Abstract

The interaction of an optical pulse with a quantum well saturable absorber is simulated using a semi-classical two-level-atom model which has been modified to approximate spectral hole burning in the carrier distribution. Saturable absorption behaviour is examined in the limit where pulse duration approaches the carrier-carrier scattering time. For long pulses bleaching dominates the absorber response but as the pulse duration approaches the carrier-carrier scattering timescale an additional pulse shaping mechanism becomes active, allowing the absorber to continue to shorten pulses beyond the limit set by bleaching. Examination of the spectral and temporal absorption profiles suggests that intense pulses experience additional pulse shortening from the optical Stark effect.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
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    [CrossRef]
  23. A. Bäumner, S. W. Koch, and J. V. Moloney, “Non-equilibrium analysis of the two-color operation in semiconductor quantum-well lasers,” Phys. Status Solidi, B Basic Res. 248(4), 843–846 (2011).
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    [CrossRef] [PubMed]
  26. W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
    [CrossRef] [PubMed]
  27. H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11(9), 736–746 (1975).
    [CrossRef]
  28. M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
    [CrossRef]

2011

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011).
[CrossRef]

A. Bäumner, S. W. Koch, and J. V. Moloney, “Non-equilibrium analysis of the two-color operation in semiconductor quantum-well lasers,” Phys. Status Solidi, B Basic Res. 248(4), 843–846 (2011).
[CrossRef]

2010

2009

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]

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]

2008

2007

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

J. V. Moloney, J. Hader, and S. W. Koch, “Quantum design of semiconductor active materials: laser and amplifier applications,” Laser Photonics Rev. 1(1), 24–43 (2007).
[CrossRef]

2005

2004

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79(3), 331–339 (2004).
[CrossRef]

2002

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

S. Balle, “Analytical description of spectral hole-burning effects in active semiconductors,” Opt. Lett. 27(21), 1923–1925 (2002).
[CrossRef] [PubMed]

1999

1998

S. Balle, “Simple analytical approximations for the gain and refractive index spectra in quantum well lasers,” Phys. Rev. A 57(2), 1304–1312 (1998).
[CrossRef]

1996

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[CrossRef]

1989

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

1986

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

1985

H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21(8), 1172–1188 (1985).
[CrossRef]

1975

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

H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11(9), 736–746 (1975).
[CrossRef]

Apostolopoulos, V.

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

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]

Aschwanden, A.

Balle, S.

J. Javaloyes and S. Balle, “Quasi-equilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81(6), 062505 (2010).
[CrossRef]

S. Balle, “Analytical description of spectral hole-burning effects in active semiconductors,” Opt. Lett. 27(21), 1923–1925 (2002).
[CrossRef] [PubMed]

S. Balle, “Simple analytical approximations for the gain and refractive index spectra in quantum well lasers,” Phys. Rev. A 57(2), 1304–1312 (1998).
[CrossRef]

Barnes, M. E.

Bäumner, A.

A. Bäumner, S. W. Koch, and J. V. Moloney, “Non-equilibrium analysis of the two-color operation in semiconductor quantum-well lasers,” Phys. Status Solidi, B Basic Res. 248(4), 843–846 (2011).
[CrossRef]

Bedford, R.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Beere, H.

K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
[CrossRef]

Chemla, D. S.

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

Cundiff, S. T.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[CrossRef]

Cunningham, J. E.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[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.

Fallahi, M.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Fan, L.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Farrer, I.

Garnache, A.

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

Gini, E.

Golling, M.

Grange, R.

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79(3), 331–339 (2004).
[CrossRef]

Griebner, U.

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011).
[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]

Hader, J.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

J. V. Moloney, J. Hader, and S. W. Koch, “Quantum design of semiconductor active materials: laser and amplifier applications,” Laser Photonics Rev. 1(1), 24–43 (2007).
[CrossRef]

Haiml, M.

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79(3), 331–339 (2004).
[CrossRef]

Haus, H. A.

H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21(8), 1172–1188 (1985).
[CrossRef]

H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11(9), 736–746 (1975).
[CrossRef]

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

Herrmann, J.

Hirlimann, C.

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

Hoffmann, M.

Hoogland, S.

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

Islam, M. N.

H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21(8), 1172–1188 (1985).
[CrossRef]

Jan, W. Y.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[CrossRef]

Javaloyes, J.

