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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 5874–5887
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Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion

Xueming Liu  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 5874-5887 (2011)
http://dx.doi.org/10.1364/OE.19.005874


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Abstract

The coexistence of weakly sech-shaped solitons and strongly dissipative solitons is experimentally observed in an ultra-large net-anomalous-dispersion mode-locked fiber laser for the first time to author’s best knowledge. Both sech-shaped and dissipative solitons appear to be the asymmetrically combined pulse state with one pulse component much smaller than the other. The energy of dissipative solitons is over three orders of magnitude larger than that of sech-shaped solitons. Two different types of pulse-shaping mechanisms coexist in the laser: one is the dissipative processes and the other is the balance between anomalous dispersion and nonlinear Kerr effect. Numerical simulations and analysis confirm the experimental observations.

© 2011 OSA

1. Introduction

Solitons as a kind of stable self-localized waves occur in various physical systems and are one of the most fascinating nonlinear phenomena [1

1. H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, and K. Loh, “Vector dissipative solitons in graphene mode locked fiber lasers,” Opt. Commun. 283(17), 3334–3338 (2010). [CrossRef]

6

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

]. Soliton formation and dynamics in optical fibers result from a balanced interaction between the anomalous dispersion of fibers and the nonlinear Kerr effect [7

7. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

]. However, solitons formed in passively mode-locked (PML) fiber lasers subject to the interplay of the laser cavity dispersion and nonlinearity and gain and losses [8

8. K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992). [CrossRef]

11

11. A. Cabasse, G. Martel, and J. L. Oudar, “High power dissipative soliton in an Erbium-doped fiber laser mode-locked with a high modulation depth saturable absorber mirror,” Opt. Express 17(12), 9537–9542 (2009). [CrossRef] [PubMed]

]. When a PML fiber laser is made of fibers with purely anomalous dispersion, the fiber dispersion balances the fiber nonlinearity to produce conventional soliton-like pulses that are well described by the nonlinear Schrödinger equation (NLSE) and have the hyperbolic-secant profile. In this case, the spectral bandwidth of solitons is much narrower than the laser gain bandwidth [9

9. D. Y. Tang, L. M. Zhao, G. Q. Xie, and L. J. Qian, “Coexistence and competition between different solitons-shaping mechanisms in a laser,” Phys. Rev. A 75(6), 063810 (2007). [CrossRef]

], and the cavity pulse peak clamping effect limits soliton to less than 0.1 nJ of the pulse energy in standard fibers [10

10. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]

,12

12. L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]

].

To increase the pulse energy, most modern ultra-short pulse cavities have the dispersion management in which a fiber laser can operate either in the positive or negative cavity dispersion regime. When the net dispersion of the laser cavity is anomalous enough, approaches zero, and is normal enough, sech-shaped solitons [12

12. L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]

], dispersion-managed solitons (i.e., stretched pulses) [13

13. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080 (1993). [CrossRef] [PubMed]

], and self-similar parabolic pulses [14

14. V. I. Kruglov, D. Méchin, and J. D. Harvey, “All-fiber ring Raman laser generating parabolic pulses,” Phys. Rev. A 81(2), 023815 (2010). [CrossRef]

] can be formed, respectively. When the laser cavity contains components without anomalous dispersion or with small anomalous dispersion together with large normal dispersion, dissipative solitons (DSs) and DS molecules can be generated [15

15. J. H. Im, S. Y. Choi, F. Rotermund, and D. I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef] [PubMed]

18

18. X. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A 82(6), 063834 (2010). [CrossRef]

]. Pulse evolutions in the aforementioned lasers are qualitatively distinct from each other and they are controlled by the distinctive types of soliton-shaping mechanisms. The influence of the laser gain on the conservative sech-shaped solitons is very weak, whereas the gain and loss play an essential role in the formation of DSs [19

19. B. Oktem, C. Ulgudur, and F. O. Ilday, “Soliton-similariton fibre laser,” Nat. Photonics 4(5), 307–311 (2010). [CrossRef]

,20

20. F. W. Wise, A. Chong, and W. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2(1-2), 58–73 (2008). [CrossRef]

].

