Abstract

The dispersive broadening of a single optical pulse traveling within a Fabry–Pérot semiconductor laser was measured for propagation over 58 round trips of the cavity, a distance of 352 mm. The interference between two copropagating pulses with variable relative phase (stabilized to within 2π×0.02 rad) was used to relate the group-velocity dispersion to the gain curvature. With both single- and double-pulse propagation measurements, the complex group-velocity dispersion (including gain curvature) was found to be 8.7+5.9i ps2/m at twice the laser-threshold bias current. When the laser bias was increased from 1.4 to 2 times the laser threshold, the gain curvature decreased by 2.8%, and the group-velocity dispersion showed less than 0.1% variation.

© 2004 Optical Society of America

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2000 (3)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

1999 (3)

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

1998 (2)

S. Haacke, R. A. Taylor, I. Bar-Joseph, M. J. S. P. Brasil, M. Hartig, and B. Deveaud, “Improving the signal-to-noise ratio of femtosecond luminescence upconversion by multichannel detection,” J. Opt. Soc. Am. B 15, 1410–1417 (1998).
[CrossRef]

M. Kauer, J. R. A. Cleaver, J. J. Baumberg, and A. P. Heberle, “Femtosecond dynamics in semiconductor lasers: dark pulse formation,” Appl. Phys. Lett. 72, 1626–1628 (1998).
[CrossRef]

1997 (3)

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in long-cavity λ/4-shifted DFB laser using its lasing beam as pump beam,” IEEE J. Quantum Electron. 33, 2002–2010 (1997).
[CrossRef]

J. W. D. Chi, K. A. Shore, and J. Le Bihan, “Highly nondegenerate four-wave mixing in uniform λ/4-shifted DFB lasers,” IEEE J. Quantum Electron. 33, 2011–2020 (1997).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

1996 (2)

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[CrossRef]

1994 (2)

B. Bauer, F. Henry, and R. Schimpe, “Gain stabilization of a semiconductor optical amplifier by distributed-feedback,” IEEE Photon. Technol. Lett. 6, 182–185 (1994).
[CrossRef]

K. L. Hall, G. Lenz, A. M. Darwish, and E. P. Ippen, “Sub-picosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

1990 (1)

M. P. Kesler and C. Harder, “Gain and index measurements in GaAlAs quantum-well lasers,” IEEE Photon. Technol. Lett. 2, 464–466 (1990).
[CrossRef]

1989 (1)

M. P. Kesler and E. P. Ippen, “Femtosecond time-domain measurements of group velocity dispersion in AlGaAs diode lasers,” Electron. Lett. 25, 640–642 (1989).
[CrossRef]

1988 (1)

J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24, 276–288 (1988).
[CrossRef]

1983 (1)

J. P. van der Ziel and R. A. Logan, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. 19, 164–168 (1983).
[CrossRef]

1975 (1)

B. W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Alphonse, G. A.

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

Bachmann, M.

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Bar-Joseph, I.

Bauer, B.

B. Bauer, F. Henry, and R. Schimpe, “Gain stabilization of a semiconductor optical amplifier by distributed-feedback,” IEEE Photon. Technol. Lett. 6, 182–185 (1994).
[CrossRef]

Baumberg, J. J.

M. Kauer, J. R. A. Cleaver, J. J. Baumberg, and A. P. Heberle, “Femtosecond dynamics in semiconductor lasers: dark pulse formation,” Appl. Phys. Lett. 72, 1626–1628 (1998).
[CrossRef]

Blow, K. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Borri, P.

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

Brasil, M. J. S. P.

Chi, J. W. D.

J. W. D. Chi, K. A. Shore, and J. Le Bihan, “Highly nondegenerate four-wave mixing in uniform λ/4-shifted DFB lasers,” IEEE J. Quantum Electron. 33, 2011–2020 (1997).
[CrossRef]

Cleaver, J. R. A.

M. Kauer, J. R. A. Cleaver, J. J. Baumberg, and A. P. Heberle, “Femtosecond dynamics in semiconductor lasers: dark pulse formation,” Appl. Phys. Lett. 72, 1626–1628 (1998).
[CrossRef]

Connolly, J. C.

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

Cotter, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Dagens, B.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

Darwish, A. M.

K. L. Hall, G. Lenz, A. M. Darwish, and E. P. Ippen, “Sub-picosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Delfyett, P. J.

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

Deveaud, B.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

S. Haacke, R. A. Taylor, I. Bar-Joseph, M. J. S. P. Brasil, M. Hartig, and B. Deveaud, “Improving the signal-to-noise ratio of femtosecond luminescence upconversion by multichannel detection,” J. Opt. Soc. Am. B 15, 1410–1417 (1998).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Doussiere, P.

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Ducellier, T.

