Abstract

Multi-channel modelocked lasers and their design have attracted much attention. Here, we use the Swift-Hohenberg equation to study dual-channel simultaneous modelocking (DSML) in a fiber laser. When a quartic filter is added to the laser cavity, the stable dual-channel simultaneous modelocking can be obtained for a given filter bandwidth when frequency separation, ωs, is less than a calculated threshold, ωth. When ωs>ωth, a multipulsing instability occurs. We use a linear stability analysis to determine the limit that the multi-pulsing instability imposes on DSML, and we propose a cavity design that avoids the multi-pulsing instability.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

R. Li, H. Shi, H. Tian, Y. Li, B. Liu, Y. Song, and M. Hu, “All-polarization-maintaining dual-wavelength mode-locked fiber laser based on sagnac loop filter,” Opt. Express 26, 28302–28311 (2018).
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X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

2017 (3)

2016 (1)

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (1)

2012 (1)

2011 (3)

2010 (5)

F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B 27, 2068–2077 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27, B51–B62 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

2009 (1)

2008 (5)

2007 (1)

2006 (2)

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet Fourier Hill method,” J. Comput. Phys. 219, 296–321 (2006).
[Crossref]

E. D. Farnum, L. Butson, and J. N. Kutz, “Theory and simulation of dual-frequency mode-locked lasers,” J. Opt. Soc. Am. B 23, 257–264 (2006).
[Crossref]

2004 (1)

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

2002 (1)

J. M. Soto-Crespo and N. Akhmediev, “Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic swift-hohenberg equation,” Phys. Rev. E 66, 066610 (2002).
[Crossref]

2001 (1)

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

1999 (1)

1998 (2)

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, 159–168 (1998).
[Crossref]

M. Quiroga-Teixeiro, C. B. Clausen, M. P. Sørensen, P. L. Christiansen, and P. A. Andrekson, “Passive mode locking by dissipative four-wave mixing,” J. Opt. Soc. Am. B 15, 1315–1321 (1998).
[Crossref]

1996 (2)

F. Kärtner, I. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

1994 (1)

O. Kamatani, S. Kawanishi, and M. Saruwatari, “Prescaled 6.3 ghz clock recovery from 50 gbit/s tdm optical signal with 50 ghz pll using four-wave mixing in a travelling-wave laser diode optical amplifier,” Electron. Lett. 30, 807–809 (1994).
[Crossref]

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Elect. 29, 983–996 (1993).
[Crossref]

1992 (2)

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1992).
[Crossref]

C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton fiber ring laser,” Opt. Lett. 17, 417–419 (1992).
[Crossref] [PubMed]

1975 (1)

H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
[Crossref]

Ablowitz, M. J.

M. J. Ablowitz and A. S. Fokas, Complex variables: introduction and applications(Cambridge University, 2003).
[Crossref]

Akhmediev, N.

J. M. Soto-Crespo and N. Akhmediev, “Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic swift-hohenberg equation,” Phys. Rev. E 66, 066610 (2002).
[Crossref]

N. Akhmediev and A. Ankiewicz, Dissipative Solitons in the Complex Ginzburg-Landau and Swift-Hohenberg Equations(SpringerBerlin Heidelberg, Berlin, Heidelberg, 2005).

Akhmediev, N. N.

Alasia, D.

Andrekson, P. A.

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, Dissipative Solitons in the Complex Ginzburg-Landau and Swift-Hohenberg Equations(SpringerBerlin Heidelberg, Berlin, Heidelberg, 2005).

Bale, B. G.

B. G. Bale, E. Farnum, and J. N. Kutz, “Theory and simulation of passive multifrequency mode-locking with waveguide arrays,” IEEE J. Quantum Elect. 44, 976–983 (2008).
[Crossref]

Barthelemy, A.

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Boudoux, C.

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

Bouma, B.

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Butson, L.

Carruthers, T. F.

Chen, C.-J.

Chen, H.-J.

Chernov, A. I.

Christiansen, P. L.

Chu, S. T.

Clausen, C. B.

Coddington, I.