Recently, the theoretical predictions and experimental observations show that with a appropriate cavity configuration a laser is expected to produce two distinctive types of pulses at the same cavity. When the net cavity dispersion βnet approaches zero, dispersion-managed solitons and sech-shaped solitons coexist in the same laser [9

9. D. Y. Tang, L. M. Zhao, G. Q. Xie, and L. J. Qian, “Coexistence and competition between different solitons-shaping mechanisms in a laser,” Phys. Rev. A 75(6), 063810 (2007). [CrossRef]

]. With the moderate normal βnet, both stretched-pulse and self-similar operation can be observed in a laser [20

20. F. W. Wise, A. Chong, and W. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2(1-2), 58–73 (2008). [CrossRef]

]. When βnet is normal enough, the fiber laser either works on a status that is similar to an all-normal-dispersion laser or generates a type of pulses exhibited as the trapezoid-spectrum profile according to the pump power [21

21. X. Liu, “Dissipative soliton evolution in ultra-large normal-cavity-dispersion fiber lasers,” Opt. Express 17(12), 9549–9557 (2009). [CrossRef] [PubMed]

]. The numerical simulations show that the high-energy DSs can even be generated by lasers operating in the anomalous dispersion regime [22

22. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009). [CrossRef]

25

25. S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17(14), 11776–11781 (2009). [CrossRef] [PubMed]

].

In this work, we experimentally observe that weakly sech-shaped solitons and strongly DSs coexist in ultra-large net-anomalous-dispersion PML lasers. Two different types of solitons attribute to two completely different soliton formation mechanisms and are governed by different theoretical modeling. The theoretical simulation and analysis successfully explain our experimental observations. Our investigation provides a better understanding of the pulse shaping in PML fiber lasers and a way to achieve high-energy nanosecond pulses.

2. Experimental setup and observations

2.1. Experimental setup

The proposed fiber laser is shown schematically in Fig. 1
Fig. 1 Schematic diagram of the proposed laser cavity. EDF, erbium-doped fiber; SMF, single-mode fiber; WDM, wavelength-division multiplexed; PC, polarization controller; PS-ISO, polarization-sensitive isolator; PAPM, polarization additive pulse mode-locking; LD, laser diode; PBS, polarization beam splitter.
. The laser cavity is a 720-m-long loop consisting of a polarization-sensitive isolator (PS-ISO), two sets of polarization controllers (PCs), a segment of standard single-mode fiber (SMF), a wavelength-division-multiplexed (WDM) coupler, a piece of erbium-doped fiber (EDF), and a fused coupler (10% output). EDF has a length of about 10 m with absorption of 6 dB/m at 980 nm, dispersion of about −42 ps/nm/km, and nonlinear coefficient of 4.5 /W/km at 1550 nm. The standard SMF has a length of about 700 m with dispersion of 17 ps/nm/km and nonlinear coefficient of 1.3 /W/km at 1550 nm. The total length of fiber pigtail of components is about 10 m. The polarization-sensitive isolator provides unidirectional operation and polarization selectivity in a ring-cavity configuration, and forms a polarization additive pulse mode-locking (PAPM) element by combining with two polarization controllers. The polarization state of lightwaves in the cavity can be controlled by adjusting two polarization controllers. The nonlinear polarization rotation technique is used for locking the laser. A 977-nm laser diode (LD) supplies the pump power of up to 500 mW. A polarization beam splitter (PBS) is used to separate the two orthogonal polarizations of the laser emission. An autocorrelator, an optical spectrum analyzer (OSA), and a 70-GHz oscilloscope (Tektronix TDS8200) together with a 50-GHz photodetector are used to simultaneously monitor the laser output.

The laser has the fundamental cavity frequency of about 278 kHz, corresponding to the round-trip time of about 3.6 μs. The laser cavity has the dispersion management with total anomalous and normal dispersion of about −15.4 ps2 and 0.5 ps2, respectively. The proposed laser system has extremely large net-anomalous dispersion so that it may exploit two soliton-shaping mechanisms. One is the balance between the anomalous dispersion and the nonlinear Kerr effect and thus the conventional soliton-like pulses are generated. The other is the balance between gain and loss processes that induce the DS pulses.

