Abstract

With increasing demand on a laser source in the gigahertz pulse repetition rate regime, clarification on the mechanism of instability in high repetition rate fiber lasers – a promising alternative to solid state lasers – is of great importance and can potentially offer guideline for continuous wave (CW) mode locking. Here we present a theoretical approach together with relevant experimental corroboration to analyze the instabilities. By means of appropriate approximations, regimes from Q-switched mode locking, CW mode locking and pulsation are theoretically identified. Meanwhile, a critical curve that characterizes pump level for triggering Q-switched mode locking and pulsation for different repetition rates is given by virtue of both analytical and numerical procedures. In experiment, a passively mode-locked fiber laser with 1.6 GHz fundamental repetition rate is realized. The three regimes and corresponding pump power intervals are revealed, which are in consistence with theoretical prediction. Pulsation, as a relatively exotic phenomenon in GHz fiber laser, is well reproduced by the present model, which further verifies the accuracy of the approach as well as enriches the nonlinear dynamics.

© 2016 Optical Society of America

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2016 (8)

J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
[Crossref]

P. W. Kuan, K. Li, L. Zhang, X. Li, C. Yu, G. Feng, and L. Hu, “0.5-GHz Repetition Rate Fundamentally Tm-Doped Mode-Locked Fiber Laser,” IEEE Photonics Technol. Lett. 28(14), 1525–1528 (2016).
[Crossref]

H. Kotb, M. Abdelalim, and H. Anis, “Generalized analytical model for dissipative soliton in all-normal- dispersion mode-locked fiber laser,” IEEE J. Sel. Top. Quantum Electron. 22(2), 25–33 (2016).
[Crossref]

M. Liu, A.-P. Luo, Y.-R. Yan, S. Hu, Y.-C. Liu, H. Cui, Z.-C. Luo, and W.-C. Xu, “Successive soliton explosions in an ultrafast fiber laser,” Opt. Lett. 41(6), 1181–1184 (2016).
[Crossref] [PubMed]

S. A. Kolpakov, H. Kbashi, and S. V. Sergeyev, “Dynamics of vector rogue waves in a fiber laser with a ring cavity,” Optica 3(8), 870–875 (2016).
[Crossref]

M. Liu, A.-P. Luo, W.-C. Xu, and Z.-C. Luo, “Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser,” Opt. Lett. 41(17), 3912–3915 (2016).
[Crossref] [PubMed]

B. Sun, J. Luo, B. P. Ng, and X. Yu, “Dispersion-compensation-free femtosecond Tm-doped all-fiber laser with a 248 MHz repetition rate,” Opt. Lett. 41(17), 4052–4055 (2016).
[Crossref] [PubMed]

M. Pang, W. He, and P. St J Russell, “Gigahertz-repetition-rate Tm-doped fiber laser passively mode-locked by optoacoustic effects in nanobore photonic crystal fiber,” Opt. Lett. 41(19), 4601–4604 (2016).
[Crossref] [PubMed]

2015 (6)

2014 (2)

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

R. Thapa, D. Nguyen, J. Zong, and A. Chavez-Pirson, “All-fiber fundamentally mode-locked 12 GHz laser oscillator based on an Er/Yb-doped phosphate glass fiber,” Opt. Lett. 39(6), 1418–1421 (2014).
[Crossref] [PubMed]

2012 (7)

A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G.-R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012).
[Crossref] [PubMed]

H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37(17), 3522–3524 (2012).
[Crossref] [PubMed]

A. Martinez and S. Yamashita, “10 GHz fundamental mode fiber laser using a graphene saturable absorber,” Appl. Phys. Lett. 101(4), 041118 (2012).
[Crossref]

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2μm mode-locked fiber lasers,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
[Crossref] [PubMed]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

2011 (2)

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively modelocked fiber lasers using carbon nanotubes,” Opt. Express 19(7), 6155–6163 (2011).
[Crossref] [PubMed]

2010 (4)

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(10), 2068–2077 (2010).
[Crossref]

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 3(1), 175–205 (2010).
[Crossref] [PubMed]

