS operation constitutes another operation regime of the Yb3+-doped mode-locked solid state lasers.

2. Experiment

Figure 1
Fig. 1 Schematic of the experimental setup. F1: Aspherical lens, f = 8 mm. F2: Plano-concave cylindrical lens, f = −25.4 mm. F3: Plano-convex cylindrical lens, f = 125 mm. F4: Plano-convex lens, f = 75 mm. M1, M2 and M3: Plano-concave mirrors, ROC = −100 mm, −300 mm and −100 mm, respectively. OC and SESAM: Flat Mirrors. L1 = 23.5 cm, L2 = 50 cm, L3 = 5.4 cm and L4 = 90 cm. OC: Output couplers with transmissions, T of 0.8% or 5%.
shows the schematic of the experimental setup. The Yb: CYA crystal used was grown with the Czochralski method and cut along the a-direction with dimensions of 2.5 (L) × 3 (W) × 3 (H) mm3. The crystal used has a Yb3+-doping concentration of 8 at. % and absorbed about 70% of the incident pump light. The amount of pump light can be increased by increasing the doing concentration of Yb3+. Both facets of the crystal were antireflection coated at the pump and laser wavelengths to minimize the Fresnel reflection loss. The crystal was also given a small tilt of about 5-8° with respect to the optical axis of the cavity. This was done to improve mode-locking stability and to suppress etalon effects. The crystal was wrapped in indium foil and placed in a water-cooled copper housing whose temperature was maintained at 14 °C throughout the experiment. A board stripe diode laser (Lumics GmBH) which emits at a central wavelength of (976 ± 4) nm was used as the pump source. The diode laser has an emitter size of 94 µm and its temperature was maintained at 15 °C by placing it in close contact with a water cooled heat sink. This diode is capable of delivering up to 12 W of pump power. The pump light is first collimated by an aspherical lens and magnified through a 5 × plano-concave and plano-convex cylindrical lens pair before being focused into the crystal by a plano-convex lens. The pump size in crystal is about (80 ± 10) µm (fast axis, horizontal direction) × (200 ± 10) µm (slow axis, vertical direction). ABCD analysis of the laser cavity revealed a spot size of 100 µm in diameter within the crystal and 60 µm in diameter on the semiconductor saturable absorber mirror (SESAM). The mode matching between the pump beam and laser beam is not ideal but acceptable and can be improved by changing the pump beam shaping optics. A commercial SESAM (BATOP GmBH) was used to initiate the mode-locking. The SESAM was designed to operate at 1064 nm with a modulation depth of 0.2%, a non-saturable absorption of 0.3%, a relaxation time of 500 fs and a saturation fluence of 90 μJ cm−2. A SESAM with low non-saturable absorption losses was selected to ensure lager output powers. The mode locked pulse train was monitored with a low noise photodetector (New Focus 1611-FC-AC) by coupling light leaking out of M3 and displayed on a 1 GHz digital oscilloscope (Tektronix DP0714). The optical spectrum was measured with a high-resolution optical spectrum analyzer (Ando, AQ-6315B), while the pulse width was measured using a commercial autocorrelator (APE, PulseCheck).

3. Experimental results

Mode-locking of the laser was investigated using output couplers (OCs) with transmission (T) of 0.8% and 5% in the setup shown in Fig. 1. It was observed that in both cases the laser initially emitted CW light. When the pump power was further increased, the laser emission switched from Q-switched mode-locking (QML) and finally into CW mode-locking as depicted in Fig. 2
Fig. 2 Output vs. absorbed power relations. Closed circles: T = 0.8%. Closed squares: T = 5%. The red, green and yellow lines represent the CW, Q-switched mode-locking, and CW mode-locking, respectively.
. Once CW mode-locking has been achieved, the laser can maintain this state of operation for hours unless its operation is disturbed. With T = 0.8% the maximum output power achieved was 0.29 W and the mode-locked slope efficiency, ηSlope, was 10%. With T = 5%, the maximum output power achieved was 1.5 W while ηSlope = 33%. Considering the fact that the cavity repetition rate was 89 MHz, the corresponding pulse energy was 3.3 nJ and 17 nJ for T = 0.8% and T = 5%, respectively. The mode-locked pulse train has a pulse to pulse separation of about 11 ns, which corresponded to the cavity repetition rate and as such demonstrates that fundamental mode-locking has been achieved. No multiple pulses were detected even under the maximum output power. The authors believe that larger output powers should be possible if the mode-matching between the pump and laser beam is improved.