2.2. Weakly sech-shaped soliton pulses

Figure 3
Fig. 3 Output optical spectra of u and v components of pulses at the pump power P = 18 mW. The ratio RP of peak power of u and v components is about 11.5. The y-axis is the linear scale, instead of the logarithmic scale in Fig. 2(b). The u and v components are indicated by the arrows.
shows the experimental observations for the optical spectra of u and v components of pulses at the pump power P = 18 mW. Note that the y-axis of Fig. 3 is the linear scale, instead of the logarithmic scale in Fig. 2(b). It is found from Fig. 3 that the ratio RP of peak power of u and v components of pulses is about 11.5. According to the theory [27

27. X. M. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82(5), 053808 (2010). [CrossRef]

], the ratio of pulse energy of u and v components also is 11.5.

The experimental observations show that the laser only produces conventional solitons with sech-shaped profile when the pump power is from about 15 mW to about 25 mW. In this operation regime, the soliton number in the cavity increases with the increase of pump power, whereas the peak and duration of solitons change slightly. The intracavity energy of each soliton is about 0.04 nJ. By comparing to the traditional fiber soliton laser [12

12. L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]

], the proposed laser generates solitons with narrower spectral width Δλ and wider pulse duration Δτ, e.g., Δλ≈1 nm and Δτ≈2.9 ps here instead of Δλ≈9 nm and Δτ≈0.45 ps in Ref [12

12. L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]

].

2.3. Coexistence of two types of weak and strong pulses

When the pump power P is beyond about 28 mW, a strange phenomenon occurs, i.e., the laser stably emits a type of pulses without spectral sidebands and with an order-of-magnitude increase in the pulse height. An experimental example for P = 29 mW is shown in Fig. 4
Fig. 4 Results of experimental observations at the pump power P = 29 mW. Oscilloscope traces (a) from 0 to 100 μs, (b) from 0 to 2.5 μs, and (c) from 3.2 to 3.4 μs. (d) Output optical spectrum. The u and v components are indicated in (d) by the arrows and the ratio RP of peak power of u and v components is about 11.1.
. Figure 4(a) is the oscilloscope trace at the range from 0 to 100 μs, and Figs. 4(b) and 4(c) are the local view of Fig. 4(a) from 0 to 2.5 μs and from 3.2 to 3.4 μs, respectively. Figure 4(d) is the optical spectra, in which the ratio RP of peak power of u and v components is about 11.1.

It is found from Figs. 4(a)4(c) that two different types of pulses coexist in the laser cavity, where weak pulses [Fig. 4(b)] are the same with the sech-shaped pulses [Fig. 2(e)] and strong pulses [Fig. 4(c)] have quasi-rectangular temporal profile with the pulse duration of about 5 ns. The strong pulse increases the pulse height by a factor of about 10 in comparison with the weak pulse. Figure 4(a) shows that the temporal spacing of strong pulses is a round-trip time of cavity and a strong pulse together with multiple weak pulses coexists within the laser cavity. By comparing Fig. 4(b) to Fig. 2(e), one can see that the height of the weak pulses is approximately the same with that of sech-shaped solitons. The experimental observations show that the energy of weak pulse varies slightly with the increase of pump power. The intracavity energy of strong pulse for P = 29 mW is about 40 nJ, increasing three orders of magnitude in comparison with the weak pulse. Comparing Fig. 4(d) to Figs. 2(b) and 2(c), we can see that the optical spectrum does not have spectral sidebands for P>28 mW rather than have spectral sidebands at the pump power range from about 10 mW to about 25 mW. It originates from the fact that the strong pulses dominate the spectral property for P>28 mW.

The experiments show that with the increase of P the height of strong pulses hardly changes while their width broadens. Some experimental examples are shown in Fig. 5(a)
Fig. 5 Results of experimental observations: (a) Oscilloscope traces at the pump power P = 40 and 50 mW; (b) Output optical spectra at P = 50, 150, 300, and 450 mW from bottom to top and the y-axis is the linear scale. Inset: output optical spectra are shown as the logarithmic scale for the y-axis.
, in which Δτ≈6.7 and 8.5 ns for P = 40 and 50 mW, respectively. No internal fine structures are observed within the pulses. We note that the trailing and leading parts of the pulses are different [three examples are shown in Figs. 4(c) and 5(a)]. The difference is caused by the response time of our measurement systems. The optical spectra for P = 50, 150, 300, 450 mW are shown in Fig. 5(b). One can see from Fig. 5(b) that the optical spectra approximately are the Gaussian profiles in the linear scale.

