## Four-wave mixing analysis on injection-locked quantum dot semiconductor lasers |

Optics Express, Vol. 21, Issue 18, pp. 21242-21253 (2013)

http://dx.doi.org/10.1364/OE.21.021242

Acrobat PDF (825 KB)

### Abstract

We derive a simplified rate equation model for the four-wave mixing (FWM) analysis on quantum dot (QD) semiconductor lasers subject to optical injection. The regenerative and the amplitude modulation spectra of the FWM signals with different intrinsic laser parameters and external injection conditions are investigated. By curve fitting the regenerative and the amplitude modulation spectra obtained experimentally, the intrinsic parameters of a commercial single-mode QD laser under different injection conditions are extracted. The linewidth enhancement factor *α* at different injection levels and detunings are shown, where a reduction of up to 39% from its free-running value is demonstrated. By increasing the injection strength, the *α* can be further reduced to minimized the chirp in optical communications.

© 2013 OSA

## 1. Introduction

1. C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express **20**, 101–110 (2012). [CrossRef] [PubMed]

3. S. Melnik, G. Huyet, and A. Uskov, “The linewidth enhancement factor α of quantum dot semiconductor lasers,” Opt. Express **14**, 2950–2955 (2006). [CrossRef] [PubMed]

*α*has been extensively studied that it determines the chirp when a laser is under modulation [4

4. S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. **183**, 195–205 (2000). [CrossRef]

5. Y. Okajima, S. K. Hwang, and J. M. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun. **219**, 357–364 (2003). [CrossRef]

*α*ranging from 0 to 60 have been reported [6

6. B. Dagens, A. Markus, J. X. Chen, J. G. Provost, D. Make, O. L. Gouezigou, J. Landreau, A. Fiore, and B. Thedrez, “Giant linewidth enhancement factor and purely frequency modulated emission from quantum dot laser,” Electron. Lett. **41**, 323–324 (2005). [CrossRef]

7. T. C. Newell, D. J. Bossert, A. Stintz, B. Fuchs, K. J. Malloy, and L. F. Lester, “Gain and linewidth enhancement factor in InAs quantum-dot laser diodes,” IEEE Photon. Technol. Lett. **11**, 1527–1529 (1999). [CrossRef]

8. K. Kechaou, F. Grillot, J. G. Provost, B. Thedrez, and D. Erasme, “Self-injected semiconductor distributed feedback lasers for frequency chirp stabilization,” Opt. Express **20**, 26062–26074 (2012). [CrossRef] [PubMed]

10. J. G. Provost and F. Grillot, “Measuring the chirp and the linewidth enhancement factor of optoelectronic devices with a Mach-Zehnder interferometer,” IEEE Photon. J. **3**, 476–488 (2011). [CrossRef]

*α*, methods utilizing the FM/AM response ratio under small signal current modulation [10

10. J. G. Provost and F. Grillot, “Measuring the chirp and the linewidth enhancement factor of optoelectronic devices with a Mach-Zehnder interferometer,” IEEE Photon. J. **3**, 476–488 (2011). [CrossRef]

11. S. Gerhard, C. Schilling, F. Gerschutz, M. Fischer, J. Koeth, I. Krestnikov, A. Kovsh, M. Kamp, S. Hofling, and A. Forchel, “Frequency-dependent linewidth enhancement factor of quantum-dot lasers,” IEEE Photon. Technol. Lett. **20**, 1736–1738 (2008). [CrossRef]

12. T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. **43**, 6–15 (2007). [CrossRef]

12. T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. **43**, 6–15 (2007). [CrossRef]

15. I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. **24**, 148–154 (1988). [CrossRef]

*α*but not other intrinsic laser parameters needed in the theoretical models. To extract the intrinsic parameters of QD lasers all at the same time, a method based on the four-wave mixing (FWM) analysis has been developed and demonstrated [1

1. C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express **20**, 101–110 (2012). [CrossRef] [PubMed]

16. J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. **30**, 957–965 (1994). [CrossRef]

*α*and other intrinsic laser parameters used in the rate equations including the carrier decay rates in the quantum dots

*γ*, the photon decay rate in the laser cavity

_{d}*γ*, the differential gain

_{s}*g*

_{0}, the interaction cross section of the carriers in the dots with the electric field

*ς*, and the gain saturation coefficient

*ε*can all be simultaneously obtained.

*α*and other intrinsic parameters of a commercial single-mode QD laser under different injection strengths and detuning frequencies are extracted. A reduction of

*α*to below its free-running value with optical injection is demonstrated.