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010).
[Crossref]

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]

2009 (3)

2008 (5)

J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express 16(21), 16509–16515 (2008).
[Crossref] [PubMed]

N. Ji, J. C. Magee, and E. Betzig, “High-speed, low-photodamage nonlinear imaging using passive pulse splitters,” Nat. Methods 5(2), 197–202 (2008).
[Crossref] [PubMed]

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

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]

2007 (2)

2005 (2)

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 025604 (2005).
[Crossref] [PubMed]

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005).
[Crossref]

2004 (1)

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 066612 (2004).
[Crossref] [PubMed]

2002 (3)

H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, “Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser,” Phys. Rev. A 65(6), 063811 (2002).
[Crossref]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
[Crossref] [PubMed]

P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002).
[Crossref] [PubMed]

2000 (3)

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]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
[Crossref]

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, “Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption,” Appl. Phys. B 70(S1), S41–S49 (2000).
[Crossref]

1999 (2)

E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
[Crossref]

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16(1), 46–56 (1999).
[Crossref]

1998 (1)

1995 (1)

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

1976 (1)

H. Haus, “Parameter ranges for CW passive mode locking,” IEEE J. Quantum Electron. 12(3), 169–176 (1976).
[Crossref]

1975 (1)

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Amrani, F.

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Anis, H.

H. Kotb, M. Abdelalim, and H. Anis, “Generalized analytical model for dissipative soliton in all-normal- dispersion mode-locked fiber laser,” IEEE J. Sel. Top. Quantum Electron. 22(2), 25–33 (2016).
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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).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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N. Ji, J. C. Magee, and E. Betzig, “High-speed, low-photodamage nonlinear imaging using passive pulse splitters,” Nat. Methods 5(2), 197–202 (2008).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Brovelli, L. R.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
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H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, “Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser,” Phys. Rev. A 65(6), 063811 (2002).
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F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Chang, G.

Chartier, T.

H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, “Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser,” Phys. Rev. A 65(6), 063811 (2002).
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Chen, H.-W.

Chen, J.

Chen, X.

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D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
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Churkin, D. V.

D. V. Churkin, S. Sugavanam, N. Tarasov, S. Khorev, S. V. Smirnov, S. M. Kobtsev, and S. K. Turitsyn, “Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers,” Nat. Commun. 6, 7004 (2015).
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F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. (Palo Alto, Calif.) 3(1), 175–205 (2010).
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Cundiff, S. T.

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S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
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T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
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Diddams, S. A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
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A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326(5953), 681 (2009).
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A. Bartels, R. Gebs, M. S. Kirchner, and S. A. Diddams, “Spectrally resolved optical frequency comb from a self-referenced 5 GHz femtosecond laser,” Opt. Lett. 32(17), 2553–2555 (2007).
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Ding, E.

Erkintalo, M.

Fendel, P.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
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Feng, G.

P. W. Kuan, K. Li, L. Zhang, X. Li, C. Yu, G. Feng, and L. Hu, “0.5-GHz Repetition Rate Fundamentally Tm-Doped Mode-Locked Fiber Laser,” IEEE Photonics Technol. Lett. 28(14), 1525–1528 (2016).
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Fortier, T. M.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
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Gebs, R.

Geis, M. W.

Geng, J.

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2μm mode-locked fiber lasers,” Proc. SPIE 8237, 82371N (2012).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
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T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
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Grapinet, M.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 066612 (2004).
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Grein, M. E.

Grelu, P.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
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C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
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J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 066612 (2004).
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P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002).
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Gutty, F.

Haboucha, A.

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).
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Hänsch, T. W.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
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H. Haus, “Parameter ranges for CW passive mode locking,” IEEE J. Quantum Electron. 12(3), 169–176 (1976).
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Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
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H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 (1975).
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He, W.

Heinecke, D.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326(5953), 681 (2009).
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Hideur, A.

H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, and F. Sanchez, “Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser,” Phys. Rev. A 65(6), 063811 (2002).
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Holzwarth, C. W.