Based on net-normal-dispersion or all-normal-dispersion laser configuration, the fiber laser oscillator can generate high-energy sub-nanosecond and nanosecond DSs [10

10. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]

,28

28. 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]

,29

29. D. Mao, X. Liu, L. Wang, H. Lu, and H. Feng, “Generation and amplification of high-energy nanosecond pulses in a compact all-fiber laser,” Opt. Express 18(22), 23024–23029 (2010). [CrossRef] [PubMed]

]. In this report, an ultra-large net-anomalous-dispersion PML laser is proposed to generate high-energy nanosecond pulses. We believe that the dissipative processes based on gain and loss in laser system dominate the pulse-shaping mechanism and the strong pulses are a class of DSs.

We can observe from Figs. 3 and 4(d) that the ratio RP of peak power of u and v components of pulses is more than 11. Then the ratio of pulse energy for u and v components of pulse is beyond 11 according to the theory [27

27. X. M. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82(5), 053808 (2010). [CrossRef]

], whether the laser delivers the weakly conventional sech-shaped solitons or the strong DSs. As a result, the pulse approximates a linearly polarized wave propagating along the fiber.

3. Theoretical simulation and analysis

3.1. Coexistence of two types of weak and strong pulses

The conventional solitons propagating in the standard fibers are usually simulated by a NLSE [7

7. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

], where the birefringence of fiber is not taken into account. However, the formation and propagation of solitons in PML fiber lasers are modeled by the coupled complex NLSEs [10

10. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]

,30

30. X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010). [CrossRef]

]. To find the physical mechanism of soliton formation in our laser, we numerically solve the coupled complex NLSEs to simulate the modeling of laser. The coupled complex NLSEs are expressed by [10

10. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]

]
uz=α2uδuTiβ222uT2+iγ(|u|2+23|v|2)u+g2u+g2Ωg22uT2,vz=α2v+δvTiβ222vT2+iγ(|v|2+23|u|2)v+g2v+g2Ωg22vT2,
(1)
where u and v denote the envelopes of the optical pulses along the two orthogonal polarization axes of the fiber, α is the loss coefficient of fiber, δ is the group velocity difference between the two polarization modes, β 2 represents the fiber dispersion, γ refers to the cubic refractive nonlinearity of the medium, Ωg is the bandwidth of the laser gain. The variable T and z indicate the time and the propagation distance, respectively. g is the net gain, which is nonzero only for the amplifier fiber. It describes the gain function of EDF and is expressed by [31

31. G. Agrawal, “Amplification of ultrashort solitons in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2(12), 875–877 (1990). [CrossRef]

]
g=g0exp(Ep/Es),
(2)
where g 0 is the small-signal gain, Es is the gain saturation energy, and Ep is the pulse energy. When the soliton propagates through the PAPM element, its intensity transmission, Ti, is expressed as
Ti=sin2(θ)sin2(φ)+cos2(θ)cos2(φ)+0.5sin(2θ)sin(2φ)cos(ϕ1+ϕ2),
(3)
where ϕ 1 is the phase delay caused by the polarization controllers and ϕ 2 is the phase delay resulted from the fiber including both the linear phase delay and the nonlinear phase delay. The polarizer and analyzer have an orientation of angle θ and φ with respect to the fast axis of the fiber, respectively [30

30. X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010). [CrossRef]

].

The coupled complex NLSEs are solved with a predictor–corrector split-step Fourier method [32

32. X. Liu and B. Lee, “A fast method for nonlinear schrödinger equation,” IEEE Photon. Technol. Lett. 15(11), 1549–1551 (2003). [CrossRef]

]. The following parameters are employed for our simulations for possibly matching the experimental conditions: α = 0.2 dB/km, g 0 = 2 m−1, γ = 4.5 W−1km−1 for EDF and 1.3 W−1km−1 for SMF, Ωg = 30 nm, and β 2 = 53.5 × 10−3 ps2/m for EDF and −21.7 × 10−3 ps2/m for SMF. The simulation starts from an arbitrary signal and converges into a stable solution when the appropriate parameters are given.