## 2. Theoretical model

*E*and a detuning frequency Δ for the injection field. The time evolution of the complex amplitude of the electric field

_{p}*E*, the occupancy probability of the energy level in quantum dots

*ρ*, and the carrier density in the surrounding quantum wells

*N*can be expressed as: [17

_{W}17. D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. **98**, 153903 (2007). [CrossRef] [PubMed]

20. B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, E. A. Viktorov, and T. Erneux, “Optically injected single-mode quantum dot lasers,” in *Quantum Dot Devices*,Zhiming M. Wang, eds. (Springer, 2012), pp. 1–22. [CrossRef]

*γ*is the photon decay rate in the laser cavity,

_{s}*γ*and

_{N}*γ*are the carrier decay rates in the quantum wells and the quantum dots, respectively,

_{d}*C*is the capture rate from the quantum wells into the quantum dots,

*J*is the bias current per quantum dot,

*ς*is the interaction cross section of the carriers in the dots with the electric field,

*α*is the linewidth enhancement factor,

*υ*is the group velocity,

_{g}*g*

_{0}is the differential gain, and

*ε*is the gain saturation coefficient, respectively.

21. M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Modeling room-temperature lasing spectra of 1.3-μ m self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injection,” J. Appl. Phys. **97**, 043523 (2005). [CrossRef]

22. M. Gioannini, A. Sevega, and I. Montrosset, “Simulations of differential gain and linewidth enhancement factor of quantum dot semiconductor lasers,” Opt. Quantum Electron. **38**, 381–394 (2006). [CrossRef]

1. C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express **20**, 101–110 (2012). [CrossRef] [PubMed]

19. T. Erneux, E. A. Viktorov, B. Kelleher, D. Goulding, S. P. Hegarty, and G. Huyet, “Optically injected quantum-dot lasers,” Opt. Lett. **35**, 937–939 (2010). [CrossRef] [PubMed]

20. B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, E. A. Viktorov, and T. Erneux, “Optically injected single-mode quantum dot lasers,” in *Quantum Dot Devices*,Zhiming M. Wang, eds. (Springer, 2012), pp. 1–22. [CrossRef]

*N*,

_{W}*γ*,

_{N}*C*,

*υ*, and

_{g}*ε*are further eliminated and the rate equations are rewritten as follows: where

*J̃*=

*J*/(2

*γ*) is the pump and

_{d}q*g*is the gain coefficient. To study the effect of optical injection on QD lasers, an additional injection term is added to the complex electric field in Eq. (4) where

*E*and Δ

_{inj}*are the respective field amplitude and frequency of the injected light. When injection-locked, the frequency of the QD laser is locked to the frequency of the injected light at Δ*

_{inj}*. (Note that, while we focus on the effects of the optical injection in this paper, similar process can be done to derive the simplified rate equation model for FWM analysis on QD lasers subject to external perturbations such as optical feedback or optoelectronic feedback.)*

_{inj}*E*= 0). In the degenerate FWM states, the electric field can be expanded approximately to the first order from the steady-state point. Thus the electric field can be expressed as the composition of the free-oscillating signal, the regenerative amplification signal, and the FWM signal: where

_{p}*E*

_{0},

*E*, and

_{r}*E*are the steady-state field amplitude of the free-oscillating signal, the complex amplitude of the regenerative amplification signal, and the complex amplitude of the FWM signal, respectively. Note that the Δ is now the frequency detuning of the probe signal from the injected light at Δ

_{f}*.*

_{inj}*ρ*will also oscillate at the frequencies of the beat signals. To the first order, the occupancy probability can be described as where

*ρ*

_{0}is the steady-state occupancy probability of the quantum dots without the perturbation from the probe signal and

*ρ*

_{1}is the amplitudes of the carrier fluctuation.

*σ*of the complex amplitude, it is generally much smaller than the steady-state field amplitude

*E*

_{0}. Therefore the higher order terms can be ignored, which gives

*E*, the FWM field

_{r}*E*, and the amplitude modulation

_{f}*σ*at different detuning frequencies Δ can be obtained: where

*α*= 1.37,

*γ*= 34.8 (ns

_{s}^{−1}),

*γ*= 0.71 (ns

_{d}^{−1}),

*g*= 29.8, and the injection parameters used are

*k*= 1.0 (

_{inj}*k*=

_{inj}*E*

_{inj}/E_{0}is the normalized injection strength) and Δ

*= 0, respectively. (Similar results are obtained with the parameters previously used in [1*

_{inj}**20**, 101–110 (2012). [CrossRef] [PubMed]