Coen, S.

J. Schröder, D. Alasia, T. Sylvestre, and S. Coen, “Dynamics of an ultrahigh-repetition-rate passively mode-locked raman fiber laser,” J. Opt. Soc. Am. B 25, 1178–1186 (2008).
[Crossref]

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

Cui, H.

De Boer, J.

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

Deconinck, B.

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet Fourier Hill method,” J. Comput. Phys. 219, 296–321 (2006).
[Crossref]

Deparis, O.

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

der Au, J. A.

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, 159–168 (1998).
[Crossref]

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Desfarges-Berthelemot, A.

Dianov, E. M.

Diddams, S. A.

Ding, E.

Docherty, A.

Droste, S.

Emplit, P.

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

Fang, Z. J.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Farnum, E.

B. G. Bale, E. Farnum, and J. N. Kutz, “Theory and simulation of passive multifrequency mode-locking with waveguide arrays,” IEEE J. Quantum Elect. 44, 976–983 (2008).
[Crossref]

Farnum, E. D.

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Fluck, R.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Fokas, A. S.

M. J. Ablowitz and A. S. Fokas, Complex variables: introduction and applications(Cambridge University, 2003).
[Crossref]

Haelterman, M.

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

Hasan, T.

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Haus, H. A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Elect. 29, 983–996 (1993).
[Crossref]

H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
[Crossref]

Honninger, C.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Hu, G.

Hu, M.

Jagadish, C.

Jiang, Y.

Jung, I.

F. Kärtner, I. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

Jung, I. D.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Kamatani, O.

O. Kamatani, S. Kawanishi, and M. Saruwatari, “Prescaled 6.3 ghz clock recovery from 50 gbit/s tdm optical signal with 50 ghz pll using four-wave mixing in a travelling-wave laser diode optical amplifier,” Electron. Lett. 30, 807–809 (1994).
[Crossref]

Kang, Z.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

X. Zhang, F. Li, Z. Kang, J. Yuan, and P. K. A. Wai, “Spectral filtering induced multi-pulsing in mode-locked soliton lasers,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), (Optical Society of America, 2016), p. JT4A.7.

Kartner, F. X.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Kärtner, F.

F. Kärtner, I. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

Kärtner, F. X.

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, 159–168 (1998).
[Crossref]

Kawanishi, S.

O. Kamatani, S. Kawanishi, and M. Saruwatari, “Prescaled 6.3 ghz clock recovery from 50 gbit/s tdm optical signal with 50 ghz pll using four-wave mixing in a travelling-wave laser diode optical amplifier,” Electron. Lett. 30, 807–809 (1994).
[Crossref]

Keller, U.

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, 159–168 (1998).
[Crossref]

F. Kärtner, I. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Kermene, V.

Kieu, K.

Konov, V. I.

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Kutz, J. N.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express 19, 23408–23419 (2011).
[Crossref] [PubMed]

F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B 27, 2068–2077 (2010).
[Crossref]

E. D. Farnum and J. N. Kutz, “Multifrequency mode-locked lasers,” J. Opt. Soc. Am. B 25, 1002–1010 (2008).
[Crossref]

B. G. Bale, E. Farnum, and J. N. Kutz, “Theory and simulation of passive multifrequency mode-locking with waveguide arrays,” IEEE J. Quantum Elect. 44, 976–983 (2008).
[Crossref]

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet Fourier Hill method,” J. Comput. Phys. 219, 296–321 (2006).
[Crossref]

E. D. Farnum, L. Butson, and J. N. Kutz, “Theory and simulation of dual-frequency mode-locked lasers,” J. Opt. Soc. Am. B 23, 257–264 (2006).
[Crossref]

Lederer, M. J.

Lhermite, J.

Li, D.

Li, F.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express 19, 23408–23419 (2011).
[Crossref] [PubMed]

F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B 27, 2068–2077 (2010).
[Crossref]

X. Zhang, F. Li, Z. Kang, J. Yuan, and P. K. A. Wai, “Spectral filtering induced multi-pulsing in mode-locked soliton lasers,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), (Optical Society of America, 2016), p. JT4A.7.