When θ = π/3.5, φ = π/10, ϕ 1 = 0.9 + π/2, and Es = 0.24 nJ, the weakly sech-shaped soliton solution is obtained, as shown in Fig. 6
Fig. 6 Results of numerical simulations: (a) Pulse profile, (b) optical spectrum, (c) autocorrelation trace, and (d) instantaneous frequency δω of the pulses. The u and v components are indicated in (a) and (b) by the arrows. The ratio RP of peak intensity of u and v components of pulses is about 11.2. The pulse duration and the spectral width are 3.1 ps and 0.9 nm, respectively. δω is nearly zero across the pulse width.
. Figures 6(a) and 6(b) illustrate the temporal and spectral domain profiles of solitons. The autocorrelation trace of soliton is shown in Fig. 6(c). It is found from Fig. 6 that there are significant spectral sidebands [Fig. 6(b)] and the pedestal of solitons has the oscillating structure [Fig. 6(a)]. It is the oscillating structure of the pedestal that causes the complex structural spectrum. The numerical results show that the pulse duration and the spectral width are 3.1 ps and 0.9 nm, respectively, corresponding to the time–bandwidth product of about 0.34. The intensity peak of soliton is about 16 W and the soliton energy is about 0.048 nJ, as are in good agreement with the experimental results. Figures 6(a) and 6(b) show that the ratio RP of peak intensity of u and v components of pulses is about 11.2. The theoretical predictions [Figs. 6(b) and 6(c)] agree well with the experimental observations (Figs. 2(b), 2(d), and 3).

Figure 6(d) exhibits that the instantaneous frequency δω of the pulses is nearly zero at the time range from −3 ps to 3 ps and hence the pulse chirp is about zero across the pulse width. So this kind of solitons is stable chirp-free pulses with low energy and solitons are static, chirp-free solutions of the coupled complex NLSEs [i.e., Eq. (1)].

3.2. Theoretical modeling and results for strongly dissipative solitons

Both the theoretical results and the experimental observations show that the weakly sech-shaped pulse approximates a linearly polarized wave propagating along the fiber (Figs. 3 and 6). The experimental results also demonstrate that the laser emits the strong DSs approximating the linearly polarized wave [Fig. 4(d)]. The sech-shaped pulse and DS appear to be the asymmetrically combined pulse state with one pulse component much smaller than the other. Then the v component can be dealt with a small perturbation on the u component. A pair of coupled complex NLSEs can be simplified to a single equation, e.g., Ginzburg-Landau equation.

It is found from Fig. 7 that, with the increase of line gain σ=σ1(110n) (corresponding to increasing n), the pulse width broadens and the pulse height hardly varies. These theoretical predictions are in good agreement with the experimental observations. Therefore, both theoretical and experimental results prove that (1) with the increase of pumping strength the width of the quasi-rectangular DSs broadens with the fixed amplitude, (2) this type of DSs is a class of the wave-breaking-free pulses, (3) the ultra-large net-anomalous-dispersion PML fiber laser exploit a new way to generate high-energy nanosecond pulses, and (4) the dissipative processes based on the balance between the energy being supplied and lost in laser system governs the formation and evolution of DSs.

Although the profiles of solitons (especially two edges) in Fig. 7 have some difference from Fig. 4(a), the evolution of pulses in theory is consistent with the experimental results. Of course, investigating CGLE in detail is beyond the range of this report and CGLE only is an equation for approximately simulating the modeling of PML fiber lasers. In this work, the theoretical and experimental results show that two different types of pulse-shaping mechanisms coexist in the proposed laser. One is the dissipative processes that govern the generation of the high-energy nanosecond pulses. The other is the balance between anomalous dispersion and nonlinear Kerr effect, which determines the formation of the low-energy picosecond sech-shaped solitons.