J. Javaloyes and S. Balle, “Quasi-equilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81(6), 062505 (2010).
[CrossRef]

Kalosha, V. P.

Keller, U.

Klehr, A.

Klopp, P.

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011).
[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]

Knox, W. H.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[CrossRef]

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

Koch, S. W.

A. Bäumner, S. W. Koch, and J. V. Moloney, “Non-equilibrium analysis of the two-color operation in semiconductor quantum-well lasers,” Phys. Status Solidi, B Basic Res. 248(4), 843–846 (2011).
[CrossRef]

J. V. Moloney, J. Hader, and S. W. Koch, “Quantum design of semiconductor active materials: laser and amplifier applications,” Laser Photonics Rev. 1(1), 24–43 (2007).
[CrossRef]

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Liero, A.

Lorenser, D.

Maas, D. J. H. C.

Mihoubi, Z.

Miller, D. A. B.

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

Moloney, J. V.

A. Bäumner, S. W. Koch, and J. V. Moloney, “Non-equilibrium analysis of the two-color operation in semiconductor quantum-well lasers,” Phys. Status Solidi, B Basic Res. 248(4), 843–846 (2011).
[CrossRef]

J. V. Moloney, J. Hader, and S. W. Koch, “Quantum design of semiconductor active materials: laser and amplifier applications,” Laser Photonics Rev. 1(1), 24–43 (2007).
[CrossRef]

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Muller, M.

Murray, J. T.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Paschotta, R.

Quarterman, A.

Quarterman, A. H.

K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
[CrossRef]

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

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.

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
[CrossRef]

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. S.

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

Sagnes, I.

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

Schmitt-Rink, S.

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

Shah, J.

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

Shank, C. V.

W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

Sieber, O. D.

Stark, J. B.

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

Stolz, W.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Südmeyer, T.

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]

Tropper, A. C.

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
[CrossRef]

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

Tsuda, S.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[CrossRef]

Unold, H. J.

Weyers, M.

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011).
[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]

Wilcox, K. G.

K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
[CrossRef]

M. E. Barnes, Z. Mihoubi, K. G. Wilcox, A. H. Quarterman, I. Farrer, D. A. Ritchie, A. Garnache, S. Hoogland, V. Apostolopoulos, and A. C. Tropper, “Gain bandwidth characterisation of surface-emitting quantum well laser gain structures for femtosecond operation,” Opt. Express 18(20), 21330–21341 (2010).
[CrossRef]

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]

Wittwer, V. J.

Zakharian, A. R.

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

Zorn, M.

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011).
[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]

Appl. Phys. B

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79(3), 331–339 (2004).
[CrossRef]

Appl. Phys. Lett.

A. Garnache, S. Hoogland, A. C. Tropper, I. Sagnes, G. Saint-Girons, and J. S. 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]

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011).
[CrossRef]

L. Fan, M. Fallahi, J. Hader, A. R. Zakharian, J. V. Moloney, W. Stolz, S. W. Koch, R. Bedford, and J. T. Murray, “Linearly polarised dual-wavelength vertical-external-cavity surface-emitting laser,” Appl. Phys. Lett. 90(18), 181124 (2007).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21(8), 1172–1188 (1985).
[CrossRef]

H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11(9), 736–746 (1975).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2(3), 454–464 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

K. G. Wilcox, A. H. Quarterman, H. Beere, D. A. Ritchie, and A. C. Tropper, “High peak power femtosecond pulse passively mode-locked vertical-external-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 22(14), 1021–1023 (2010).
[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]

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Laser Photonics Rev.

J. V. Moloney, J. Hader, and S. W. Koch, “Quantum design of semiconductor active materials: laser and amplifier applications,” Laser Photonics Rev. 1(1), 24–43 (2007).
[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]

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Phys. Rev. A

S. Balle, “Simple analytical approximations for the gain and refractive index spectra in quantum well lasers,” Phys. Rev. A 57(2), 1304–1312 (1998).
[CrossRef]

J. Javaloyes and S. Balle, “Quasi-equilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81(6), 062505 (2010).
[CrossRef]

