Abstract

A complete characterization is given of the effects of homogeneous and inhomogeneous gain broadening on the mode-locking dynamics and stability of a laser operating simultaneously at N frequency channels. Using a low-dimensional model for the wavelength-division multiplexing interactions of the governing cubic-quintic master mode-locking equation, the interplay of the gain dynamics can be completely classified. This gives a simple way to characterize the laser performance and the parameter regimes under which stable multifrequency operation can be achieved. The analysis shows that a small amount of inhomogeneous gain broadening is critical for the multifrequency operation. The model further provides a simple framework for understanding the stability of mode-locked pulses at multiple frequencies, thus contributing to the characterization of the increasingly important and timely technology of dual-frequency and multifrequency mode-locked laser cavities.

© 2008 Optical Society of America

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    [CrossRef]
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2008

2007

2006

2005

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

2003

2002

2001

D. Anderson, M. Lisak, and A. Berntson, “A variational approach to nonlinear evolution equations in optics,” Pramana, J. Phys. 57, 917-936 (2001).
[CrossRef]

2000

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

C. Wu and N. K. Dutta, “High repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145-150 (2000).
[CrossRef]

Z. Li, C. Lou, Y. Gao, and K. T. Chan, “A dual-wavelength and dual-repetition-rate actively mode-locked fiber ring laser,” Opt. Commun. 185, 381-385 (2000).
[CrossRef]

1996

Z. Ahned and N. Onodera, “High repetition rate optical pulse generation by frequency multiplication in actively mode-locked fiber ring lasers,” Electron. Lett. 32, 455455 (1996).

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

1991

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-longdistance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362-367 (1991); see Appendix.
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley-Interscience, 2002).

Ahned, Z.

Z. Ahned and N. Onodera, “High repetition rate optical pulse generation by frequency multiplication in actively mode-locked fiber ring lasers,” Electron. Lett. 32, 455455 (1996).

Anderson, D.

D. Anderson, M. Lisak, and A. Berntson, “A variational approach to nonlinear evolution equations in optics,” Pramana, J. Phys. 57, 917-936 (2001).
[CrossRef]

Antonelli, C.

Bale, B. G.

B. G. Bale, J. N. Kutz, A. Chong, W. H. Renninger, and F. W. Wise, “Spectral filtering for mode-locking in the normal dispersive regime,” Opt. Lett. 33, 941-943 (2008).
[CrossRef]

B. G. Bale and J. N. Kutz, “Variational method for mode-locked lasers,” J. Opt. Soc. Am. B 25, 1193-1202 (2008).
[CrossRef]

B. G. Bale, J. N. Kutz, A. Chong, W. H. Renninger, and F. W. Wise, “Spectral filtering for high-energy mode-locking in normal dispersion lasers,” J. Opt. Soc. Am. B (to be published).

B. G. Bale, E. Farnum, and J. N. Kutz, “Theory and simulation of passive multi-frequency mode-locking with waveguide arrays,” IEEE J. Quantum Electron. (to be published).

Berntson, A.

D. Anderson, M. Lisak, and A. Berntson, “A variational approach to nonlinear evolution equations in optics,” Pramana, J. Phys. 57, 917-936 (2001).
[CrossRef]

Brunel, M.

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, 063811 (2002).
[CrossRef]

Buckley, J.

Butson, L.

Chan, K. T.

Z. Li, C. Lou, Y. Gao, and K. T. Chan, “A dual-wavelength and dual-repetition-rate actively mode-locked fiber ring laser,” Opt. Commun. 185, 381-385 (2000).
[CrossRef]

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, 063811 (2002).
[CrossRef]

Chen, J.

Chong, A.

Dennis, M. L.

I. N. Duling III and M. L. Dennis, Compact Sources of Ultrashort Pulses (Cambridge U. Press, 1995).

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifiers Principles and Applications (Wiley-Interscience, 1994).

Dong, H.

H. Dong, G. Zhu, Q. Wang, and N. K. Dutta, “Simultaneous mode locked operation of a fiber laser at two wavelengths,” in Physics and Simulation of Optoelectronic Devices XII, M.Osinski, H.Amano, and F.Henneberger, eds., Proc. SPIE 5349, 117-121 (2004).

Drazin, P. G.

P. G. Drazin, Nonlinear Systems (Cambridge U. Press, 1992).

Duling, I. N.

I. N. Duling III and M. L. Dennis, Compact Sources of Ultrashort Pulses (Cambridge U. Press, 1995).

Dutta, N. K.

C. Wu and N. K. Dutta, “High repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145-150 (2000).
[CrossRef]

H. Dong, G. Zhu, Q. Wang, and N. K. Dutta, “Simultaneous mode locked operation of a fiber laser at two wavelengths,” in Physics and Simulation of Optoelectronic Devices XII, M.Osinski, H.Amano, and F.Henneberger, eds., Proc. SPIE 5349, 117-121 (2004).

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-longdistance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362-367 (1991); see Appendix.
[CrossRef]

Farnum, E.

Gao, Y.

Z. Li, C. Lou, Y. Gao, and K. T. Chan, “A dual-wavelength and dual-repetition-rate actively mode-locked fiber ring laser,” Opt. Commun. 185, 381-385 (2000).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-longdistance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362-367 (1991); see Appendix.
[CrossRef]

Guiyun, K.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications, (Oxford U. Press, 1995), Chap. 10.

