Nonlinear dynamics of semiconductor lasers with feedback and modulation |
Optics Express, Vol. 18, Issue 16, pp. 16955-16972 (2010)
http://dx.doi.org/10.1364/OE.18.016955
Acrobat PDF (7673 KB)
Abstract
The nonlinear dynamics of two semiconductor laser systems: (i) with optical feedback, and (ii) with optical feedback and direct current modulation are evaluated from multi-GHz-bandwidth output power time-series. Animations of compilations of the RF spectrum (from the FFT of the time-series) as a function of optical feedback level, injection current and modulation signal strength is demonstrated as a new tool to give insight into the dynamics. The results are contrasted with prior art and new observations include fine structure in the RF spectrum at low levels of optical feedback and non-stationary switching between periodic and chaotic dynamics for some sets of laser system parameters. Correlation dimension analysis successfully identifies periodic dynamics but most of the dynamical states are too complex to be extracted using standard algorithms.
© 2010 OSA
1. Introduction
2. G. C. Dente, P. S. Durkin, K. A. Wilson, and C. E. Moeller, “Chaos in the coherence collapse of semiconductor lasers,” IEEE J. Quantum Electron. 24(12), 2441–2447 (1988). [CrossRef]
6. J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990). [CrossRef] [PubMed]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
8. C. H. Lee, T. H. Yoon, and S. Y. Shin, “Period doubling and chaos in a directly modulated laser diode,” Appl. Phys. Lett. 46(1), 95–97 (1985). [CrossRef]
10. Y. H. Kao and H. T. Lin, “Virtual Hopf precursor of period-doubling route in directly modulated semiconductor-lasers,” IEEE J. Quantum Electron. 29(6), 1617–1623 (1993). [CrossRef]
11. L. Chusseau, E. Hemery, and J. M. Lourtioz, “Period doubling in directly modulated InGaAsP semiconductor-lasers,” Appl. Phys. Lett. 55(9), 822–824 (1989). [CrossRef]
13. S. Bennett, C. M. Snowden, and S. Iezekiel, “Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum Electron. 33(11), 2076–2083 (1997). [CrossRef]
14. H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 um InGaAsP distributed-feedback semiconductor-laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993). [CrossRef]
15. R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol. 4(11), 1655–1661 (1986). [CrossRef]
16. D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985). [CrossRef]
17. Y. Cho and T. Umeda, “Observation of chaos in a semiconductor laser with delayed feedback,” Opt. Commun. 59(2), 131–136 (1986). [CrossRef]
18. H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986). [CrossRef]
19. R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef]
3. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor-lasers with optical feedback - Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992). [CrossRef]
15. R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol. 4(11), 1655–1661 (1986). [CrossRef]
21. J. Sacher, D. Baums, P. Panknin, W. Elsässer, and E. O. Göbel, “Intensity instabilities of semiconductor lasers under current modulation, external light injection, and delayed feedback,” Phys. Rev. A 45(3), 1893–1905 (1992). [CrossRef] [PubMed]
22. J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef]
22. J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef]
15. R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol. 4(11), 1655–1661 (1986). [CrossRef]
25. T. Heil, I. Fischer, and W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58(4), R2672–R2675 (1998). [CrossRef]
26. T. Heil, I. Fischer, and W. Elsasser, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60(1), 634–641 (1999). [CrossRef]
5. S. Eriksson and A. M. Lindberg, “Observations on the dynamics of semiconductor lasers subjected to external optical injection,” J. Opt. B Quantum Semiclassical Opt. 4(2), 149–154 (2002). [CrossRef]
27. S. Eriksson, “Dependence of the experimental stability diagram of an optically injected semiconductor laser on the laser current,” Opt. Commun. 210(3-6), 343–353 (2002). [CrossRef]
29. S. Wieczorek, T. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2A), 045207 (2002). [CrossRef] [PubMed]
22. J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef]
30. M. T. Rosenstein, J. J. Collins, and C. J. Deluca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993). [CrossRef]
31. H. Kantz, “A robust method to estimate the maximal Lyapunov exponent of a time-series,” Phys. Lett. A 185(1), 77–87 (1994). [CrossRef]
32. K. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216(4-6), 405–412 (2003). [CrossRef]
33. T. Fordell and A. M. Lindberg, “Numerical stability maps of an optically injected semiconductor laser,” Opt. Commun. 242(4-6), 613–622 (2004). [CrossRef]
34. P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D 9(1-2), 189–208 (1983). [CrossRef]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
36. D. M. Kane, J. P. Toomey, M. W. Lee, and K. A. Shore, “Correlation dimension signature of wideband chaos synchronization of semiconductor lasers,” Opt. Lett. 31(1), 20–22 (2006). [CrossRef] [PubMed]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
37. S. Donati and C. R. Mirasso, “Introduction to the feature section on Optical Chaos and Applications to Cryptography,” IEEE J. Quantum Electron. 38(9), 1138–1140 (2002). [CrossRef]
38. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005). [CrossRef]
19. R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef]
40. I. Pierce, P. Rees, and P. S. Spencer, “Multimode dynamics in laser diodes with optical feedback,” Phys. Rev. A 61(5), 053801 (2000). [CrossRef]
2. Semiconductor laser with optical feedback
2.1 Experimental setup
41. S. Sivaprakasam and K. A. Shore, “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24(7), 466–468 (1999). [CrossRef]
43. J. Paul, S. Sivaprakasam, and K. A. Shore, “Dual-channel chaotic optical communications using external-cavity semiconductor lasers,” J. Opt. Soc. Am. B 21(3), 514–521 (2004). [CrossRef]
44. R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: The TISEAN package,” Chaos 9(2), 413–435 (1999). [CrossRef]
2.2 Results and discussion
45. C. McMahon, D. M. Kane, J. P. Toomey, and J. S. Lawrence, “High Accuracy Measurement of Relaxation Oscillation Frequency in Heavily Damped Quantum Well Lasers,” in Proceedings of the International Conference on Nanoscience and Nanotechnology, C. Jagadish, and G. Q. M. Lu, eds. (IEEE, Brisbane, 2006), pp. 497–500.
47. D. M. Kane and C. J. McMahon, “Instantaneous frequency measurement applied to semiconductor laser relaxation oscillations,” Appl. Phys. B 98(4), 759–765 (2010). [CrossRef]
19. R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef]
15. R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol. 4(11), 1655–1661 (1986). [CrossRef]
2.3 Correlation dimension analysis
34. P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D 9(1-2), 189–208 (1983). [CrossRef]
36. D. M. Kane, J. P. Toomey, M. W. Lee, and K. A. Shore, “Correlation dimension signature of wideband chaos synchronization of semiconductor lasers,” Opt. Lett. 31(1), 20–22 (2006). [CrossRef] [PubMed]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
7. J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
3. Directly modulated semiconductor laser with optical feedback
3.1 Experimental setup
44. R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: The TISEAN package,” Chaos 9(2), 413–435 (1999). [CrossRef]
3.2 Results and discussion
22. J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef]
22. J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef]
4. Conclusion
34. P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D 9(1-2), 189–208 (1983). [CrossRef]
Acknowledgements
References and links
1. | J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer-Verlag, Berlin, 2006). |
2. | G. C. Dente, P. S. Durkin, K. A. Wilson, and C. E. Moeller, “Chaos in the coherence collapse of semiconductor lasers,” IEEE J. Quantum Electron. 24(12), 2441–2447 (1988). [CrossRef] |
3. | J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor-lasers with optical feedback - Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992). [CrossRef] |
4. | H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993). [CrossRef] |
5. | S. Eriksson and A. M. Lindberg, “Observations on the dynamics of semiconductor lasers subjected to external optical injection,” J. Opt. B Quantum Semiclassical Opt. 4(2), 149–154 (2002). [CrossRef] |
6. | J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990). [CrossRef] [PubMed] |
7. | J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed] |
8. | C. H. Lee, T. H. Yoon, and S. Y. Shin, “Period doubling and chaos in a directly modulated laser diode,” Appl. Phys. Lett. 46(1), 95–97 (1985). [CrossRef] |
9. | T. H. Yoon, C. H. Lee, and S. Y. Shin, “Perturbation analysis of bistability and period doubling bifurcations in directly-modulated laser-diodes,” IEEE J. Quantum Electron. 25(9), 1993–2000 (1989). [CrossRef] |
10. | Y. H. Kao and H. T. Lin, “Virtual Hopf precursor of period-doubling route in directly modulated semiconductor-lasers,” IEEE J. Quantum Electron. 29(6), 1617–1623 (1993). [CrossRef] |
11. | L. Chusseau, E. Hemery, and J. M. Lourtioz, “Period doubling in directly modulated InGaAsP semiconductor-lasers,” Appl. Phys. Lett. 55(9), 822–824 (1989). [CrossRef] |
12. | E. Hemery, L. Chusseau, and J. M. Lourtioz, “Dynamic behaviors of semiconductor lasers under strong sinusoidal current modulation: modeling and experiments at 1.3 mm,” IEEE J. Quantum Electron. 26(4), 633–641 (1990). [CrossRef] |
13. | S. Bennett, C. M. Snowden, and S. Iezekiel, “Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum Electron. 33(11), 2076–2083 (1997). [CrossRef] |
14. | H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 um InGaAsP distributed-feedback semiconductor-laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993). [CrossRef] |
15. | R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol. 4(11), 1655–1661 (1986). [CrossRef] |
16. | D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985). [CrossRef] |
17. | Y. Cho and T. Umeda, “Observation of chaos in a semiconductor laser with delayed feedback,” Opt. Commun. 59(2), 131–136 (1986). [CrossRef] |
18. | H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986). [CrossRef] |
19. | R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef] |
20. | A. T. Gavrielides, and D. W. Sukow, “Experimental Observations,” in Unlocking Dynamical Diverstiy: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane, and K. A. Shore, eds. (John Wiley & Sons, West Sussex, 2005), pp. 81–145. |
21. | J. Sacher, D. Baums, P. Panknin, W. Elsässer, and E. O. Göbel, “Intensity instabilities of semiconductor lasers under current modulation, external light injection, and delayed feedback,” Phys. Rev. A 45(3), 1893–1905 (1992). [CrossRef] [PubMed] |
22. | J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef] |
23. | P. Spencer, P. Rees, and I. Pierce, “Theoretical Analysis,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane, and K. A. Shore, eds. (John Wiley & Sons, West Sussex, 2005), pp. 23–54. |
24. | D. Lenstra, G. Vemuri, and M. Yousefi, “Generalized Optical Feedback,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane, and K. A. Shore, eds. (John Wiley & Sons, West Sussex, 2005), pp. 55–80. |
25. | T. Heil, I. Fischer, and W. Elsasser, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58(4), R2672–R2675 (1998). [CrossRef] |
26. | T. Heil, I. Fischer, and W. Elsasser, “Influence of amplitude-phase coupling on the dynamics of semiconductor lasers subject to optical feedback,” Phys. Rev. A 60(1), 634–641 (1999). [CrossRef] |
27. | S. Eriksson, “Dependence of the experimental stability diagram of an optically injected semiconductor laser on the laser current,” Opt. Commun. 210(3-6), 343–353 (2002). [CrossRef] |
28. | T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” J. Opt. B Quantum Semiclassical Opt. 9(5), 765–784 (1997). [CrossRef] |
29. | S. Wieczorek, T. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2A), 045207 (2002). [CrossRef] [PubMed] |
30. | M. T. Rosenstein, J. J. Collins, and C. J. Deluca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993). [CrossRef] |
31. | H. Kantz, “A robust method to estimate the maximal Lyapunov exponent of a time-series,” Phys. Lett. A 185(1), 77–87 (1994). [CrossRef] |
32. | K. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216(4-6), 405–412 (2003). [CrossRef] |
33. | T. Fordell and A. M. Lindberg, “Numerical stability maps of an optically injected semiconductor laser,” Opt. Commun. 242(4-6), 613–622 (2004). [CrossRef] |
34. | P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D 9(1-2), 189–208 (1983). [CrossRef] |
35. | J. C. Sprott, “Chaos Data Analyzer The Professional Version,” (Physics Academic Software, 2003). |
36. | D. M. Kane, J. P. Toomey, M. W. Lee, and K. A. Shore, “Correlation dimension signature of wideband chaos synchronization of semiconductor lasers,” Opt. Lett. 31(1), 20–22 (2006). [CrossRef] [PubMed] |
37. | S. Donati and C. R. Mirasso, “Introduction to the feature section on Optical Chaos and Applications to Cryptography,” IEEE J. Quantum Electron. 38(9), 1138–1140 (2002). [CrossRef] |
38. | A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005). [CrossRef] |
39. | F. Sporleder, “Proceedings of the URSI International Symposium on Electromagnetic Theory,” in Proceedings of the URSI International Symposium on Electromagnetic Theory(Brussels, Belgium, 1983), p. 585. |
40. | I. Pierce, P. Rees, and P. S. Spencer, “Multimode dynamics in laser diodes with optical feedback,” Phys. Rev. A 61(5), 053801 (2000). [CrossRef] |
41. | S. Sivaprakasam and K. A. Shore, “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24(7), 466–468 (1999). [CrossRef] |
42. | S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, “Regimes of chaotic synchronization in external-cavity laser diodes,” IEEE J. Quantum Electron. 38(9), 1155–1161 (2002). [CrossRef] |
43. | J. Paul, S. Sivaprakasam, and K. A. Shore, “Dual-channel chaotic optical communications using external-cavity semiconductor lasers,” J. Opt. Soc. Am. B 21(3), 514–521 (2004). [CrossRef] |
44. | R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: The TISEAN package,” Chaos 9(2), 413–435 (1999). [CrossRef] |
45. | C. McMahon, D. M. Kane, J. P. Toomey, and J. S. Lawrence, “High Accuracy Measurement of Relaxation Oscillation Frequency in Heavily Damped Quantum Well Lasers,” in Proceedings of the International Conference on Nanoscience and Nanotechnology, C. Jagadish, and G. Q. M. Lu, eds. (IEEE, Brisbane, 2006), pp. 497–500. |
46. | D. M. Kane, and J. P. Toomey, “Precision threshold current measurement for semiconductor lasers based on relaxation oscillation frequency,” J. Lightwave Tech. (2009). |
47. | D. M. Kane and C. J. McMahon, “Instantaneous frequency measurement applied to semiconductor laser relaxation oscillations,” Appl. Phys. B 98(4), 759–765 (2010). [CrossRef] |
OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.1540) Lasers and laser optics : Chaos
(140.5960) Lasers and laser optics : Semiconductor lasers
(190.0190) Nonlinear optics : Nonlinear optics
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
ToC Category:
Lasers and Laser Optics
History
Original Manuscript: May 19, 2010
Revised Manuscript: June 26, 2010
Manuscript Accepted: July 12, 2010
Published: July 26, 2010
Citation
J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Nonlinear dynamics of semiconductor lasers with feedback and modulation," Opt. Express 18, 16955-16972 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16955
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References
- J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer-Verlag, Berlin, 2006).
- G. C. Dente, P. S. Durkin, K. A. Wilson, and C. E. Moeller, “Chaos in the coherence collapse of semiconductor lasers,” IEEE J. Quantum Electron. 24(12), 2441–2447 (1988). [CrossRef]
- J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor-lasers with optical feedback - Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992). [CrossRef]
- H. Li, J. Ye, and J. G. McInerney, “Detailed analysis of coherence collapse in semiconductor lasers,” IEEE J. Quantum Electron. 29(9), 2421–2432 (1993). [CrossRef]
- S. Eriksson and A. M. Lindberg, “Observations on the dynamics of semiconductor lasers subjected to external optical injection,” J. Opt. B Quantum Semiclassical Opt. 4(2), 149–154 (2002). [CrossRef]
- J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65(16), 1999–2002 (1990). [CrossRef] [PubMed]
- J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, “Automated correlation dimension analysis of optically injected solid state lasers,” Opt. Express 17(9), 7592–7608 (2009). [CrossRef] [PubMed]
- C. H. Lee, T. H. Yoon, and S. Y. Shin, “Period doubling and chaos in a directly modulated laser diode,” Appl. Phys. Lett. 46(1), 95–97 (1985). [CrossRef]
- T. H. Yoon, C. H. Lee, and S. Y. Shin, “Perturbation analysis of bistability and period doubling bifurcations in directly-modulated laser-diodes,” IEEE J. Quantum Electron. 25(9), 1993–2000 (1989). [CrossRef]
- Y. H. Kao and H. T. Lin, “Virtual Hopf precursor of period-doubling route in directly modulated semiconductor-lasers,” IEEE J. Quantum Electron. 29(6), 1617–1623 (1993). [CrossRef]
- L. Chusseau, E. Hemery, and J. M. Lourtioz, “Period doubling in directly modulated InGaAsP semiconductor-lasers,” Appl. Phys. Lett. 55(9), 822–824 (1989). [CrossRef]
- E. Hemery, L. Chusseau, and J. M. Lourtioz, “Dynamic behaviors of semiconductor lasers under strong sinusoidal current modulation: modeling and experiments at 1.3 mm,” IEEE J. Quantum Electron. 26(4), 633–641 (1990). [CrossRef]
- S. Bennett, C. M. Snowden, and S. Iezekiel, “Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes,” IEEE J. Quantum Electron. 33(11), 2076–2083 (1997). [CrossRef]
- H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 um InGaAsP distributed-feedback semiconductor-laser,” IEEE J. Quantum Electron. 29(6), 1668–1675 (1993). [CrossRef]
- R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5μm distributed feedback lasers,” J. Lightwave Technol. 4(11), 1655–1661 (1986). [CrossRef]
- D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985). [CrossRef]
- Y. Cho and T. Umeda, “Observation of chaos in a semiconductor laser with delayed feedback,” Opt. Commun. 59(2), 131–136 (1986). [CrossRef]
- H. Olesen, J. Osmundsen, and B. Tromborg, “Nonlinear dynamics and spectral behavior for an external cavity laser,” IEEE J. Quantum Electron. 22(6), 762–773 (1986). [CrossRef]
- R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef]
- A. T. Gavrielides, and D. W. Sukow, “Experimental Observations,” in Unlocking Dynamical Diverstiy: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane, and K. A. Shore, eds. (John Wiley & Sons, West Sussex, 2005), pp. 81–145.
- J. Sacher, D. Baums, P. Panknin, W. Elsässer, and E. O. Göbel, “Intensity instabilities of semiconductor lasers under current modulation, external light injection, and delayed feedback,” Phys. Rev. A 45(3), 1893–1905 (1992). [CrossRef] [PubMed]
- J. S. Lawrence and D. M. Kane, “Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation,” IEEE J. Quantum Electron. 38(2), 185–192 (2002). [CrossRef]
- P. Spencer, P. Rees, and I. Pierce, “Theoretical Analysis,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane, and K. A. Shore, eds. (John Wiley & Sons, West Sussex, 2005), pp. 23–54.
- D. Lenstra, G. Vemuri, and M. Yousefi, “Generalized Optical Feedback,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane, and K. A. Shore, eds. (John Wiley & Sons, West Sussex, 2005), pp. 55–80.
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