X. Zhang, S. Wang, F. Li, C. R. Menyuk, and P. Wai, “Design of a dual-channel modelocked fiber laser that avoids multi-pulsing,” in CLEO: Applications and Technology, (Optical Society of America, 2018), pp. JTh2A.

Li, R.

Li, Y.

Little, B. E.

Liu, B.

Liu, J. R.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Liu, L.

Liu, X.

X. Liu, “Interaction and motion of solitons in passively-mode-locked fiber lasers,” Phys. Rev. A 84, 053828 (2011).
[Crossref]

Liu, Y.

Lobach, A. S.

Luo, A. P.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Luo, A.-P.

Luo, Z. C.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Luo, Z.-C.

Luther-Davies, B.

Lv, Y.-K.

Marks, B. S.

Matsas, V. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1992).
[Crossref]

Matuschek, N.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Elect. 29, 983–996 (1993).
[Crossref]

Menyuk, C.

S. Wang and C. Menyuk, “Computational methods for determining the stability of pulses in passively modelocked laser systems,” in 2013 IEEE Photonics Conference (IPC), (2013), pp. 392–393.
[Crossref]

Menyuk, C. R.

Morandotti, R.

Moss, D. J.

Nakkeeran, K.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

Newbury, N. R.

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1992).
[Crossref]

Obraztsova, E. D.

Oudar, J.-L.

Pan, Y.

Pasquazi, A.

Payne, D. N.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1992).
[Crossref]

Peccianti, M.

Pierce, M.

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

Quiroga-Teixeiro, M.

Richardson, D. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1992).
[Crossref]

Rozhin, A. G.

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Sabourdy, D.

Saruwatari, M.

O. Kamatani, S. Kawanishi, and M. Saruwatari, “Prescaled 6.3 ghz clock recovery from 50 gbit/s tdm optical signal with 50 ghz pll using four-wave mixing in a travelling-wave laser diode optical amplifier,” Electron. Lett. 30, 807–809 (1994).
[Crossref]

Schröder, J.

Shen, D.

Shi, H.

Sinclair, L. C.

Solodyankin, M. A.

Song, Y.

Sørensen, M. P.

Soto-Crespo, J. M.

J. M. Soto-Crespo and N. Akhmediev, “Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic swift-hohenberg equation,” Phys. Rev. E 66, 066610 (2002).
[Crossref]

M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, “Multipulse operation of a ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror,” J. Opt. Soc. Am. B 16, 895–904 (1999).
[Crossref]

Strogatz, S.

S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Studies in Nonlinearity Series (Perseus Books Publishing, 1994).

Sun, Z.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Sylvestre, T.

J. Schröder, D. Alasia, T. Sylvestre, and S. Coen, “Dynamics of an ultrahigh-repetition-rate passively mode-locked raman fiber laser,” J. Opt. Soc. Am. B 25, 1178–1186 (2008).
[Crossref]

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

Tan, H. H.

Tan, X.-M.

Tang, D.

Tang, D. Y.

Tausenev, A. V.

Tearney, G.

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

Tian, H.

Wai, P.

X. Zhang, S. Wang, F. Li, C. R. Menyuk, and P. Wai, “Design of a dual-channel modelocked fiber laser that avoids multi-pulsing,” in CLEO: Applications and Technology, (Optical Society of America, 2018), pp. JTh2A.

Wai, P. K. A.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express 19, 23408–23419 (2011).
[Crossref] [PubMed]

F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B 27, 2068–2077 (2010).
[Crossref]

C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton fiber ring laser,” Opt. Lett. 17, 417–419 (1992).
[Crossref] [PubMed]

X. Zhang, F. Li, Z. Kang, J. Yuan, and P. K. A. Wai, “Spectral filtering induced multi-pulsing in mode-locked soliton lasers,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), (Optical Society of America, 2016), p. JT4A.7.

Wang, F.

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Wang, S.