## 3. Characteristics of the FWM spectra of a QD laser subject to optical injection

*α*,

*γ*,

_{s}*γ*, and

_{d}*g*are shown in Fig. 2. Since the regenerative and the amplitude modulation signals contain all the information of the FWM signal [16

16. J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. **30**, 957–965 (1994). [CrossRef]

*α*only alters the depth of the valley in the regenerative spectrum [1

**20**, 101–110 (2012). [CrossRef] [PubMed]

*α*alters both the depths of the valleys in the regenerative and amplitude modulation spectra for a QD laser subject to optical injection. When

*γ*increases, as shown in Figs. 2(b) and 2(f), the valleys in the spectra become deeper and shift toward higher detuning frequency. Meanwhile, the peaks in the spectra of the amplitude modulation are shifted away from zero detuning. Figures 2(c) and 2(g) show the spectra when

_{s}*γ*increases. As can be seen, the valleys and the peaks are shifted away from zero detuning while the valleys become shallower and the peaks reduce in their magnitudes. For the effect of the gain coefficient

_{d}*g*, similar behaviors are observed for the spectra of the regenerative and amplitude modulation signals shown in Figs. 2(d) and 2(h) as those shown in Figs. 2(b) and 2(g), respectively. Moreover, the peaks in the spectra of the amplitude modulation become more symmetric as the

*g*increases.

*k*

_{0}increases. At the same time, the peaks in the spectra of the amplitude modulation shown in Fig. 3(c) become more asymmetric. On the other hand, increasing the detuning frequency of the injected light Δ

*makes the valleys deeper in both the spectra of the regenerative and amplitude modulation signals as shown in Figs. 3(b) and 3(d), respectively. Also, the peaks in the spectra of the amplitude modulation become more asymmetric. With the distinct features of each parameter on the characteristic peaks and valleys shown in Figs. 2 and 3, the parameters of a QD laser subject to optical injection are expected to be extracted effectively by curve fitting with the analytical model.*

_{inj}## 4. Experimental setup

## 5. Experimental results

*P*= 0 mW, 0.1 mW, 0.2 mW, and 0.3 mW at a detuning frequency Δ

_{inj}*= 0, respectively. Here the injection power*

_{inj}*P*is measured before the injection light being coupled into the QD laser. Figures 6(a)–6(d) and 6(e)–6(h) show the respective spectra at detuning frequencies of Δ

_{inj}*= −1.22, −0.67, 0, and 0.67 GHz with an injection power of*

_{inj}*P*= 0.15 mW. By the least squares fitting with the analytically derived curves from Eqs. (9)–(11) (blue curves), the laser parameters including the linewidth enhancement factor

_{inj}*α*, the photon decay rate

*γ*, the carrier decay rates in the quantum dots

_{s}*γ*, the gain coefficient

_{d}*g*, and the normalized injection strength within the laser cavity

*k*are extracted and listed in Table 1. Note that, from the previous study of the FWM analysis on QD lasers, the error ranges of the

_{inj}*α*extracted with this method is expected to be less than 5% while the

*γ*,

_{s}*γ*, and

_{d}*g*are expected to be less than 15%, respectively [1

**20**, 101–110 (2012). [CrossRef] [PubMed]

*α*decreases as the injection power increases. Moreover, it has a minimum value at around Δ

*= 0. Figure 7(a) shows the*

_{inj}*α*of the injection-locked QD laser for different injection powers with Δ

*= 0. As can be seen, the*

_{inj}*α*decreases distinctly as the injection power increases. A minimum

*α*of 0.84 is observed at an injection power of 0.9 mW, which is reduced by 39% from its free-running value. (Note that similar behavior of the reduction of the

*α*in optically-injected Fabry-P

*é*rot quantum dash lasers at zero detuning has also been reported [23

23. L. F. Lester, F. Grillot, N. A. Naderi, and V. Kovanis, “Differential gain enhancement in a quantum dash laser using strong optical injection,” Proc. SPIE **8619**, 861907, (2013). [CrossRef]

*α*under different detuning frequencies, Fig. 7(b) shows the

*α*of the QD laser with different injection conditions in the stable locking region (bounded by the green curves). As can be seen, while the

*α*in general decreases as the injection power increases, local minima occur around zero detuning under different injection powers. To the best of our knowledge, this variations of the

*α*for the single-mode DFB QD laser under different injection powers and detuning frequencies are experimentally demonstrated the first time. The behaviors shown in Fig. 7 qualitatively agree with those previously reported in the theoretical study [2

2. B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E **86**, 065201 (2012). [CrossRef]

## 6. Conclusion

*α*, the photon decay rate

*γ*, the carrier decay rates in the quantum dots

_{s}*γ*, the gain coefficient

_{d}*g*, and the normalized injection strength

*k*are successfully extracted. To the best of our knowledge, the variations of the

_{inj}*α*in an injection-locked single-mode DFB QD laser at different injection powers and detuning frequencies are experimentally demonstrated the first time. A reduction of

*α*up to 39% from its free-running value is shown, which is expected to reduce the chirp in optical communications for long distance transmission. While in this paper we focus on the effects of the optical injection, similar process can be done to derive the simplified rate equation model for FWM analysis on QD lasers subject to external perturbations such as optical feedback or optoelectronic feedback. How the external feedback affects the laser parameters will be next studied.

