Abstract

We present a method to experimentally characterize the gain filter and calculate a corresponding parabolic gain bandwidth of lasers that are described by “class A” dynamics by solving the master equation of spectral condensation for Gaussian spectra. We experimentally determine the gain filter, with an equivalent parabolic gain bandwidth of up to 51 nm, for broad-band InGaAs/GaAs quantum well gain surface-emitting semiconductor laser structures capable of producing pulses down to 60 fs width when mode-locked with an optical Stark saturable absorber mirror.

© 2010 OSA

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  1. A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
    [CrossRef]
  2. U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006).
    [CrossRef]
  3. P. Klopp, U. Griebner, M. Zorn, A. Klehr, A. Liero, M. Weyers, and G. Erbert, “Mode-locked InGaAs-AlGaAs disk laser generating sub-200-fs pulses, pulse picking and amplification by a tapered diode amplifier,” Opt. Express 17(13), 10820–10834 (2009).
    [CrossRef] [PubMed]
  4. H. A. Haus, “Theory of mode-locking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 (1975).
    [CrossRef]
  5. Z. Mihoubi, G. J. Daniell, K. G. Wilcox, and A. C. Tropper, “Numerical model of the optical Stark effect as a mode-locking mechanism for femtosecond vertical-external-cavity surface-emitting semiconductor lasers,” in CLEO/QELS'08 (San Jose CA, 2008).
  6. A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
    [CrossRef]
  7. K. G. Wilcox, Z. Mihoubi, G. J. Daniell, S. Elsmere, A. Quarterman, I. Farrer, D. A. Ritchie, and A. Tropper, “Ultrafast optical Stark mode-locked semiconductor laser,” Opt. Lett. 33(23), 2797–2799 (2008).
    [CrossRef] [PubMed]
  8. S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
    [CrossRef]
  9. A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
    [CrossRef]
  10. A. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
    [CrossRef]
  11. V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).
  12. V. Baev, T. Latz, and P. Toschek, “Laser intracavity absorption spectroscopy,” Appl. Phys. B 69(3), 171–202 (1999).
    [CrossRef]
  13. A. Garnache, A. A. Kachanov, F. Stoeckel, and R. Houdre, “Diode-pumped broadband vertical-external-cavity surface-emitting semiconductor laser applied to high-sensitivity intracavity absorption spectroscopy,” J. Opt. Soc. Am. B 17(9), 1589–1598 (2000).
    [CrossRef]
  14. A. Garnache, A. Ouvrard, and D. Romanini, “Single-Frequency operation of External-Cavity VCSELs: Non-linear multimode temporal dynamics and quantum limit,” Opt. Express 15(15), 9403–9417 (2007).
    [CrossRef] [PubMed]
  15. D. Findlay and R. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966).
    [CrossRef]
  16. M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
    [CrossRef]
  17. A. Siegman, Lasers, (University Science Books, 1986) p. 359.

2009

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

P. Klopp, U. Griebner, M. Zorn, A. Klehr, A. Liero, M. Weyers, and G. Erbert, “Mode-locked InGaAs-AlGaAs disk laser generating sub-200-fs pulses, pulse picking and amplification by a tapered diode amplifier,” Opt. Express 17(13), 10820–10834 (2009).
[CrossRef] [PubMed]

2008

2007

2006

A. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
[CrossRef]

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006).
[CrossRef]

2005

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

2004

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

2002

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

2000

1999

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
[CrossRef]

V. Baev, T. Latz, and P. Toschek, “Laser intracavity absorption spectroscopy,” Appl. Phys. B 69(3), 171–202 (1999).
[CrossRef]

1992

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

1975

H. A. Haus, “Theory of mode-locking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 (1975).
[CrossRef]

1966

D. Findlay and R. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966).
[CrossRef]

Apostolopoulos, V.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

Baev, V.

V. Baev, T. Latz, and P. Toschek, “Laser intracavity absorption spectroscopy,” Appl. Phys. B 69(3), 171–202 (1999).
[CrossRef]

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

Clay, R.

D. Findlay and R. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966).
[CrossRef]

Daniell, G. J.

Elsmere, S.

Elsmere, S. P.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

Erbert, G.

Eschner, J.

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

Farrer, I.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

K. G. Wilcox, Z. Mihoubi, G. J. Daniell, S. Elsmere, A. Quarterman, I. Farrer, D. A. Ritchie, and A. Tropper, “Ultrafast optical Stark mode-locked semiconductor laser,” Opt. Lett. 33(23), 2797–2799 (2008).
[CrossRef] [PubMed]

Findlay, D.

D. Findlay and R. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966).
[CrossRef]

Foreman, H. D.

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

Garnache, A.