4. Discussions

The laser oscillator has a 10-m length of EDF with normal dispersion of about 0.5 ps2 in current work, instead of a 0.8-m length of EDF with normal dispersion of about 0.01 ps2 in Ref [29

29. D. Mao, X. Liu, L. Wang, H. Lu, and H. Feng, “Generation and amplification of high-energy nanosecond pulses in a compact all-fiber laser,” Opt. Express 18(22), 23024–23029 (2010). [CrossRef] [PubMed]

]. The total length of laser cavity here is about 720 m rather than about 530 m in Ref [29

29. D. Mao, X. Liu, L. Wang, H. Lu, and H. Feng, “Generation and amplification of high-energy nanosecond pulses in a compact all-fiber laser,” Opt. Express 18(22), 23024–23029 (2010). [CrossRef] [PubMed]

]. We can conclude that the sech-shaped solitons depend on not only the angles of polarizer and analyzer, φ and θ, but also the cavity parameters (e.g., the total normal and anomalous dispersions of cavity, the length of EDF and SMF, and even their location in cavity). The experimental results here show that, if the polarization controllers are not set to the appropriate orientation and pressure, the proposed laser does not deliver the weakly sech-shaped solitons and its operation is very similar to reports in Ref [29

29. D. Mao, X. Liu, L. Wang, H. Lu, and H. Feng, “Generation and amplification of high-energy nanosecond pulses in a compact all-fiber laser,” Opt. Express 18(22), 23024–23029 (2010). [CrossRef] [PubMed]

]. To achieve the sech-shaped solitons, in fact, the length of EDF and SMF in the cavity here is adjusted again and again.

By comparing our pulses to the vector solitons reported on Ref [1

1. H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, and K. Loh, “Vector dissipative solitons in graphene mode locked fiber lasers,” Opt. Commun. 283(17), 3334–3338 (2010). [CrossRef]

], their behaviors have very distinct difference. For instance, the u and v components along the two orthogonal polarization axes of the fiber almost have the same spectral and temporal profiles (see Figs. 3, 4(d), 6(a), and 6(b) in this paper), except the intensity difference of u and v. For the vector solitons, however, the spectral and temporal profiles for the horizontal axis are completely different from those for the vertical axis (see Figs. 4(c), 5, and 6(b) in Ref [1

1. H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, and K. Loh, “Vector dissipative solitons in graphene mode locked fiber lasers,” Opt. Commun. 283(17), 3334–3338 (2010). [CrossRef]

].). Therefore, we believe that the solitons here are not a sort of vector solitons.

5. Conclusions

We have experimentally observed the coexistence of weakly sech-shaped solitons and strongly DSs in an ultra-large net-anomalous-dispersion PML fiber laser for the first time to author’s best knowledge. The sech-shaped solitons here have the pulse duration Δτ of about 2.9 ps and the spectral width Δλ of about 1 nm, which are much wider and narrower than Δτ and Δλ of the typical sech-shaped solitons [12

12. L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]

], respectively. The laser generates a new class of DSs exhibiting as the quasi-rectangular temporal and quasi-Gaussian spectral profiles in linear scale. The pulse energy of DSs increases more than three orders of magnitude by comparing to the pulse energy of sech-shaped solitons. The experimental observations show that two different types of pulse-shaping mechanisms exist simultaneously in our laser. One is the dissipative processes that play an essential role in the formation of nanosecond DSs. The other is the balance between anomalous dispersion and nonlinear Kerr effect, which governs the generation and evolution of picosecond sech-shaped solitons. Both sech-shaped and dissipative solitons appear to be the asymmetrically combined pulse state with one pulse component much smaller than the other. The theoretical predictions and experimental observations show that the energy of pulses along one of the two orthogonal polarization axes of the fiber is over 11 times lower than the energy along the other axis. The theoretical results are in good agreement with the experimental observations. The proposed laser provides a new way to generate high-energy nanosecond pulses and the investigation here provides a better understanding of the pulse shaping in PML fiber lasers.

Acknowledgments

This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grants 10874239, 10604066, and 60537060. The author would especially like to thank Xiaohui Li and Dong Mao for help with the experiments.

References and links

1.

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2.

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D. Mao, X. M. Liu, L. R. Wang, X. H. Hu, and H. Lu, “Partially polarized wave-breaking-free dissipative soliton with super-broad spectrum in a mode-locked fiber laser,” Laser Phys. Lett. 8(2), 134–138 (2011). [CrossRef]

6.

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

7.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

8.

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992). [CrossRef]

9.