## Acknowledgments

## References and links

1. | C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express |

2. | B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E |

3. | S. Melnik, G. Huyet, and A. Uskov, “The linewidth enhancement factor α of quantum dot semiconductor lasers,” Opt. Express |

4. | S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. |

5. | Y. Okajima, S. K. Hwang, and J. M. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun. |

6. | B. Dagens, A. Markus, J. X. Chen, J. G. Provost, D. Make, O. L. Gouezigou, J. Landreau, A. Fiore, and B. Thedrez, “Giant linewidth enhancement factor and purely frequency modulated emission from quantum dot laser,” Electron. Lett. |

7. | T. C. Newell, D. J. Bossert, A. Stintz, B. Fuchs, K. J. Malloy, and L. F. Lester, “Gain and linewidth enhancement factor in InAs quantum-dot laser diodes,” IEEE Photon. Technol. Lett. |

8. | K. Kechaou, F. Grillot, J. G. Provost, B. Thedrez, and D. Erasme, “Self-injected semiconductor distributed feedback lasers for frequency chirp stabilization,” Opt. Express |

9. | F. Grillot, B. Dagens, J. G. Provost, H. Su, and L. F. Lester, “Gain compression and above-threshold linewidth enhancement factor in 1.3-μ m InAs-GaAs quantum-dot lasers,” IEEE J. Quantum Electron. |

10. | J. G. Provost and F. Grillot, “Measuring the chirp and the linewidth enhancement factor of optoelectronic devices with a Mach-Zehnder interferometer,” IEEE Photon. J. |

11. | S. Gerhard, C. Schilling, F. Gerschutz, M. Fischer, J. Koeth, I. Krestnikov, A. Kovsh, M. Kamp, S. Hofling, and A. Forchel, “Frequency-dependent linewidth enhancement factor of quantum-dot lasers,” IEEE Photon. Technol. Lett. |

12. | T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. |

13. | K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett. |

14. | R. Hui, A. Mecozzi, A. D’ottavi, and P. Spano, “Novel measurement technique of alpha factor in DFB semiconductor lasers by injection locking,” Electron. Lett. |

15. | I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron. |

16. | J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron. |

17. | D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett. |

18. | D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, “Sensitivity of quantum-dot semiconductor lasers to optical feedback,” Opt. Lett. |

19. | T. Erneux, E. A. Viktorov, B. Kelleher, D. Goulding, S. P. Hegarty, and G. Huyet, “Optically injected quantum-dot lasers,” Opt. Lett. |

20. | B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, E. A. Viktorov, and T. Erneux, “Optically injected single-mode quantum dot lasers,” in |

21. | M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Modeling room-temperature lasing spectra of 1.3-μ m self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injection,” J. Appl. Phys. |

22. | M. Gioannini, A. Sevega, and I. Montrosset, “Simulations of differential gain and linewidth enhancement factor of quantum dot semiconductor lasers,” Opt. Quantum Electron. |

23. | L. F. Lester, F. Grillot, N. A. Naderi, and V. Kovanis, “Differential gain enhancement in a quantum dash laser using strong optical injection,” Proc. SPIE |

24. | N. A. Naderi, F. Grillot, V. Kovanis, and L. F. Lester, “Simultaneous low linewidth enhancement factor and high bandwidth quantum-dash injection-locked laser,” in Proceedings of IEEE Photonics Conference (IEEE, 2011), pp. 115–116. |

**OCIS Codes**

(140.3520) Lasers and laser optics : Lasers, injection-locked

(140.5960) Lasers and laser optics : Semiconductor lasers

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(290.3700) Scattering : Linewidth

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: July 8, 2013

Revised Manuscript: August 23, 2013

Manuscript Accepted: August 25, 2013

Published: September 3, 2013

**Citation**

Chih-Hao Lin and Fan-Yi Lin, "Four-wave mixing analysis on injection-locked quantum dot semiconductor lasers," Opt. Express **21**, 21242-21253 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21242