S. Wang, S. Droste, L. C. Sinclair, I. Coddington, N. R. Newbury, T. F. Carruthers, and C. R. Menyuk, “Wake mode sidebands and instability in mode-locked lasers with slow saturable absorbers,” Opt. Lett. 42, 2362–2365 (2017).
[Crossref] [PubMed]

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

S. Wang, A. Docherty, B. S. Marks, and C. R. Menyuk, “Boundary tracking algorithms for determining the stability of mode-locked pulses,” J. Opt. Soc. Am. B 31, 2914–2930 (2014).
[Crossref]

S. Wang, A. Docherty, B. S. Marks, and C. R. Menyuk, “Comparison of numerical methods for modeling laser mode locking with saturable gain,” J. Opt. Soc. Am. B 30, 3064–3074 (2013).
[Crossref]

X. Zhang, S. Wang, F. Li, C. R. Menyuk, and P. Wai, “Design of a dual-channel modelocked fiber laser that avoids multi-pulsing,” in CLEO: Applications and Technology, (Optical Society of America, 2018), pp. JTh2A.

S. Wang and C. Menyuk, “Computational methods for determining the stability of pulses in passively modelocked laser systems,” in 2013 IEEE Photonics Conference (IPC), (2013), pp. 392–393.
[Crossref]

Weingarten, K. J.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

White, I. H.

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Wise, F. W.

Wu, X.

Xu, W. C.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Xu, W.-C.

Yang, X.

Ye, Q.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Yin, H. S.

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

Yin, S.

Yuan, J.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

X. Zhang, F. Li, Z. Kang, J. Yuan, and P. K. A. Wai, “Spectral filtering induced multi-pulsing in mode-locked soliton lasers,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), (Optical Society of America, 2016), p. JT4A.7.

Yun, S.

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

Zhang, H.

Zhang, M.

Zhang, X.

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

X. Zhang, F. Li, Z. Kang, J. Yuan, and P. K. A. Wai, “Spectral filtering induced multi-pulsing in mode-locked soliton lasers,” in Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), (Optical Society of America, 2016), p. JT4A.7.

X. Zhang, S. Wang, F. Li, C. R. Menyuk, and P. Wai, “Design of a dual-channel modelocked fiber laser that avoids multi-pulsing,” in CLEO: Applications and Technology, (Optical Society of America, 2018), pp. JTh2A.

Zhao, G.-K.

Zhao, L.

Zhao, L. M.

Zhao, X.

Zheng, Z.

Zhu, J.

Electron. Lett. (3)

O. Kamatani, S. Kawanishi, and M. Saruwatari, “Prescaled 6.3 ghz clock recovery from 50 gbit/s tdm optical signal with 50 ghz pll using four-wave mixing in a travelling-wave laser diode optical amplifier,” Electron. Lett. 30, 807–809 (1994).
[Crossref]

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28, 1391–1393 (1992).
[Crossref]

T. Sylvestre, S. Coen, O. Deparis, P. Emplit, and M. Haelterman, “Demonstration of passive modelocking through dissipative four-wave mixing in fibre laser,” Electron. Lett. 37, 881–882 (2001).
[Crossref]

IEEE J. Quantum Elect. (2)

B. G. Bale, E. Farnum, and J. N. Kutz, “Theory and simulation of passive multifrequency mode-locking with waveguide arrays,” IEEE J. Quantum Elect. 44, 976–983 (2008).
[Crossref]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Elect. 29, 983–996 (1993).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (4)

F. Kärtner, I. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

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, 159–168 (1998).
[Crossref]

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (sesam’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[Crossref]

X. Zhang, F. Li, K. Nakkeeran, J. Yuan, Z. Kang, J. N. Kutz, and P. K. A. Wai, “Impact of spectral filtering on multipulsing instability in mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).

