Abstract

A new method for measuring the linewidth enhancement factor (α-parameter) of semiconductor lasers is proposed and discussed. The method itself provides an estimation of the measurement error, thus self-validating the entire procedure. The α-parameter is obtained from the temporal profile and the instantaneous frequency (chirp) of the pulses generated by gain switching. The time resolved chirp is measured with a polarization based optical differentiator. The accuracy of the obtained values of the α-parameter is estimated from the comparison between the directly measured pulse spectrum and the spectrum reconstructed from the chirp and the temporal profile of the pulse. The method is applied to a VCSEL and to a DFB laser emitting around 1550 nm at different temperatures, obtaining a measurement error lower than ± 8%.

©2012 Optical Society of America

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References

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  1. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
    [Crossref]
  2. I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19(22), 927–929 (1983).
    [Crossref]
  3. Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
    [Crossref]
  4. C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor alpha of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983).
    [Crossref]
  5. F. Devaux, Y. Sorel, and J. K. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993).
    [Crossref]
  6. M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21(21), 981–982 (1985).
    [Crossref]
  7. J. Jeong and Y. K. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33(7), 605–606 (1997).
    [Crossref]
  8. P. Lazaridis, G. Debarge, and P. Gallion, “Time-bandwidth product of chirped sech(2) pulses: application to phase-amplitude-coupling factor measurement,” Opt. Lett. 20(10), 1160–1162 (1995).
    [Crossref] [PubMed]
  9. 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(14), 997–998 (1990).
    [Crossref]
  10. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
    [Crossref]
  11. M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers - an overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
    [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(1), 6–15 (2007).
    [Crossref]
  13. T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a Vertical-Cavity Surface-Emitting Laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
    [Crossref]
  14. K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52(4), 257–259 (1988).
    [Crossref]
  15. F. Li, Y. Park, and J. Azaña, “Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD),” Opt. Lett. 32(22), 3364–3366 (2007).
    [Crossref] [PubMed]
  16. A. Consoli, J. M. Tijero, and I. Esquivias, “Time resolved chirp measurements of gain switched semiconductor laser using a polarization based optical differentiator,” Opt. Express 19(11), 10805–10812 (2011).
    [Crossref] [PubMed]
  17. R. Tucker, “High-speed modulation of semiconductor lasers,” J. Lightwave Technol. 3(6), 1180–1192 (1985).
    [Crossref]
  18. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., 1995).
  19. A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
    [Crossref]
  20. F. Li, Y. Park, and J. Azaña, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” J. Lightwave Technol. 27(21), 4623–4633 (2009).
    [Crossref]

2011 (1)

2010 (1)

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

2009 (1)

2008 (1)

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a Vertical-Cavity Surface-Emitting Laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
[Crossref]

2007 (2)

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a Vertical-Cavity Surface-Emitting Laser,” IEEE J. Quantum Electron. 43(1), 6–15 (2007).
[Crossref]

F. Li, Y. Park, and J. Azaña, “Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD),” Opt. Lett. 32(22), 3364–3366 (2007).
[Crossref] [PubMed]

2004 (1)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

1997 (1)

J. Jeong and Y. K. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33(7), 605–606 (1997).
[Crossref]

1995 (1)

1993 (1)

F. Devaux, Y. Sorel, and J. K. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993).
[Crossref]

1992 (1)

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
[Crossref]

1990 (1)

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(14), 997–998 (1990).
[Crossref]

1988 (1)

K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52(4), 257–259 (1988).
[Crossref]

1987 (1)

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers - an overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

1985 (2)

R. Tucker, “High-speed modulation of semiconductor lasers,” J. Lightwave Technol. 3(6), 1180–1192 (1985).
[Crossref]

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21(21), 981–982 (1985).
[Crossref]

1983 (2)

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor alpha of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983).
[Crossref]

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19(22), 927–929 (1983).
[Crossref]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Azaña, J.

Balle, S.

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

Birocheau, C.

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
[Crossref]

Buus, J.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers - an overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

Collins, J. V.

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19(22), 927–929 (1983).
[Crossref]

Consoli, A.

A. Consoli, J. M. Tijero, and I. Esquivias, “Time resolved chirp measurements of gain switched semiconductor laser using a polarization based optical differentiator,” Opt. Express 19(11), 10805–10812 (2011).
[Crossref] [PubMed]

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

Debarge, G.

Destrez, A.

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
[Crossref]

Devaux, F.

F. Devaux, Y. Sorel, and J. K. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993).
[Crossref]

Donati, S.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

D'Ottavi, A.

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(14), 997–998 (1990).
[Crossref]

Esquivias, I.

A. Consoli, J. M. Tijero, and I. Esquivias, “Time resolved chirp measurements of gain switched semiconductor laser using a polarization based optical differentiator,” Opt. Express 19(11), 10805–10812 (2011).
[Crossref] [PubMed]

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

Fordell, T.

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a Vertical-Cavity Surface-Emitting Laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (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(1), 6–15 (2007).
[Crossref]

Gallagher, D. F. G.

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21(21), 981–982 (1985).
[Crossref]

Gallion, P.