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### References

- C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express20, 101–110 (2012). [CrossRef] [PubMed]
- B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E86, 065201 (2012). [CrossRef]
- S. Melnik, G. Huyet, and A. Uskov, “The linewidth enhancement factor α of quantum dot semiconductor lasers,” Opt. Express14, 2950–2955 (2006). [CrossRef] [PubMed]
- S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun.183, 195–205 (2000). [CrossRef]
- Y. Okajima, S. K. Hwang, and J. M. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun.219, 357–364 (2003). [CrossRef]
- B. Dagens, A. Markus, J. X. Chen, J. G. Provost, D. Make, O. L. Gouezigou, J. Landreau, A. Fiore, and B. Thedrez, “Giant linewidth enhancement factor and purely frequency modulated emission from quantum dot laser,” Electron. Lett.41, 323–324 (2005). [CrossRef]
- T. C. Newell, D. J. Bossert, A. Stintz, B. Fuchs, K. J. Malloy, and L. F. Lester, “Gain and linewidth enhancement factor in InAs quantum-dot laser diodes,” IEEE Photon. Technol. Lett.11, 1527–1529 (1999). [CrossRef]
- K. Kechaou, F. Grillot, J. G. Provost, B. Thedrez, and D. Erasme, “Self-injected semiconductor distributed feedback lasers for frequency chirp stabilization,” Opt. Express20, 26062–26074 (2012). [CrossRef] [PubMed]
- F. Grillot, B. Dagens, J. G. Provost, H. Su, and L. F. Lester, “Gain compression and above-threshold linewidth enhancement factor in 1.3-μ m InAs-GaAs quantum-dot lasers,” IEEE J. Quantum Electron.44, 946–951 (2008). [CrossRef]
- J. G. Provost and F. Grillot, “Measuring the chirp and the linewidth enhancement factor of optoelectronic devices with a Mach-Zehnder interferometer,” IEEE Photon. J.3, 476–488 (2011). [CrossRef]
- S. Gerhard, C. Schilling, F. Gerschutz, M. Fischer, J. Koeth, I. Krestnikov, A. Kovsh, M. Kamp, S. Hofling, and A. Forchel, “Frequency-dependent linewidth enhancement factor of quantum-dot lasers,” IEEE Photon. Technol. Lett.20, 1736–1738 (2008). [CrossRef]
- T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron.43, 6–15 (2007). [CrossRef]
- K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett.17, 1128–1130 (1992). [CrossRef] [PubMed]
- R. Hui, A. Mecozzi, A. D’ottavi, and P. Spano, “Novel measurement technique of alpha factor in DFB semiconductor lasers by injection locking,” Electron. Lett.26, 997–998 (1990). [CrossRef]
- I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24, 148–154 (1988). [CrossRef]
- J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron.30, 957–965 (1994). [CrossRef]
- D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a quantum dot semiconductor laser with optical injection,” Phys. Rev. Lett.98, 153903 (2007). [CrossRef] [PubMed]
- D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, “Sensitivity of quantum-dot semiconductor lasers to optical feedback,” Opt. Lett.29, 1072–1074 (2004). [CrossRef]
- T. Erneux, E. A. Viktorov, B. Kelleher, D. Goulding, S. P. Hegarty, and G. Huyet, “Optically injected quantum-dot lasers,” Opt. Lett.35, 937–939 (2010). [CrossRef] [PubMed]
- B. Kelleher, D. Goulding, S. P. Hegarty, G. Huyet, E. A. Viktorov, and T. Erneux, “Optically injected single-mode quantum dot lasers,” in Quantum Dot Devices,Zhiming M. Wang, eds. (Springer, 2012), pp. 1–22. [CrossRef]
- M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Modeling room-temperature lasing spectra of 1.3-μ m self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening of optical gain under current injection,” J. Appl. Phys.97, 043523 (2005). [CrossRef]
- M. Gioannini, A. Sevega, and I. Montrosset, “Simulations of differential gain and linewidth enhancement factor of quantum dot semiconductor lasers,” Opt. Quantum Electron.38, 381–394 (2006). [CrossRef]
- L. F. Lester, F. Grillot, N. A. Naderi, and V. Kovanis, “Differential gain enhancement in a quantum dash laser using strong optical injection,” Proc. SPIE8619, 861907, (2013). [CrossRef]
- N. A. Naderi, F. Grillot, V. Kovanis, and L. F. Lester, “Simultaneous low linewidth enhancement factor and high bandwidth quantum-dash injection-locked laser,” in Proceedings of IEEE Photonics Conference (IEEE, 2011), pp. 115–116.

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