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Dupertuis, M. A.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Ellis, A. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Emery, J. Y.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Gee, S.

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

Goldstein, L.

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Haacke, S.

S. Haacke, R. A. Taylor, I. Bar-Joseph, M. J. S. P. Brasil, M. Hartig, and B. Deveaud, “Improving the signal-to-noise ratio of femtosecond luminescence upconversion by multichannel detection,” J. Opt. Soc. Am. B 15, 1410–1417 (1998).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Hakki, B. W.

B. W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Hall, K. L.

K. L. Hall, G. Lenz, A. M. Darwish, and E. P. Ippen, “Sub-picosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Harder, C.

M. P. Kesler and C. Harder, “Gain and index measurements in GaAlAs quantum-well lasers,” IEEE Photon. Technol. Lett. 2, 464–466 (1990).
[CrossRef]

Hartig, M.

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

Heberle, A. P.

M. Kauer, J. R. A. Cleaver, J. J. Baumberg, and A. P. Heberle, “Femtosecond dynamics in semiconductor lasers: dark pulse formation,” Appl. Phys. Lett. 72, 1626–1628 (1998).
[CrossRef]

Henry, F.

B. Bauer, F. Henry, and R. Schimpe, “Gain stabilization of a semiconductor optical amplifier by distributed-feedback,” IEEE Photon. Technol. Lett. 6, 182–185 (1994).
[CrossRef]

Hessler, T.

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Hessler, T. P.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

Hvam, J. M.

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

Ippen, E. P.

K. L. Hall, G. Lenz, A. M. Darwish, and E. P. Ippen, “Sub-picosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Femtosecond time-domain measurements of group velocity dispersion in AlGaAs diode lasers,” Electron. Lett. 25, 640–642 (1989).
[CrossRef]

Ishikawa, H.

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in long-cavity λ/4-shifted DFB laser using its lasing beam as pump beam,” IEEE J. Quantum Electron. 33, 2002–2010 (1997).
[CrossRef]

Jourdan, A.

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Kauer, M.

M. Kauer, J. R. A. Cleaver, J. J. Baumberg, and A. P. Heberle, “Femtosecond dynamics in semiconductor lasers: dark pulse formation,” Appl. Phys. Lett. 72, 1626–1628 (1998).
[CrossRef]

Kelly, A. E.

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Kesler, M. P.

M. P. Kesler and C. Harder, “Gain and index measurements in GaAlAs quantum-well lasers,” IEEE Photon. Technol. Lett. 2, 464–466 (1990).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Femtosecond time-domain measurements of group velocity dispersion in AlGaAs diode lasers,” Electron. Lett. 25, 640–642 (1989).
[CrossRef]

Kotaki, Y.

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

Kuwatsuka, H.

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in long-cavity λ/4-shifted DFB laser using its lasing beam as pump beam,” IEEE J. Quantum Electron. 33, 2002–2010 (1997).
[CrossRef]

Langbein, W.

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

Le Bihan, J.

J. W. D. Chi, K. A. Shore, and J. Le Bihan, “Highly nondegenerate four-wave mixing in uniform λ/4-shifted DFB lasers,” IEEE J. Quantum Electron. 33, 2011–2020 (1997).
[CrossRef]

Lenz, G.

K. L. Hall, G. Lenz, A. M. Darwish, and E. P. Ippen, “Sub-picosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Little, B. E.

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

Logan, R. A.

J. P. van der Ziel and R. A. Logan, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. 19, 164–168 (1983).
[CrossRef]

Manning, R. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Matsuda, M.

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in long-cavity λ/4-shifted DFB laser using its lasing beam as pump beam,” IEEE J. Quantum Electron. 33, 2002–2010 (1997).
[CrossRef]

Mecozzi, A.

Mørk, J.

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

J. Mørk and A. Mecozzi, “Theory of the ultrafast optical response of active semiconductor waveguides,” J. Opt. Soc. Am. B 13, 1803–1816 (1996).
[CrossRef]

Nesset, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

NGo, R.

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Nitta, I.

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

Paoli, T. L.

B. W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

Phillips, I. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Pleumeekers, J. L.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Pommereau, F.

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Poustie, A. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Rogers, D. C.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Romstad, F.

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

Schimpe, R.

B. Bauer, F. Henry, and R. Schimpe, “Gain stabilization of a semiconductor optical amplifier by distributed-feedback,” IEEE Photon. Technol. Lett. 6, 182–185 (1994).
[CrossRef]

Selbmann, P. E.

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Shah, J.

J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24, 276–288 (1988).
[CrossRef]

Shi, H.

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

Shoji, H.

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in long-cavity λ/4-shifted DFB laser using its lasing beam as pump beam,” IEEE J. Quantum Electron. 33, 2002–2010 (1997).
[CrossRef]

Shore, K. A.