Holzwarth, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
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Hönninger, C.

Hoyt, J. L.

Hu, L.

P. W. Kuan, K. Li, L. Zhang, X. Li, C. Yu, G. Feng, and L. Hu, “0.5-GHz Repetition Rate Fundamentally Tm-Doped Mode-Locked Fiber Laser,” IEEE Photonics Technol. Lett. 28(14), 1525–1528 (2016).
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Ippen, E. P.

A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G.-R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012).
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T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, “Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption,” Appl. Phys. B 70(S1), S41–S49 (2000).
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E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
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Jalali, B.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
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Ji, N.

N. Ji, J. C. Magee, and E. Betzig, “High-speed, low-photodamage nonlinear imaging using passive pulse splitters,” Nat. Methods 5(2), 197–202 (2008).
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Jiang, S.

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2μm mode-locked fiber lasers,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

Jiang, Y.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
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Joschko, M.

E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
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Kaertner, F. X.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
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Kamp, M.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
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A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G.-R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012).
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H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37(17), 3522–3524 (2012).
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J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express 16(21), 16509–16515 (2008).
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C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, “Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption,” Appl. Phys. B 70(S1), S41–S49 (2000).
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E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
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Keller, U.

Khilo, A.

Khorev, S.

D. V. Churkin, S. Sugavanam, N. Tarasov, S. Khorev, S. V. Smirnov, S. M. Kobtsev, and S. K. Turitsyn, “Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers,” Nat. Commun. 6, 7004 (2015).
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J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
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J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express 16(21), 16509–16515 (2008).
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Kirchner, M. S.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

A. Bartels, R. Gebs, M. S. Kirchner, and S. A. Diddams, “Spectrally resolved optical frequency comb from a self-referenced 5 GHz femtosecond laser,” Opt. Lett. 32(17), 2553–2555 (2007).
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Klenner, A.

Kobtsev, S.

Kobtsev, S. M.

D. V. Churkin, S. Sugavanam, N. Tarasov, S. Khorev, S. V. Smirnov, S. M. Kobtsev, and S. K. Turitsyn, “Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers,” Nat. Commun. 6, 7004 (2015).
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Kolodziejski, L. A.

E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
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Kolpakov, S. A.

Komarov, A.

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).
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A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005).
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A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 025604 (2005).
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Koontz, E. M.

E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
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Kopf, D.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
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Kotb, H.

H. Kotb, M. Abdelalim, and H. Anis, “Generalized analytical model for dissipative soliton in all-normal- dispersion mode-locked fiber laser,” IEEE J. Sel. Top. Quantum Electron. 22(2), 25–33 (2016).
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Kuan, P. W.

P. W. Kuan, K. Li, L. Zhang, X. Li, C. Yu, G. Feng, and L. Hu, “0.5-GHz Repetition Rate Fundamentally Tm-Doped Mode-Locked Fiber Laser,” IEEE Photonics Technol. Lett. 28(14), 1525–1528 (2016).
[Crossref]

Kukarin, S.

Kutz, J. N.

Laghezza, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Langlois, P.

E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999).
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Latkin, A.

Lazzeri, E.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
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Figures (8)

