PapersNo Access

THE ECM-BACKBONE OF THE LANG–KOBAYASHI EQUATIONS: A GEOMETRIC PICTURE

VIVI ROTTSCHÄFER

Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Search for more papers by this author

and

BERND KRAUSKOPF

Engineering Mathematics, University of Bristol, University Walk, Bristol BS8 1TR, UK

Search for more papers by this author

https://doi.org/10.1142/S0218127407017914Cited by:37 (Source: Crossref)

Abstract

We perform an analytical study of the external cavity modes of a semiconductor laser subject to conventional optical feedback as modeled by the well-known Lang–Kobayashi equations. Specifically, the bifurcation set is derived in the three-dimensional parameter space of feedback phase, feedback strength and pump current of the laser. Different open regions in this space correspond to different numbers of physically relevant external cavity modes of the laser. Some of their stability properties are determined from the characteristic equation.

Keywords:

References

O. Diekmann et al. , Delay Equations: Functional-, Complex-, and Nonlinear Analysis ( Springer-Verlag , NY , 1995 ) . Crossref, Google Scholar
E. Doedel et al. , AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations, 1997 ( 1997 ) , http://indy.cs.concordia.ca/auto/main.html . Google Scholar
Engelborghs, K., Luzyanina, T. & Samaey, G. [2000] DDE-BIFTOOL v2.00: A Matlab Package for Bifurcation Analysis of Delay Differential Equations, Tech. Rep. TW-330, Department of Computer Science, Katholieke Universiteit Leuven, Belguim, 2000 (http://www.cs.kuleuven.ac.be/~koen/delay/ddebiftool.shtml) . Google Scholar
I. Fischer, T. Heil and W. Elsäßer, Fundamental Issues of Nonlinear Laser Dynamics (2000) pp. 218–237. Google Scholar
I. Fischer, Y. Liu and P. Davis, Phys. Rev. A 62, 011801 (2000), DOI: 10.1103/PhysRevA.62.011801. Crossref, Web of Science, Google Scholar
A. Gavrielides, Fundamental Issues of Nonlinear Laser Dynamics (2000) pp. 191–217. Google Scholar
B. Haegemanet al., Phys. Rev. E 66, 046216 (2002), DOI: 10.1103/PhysRevE.66.046216. Crossref, Web of Science, Google Scholar
J. K. Hale and S. M. Verduyn Lunel , Introduction to Functional Differential Equations ( Springer-Verlag , NY , 1993 ) . Crossref, Google Scholar
T. Heilet al., Phys. Rev. E 67, 066214 (2003), DOI: 10.1103/PhysRevE.67.066214. Crossref, Web of Science, Google Scholar
D. M. Kane and K. A. Shore (eds.) , Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers ( Wiley , 2005 ) . Crossref, Google Scholar
B. Krauskopf and D. Lenstra (eds.) , Fundamental Issues of Nonlinear Laser Dynamics , AIP Conf. Proc. 548 ( American Institute of Physics Publishing , Melville, NY , 2000 ) . Google Scholar
B. Krauskopf, G. H. M. Van Tartwijk and G. R. Gray, Opt. Commun. 177, 347 (2000), DOI: 10.1016/S0030-4018(00)00574-5. Crossref, Web of Science, Google Scholar
B. Krauskopf, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (2005) pp. 147–183. Crossref, Google Scholar
R. Lang and K. Kobayashi, IEEE J. Quant. Electron. 16, 347 (1980), DOI: 10.1109/JQE.1980.1070479. Crossref, Web of Science, Google Scholar
D. Lenstra, G. Vemuri and M. Yousefi, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (2005) pp. 55–80. Crossref, Google Scholar
J. Mørk, B. Tromborg and J. Mark, IEEE J. Quant. Elec. 28, 93 (1992). Crossref, Web of Science, Google Scholar
J. Ohtsubo and P. Davis, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (2005) pp. 307–334. Crossref, Google Scholar
G. H. M. Van Tartwijk and G. P. Agrawal, Prog. Quant. Electron. 22, 43 (1998), DOI: 10.1016/S0079-6727(98)00008-1. Crossref, Web of Science, Google Scholar
G. D. Van Wiggeren and R. Roy, Science 279, 1198 (1998), DOI: 10.1126/science.279.5354.1198. Crossref, Web of Science, Google Scholar
S. M. Verduyn Lunel and B. Krauskopf, Fundamental Issues of Nonlinear Laser Dynamics (2000) pp. 66–86. Google Scholar