J. W. D. Chi, K. A. Shore, and J. Le Bihan, “Highly nondegenerate four-wave mixing in uniform λ/4-shifted DFB lasers,” IEEE J. Quantum Electron. 33, 2011–2020 (1997).
[CrossRef]

Simoyama, T.

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

Soulage, G.

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

Taylor, R. A.

S. Haacke, R. A. Taylor, I. Bar-Joseph, M. J. S. P. Brasil, M. Hartig, and B. Deveaud, “Improving the signal-to-noise ratio of femtosecond luminescence upconversion by multichannel detection,” J. Opt. Soc. Am. B 15, 1410–1417 (1998).
[CrossRef]

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

van der Ziel, J. P.

J. P. van der Ziel and R. A. Logan, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. 19, 164–168 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

M. Kauer, J. R. A. Cleaver, J. J. Baumberg, and A. P. Heberle, “Femtosecond dynamics in semiconductor lasers: dark pulse formation,” Appl. Phys. Lett. 72, 1626–1628 (1998).
[CrossRef]

P. E. Selbmann, T. P. Hessler, J. L. Pleumeekers, M. A. Dupertuis, B. Deveaud, B. Dagens, and J. Y. Emery, “Observation of dark-pulse formation in gain-clamped semiconductor optical amplifiers by cross-gain modulation,” Appl. Phys. Lett. 75, 3760–3762 (1999).
[CrossRef]

Electron. Lett. (2)

M. Bachmann, P. Doussiere, J. Y. Emery, R. NGo, F. Pommereau, L. Goldstein, G. Soulage, and A. Jourdan, “Polarisation-insensitive clamped-gain SOA with integrated spot-size convertor and DBR gratings for WDM applications at 1.55 μm wavelength,” Electron. Lett. 32, 2076–2078 (1996).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Femtosecond time-domain measurements of group velocity dispersion in AlGaAs diode lasers,” Electron. Lett. 25, 640–642 (1989).
[CrossRef]

IEEE J. Quantum Electron. (6)

J. P. van der Ziel and R. A. Logan, “Dispersion of the group velocity refractive index in GaAs double heterostructure lasers,” IEEE J. Quantum Electron. 19, 164–168 (1983).
[CrossRef]

J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24, 276–288 (1988).
[CrossRef]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

P. J. Delfyett, H. Shi, S. Gee, I. Nitta, J. C. Connolly, and G. A. Alphonse, “Joint time–frequency measurements of mode-locked semiconductor diode lasers and dynamics using frequency-resolved optical gating,” IEEE J. Quantum Electron. 35, 487–500 (1999).
[CrossRef]

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in long-cavity λ/4-shifted DFB laser using its lasing beam as pump beam,” IEEE J. Quantum Electron. 33, 2002–2010 (1997).
[CrossRef]

J. W. D. Chi, K. A. Shore, and J. Le Bihan, “Highly nondegenerate four-wave mixing in uniform λ/4-shifted DFB lasers,” IEEE J. Quantum Electron. 33, 2011–2020 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

T. Simoyama, H. Kuwatsuka, B. E. Little, M. Matsuda, Y. Kotaki, and H. Ishikawa, “High-efficiency wavelength conversion using FWM in an SOA integrated DFB laser,” IEEE Photon. Technol. Lett. 12, 576–578 (2000).
[CrossRef]

B. Bauer, F. Henry, and R. Schimpe, “Gain stabilization of a semiconductor optical amplifier by distributed-feedback,” IEEE Photon. Technol. Lett. 6, 182–185 (1994).
[CrossRef]

M. P. Kesler and C. Harder, “Gain and index measurements in GaAlAs quantum-well lasers,” IEEE Photon. Technol. Lett. 2, 464–466 (1990).
[CrossRef]

J. Appl. Phys. (1)

B. W. Hakki and T. L. Paoli, “Gain spectra in GaAs double-heterostructure injection lasers,” J. Appl. Phys. 46, 1299–1306 (1975).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

K. L. Hall, G. Lenz, A. M. Darwish, and E. P. Ippen, “Sub-picosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Opt. Express (1)

P. Borri, F. Romstad, W. Langbein, A. E. Kelly, J. Mørk, and J. M. Hvam, “Separation of coherent and incoherent nonlin-earities in a heterodyne pump–probe experiment,” Opt. Express 3, 107–112 (2000).
[CrossRef]

Quantum Semiclassic. Opt. (1)

T. Hessler, S. Haacke, J. L. Pleumeekers, P. E. Selbmann, M. A. Dupertuis, B. Deveaud, R. A. Taylor, P. Doussiere, M. Bachmann, T. Ducellier, and J. Y. Emery, “Time-resolved relaxation oscillations in gain-clamped semiconductor optical amplifiers by pump and probe measurements,” Quantum Semiclassic. Opt. 9, 675–679 (1997).
[CrossRef]

Science (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef] [PubMed]

Other (2)

G. Guekos, Photonic Devices for Telecommunications (Springer-Verlag, Berlin, 1999).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995).