Figures 4
Fig. 4 Autocorrelation traces when T = 0.8%. a) Uncompressed trace and b) compressed trace. Closed circles are experimental data while the solid blue line is a sech2 fit.
and 5
Fig. 5 Autocorrelation traces when T = 5%. a) Uncompressed trace and b) compressed trace. Closed circles are experimental data while the solid blue line is a sech2 fit.
[parts (a)] further show the autocorrelation traces measured at the maximum output powers. Assuming that the pulses have a sech2 profile, the emitted pulse widths were 7.4 ps and 8.5 ps, respectively. The time-bandwidth-products (TBPs) were 26 and 19, which were 80 and 60 times of the Fourier transform-limited value. It means that the pulses are strongly chirped. Strongly chirped pulses that are tens of times above the transform-limit is another distinctive characteristics of DSs which further shows that the existence of DSs in Yb: CYA. Using a pair of reflection gratings (Spectrogon, 1200 lines per mm) separated by 7 cm, the pulses were extra cavity compressed. The narrowest pulses obtained were 340 fs and 380 fs, respectively, as shown in Figs. 4b and 5b. Weak pedestals are clearly observable on the bases of the compressed autocorrelation traces, which indicate the presence of non-linear chirp. No transform-limited pulses could be obtained [5

5. B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18(19), 1654–1656 (1993). [CrossRef] [PubMed]

]. The authors believe that to obtain the transform-limited pulses from the Yb: CYA laser a non-linear pulse compression method would be needed, e. g. via a piece of optical fiber [15

15. J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Femtosecond passively mode-locked Ti:Al(2)O(3) laser with a nonlinear external cavity,” Opt. Lett. 14(20), 1125–1127 (1989). [CrossRef] [PubMed]

].

The mode locked pulses of the laser exhibit the typical features of the DSs observed in fiber lasers [8

8. L. M. Zhao, D. Y. Tang, and J. Wu, “Gain-guided soliton in a positive group-dispersion fiber laser,” Opt. Lett. 31(12), 1788–1790 (2006). [CrossRef] [PubMed]

,9

9. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006). [CrossRef] [PubMed]

,14

14. A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25(2), 140 (2008). [CrossRef]

], which suggests that DS mode locking should also be an accessible operation regime for Yb3+ mode locked solid state lasers. One of the requirements for DS operation is the existence of large nonlinear phase shift accumulation of the pulse in the cavity. For lasers with large Kerr nonlinearity gain this could be relatively easily achieved. In addition, one could also insert a piece of large Kerr nonlinearity material in cavity to achieve the same result. Another requirement is the spectral filtering, which causes a kind of pulse intensity dependent loss in the Yb: CYA laser. In our laser the effective gain bandwidth filtering plays the role. The advantage of operating a laser in the positive dispersion regime to generate DSs is that the pulses are chirped everywhere within the cavity and as such the threshold intensity required for pulse breakup and distortion is not reached. Hence operating a laser in the DS regime allows the generation of femtosecond lasers with higher output powers than that normally achievable with solitary lasers. Furthermore, DS mode-locked lasers would be an ideal seed pulse source for large energy pulse amplification which can be compressible to generate high energy femtosecond pulses. Moreover the requirement for additional optics to generate femtosecond pulses is also lifted. Recognizing the DS operation of a laser could help to better design a laser, for example, by exploiting the DS resonance [16

16. W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative solitons resonances,” Phys. Rev. A 78(2), 023830 (2008). [CrossRef]

], the energy of achievable mode locked pulses could be significantly increased. Wu et. al. [17

17. X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009). [CrossRef] [PubMed]

] have demonstrated DS resonance in an Er3+ doped fiber laser in which single pulse energy as large as 280 nJ was obtained. However such a regime may be difficult to access in a solid state laser.

