Stability of mode-locked pulse solutions subject to saturable gain: Computing linear stability with the Floquet-Fourier-Hill method

Journal of the Optical Society of America B: Optical Physics

Volumn 27, Issue 6, 2010, Pages 1184-1194

  Jones, Christopher R ^a   Kutz, J Nathan ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LASERS; MODE-LOCKED FIBER LASERS;

COMMONLY USED; FLOQUET; FOURIER; LINEAR STABILITY; LOCAL STRUCTURE; MODE-LOCKED LASER; MODE-LOCKED PULSE; NONLOCAL; SATURABLE GAIN; STABILITY PREDICTION;

STABILITY;

EID: 77955680280     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.27.001184     Document Type: Article

References (27)

1. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge Univ. Press, 1981).
2. J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications (Springer-Verlag, 2003).
3. A. Hasegawa, Optical Solitons in Fibers, 2nd ed. (Springer- Verlag, 1990).
4. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, 1984).
5. J. N. Kutz, "Mode-locked soliton lasers," SIAM Rev. 48, 629-678 (2006).
6. H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
7. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Structures for additive pulse mode locking," J. Opt. Soc. Am. B 8, 2068-2076 (1991).
8. S. Namiki, E. P. Ippen, H. A. Haus, and C. X. Yu, "Energy rate equations for mode-locked lasers," J. Opt. Soc. Am. B 14, 2099-2111 (1997).
9. T. Kapitula, J. N. Kutz, and B. Sandstede, "Stability of pulses in the master-mode-locking equation," J. Opt. Soc. Am. B 19, 740-746 (2002).
10. T. Kapitula, J. N. Kutz, and B. Sandstede, "The Evans function for nonlocal equations," Indiana Univ. Math. J. 53, 1095-1126 (2004).
11. B. Deconinck and J. N. Kutz, "Computing spectra of linear operators using the Floquet-Fourier-Hill method," J. Comput. Phys. 219, 296-321 (2006).
12. B. Deconinck, F. Kiyak, J. Carter, and J. N. Kutz, "SpectrUW: a laboratory for the numerical exploration of spectra of linear operators," Math. Comput. Simul. 74, 370-378 (2007).
13. G. W. Hill, "On the part of the lunar perigee which is a function of the mean motions of the sun and the moon," Acta Math. 8, 1-36 (1886).
14. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
15. B. Fornberg, A Practical Guide to Pseudospectral Methods (Cambridge Univ. Press, 1998).
16. L. N. Trefethen, Spectral Methods in Matlab (SIAM, 2000).
17. G. Floquet, "Sur les équations différentielles linéaires à coefficients périodiques," Ann. Sci. Ec. Normale Super. 2, 47-89 (1883).
18. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, 1955).
19. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).
20. E. Farnum and J. N. Kutz, "Multi-frequency mode-locked lasers," J. Opt. Soc. Am. B 25, 1002-1010 (2008).
21. B. Bale, E. Farnum, and J. N. Kutz, "Theory and simulation of passive multifrequency mode-locking with waveguide arrays," IEEE J. Quantum Electron. 44, 976-983 (2008).
22. J. N. Kutz, "Passive mode-locking using phase-sensitive amplification," Phys. Rev. A 78, 013845 (2008).
23. B. Bale, E. Farnum, and J. N. Kutz, "Dynamics of multifrequency mode-locking driven by homogenous and inhomogenous gain broadening effects," J. Opt. Soc. Am. B 25, 1479-1487 (2008).
24. N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, 1997).
25. J. Proctor and J. N. Kutz, "Passive mode-locking by use of waveguide arrays," Opt. Lett. 30, 2013-2015 (2005).
26. J. N. Kutz and B. Sandstede, "Theory of passive harmonic mode-locking using waveguide arrays," Opt. Express 16, 636-650 (2008).
27. B. Bale, J. N. Kutz, and B. Sandstede, "Optimizing waveguide array mode-locking for high-power fiber lasers," IEEE J. Sel. Top. Quantum Electron. 15, 220-231 (2009).