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Figures (8)

Fig. 1
Fig. 1

Schematic of experimental configuration: sub-100-fs pulses with 790-nm central wavelength were generated in a mode-locked Ti:sapphire laser, pumped with an argon-ion laser. A half-wave plate (λ/2) was used to match the polarization to the Brewster angle of the prism in the dispersion compensator. A Fresnel rhomb (FR) was tuned to divide the pulse into sampling and injection beam lines at a polarizing beam splitter (PBS). A wobbler scanned short time delays, and a computer-controlled delay stage was used for larger displacements. A Michelson interferometer split the injected pulse into two time-delayed pulses. The interferometer was actively stabilized with a data-acquisition processor (DAP) board by adjusting the piezoelectric (PZT) mirror to maintain the fringe pattern of the He–Ne laser on two photodiodes (PDs). The pulses were injected into a semiconductor laser (SL) through a microscope objective (MO), coupled in with a beam splitter (BS). The emission from the SL was upconverted when coincident with the sampling pulse on the β-BBO nonlinear crystal. The upconverted light was filtered out and detected with a photomultiplier tube.

Fig. 2
Fig. 2

Observed pulse-echo measurements for single-pulse injection at laser-diode bias currents of 25 and 35 mA. At 25 mA, the pulse persisted for long times, whereas at 35 mA, a dark pulse formed, and the original bright pulse died out after 300 ps.

Fig. 3
Fig. 3

Circles show the measured pulse width of a recirculating pulse within a FP laser diode biased at 25 mA. The dashed curve is the best fit with the GVD without including GC. The thin solid curve is the best fit including the GC and GVD. The thick solid curve is the best fit including the GC and GVD, with an additional constraint from the double-pulse measurements (see Subsection 3.C).

Fig. 4
Fig. 4

Emission from FP laser diode (bias of 36 mA) after injection of two pulses for two different time spans. Two phase values are shown, separated by π. The top curve is displaced by 1.2 mW.

Fig. 5
Fig. 5

Array of contour plots showing intensity emission from FP lasers biased at 36 mA after double-pulse injection. Horizontal axis of each contour plot is 6.8 ps wide, showing the emission pattern of one round trip. Vertical axis is the relative phase increment between the pulses, from 0 to 2π. The contour plots are arranged with different rows corresponding to different initial time separations between pulses: 0.3, 0.6, and 0.9 ps. Columns show emission pattern after different propagation distances within the laser diode: 3, 10.2, 17.4, and 24.6 mm.

Fig. 6
Fig. 6

Array of contour plots of intensity distribution for two interfering Gaussian field distributions of varying separation (rows from top to bottom use τ12=0.3, 0.6, and 0.9 ps) and chirp (columns use C=0, 1, 2, 3). Vertical and horizontal axes are the phase increment (from 0 to 2π) and the time delay (span of 6.8 ps).

Fig. 7
Fig. 7

Pattern of two pulses, separated by 0.75 ps, interfering after propagating 32 round trips in the laser diode, biased at 37 mA. Triangles show the peak location of each pulse when injected alone. Three pulse energies are shown (scaled by the injected pulse energy and offset to allow for comparison), with little variation in the interference pattern.

Fig. 8
Fig. 8

Interference of two pulses after propagating 19 round trips within the laser diode for two phase values (separated by π) and three different bias currents. Experimentally measured values shown with dots, offset to remove the laser-diode emission background. The best fit, with Eq. (9), is shown with a solid curve. Three fitting parameters were used at 25 mA: A, C, and ϕ. The phase values, ϕ, were then fixed for the remaining fits, leaving only two free parameters. The chirp parameter was found to vary from 1.39 to 1.57; however, the average over both independent phase fits varied from 1.45 to 1.48 only.

Equations (9)

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Uz=-i2β2 2UT2,
U(z, T)=U(0, T)1-iβ2z exp-iT22β2z,
U(z, T)1-iβ2z exp-iT22β2z.
Tw2=β2R2+β2I2β2Rz,
U(T)=exp-(1+iC)T22Tw2.
C=β2RzTw(0)2+β2Iz.
U(z, T)=Tw(0)Tw(0)2-iβ2z exp-T22[Tw(0)2-iβ2z]=Tw(0)Tw(0)2-iβ2z×exp-[Tw(0)2+β2Iz+iβ2Rz]T22[(Tw(0)2+β2Iz)2+(β2Rz)2].
F=Tw2Tw2+β2Iz.
I(ϕ, τ12, T)=Aexp-(1+iC)T22Tw2+exp-(1+iC)(T-τ12)22Tw2+iϕ2.

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