Giuliani, G.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

Harder, C.

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor alpha of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983).
[Crossref]

Hassine, L.

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
[Crossref]

Henning, I. D.

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19(22), 927–929 (1983).
[Crossref]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Hernandez, F. J. L.

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

Hui, R.

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(14), 997–998 (1990).
[Crossref]

Jeong, J.

J. Jeong and Y. K. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33(7), 605–606 (1997).
[Crossref]

Kerdiles, J. K.

F. Devaux, Y. Sorel, and J. K. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993).
[Crossref]

Lau, K. Y.

K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52(4), 257–259 (1988).
[Crossref]

Lazaridis, P.

Li, F.

Lindberg, A. M.

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a Vertical-Cavity Surface-Emitting Laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (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(1), 6–15 (2007).
[Crossref]

Mecozzi, A.

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(14), 997–998 (1990).
[Crossref]

Mulet, J.

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

Osinski, M.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers - an overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[Crossref]

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21(21), 981–982 (1985).
[Crossref]

Park, Y.

Park, Y. K.

J. Jeong and Y. K. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33(7), 605–606 (1997).
[Crossref]

Sorel, Y.

F. Devaux, Y. Sorel, and J. K. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993).
[Crossref]

Spano, P.

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(14), 997–998 (1990).
[Crossref]

Tijero, J. M.

Toffano, Z.

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
[Crossref]

Tucker, R.

R. Tucker, “High-speed modulation of semiconductor lasers,” J. Lightwave Technol. 3(6), 1180–1192 (1985).
[Crossref]

Vahala, K.

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor alpha of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983).
[Crossref]

White, I. H.

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21(21), 981–982 (1985).
[Crossref]

Yariv, A.

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor alpha of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983).
[Crossref]

Yu, Y.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

Appl. Phys. Lett. (2)

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor alpha of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983).
[Crossref]

K. Y. Lau, “Gain switching of semiconductor injection lasers,” Appl. Phys. Lett. 52(4), 257–259 (1988).
[Crossref]

Electron. Lett. (5)

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19(22), 927–929 (1983).
[Crossref]

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28(1), 9–11 (1992).
[Crossref]

M. Osinski, D. F. G. Gallagher, and I. H. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21(21), 981–982 (1985).
[Crossref]

J. Jeong and Y. K. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33(7), 605–606 (1997).
[Crossref]

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(14), 997–998 (1990).
[Crossref]

IEEE J. Quantum Electron. (3)

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers - an overview,” IEEE J. Quantum Electron. 23(1), 9–29 (1987).
[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(1), 6–15 (2007).
[Crossref]

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

IEEE Photon. Technol. Lett. (3)

T. Fordell and A. M. Lindberg, “Noise correlation, regenerative amplification, and the linewidth enhancement factor of a Vertical-Cavity Surface-Emitting Laser,” IEEE Photon. Technol. Lett. 20(9), 667–669 (2008).
[Crossref]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004).
[Crossref]

A. Consoli, I. Esquivias, F. J. L. Hernandez, J. Mulet, and S. Balle, “Characterization of gain-switched pulses from 1.55-µm VCSEL,” IEEE Photon. Technol. Lett. 22(11), 772–774 (2010).
[Crossref]

J. Lightwave Technol. (3)

F. Li, Y. Park, and J. Azaña, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” J. Lightwave Technol. 27(21), 4623–4633 (2009).
[Crossref]

F. Devaux, Y. Sorel, and J. K. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993).
[Crossref]

R. Tucker, “High-speed modulation of semiconductor lasers,” J. Lightwave Technol. 3(6), 1180–1192 (1985).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Other (1)

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., 1995).

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Figures (5)

Fig. 1
Fig. 1 Simulation results. Solid line: pulse intensity (left and bottom axes). Dashed line: time resolved chirp (right and bottom axes). The open circles represent the chirp plotted as a function of (4πP(t))−1dP(t)/dt (right and upper axes).

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Fig. 2
Fig. 2 Experimental results obtained with the 1550 nm VCSEL. Solid line: pulse intensity (left and bottom axes). Dashed line: time resolved chirp (right and bottom axes). The open circles represent the chirp plotted as a function of (4πP(t))−1dP(t)/dt (right and upper axes).

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Fig. 3
Fig. 3 Comparison between the measured (black solid line), reconstructed (open circles) and convolved (solid squares) spectra of the pulse shown in Fig. 2.

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Fig. 4
Fig. 4 Linewidth enhancement factor obtained at different temperatures for the DFB laser (solid circles) and for the VCSEL (open squares).

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Fig. 5
Fig. 5 α-parameter error as a function of the differentiator slope normalized to the nominal value, and spectral error for different OSA bandwidths.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ν(t)= α 4π ( 1 P(t) dP(t) dt +κP(t) )
ε S =100⋅ ∫ | I m ( f )− I r ( f ) | df ∫ I m ( f ) df
ν(t)= [ ( Q(t) A ) 2 − ( d( P(t) ) dt ) 2 ] / P(t) −Δf
ε α =100⋅ | α RE − α rec | α RE

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