A. Garnache, A. Ouvrard, and D. Romanini, “Single-Frequency operation of External-Cavity VCSELs: Non-linear multimode temporal dynamics and quantum limit,” Opt. Express 15(15), 9403–9417 (2007).
[CrossRef] [PubMed]

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

A. Garnache, A. A. Kachanov, F. Stoeckel, and R. Houdre, “Diode-pumped broadband vertical-external-cavity surface-emitting semiconductor laser applied to high-sensitivity intracavity absorption spectroscopy,” J. Opt. Soc. Am. B 17(9), 1589–1598 (2000).
[CrossRef]

Griebner, U.

Hakimi, F.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
[CrossRef]

Haus, H. A.

H. A. Haus, “Theory of mode-locking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 (1975).
[CrossRef]

Hoogland, S.

A. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
[CrossRef]

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

Hoogland, S. H.

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

Houdre, R.

Kachanov, A. A.

Keller, U.

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006).
[CrossRef]

Klehr, A.

Klopp, P.

Kuznetsov, M.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
[CrossRef]

Latz, T.

V. Baev, T. Latz, and P. Toschek, “Laser intracavity absorption spectroscopy,” Appl. Phys. B 69(3), 171–202 (1999).
[CrossRef]

Liero, A.

Mihoubi, Z.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

K. G. Wilcox, Z. Mihoubi, G. J. Daniell, S. Elsmere, A. Quarterman, I. Farrer, D. A. Ritchie, and A. Tropper, “Ultrafast optical Stark mode-locked semiconductor laser,” Opt. Lett. 33(23), 2797–2799 (2008).
[CrossRef] [PubMed]

Mooradian, A.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
[CrossRef]

Ouvrard, A.

Paeth, E.

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

Quarterman, A.

Quarterman, A. H.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

Ritchie, D. A.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

K. G. Wilcox, Z. Mihoubi, G. J. Daniell, S. Elsmere, A. Quarterman, I. Farrer, D. A. Ritchie, and A. Tropper, “Ultrafast optical Stark mode-locked semiconductor laser,” Opt. Lett. 33(23), 2797–2799 (2008).
[CrossRef] [PubMed]

Roberts, J.

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

Roberts, J. S.

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

Romanini, D.

Sagnes, I.

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

Saint-Girons, G.

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

Schuler, R.

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

Sprague, R.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
[CrossRef]

Stoeckel, F.

Toschek, P.

V. Baev, T. Latz, and P. Toschek, “Laser intracavity absorption spectroscopy,” Appl. Phys. B 69(3), 171–202 (1999).
[CrossRef]

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

Tropper, A.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

K. G. Wilcox, Z. Mihoubi, G. J. Daniell, S. Elsmere, A. Quarterman, I. Farrer, D. A. Ritchie, and A. Tropper, “Ultrafast optical Stark mode-locked semiconductor laser,” Opt. Lett. 33(23), 2797–2799 (2008).
[CrossRef] [PubMed]

A. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
[CrossRef]

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

Tropper, A. C.

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006).
[CrossRef]

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

Weyers, M.

Wilcox, K. G.

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

K. G. Wilcox, Z. Mihoubi, G. J. Daniell, S. Elsmere, A. Quarterman, I. Farrer, D. A. Ritchie, and A. Tropper, “Ultrafast optical Stark mode-locked semiconductor laser,” Opt. Lett. 33(23), 2797–2799 (2008).
[CrossRef] [PubMed]

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

Zorn, M.

Appl. Phys. B

V. Baev, T. Latz, and P. Toschek, “Laser intracavity absorption spectroscopy,” Appl. Phys. B 69(3), 171–202 (1999).
[CrossRef]

Appl. Phys. Lett.

A. Garnache, S. Hoogland, A. Tropper, I. Sagnes, G. Saint-Girons, and J. Roberts, “Sub-500-fs soliton-like pulse in a passively mode-locked broadband surface-emitting laser with 100 mW average power,” Appl. Phys. Lett. 80(21), 3892–3894 (2002).
[CrossRef]

B-Photo

V. Baev, J. Eschner, E. Paeth, R. Schuler, and P. Toschek, ““Intracavity spectroscopy with diode-lasers,” Appl. Phys,” B-Photo 55, 463–477 (1992).

IEEE J. Sel. Top. Quantum Electron.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “Design and characteristics of high-power (> 0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE J. Sel. Top. Quantum Electron. 5(3), 561–573 (1999).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Hoogland, A. Garnache, I. Sagnes, J. S. Roberts, and A. C. Tropper, “10-GHz train of sub-500-fs optical soliton-like pulses from a surface-emitting semiconductor laser,” IEEE Photon. Technol. Lett. 17(2), 267–269 (2005).
[CrossRef]

J. Appl. Phys.

H. A. Haus, “Theory of mode-locking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 (1975).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D Appl. Phys.

A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D Appl. Phys. 37(9), R75–R85 (2004).
[CrossRef]

Nat. Photonics

A. H. Quarterman, K. G. Wilcox, V. Apostolopoulos, Z. Mihoubi, S. P. Elsmere, I. Farrer, D. A. Ritchie, and A. Tropper, “A passively mode-locked external-cavity semiconductor laser emitting 60-fs pulses,” Nat. Photonics 3(12), 729–731 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett.