D. Y. Tang, L. M. Zhao, G. Q. Xie, and L. J. Qian, “Coexistence and competition between different solitons-shaping mechanisms in a laser,” Phys. Rev. A 75(6), 063810 (2007). [CrossRef]

10.

X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]

11.

A. Cabasse, G. Martel, and J. L. Oudar, “High power dissipative soliton in an Erbium-doped fiber laser mode-locked with a high modulation depth saturable absorber mirror,” Opt. Express 17(12), 9537–9542 (2009). [CrossRef] [PubMed]

12.

L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]

13.

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080 (1993). [CrossRef] [PubMed]

14.

V. I. Kruglov, D. Méchin, and J. D. Harvey, “All-fiber ring Raman laser generating parabolic pulses,” Phys. Rev. A 81(2), 023815 (2010). [CrossRef]

15.

J. H. Im, S. Y. Choi, F. Rotermund, and D. I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef] [PubMed]

16.

M. A. Abdelalim, Y. Logvin, D. A. Khalil, and H. Anis, “Steady and oscillating multiple dissipative solitons in normal-dispersion mode-locked Yb-doped fiber laser,” Opt. Express 17(15), 13128–13139 (2009). [CrossRef] [PubMed]

17.

X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]

18.

X. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A 82(6), 063834 (2010). [CrossRef]

19.

B. Oktem, C. Ulgudur, and F. O. Ilday, “Soliton-similariton fibre laser,” Nat. Photonics 4(5), 307–311 (2010). [CrossRef]

20.

F. W. Wise, A. Chong, and W. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2(1-2), 58–73 (2008). [CrossRef]

21.

X. Liu, “Dissipative soliton evolution in ultra-large normal-cavity-dispersion fiber lasers,” Opt. Express 17(12), 9549–9557 (2009). [CrossRef] [PubMed]

22.

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009). [CrossRef]

23.

A. Komarov and F. Sanchez, “Structural dissipative solitons in passive mode-locked fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6), 066201 (2008). [CrossRef] [PubMed]

24.

S. Chouli and P. Grelu, “Soliton rains in a fiber laser: An experimental study,” Phys. Rev. A 81(6), 063829 (2010). [CrossRef]

25.

S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17(14), 11776–11781 (2009). [CrossRef] [PubMed]

26.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantization in figure eight fiber laser,” Electron. Lett. 28(1), 67 (1992). [CrossRef]

27.

X. M. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82(5), 053808 (2010). [CrossRef]

28.

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]

29.

D. Mao, X. Liu, L. Wang, H. Lu, and H. Feng, “Generation and amplification of high-energy nanosecond pulses in a compact all-fiber laser,” Opt. Express 18(22), 23024–23029 (2010). [CrossRef] [PubMed]

30.

X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010). [CrossRef]

31.

G. Agrawal, “Amplification of ultrashort solitons in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2(12), 875–877 (1990). [CrossRef]

32.

X. Liu and B. Lee, “A fast method for nonlinear schrödinger equation,” IEEE Photon. Technol. Lett. 15(11), 1549–1551 (2003). [CrossRef]

33.

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000). [CrossRef] [PubMed]

34.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016613 (2007). [CrossRef] [PubMed]

35.

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

36.

N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036613 (2004). [CrossRef] [PubMed]

37.

W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of an external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009). [CrossRef]

38.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996). [CrossRef] [PubMed]

39.

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

40.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997). [CrossRef]

41.

S. Chen, “Theory of dissipative solitons in complex Ginzburg-Landau systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025601 (2008). [CrossRef] [PubMed]

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.3500) Lasers and laser optics : Lasers, erbium
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 4, 2011
Revised Manuscript: February 11, 2011
Manuscript Accepted: March 9, 2011
Published: March 15, 2011

Citation
Xueming Liu, "Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion," Opt. Express 19, 5874-5887 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-5874