4. Conclusion

In conclusion, the authors have shown experimental evidence of DS operation of a diode pumped Yb: CYA laser. Theses experimental results demonstrate that apart from the conventional soliton mode-locking, a Yb3+ doped solid-state laser can also operate in positive dispersion regime as DSs, where they are strongly chirped and have characteristic steep spectral edges. An advantage of DS operation of a laser is that apart from having the same stability as the conventional soliton mode-locking, much larger pulse energies can be directly achieved. The authors believe that the DS mode-locking could be another useful operation regime for Yb3+ mode-locked solid state lasers, which deserves to be explored.

Acknowledgments

The authors acknowledge support from the National Research Foundation of Singapore under contract NRF-G-CRP-2007-01, and the National Natural Science Foundation of China (NSFC) under projects no. 60938001, 60908030 and 61078054. D. Y. Tang acknowledges support from the AOARD under the contract no. FA2386-11-4010.

References and links

1.

F. X. Kärtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers–­-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998). [CrossRef]

2.

W. De Tan, D. Y. Tang, X. D. Xu, J. Zhang, C. W. Xu, F. Xu, L. H. Zheng, L. B. Su, and J. Xu, “Passive femtosecond mode-locking and cw laser performance of Yb3+: Sc2SiO5.,” Opt. Express 18(16), 16739–16744 (2010). [CrossRef] [PubMed]

3.

W. D. Tan, D. Y. Tang, X. D. Xu, D. Z. Li, J. Zhang, C. W. Xu, and J. Xu, “Femtosecond and continuous-wave laser performance of a diode-pumped Yb3+:CaYAlO4 laser,” Opt. Lett. 36(2), 259–261 (2011). [CrossRef] [PubMed]

4.

Y. Zaouter, J. Didierjean, F. Balembois, G. Lucas Leclin, F. Druon, P. Georges, J. Petit, P. Goldner, and B. Viana, “47-fs diode-pumped Yb3+:CaGdAlO4 laser,” Opt. Lett. 31(1), 119–121 (2006). [CrossRef] [PubMed]

5.

B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18(19), 1654–1656 (1993). [CrossRef] [PubMed]

6.

S. H. Cho, F. X. Kärtner, U. Morgner, E. P. Ippen, J. G. Fujimoto, J. E. Cunningham, and W. H. Knox, “Generation of 90-nJ pulses with 4-MHz repetition-rate Kerr-lens mode-locked Ti: Al2O3 laser operating with net positive and negative intracavity dispersion,” Opt. Lett. 26(8), 560–562 (2001). [CrossRef] [PubMed]

7.

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett. 29(12), 1366–1368 (2004). [CrossRef] [PubMed]

8.

L. M. Zhao, D. Y. Tang, and J. Wu, “Gain-guided soliton in a positive group-dispersion fiber laser,” Opt. Lett. 31(12), 1788–1790 (2006). [CrossRef] [PubMed]

9.

A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006). [CrossRef] [PubMed]

10.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5 Pt 2), 056602 (2001). [CrossRef] [PubMed]

11.

J. M. Soto-Crespo, N. Akhmediev, and G. Town, “Interrelation between various branches of stable solitons in dissipative systems––conjecture for stability criterion,” Opt. Commun. 199(1-4), 283–293 (2001). [CrossRef]

12.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372(17), 3124–3128 (2008). [CrossRef]

13.

V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: a unified standpoint,” Phys. Rev. A 79(4), 043829 (2009). [CrossRef]

14.

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25(2), 140 (2008). [CrossRef]

15.

J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Femtosecond passively mode-locked Ti:Al(2)O(3) laser with a nonlinear external cavity,” Opt. Lett. 14(20), 1125–1127 (1989). [CrossRef] [PubMed]

16.