D. Findlay and R. Clay, “The measurement of internal losses in 4-level lasers,” Phys. Lett. 20(3), 277–278 (1966).
[CrossRef]

Phys. Rep.

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006).
[CrossRef]

Prog. Quantum Electron.

A. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
[CrossRef]

Other

Z. Mihoubi, G. J. Daniell, K. G. Wilcox, and A. C. Tropper, “Numerical model of the optical Stark effect as a mode-locking mechanism for femtosecond vertical-external-cavity surface-emitting semiconductor lasers,” in CLEO/QELS'08 (San Jose CA, 2008).

A. Siegman, Lasers, (University Science Books, 1986) p. 359.

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Figures (6)

Fig. 1
Fig. 1

The electric field inside the microcavity of the A4226 gain sample. The quantum wells are positioned in the maxima of the modulus of the electric field.

Fig. 2
Fig. 2

Experimental apparatus for the spectrotemporal measurements. The VECSEL cavity is formed between mirrors M1, M2, M3, the gain sample and the output coupler, OC.

Fig. 3
Fig. 3

Spectra acquired from gain sample QT1544 in a range of time intervals from 18.75 to 45.00 μs, for a pump power of 1.2 W. The ripples in the spectra are due to modulations of the cavity formed between the back surface of the gain chip and the DBR.

Fig. 4
Fig. 4

Evolution of A = 1 / 2 μ 2 with generation time for sample QT1544 corresponding to the graph depicted in Fig. 3. The slope of the fit is 3.74x10−21 s/rad2.

Fig. 5
Fig. 5

Spectra acquired from gain sample A4226 in a range of time intervals from 18.75 to 45.00 μs, for a pump power of 1.2 W.

Fig. 6
Fig. 6

Corresponding graph to the graph of Fig. 5 which shows the evolution of A = 1 / 2 μ 2 with generation time for sample A4226. The slope of the fit is 4.06x10−21s/rad2.

Tables (3)

Tables Icon

Table 1 Values for the loss analysis for samples QT1544 and A4226

Tables Icon

Table 2 QT1544 bandwidth for different pump powers

Tables Icon

Table 3 A4226 bandwidth for different pump powers

Equations (21)

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

d ϕ q d t = ϕ q τ + G q ( N ) ϕ q ,
G q ( N ) = ( N N t ) γ q ,
d Φ d t = q d ϕ q d t = 0.
( N N t ) q γ q ϕ q = Φ τ .
d ϕ q d t = ϕ q τ ( 1 γ q 1 Φ q γ q ϕ q ) .
ω n ¯ = 1 Φ q ω q n ϕ q .
μ n = ( ω ω ¯ ) n ¯ = q ( ω ω ¯ ) n ϕ q .
ω 2 ¯ = μ 2 + ω ¯ 2 , ω 3 ¯ = μ 3 + 3 μ 2 ω ¯ + ω ¯ 3 , ω 4 ¯ = μ 4 + 4 μ 3 ω ¯ + 6 μ 2 ω ¯ 2 + ω ¯ 4 .
γ q = γ 0 ( 1 ( ω q ω 0 Ω g ) 2 ) ,
d ϕ q d t = ϕ q τ Ω 2 g ( 1 1 ( ω q ω 0 Ω g ) 2 1 Φ q ( 1 ( ω q ω 0 Ω g ) 2 ) ϕ q ) ,
1 Φ q ( 1 ( ω g ω 0 Ω g ) 2 ) ϕ q = 1 ( ( ω ω 0 ) 2 ¯ Ω 2 g ) .
d ϕ q d t = ϕ q τ Ω 2 g ( ( ω q ω 0 ) 2 ( ω ω 0 ) 2 ¯ ) ,
( ω ω 0 ) 2 ¯ = 1 Φ ( ω q ω 0 ) 2 ϕ q = ω 2 ¯ 2 ω 0 ω ¯ + ω 2 0 .
d d t ω ¯ = q ω q d ϕ q d t = q [ ϕ q ω q τ Ω g ( ( ω q ω 0 ) 2 ( ω ω 0 ) 2 ¯ ) ] = 1 τ Ω g ( ω ( ω q ω 0 ) 2 ¯ ω ¯ ( ω ω 0 ) 2 ¯ ) .
d ω ¯ d t = 1 τ Ω g 2 ( μ 3 + 2 μ 2 ( ω ¯ ω 0 ) ) .
d μ 2 d t = 2 μ 2 2 τ Ω g 2 [ μ 4 + 2 μ 3 ( ω ¯ ω 0 ) μ 2 2 ] .
Φ = exp ( A ( ω B ) 2 ) .
d ω ¯ d t = 1 τ Ω g 2 2 μ 2 ( ω ¯ ω 0 ) ,
d μ 2 d t = 2 μ 2 2 τ Ω g 2 .
d A d t = 1 2 μ 2 2 d μ 2 d t = 1 τ Ω g 2 .
Ω g = 1 τ d A d t .

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