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References

  1. H. Zhang, D. Y. Tang, L. M. Zhao, Q. Bao, and K. Loh, “Vector dissipative solitons in graphene mode locked fiber lasers,” Opt. Commun. 283(17), 3334–3338 (2010). [CrossRef]
  2. L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7(1), 63–67 (2010). [CrossRef]
  3. A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008). [CrossRef]
  4. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode- locked fiber lasers,” Phys. Rev. A 80(4), 043829 (2009). [CrossRef]
  5. D. Mao, X. M. Liu, L. R. Wang, X. H. Hu, and H. Lu, “Partially polarized wave-breaking-free dissipative soliton with super-broad spectrum in a mode-locked fiber laser,” Laser Phys. Lett. 8(2), 134–138 (2011). [CrossRef]
  6. V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: a unified standpoint,” Phys. Rev. A 79(4), 043829 (2009). [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
  8. K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fibre ring laser,” Electron. Lett. 28(24), 2226–2228 (1992). [CrossRef]
  9. D. Y. Tang, L. M. Zhao, G. Q. Xie, and L. J. Qian, “Coexistence and competition between different solitons-shaping mechanisms in a laser,” Phys. Rev. A 75(6), 063810 (2007). [CrossRef]
  10. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]
  11. A. Cabasse, G. Martel, and J. L. Oudar, “High power dissipative soliton in an Erbium-doped fiber laser mode-locked with a high modulation depth saturable absorber mirror,” Opt. Express 17(12), 9537–9542 (2009). [CrossRef] [PubMed]
  12. L. E. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). [CrossRef]
  13. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080 (1993). [CrossRef] [PubMed]
  14. V. I. Kruglov, D. Méchin, and J. D. Harvey, “All-fiber ring Raman laser generating parabolic pulses,” Phys. Rev. A 81(2), 023815 (2010). [CrossRef]
  15. J. H. Im, S. Y. Choi, F. Rotermund, and D. I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef] [PubMed]
  16. M. A. Abdelalim, Y. Logvin, D. A. Khalil, and H. Anis, “Steady and oscillating multiple dissipative solitons in normal-dispersion mode-locked Yb-doped fiber laser,” Opt. Express 17(15), 13128–13139 (2009). [CrossRef] [PubMed]
  17. X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]
  18. X. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A 82(6), 063834 (2010). [CrossRef]
  19. B. Oktem, C. Ulgudur, and F. O. Ilday, “Soliton-similariton fibre laser,” Nat. Photonics 4(5), 307–311 (2010). [CrossRef]
  20. F. W. Wise, A. Chong, and W. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2(1-2), 58–73 (2008). [CrossRef]
  21. X. Liu, “Dissipative soliton evolution in ultra-large normal-cavity-dispersion fiber lasers,” Opt. Express 17(12), 9549–9557 (2009). [CrossRef] [PubMed]
  22. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009). [CrossRef]
  23. A. Komarov and F. Sanchez, “Structural dissipative solitons in passive mode-locked fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6), 066201 (2008). [CrossRef] [PubMed]
  24. S. Chouli and P. Grelu, “Soliton rains in a fiber laser: An experimental study,” Phys. Rev. A 81(6), 063829 (2010). [CrossRef]
  25. S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17(14), 11776–11781 (2009). [CrossRef] [PubMed]
  26. A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantization in figure eight fiber laser,” Electron. Lett. 28(1), 67 (1992). [CrossRef]
  27. X. M. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82(5), 053808 (2010). [CrossRef]
  28. 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]
  29. D. Mao, X. Liu, L. Wang, H. Lu, and H. Feng, “Generation and amplification of high-energy nanosecond pulses in a compact all-fiber laser,” Opt. Express 18(22), 23024–23029 (2010). [CrossRef] [PubMed]
  30. X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010). [CrossRef]
  31. G. Agrawal, “Amplification of ultrashort solitons in erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 2(12), 875–877 (1990). [CrossRef]
  32. X. Liu and B. Lee, “A fast method for nonlinear schrödinger equation,” IEEE Photon. Technol. Lett. 15(11), 1549–1551 (2003). [CrossRef]
  33. J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000). [CrossRef] [PubMed]
  34. J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016613 (2007). [CrossRef] [PubMed]
  35. N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372(17), 3124–3128 (2008). [CrossRef]
  36. N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036613 (2004). [CrossRef] [PubMed]
  37. W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of an external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009). [CrossRef]
  38. N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996). [CrossRef] [PubMed]
  39. W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008). [CrossRef]
  40. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997). [CrossRef]
  41. S. Chen, “Theory of dissipative solitons in complex Ginzburg-Landau systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025601 (2008). [CrossRef] [PubMed]

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