Fig. 1
Fig. 1 Schematic of the model used in the simulation
Fig. 2
Fig. 2 (a,b) Bell-shaped and flat-top profile of the energy variation towards g0 = 50 and 190, the inset of (b) is the zoom-in of the energy variation from 8000th to 10000th roundtrip. (c) A typical stationary state for g0 = 250 with no energy fluctuation. (d) Temporal profile of the stable pulse solution for g0 = 250.
Fig. 3
Fig. 3 Analytical threshold curve for CW mode-locking at different repetition rate, g0p represents the threshold for 0.5 GHz repetition rate.
Fig. 4
Fig. 4 (a) Evolution of pulse energy at stable CW mode-locking for g0 = 270 and regular pulsating for g0 = 290. Evolution of the temporal (b) and spectral (c) profile for the pulse over 5000 roundtrips.
Fig. 5
Fig. 5 (a) The curve of pulse energy versus small-signal gain coefficient g0 in terms of the analytical solution. (b) The comparison between numerical and analytical normalized results in the most energetic case of CW mode locking. The exact saturable loss and pulse profile as to the numerical (c) and analytical (d) calculation.
Fig. 6
Fig. 6 Area of CW mode locking (ML) with respect to the parameter g0. The colored cyan and gray shades are analytically and numerically achieved, respectively. The cross represents the point that directly obtained by numerical simulation, while the dash line is the corresponding fitted curve by exponential function.
Fig. 7
Fig. 7 (a) Schematic of the experimental setup, the insets inside shows the transmission curve of the film, the photographs of the ferrules with the film and the SESAM chip, respectively. (b) Continuous transition of the laser operations from Q-switched mode locking, CW mode locking to pulsation.
Fig. 8
Fig. 8 (a) Intervals in the pump axis (in experiment) and towards values of parameter g0 (in numerical simulation) with respect to the three operating regimes (QS. for Q-switched mode locking, ML. for CW mode locking and Pu. for pulsation). Characteristics of the pulsation from the numerical calculations and experimental measurements in (b) optical spectrum, (c) oscilloscope trace and (d) RF spectrum

Tables (1)

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Table 1 Parameters and relevant values in the model of Tm-doped mode-locked fiber laser

Equations (14)

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dg dt = g g 0 T g g E g P( t ).
dg dτ = g g 0 T g g E g lim T+ ( 1 T T 0 T P( T ,τ ) T ),
u i ( z,T ) z =i β 2 2 2 u i ( z,T ) T 2 +iγ | u i ( z,T ) | 2 u i ( z,T )+g( τ ) u i ( z,T )+ g( τ ) Ω 2 2 u i ( z,T ) T 2 .
dg( z,τ ) dτ = g( z,τ ) g 0 T g g( z,τ ) E g u i ( z,T ) T r .
q( T )= q 0 1+P( L c ,T ) T a / E a .
T r d u dτ =2( 2g L c q a + q l +q 2 ) u T r dg dτ = g g 0 T g / T r g E g u .
T r d dτ δ u =2( 2 L c δg D u ( q )δ u ) u s T r d dτ δg=δg( 1 T g / T r + u s E g ) g s δ u E g in which D u ( q )= q 0 2 E a 1 e u s / E a ( 1+ u s / E a ) ( u s / E a ) 2 .
q 0 1 e u s / E a ( 1+ u s / E a ) u s / E a < T r T g + u s E g u s E g 2 L c g 0 1+ u s T g /( E g T r ) q a + q l 2 q 0 2 1 e u s / E a u s / E a =0.
u i ( z,T ) z =i β 2 2 2 u i ( z,T ) T 2 +iγ | u i ( z,T ) | 2 u i ( z,T )+g u i ( z,T )+ g Ω 2 2 u i ( z,T ) T 2 in which g( z )= g 0 1+ T g u i ( z,T ) /( E g T r ) .
dq dT = q( T ) q 0 T a q( T ) E a P( L c ,T ).
i u Z β 2 2 2 u T 2 +γ | u | 2 u=iδu+iβ 2 u T 2 +iαu T | u | 2 d T in which δ= g 0 1+ T g u /( E g T r ) ( q a + q l + q 0 4 L c ), β= g Ω 2 , α= q 0 4 E a L c .
u=Cτsech( τ( TvZ ) ) e idln( Cτsech( τ( TvZ ) ) ) e ikTiwZ .
d= 3 β 2 + 9 β 2 2 +32 β 2 4β , C 2 = 3d( β 2 2 +4 β 2 ) 4βγ , k= α C 2 d 2β( d 2 +1 ) , v=α C 2 +2βkd β 2 d, τ= α C 2 α 2 C 4 2( β k 2 δ )( 2β+Dd ) 2β+ β 2 d , w=βd τ 2 γ C 2 τ 2 β 2 2 ( k 2 + τ 2 ).
g 0 =g( 1+ T g u /( E g T r ) ).

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