IEEE Photonics J. (1)

Z. C. Luo, A. P. Luo, W. C. Xu, H. S. Yin, J. R. Liu, Q. Ye, and Z. J. Fang, “Tunable multiwavelength passively mode-locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2, 571–577 (2010).
[Crossref]

IEEE Photonics Tech. L. (1)

S. Yun, C. Boudoux, M. Pierce, J. De Boer, G. Tearney, and B. Bouma, “Extended-cavity semiconductor wavelength-swept laser for biomedical imaging,” IEEE Photonics Tech. L. 16, 293–295 (2004).
[Crossref]

J. Appl. Phys. (1)

H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
[Crossref]

J. Comput. Phys. (1)

B. Deconinck and J. N. Kutz, “Computing spectra of linear operators using the Floquet Fourier Hill method,” J. Comput. Phys. 219, 296–321 (2006).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (9)

S. Wang, A. Docherty, B. S. Marks, and C. R. Menyuk, “Comparison of numerical methods for modeling laser mode locking with saturable gain,” J. Opt. Soc. Am. B 30, 3064–3074 (2013).
[Crossref]

S. Wang, A. Docherty, B. S. Marks, and C. R. Menyuk, “Boundary tracking algorithms for determining the stability of mode-locked pulses,” J. Opt. Soc. Am. B 31, 2914–2930 (2014).
[Crossref]

M. Quiroga-Teixeiro, C. B. Clausen, M. P. Sørensen, P. L. Christiansen, and P. A. Andrekson, “Passive mode locking by dissipative four-wave mixing,” J. Opt. Soc. Am. B 15, 1315–1321 (1998).
[Crossref]

M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, “Multipulse operation of a ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror,” J. Opt. Soc. Am. B 16, 895–904 (1999).
[Crossref]

E. D. Farnum, L. Butson, and J. N. Kutz, “Theory and simulation of dual-frequency mode-locked lasers,” J. Opt. Soc. Am. B 23, 257–264 (2006).
[Crossref]

E. D. Farnum and J. N. Kutz, “Multifrequency mode-locked lasers,” J. Opt. Soc. Am. B 25, 1002–1010 (2008).
[Crossref]

J. Schröder, D. Alasia, T. Sylvestre, and S. Coen, “Dynamics of an ultrahigh-repetition-rate passively mode-locked raman fiber laser,” J. Opt. Soc. Am. B 25, 1178–1186 (2008).
[Crossref]

F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B 27, 2068–2077 (2010).
[Crossref]

S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27, B51–B62 (2010).
[Crossref]

Nano Res. (1)

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Nanophotonics (1)

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

Nat. Photonics (1)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Opt. Express (7)

X. Zhao, Z. Zheng, L. Liu, Y. Liu, Y. Jiang, X. Yang, and J. Zhu, “Switchable, dual-wavelength passively mode-locked ultrafast fiber laser based on a single-wall carbon nanotube modelocker and intracavity loss tuning,” Opt. Express 19, 1168–1173 (2011).
[Crossref] [PubMed]

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express 19, 23408–23419 (2011).
[Crossref] [PubMed]

A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27363 (2012).
[Crossref] [PubMed]

K. Kieu and F. W. Wise, “All-fiber normal-dispersion femtosecond laser,” Opt. Express 16, 11453–11458 (2008).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 The filter profile in the Fourier domain and the filter parameters.
Fig. 2
Fig. 2 The temporal profiles and the normalized Fourier spectra of stable modelocked states that we obtain by evolving Eq. (1) when (a)(b) E sat = 0.50, and (c)(d) E sat = 1.00. The parameters are ω s = 1.20 and ω b = 0.30 ( α 2 = 23.76 and α 4 = 32.92).
Fig. 3
Fig. 3 The temporal profiles and the normalized Fourier spectra of modelocked states that we obtain by solving Eq. (1) when E sat = 2.50. We set ω s = 1.60 and ω b = 0.30 ( α 2 = 23.04, α 4 = 17.98).
Fig. 4
Fig. 4 The dynamical spectrum of J when E sat = 0.5, α 2 = 23.76, and α 4 = 32.92, corresponding to the single-channel modelocked solution that we show in Figs. 2(a) and 2(b).
Fig. 5
Fig. 5 The dynamical spectrum of J (for the single-channel modelocked solution) when E sat = 1.00, α 2 = 23.76, and α 4 = 32.92.
Fig. 6
Fig. 6 Transients evolution from single pulse modelocking to dual-channel simultaneous modelocking in (a) the time and (b) the frequency domains.
Fig. 7
Fig. 7 The dynamical spectrum of the single channel modelocked pulse when E sat = 2.5. The filter parameters are α 2 = 23.04, α 4 = 17.98. The continuous spectrum crosses the imaginary axis, which indicates that a small perturbation that is separated from the modelocked pulse experiences net gain.
Fig. 8
Fig. 8 Transition of a single-channel modelocked state to a multi-pulsing state (a) in the time and (b) in the frequency domain. We set E sat = 2.5. In the time domain, a new pulse appears, which leads to a rapid modulation in the frequencydomain.

Tables (1)

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Table 1 Values of Parameters We Use in Validating the Experimental Results

Equations (17)

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q z = i ϕ q D 1 q z + g ( | q | ) 2 q l 2 q + i 2 2 q t 2 + ( i + δ ) | q | 2 q σ | q | 4 q + α 2 2 q t 2 + α 4 4 q t 4 ,
q = A ( γ L c ) 1 / 2 , t = τ ( | β 2 | L c ) 1 / 2 ,
g ( | q | ) = g 0 [ 1 + 0 T R | q | 2 d t E sat ] 1 ,
T ( ω ) = exp  { α 4 [ ω 2 ( ω s / 2 ) 2 ] 2 } ,
α 2 = α 4 ω s 2 / 8 ,
l = l cavity + α 4 ω s 4 / 16 ,
Ω s = ( | β 2 | L c ) 1 / 2 ω s / 2 .
q 0 ( t ) z = 0 .
q 0 ( t ) = R 0 ( t ) + i I 0 ( t ) , R ( t , z ) = R 0 ( t ) + Δ R ( t , z ) , I ( t , z ) = I 0 ( t ) + Δ I ( t , z ) ,
d d z [ Δ R Δ I ] = J [ Δ R Δ I ] = [ L 11 L 12 L 21 L 22 ] [ Δ R Δ I ] ,
L 11 = D 1 D t + α 2 D t 2 + α 4 D t 4 + g l 2 I + g 1 R 0 R 0 T + P R , L 12 = ϕ 0 I 1 2 D t 2 + g 1 R 0 I 0 T + P I , L 21 = ϕ 0 I + 1 2 D t 2 + g 1 I 0 R 0 T + Q R , L 22 = D 1 D t + α 2 D t 2 + α 4 D t 4 + g l 2 I + g 1 I 0 I 0 T + Q I .
g 1 = g 0 [ 1 + Δ t ( R 0 T R 0 + I 0 T I 0 ) / E sat ] 2 Δ t E sat .
P R , j j = 2 R j I j + δ ( 3 R j 2 + I j 2 ) σ [ ( R j 2 + I j 2 ) 2 + 4 R j 2 ( R j 2 + I j 2 ) 2 ] , P I , j j = ( R j 2 + 3 I j 2 ) + 2 δ R j I j 4 σ R j I j ( R j 2 + I j 2 ) , Q R , j j = ( I j 2 + 3 R j 2 ) + 2 δ R j I j 4 σ R j I j ( R j 2 + I j 2 ) , Q I , j j = 2 R j I j + δ ( 3 I j 2 + R j 2 ) σ [ ( R j 2 + I j 2 ) 2 + 4 R j 2 ( R j 2 + I j 2 ) 2 ] .
J = [ i D 1 ω α 2 ω 2 + α 4 ω 4 + g l 2 ϕ + ω 2 2 ϕ ω 2 2 i D 1 ω α 2 ω 2 + α 4 ω 4 + g l 2 ] ,
λ ( ω ) = g l 2 α 2 ω 2 + α 4 ω 4 + i D 1 ω ± i ( ϕ + ω 2 2 ) .
max  [ Re ( λ ) ] = max  [ g l cavity 2 + α 4 ( ω 2 ω s 2 4 ) 2 ] = g l cavity 2 < 0
| Ω s | > 1.54 ( β 2 L c ) 0.5 .

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