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative solitons resonances,” Phys. Rev. A 78(2), 023830 (2008). [CrossRef]

17.

X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009). [CrossRef] [PubMed]

OCIS Codes
(140.3580) Lasers and laser optics : Lasers, solid-state
(140.4050) Lasers and laser optics : Mode-locked lasers
(140.5680) Lasers and laser optics : Rare earth and transition metal solid-state lasers
(140.7090) Lasers and laser optics : Ultrafast lasers
(160.5690) Materials : Rare-earth-doped materials

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: August 8, 2011
Revised Manuscript: August 19, 2011
Manuscript Accepted: August 25, 2011
Published: September 6, 2011

Citation
W. D. Tan, D. Y. Tang, C. W. Xu, J. Zhang, X. D. Xu, D. Z. Li, and J. Xu, "Evidence of dissipative solitons in Yb3+:CaYAlO4," Opt. Express 19, 18495-18500 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18495


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. X. Kärtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers–­-what’s the difference?” IEEE J. Sel. Top. Quantum Electron.4(2), 159–168 (1998). [CrossRef]
  2. W. De Tan, D. Y. Tang, X. D. Xu, J. Zhang, C. W. Xu, F. Xu, L. H. Zheng, L. B. Su, and J. Xu, “Passive femtosecond mode-locking and cw laser performance of Yb3+: Sc2SiO5.,” Opt. Express18(16), 16739–16744 (2010). [CrossRef] [PubMed]
  3. W. D. Tan, D. Y. Tang, X. D. Xu, D. Z. Li, J. Zhang, C. W. Xu, and J. Xu, “Femtosecond and continuous-wave laser performance of a diode-pumped Yb3+:CaYAlO4 laser,” Opt. Lett.36(2), 259–261 (2011). [CrossRef] [PubMed]
  4. Y. Zaouter, J. Didierjean, F. Balembois, G. Lucas Leclin, F. Druon, P. Georges, J. Petit, P. Goldner, and B. Viana, “47-fs diode-pumped Yb3+:CaGdAlO4 laser,” Opt. Lett.31(1), 119–121 (2006). [CrossRef] [PubMed]
  5. B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett.18(19), 1654–1656 (1993). [CrossRef] [PubMed]
  6. S. H. Cho, F. X. Kärtner, U. Morgner, E. P. Ippen, J. G. Fujimoto, J. E. Cunningham, and W. H. Knox, “Generation of 90-nJ pulses with 4-MHz repetition-rate Kerr-lens mode-locked Ti: Al2O3 laser operating with net positive and negative intracavity dispersion,” Opt. Lett.26(8), 560–562 (2001). [CrossRef] [PubMed]
  7. A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett.29(12), 1366–1368 (2004). [CrossRef] [PubMed]
  8. L. M. Zhao, D. Y. Tang, and J. Wu, “Gain-guided soliton in a positive group-dispersion fiber laser,” Opt. Lett.31(12), 1788–1790 (2006). [CrossRef] [PubMed]
  9. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express14(21), 10095–10100 (2006). [CrossRef] [PubMed]
  10. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg–Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(5 Pt 2), 056602 (2001). [CrossRef] [PubMed]
  11. J. M. Soto-Crespo, N. Akhmediev, and G. Town, “Interrelation between various branches of stable solitons in dissipative systems––conjecture for stability criterion,” Opt. Commun.199(1-4), 283–293 (2001). [CrossRef]
  12. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A372(17), 3124–3128 (2008). [CrossRef]
  13. V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: a unified standpoint,” Phys. Rev. A79(4), 043829 (2009). [CrossRef]
  14. A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B25(2), 140 (2008). [CrossRef]
  15. J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Femtosecond passively mode-locked Ti:Al(2)O(3) laser with a nonlinear external cavity,” Opt. Lett.14(20), 1125–1127 (1989). [CrossRef] [PubMed]
  16. W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative solitons resonances,” Phys. Rev. A78(2), 023830 (2008). [CrossRef]
  17. X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express17(7), 5580–5584 (2009). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited