Self-induced transparency modelocking of quantum cascade lasers in the presence of saturable nonlinearity and group velocity dispersion
Optics Express, Vol. 18, Issue 6, pp. 5639-5653 (2010)
http://dx.doi.org/10.1364/OE.18.005639
Acrobat PDF (5676 KB)
Abstract
We consider the impact of saturable nonlinearity and group velocity dispersion on self-induced transparency (SIT) modelocking of quantum cascade lasers (QCLs). We find that self-induced transparency modelocking in QCLs can be obtained in the presence of saturable nonlinearity if the saturable loss or gain is below a critical limit. The limit for the saturable loss is significantly more stringent than the limit for the saturable gain. Stable modelocked pulses are also obtained in the presence of both normal and anomalous group velocity dispersion when its magnitude is below a critical value. The stability limit for the saturable loss becomes less stringent when group velocity dispersion is simultaneously present. However, the stability limit for the saturable gain is not significantly affected. All these limits depend on the ratio of the SIT-induced gain and absorption to the linear loss. Realistic values for both the saturable nonlinearity and chromatic dispersion are within the range in which SIT modelocking is predicted to be stable.
© 2010 Optical Society of America
1. Introduction
1. J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994). [CrossRef] [PubMed]
2. C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express 17, 12929–12943 (2009). [CrossRef] [PubMed]
3. C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007). [CrossRef]
5. H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100, 167401 (2008). [CrossRef] [PubMed]
6. H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition,” IEEE J. Quantum Electron. 45, 307–321 (2009). [CrossRef]
7. H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968); R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser-active medium,” Z. Phys. 213, 420–450 (1968). [CrossRef]
8. P. W. Smith, “The self-pulsing laser oscillator,” IEEE J. Quantum Electron. 3, 627–635 (1967). [CrossRef]
11. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–912 (1967). [CrossRef]
15. C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett. 102, 023903 (2009). [CrossRef] [PubMed]
18. R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites,” Science 290, 1739–1742 (2000). [CrossRef] [PubMed]
3. C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007). [CrossRef]
19. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008). [CrossRef]
20. H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Höfler, and T. B. Norris, “Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers,” Opt. Express 15, 15898 (2007). [CrossRef] [PubMed]
15. C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett. 102, 023903 (2009). [CrossRef] [PubMed]
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
17. M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
21. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Quantum. Electron. 6, 1173–1185 (2000). [CrossRef]
17. M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
17. M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
17. M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
2. Theoretical model
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
21. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Quantum. Electron. 6, 1173–1185 (2000). [CrossRef]
19. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008). [CrossRef]
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
19. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008). [CrossRef]
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
17. M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
17. M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
3. Nonlinearity
3.1. Saturable loss (γ > 0)
15. C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett. 102, 023903 (2009). [CrossRef] [PubMed]
16. M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef]
3.2. Saturable gain (γ < 0)
4. Group velocity dispersion
5. Saturable nonlinearity and group velocity dispersion
6. Conclusion
19. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008). [CrossRef]
20. H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Höfler, and T. B. Norris, “Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers,” Opt. Express 15, 15898 (2007). [CrossRef] [PubMed]
References and links
1. | J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994). [CrossRef] [PubMed] |
2. | C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kärtner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, “Mode-locked pulses from mid-infrared quantum cascade lasers,” Opt. Express 17, 12929–12943 (2009). [CrossRef] [PubMed] |
3. | C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, M. Troccoli, J. Faist, and F. Capasso, “Coherent instabilities in a semiconductor laser with fast gain recovery,” Phys. Rev. A 75, 031802 (2007). [CrossRef] |
4. | C. Sirtori and R. Teissier, “Quantum Cascade Lasers: Overview of Basic Principles of Operation and State of the Art,” in Intersubband Transitions in Quantum Structures, R. Paiella, ed. (McGraw-Hill, New York, 2006). |
5. | H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Gain recovery dynamics and photon-driven transport in quantum cascade lasers,” Phys. Rev. Lett. 100, 167401 (2008). [CrossRef] [PubMed] |
6. | H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, “Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition,” IEEE J. Quantum Electron. 45, 307–321 (2009). [CrossRef] |
7. | H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968); R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser-active medium,” Z. Phys. 213, 420–450 (1968). [CrossRef] |
8. | P. W. Smith, “The self-pulsing laser oscillator,” IEEE J. Quantum Electron. 3, 627–635 (1967). [CrossRef] |
9. | T. Uchida and A. Ueki, “Self locking of gas lasers,” IEEE J. Quantum Electron. 3, 17–30 (1967). [CrossRef] |
10. | H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975). [CrossRef] |
11. | S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–912 (1967). [CrossRef] |
12. | S. L. McCall and E. L. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–489 (1969). [CrossRef] |
13. | V. V. Kozlov, “Self-induced transparency soliton laser via coherent mode locking,” Phys. Rev. A 56, 1607–1612 (1997). [CrossRef] |
14. | V. V. Kozlov, “Self-induced transparency soliton laser,” JETP Lett. 69, 906–911 (1999) [Pis’ma Zh. Eksp. Teor. Fiz. 69, 856 (1999)]. [CrossRef] |
15. | C. R. Menyuk and M. A. Talukder, “Self-induced transparency modelocking of quantum cascade lasers,” Phys. Rev. Lett. 102, 023903 (2009). [CrossRef] [PubMed] |
16. | M. A. Talukder and C. R. Menyuk, “Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers,” Phys. Rev. A 79, 063841 (2009). [CrossRef] |
17. | M. A. Talukder and C. R. Menyuk, “Effects of backward propagating waves and lumped mirror losses on self-induced transparency modelocking in quantum cascade lasers,” Appl. Phys. Lett. 95, 071109 (2009). [CrossRef] |
18. | R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, “Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites,” Science 290, 1739–1742 (2000). [CrossRef] [PubMed] |
19. | A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 053804 (2008). [CrossRef] |
20. | H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Höfler, and T. B. Norris, “Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers,” Opt. Express 15, 15898 (2007). [CrossRef] [PubMed] |
21. | H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Quantum. Electron. 6, 1173–1185 (2000). [CrossRef] |
22. | L. Allen and J. H. Eberley, Optical Resonance and Two Level Atoms (Dover, New York, 1987). |
23. | R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, London, 2003). |
OCIS Codes
(140.4050) Lasers and laser optics : Mode-locked lasers
(140.5965) Lasers and laser optics : Semiconductor lasers, quantum cascade
ToC Category:
Lasers and Laser Optics
History
Original Manuscript: December 22, 2009
Revised Manuscript: January 28, 2010
Manuscript Accepted: February 21, 2010
Published: March 4, 2010
Citation
Muhammad Anisuzzaman Talukder and Curtis R. Menyuk, "Self-induced transparency modelocking of quantum cascade lasers in the presence of saturable nonlinearity and group velocity dispersion," Opt. Express 18, 5639-5653 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5639
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References
- J. Faist, F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho, "Quantum cascade laser," Science 264, 553?556 (1994). [CrossRef] [PubMed]
- C. Y. Wang, L. Kuznetsova, V. M. Gkortsas, L. Diehl, F. X. Kartner, M. A. Belkin, A. Belyanin, X. Li, D. Ham, H. Schneider, P. Grant, C. Y. Song, S. Haffouz, Z. R. Wasilewski, H. C. Liu, and F. Capasso, "Mode-locked pulses from mid-infrared quantum cascade lasers," Opt. Express 17, 12929?12943 (2009). [CrossRef] [PubMed]
- C. Y. Wang, L. Diehl, A. Gordon, C. Jirauschek, F. X. K¨artner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, M. Troccoli, J. Faist, and F. Capasso, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802 (2007). [CrossRef]
- C. Sirtori and R. Teissier, "Quantum Cascade Lasers: Overview of Basic Principles of Operation and State of the Art," in Intersubband Transitions in Quantum Structures, R. Paiella, ed., (McGraw-Hill, New York, 2006).
- H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Gain recovery dynamics and photon-driven transport in quantum cascade lasers," Phys. Rev. Lett. 100, 167401 (2008). [CrossRef] [PubMed]
- H. Choi, L. Diehl, Z.-K. Wu, M. Giovannini, J. Faist, F. Capasso, and T. B. Norris, "Time-resolved investigations of electronic transport dynamics in quantum cascade lasers based on diagonal lasing transition," IEEE J. Quantum Electron. 45, 307?321 (2009). [CrossRef]
- H. Risken and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662?4672 (1968);R. Graham and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420?450 (1968). [CrossRef]
- P. W. Smith, "The self-pulsing laser oscillator," IEEE J. Quantum Electron. 3, 627?635 (1967). [CrossRef]
- T. Uchida and A. Ueki, "Self locking of gas lasers," IEEE J. Quantum Electron. 3, 17?30 (1967). [CrossRef]
- H. A. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049?3058 (1975). [CrossRef]
- S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908?912 (1967). [CrossRef]
- S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457?489 (1969). [CrossRef]
- V. V. Kozlov, "Self-induced transparency soliton laser via coherent mode locking," Phys. Rev. A 56, 1607?1612 (1997). [CrossRef]
- V. V. Kozlov, "Self-induced transparency soliton laser," JETP Lett. 69, 906?911 (1999) [Pis’ma Zh. Eksp. Teor. Fiz. 69, 856 (1999)]. [CrossRef]
- C. R. Menyuk and M. A. Talukder, "Self-induced transparency modelocking of quantum cascade lasers," Phys. Rev. Lett. 102, 023903 (2009). [CrossRef] [PubMed]
- M. A. Talukder and C. R. Menyuk, "Analytical and computational study of self-induced transparency modelocking in quantum cascade lasers," Phys. Rev. A 79, 063841 (2009). [CrossRef]
- M. A. Talukder and C. R. Menyuk, "Effects of backward propagating waves and lumped mirror losses on selfinduced transparency modelocking in quantum cascade lasers," Appl. Phys. Lett. 95, 071109 (2009). [CrossRef]
- R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, "Self-mode-locking of quantum cascade lasers with giant ultrafast optical nonlinearites," Science 290, 1739?1742 (2000). [CrossRef] [PubMed]
- A. Gordon, C. Y. Wang, L. Diehl, F. X. Kartner, A. Belyanin, D. Bour, S. Corzine, G. Hofler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, "Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning," Phys. Rev. A 77, 053804 (2008). [CrossRef]
- H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, "Time-domain upconversion measurements of group-velocity dispersion in quantum cascade lasers," Opt. Express 15, 15898 (2007). [CrossRef] [PubMed]
- H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Quantum. Electron. 6, 1173?1185 (2000). [CrossRef]
- L. Allen and J. H. Eberley, Optical Resonance and Two Level Atoms (Dover, New York, 1987).
- R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, London, 2003).
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