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, 1989).

Haus, H. A.

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

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

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, 063811 (2002).
[CrossRef]

Jirauschek, C.

Kapitula, T.

Kärtner, F. X.

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications, (Oxford U. Press, 1995), Chap. 10.

Komarov, A.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

Kutz, J. N.

Leblond, H.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

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, 063811 (2002).
[CrossRef]

Li, Z.

Z. Li, C. Lou, Y. Gao, and K. T. Chan, “A dual-wavelength and dual-repetition-rate actively mode-locked fiber ring laser,” Opt. Commun. 185, 381-385 (2000).
[CrossRef]

Lisak, M.

D. Anderson, M. Lisak, and A. Berntson, “A variational approach to nonlinear evolution equations in optics,” Pramana, J. Phys. 57, 917-936 (2001).
[CrossRef]

Lou, C.

Z. Li, C. Lou, Y. Gao, and K. T. Chan, “A dual-wavelength and dual-repetition-rate actively mode-locked fiber ring laser,” Opt. Commun. 185, 381-385 (2000).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-longdistance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362-367 (1991); see Appendix.
[CrossRef]

Morgner, U.

Onodera, N.

Z. Ahned and N. Onodera, “High repetition rate optical pulse generation by frequency multiplication in actively mode-locked fiber ring lasers,” Electron. Lett. 32, 455455 (1996).

Qida, Z.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

Renninger, W.

Renninger, W. H.

Salhi, M.

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, 063811 (2002).
[CrossRef]

Sanchez, F.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

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, 063811 (2002).
[CrossRef]

Sandstede, B.

Shiquan, Y.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

Shuzhong, Y.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Wang, Q.

H. Dong, G. Zhu, Q. Wang, and N. K. Dutta, “Simultaneous mode locked operation of a fiber laser at two wavelengths,” in Physics and Simulation of Optoelectronic Devices XII, M.Osinski, H.Amano, and F.Henneberger, eds., Proc. SPIE 5349, 117-121 (2004).

Whitham, G.

G. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, 1974).

Wise, F.

Wise, F. W.

Wong, W. S.

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

Wu, C.

C. Wu and N. K. Dutta, “High repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145-150 (2000).
[CrossRef]

Xiaoyyi, D.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

Zhaohui, L.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

Zhu, G.

H. Dong, G. Zhu, Q. Wang, and N. K. Dutta, “Simultaneous mode locked operation of a fiber laser at two wavelengths,” in Physics and Simulation of Optoelectronic Devices XII, M.Osinski, H.Amano, and F.Henneberger, eds., Proc. SPIE 5349, 117-121 (2004).

Electron. Lett.

Z. Ahned and N. Onodera, “High repetition rate optical pulse generation by frequency multiplication in actively mode-locked fiber ring lasers,” Electron. Lett. 32, 455455 (1996).

IEEE J. Quantum Electron.

C. Wu and N. K. Dutta, “High repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145-150 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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

J. Lightwave Technol.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-longdistance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362-367 (1991); see Appendix.
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

Z. Li, C. Lou, Y. Gao, and K. T. Chan, “A dual-wavelength and dual-repetition-rate actively mode-locked fiber ring laser,” Opt. Commun. 185, 381-385 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. 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, 063811 (2002).
[CrossRef]

Phys. Rev. E

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604 (2005).
[CrossRef]

Pramana, J. Phys.

D. Anderson, M. Lisak, and A. Berntson, “A variational approach to nonlinear evolution equations in optics,” Pramana, J. Phys. 57, 917-936 (2001).
[CrossRef]

Rev. Mod. Phys.

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

SIAM Rev.

J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48, 629-678 (2006).
[CrossRef]

Other

B. G. Bale, J. N. Kutz, A. Chong, W. H. Renninger, and F. W. Wise, “Spectral filtering for high-energy mode-locking in normal dispersion lasers,” J. Opt. Soc. Am. B (to be published).

G. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, 1974).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications, (Oxford U. Press, 1995), Chap. 10.

Y. Shiquan, L. Zhaohui, Y. Shuzhong, D. Xiaoyyi, K. Guiyun, and Z. Qida, “Dual-wavelength actively mode-locked erbium dobed fiber laser using FBGs,” in Advances in Fiber Lasers, L.N.Duprasula, ed., Proc. SPIE 4974, 43-49 (2003).

H. Dong, G. Zhu, Q. Wang, and N. K. Dutta, “Simultaneous mode locked operation of a fiber laser at two wavelengths,” in Physics and Simulation of Optoelectronic Devices XII, M.Osinski, H.Amano, and F.Henneberger, eds., Proc. SPIE 5349, 117-121 (2004).

A. E. Siegman, Lasers (University Science Books, 1986).

I. N. Duling III and M. L. Dennis, Compact Sources of Ultrashort Pulses (Cambridge U. Press, 1995).

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley-Interscience, 2002).

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, 1989).

B. G. Bale, E. Farnum, and J. N. Kutz, “Theory and simulation of passive multi-frequency mode-locking with waveguide arrays,” IEEE J. Quantum Electron. (to be published).

E. Desurvire, Erbium-Doped Fiber Amplifiers Principles and Applications (Wiley-Interscience, 1994).

P. G. Drazin, Nonlinear Systems (Cambridge U. Press, 1992).

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