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W. H. Knox, C. Hirlimann, D. A. B. Miller, J. Shah, D. S. Chemla, and C. V. Shank, “Femtosecond excitation of nonthermal carrier populations in GaAs quantum wells,” Phys. Rev. Lett. 56(11), 1191–1193 (1986).
[CrossRef] [PubMed]

W. H. Knox, D. S. Chemla, D. A. B. Miller, J. B. Stark, and S. Schmitt-Rink, “Femtosecond ac Stark effect in semiconductor quantum wells: Extreme low- and high-intensity limits,” Phys. Rev. Lett. 62(10), 1189–1192 (1989).
[CrossRef] [PubMed]

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A. Bäumner, S. W. Koch, and J. V. Moloney, “Non-equilibrium analysis of the two-color operation in semiconductor quantum-well lasers,” Phys. Status Solidi, B Basic Res. 248(4), 843–846 (2011).
[CrossRef]

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O. D. Sieber, M. Hoffmann, D. J. Maas, V. J. Wittwer, M. Golling, T. Sudmeyer, and U. Keller, “Experimental confirmation of quasi-soliton pulse formation in ultrafast VECSELs,” in Advanced Solid State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper AMB26.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th edition (World Scientific, 2004).

G. J. Daniell, Z. Mihoubi, 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 Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonics Applications Systems Technologies. OSA Technical Digest (CD)(Optical Society of America, 2008), paper CThF3.

Z. Mihoubi, G. J. Daniell, K. G. Wilcox, and A. C. Tropper, “Numerical model of a vertical-external-cavity surface-emitting semiconductor lasers mode-locked by the optical Stark effect,” in Proceedings of the 8th International Conference on Numerical Simulation of Optoelectronic Devices. (IEEE, 2008), pp. 91–92.

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Figures (6)

Fig. 1
Fig. 1

Energy level diagram of the live-dead two-level atom system. Populations of the levels are indicated by N 14 . Non-radiative transition rates between levels are also shown.

Fig. 2
Fig. 2

Transmission through the population of two level atoms as a function of input pulse fluence for 1.5 ps sech squared profile pulses. The curve is fit using the method in [15], giving a saturation fluence of 0.447 E2Starkτp and a modulation depth of 0.75%. The parameters used are shown in Table 1. The top x-axis is based on the value of saturation fluence in [5].

Fig. 3
Fig. 3

Time-resolved absorption for pulses with durations of 10 τ p (Fig. 3a) and τ p (Fig. 3b) and fluence 6.66 E Stark 2 τ p . Figure 3a shows a slow saturable absorber type absorption profile where the absorption recovery is long compared to the pulse duration. In Fig. 3b there is still a slow component to the absorption recovery but there is also a fast, nearly-intensity-dependent component.

Fig. 4
Fig. 4

Calculated absorption spectra of the two-level atom medium when interacting with sech2 pulses of duration τ p and with different peak intensities. As the peak intensity increases the optical Stark effect alters the resonance profile, broadening it and reducing its peak amplitude.

Fig. 5
Fig. 5

Pulse shortening and change in pulse energy per single pass of the absorber as a function of pulse duration for a sech2 pulse with fluence 6.66 E Stark 2 τ p . Spectral hole burning causes a significant drop in absorption for pulses shorter than 5 τ p . An increase in pulse shortening can be seen over the same range of pulse durations.

Fig. 6
Fig. 6

Pulse shortening per round trip due to simulated saturable absorbers with 0.75% and 0.3% modulation depths, and pulse lengthening per round trip due to gain filters with 37 nm and 51 nm effective bandwidths. Intersections between the curves represent steady state pulse durations.

Tables (1)

Tables Icon

Table 1 Parameters of the two level atom distribution used to simulate an 8 nm thick In0.25Ga0.75As quantum well.

Equations (34)

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

Φ(r,t)= c 1 (t) ϕ 1 (r)exp( i ω 1 t )+ c 2 (t) ϕ 2 (r)exp( i ω 2 t ),
c ˙ 1 =i μ E(t)exp( iωt ) c 2 ,
c ˙ 2 =i μ E(t)exp( iωt ) c 1 ,
Φ * ( q e z)Φ d 3 r=μ[ c 1 * c 2 exp( iωt )+ c 1 c 2 * exp( iωt )]= p 1 + p 2 ,
μ= ϕ 1 * ( q e z) ϕ 2 d 3 r .
p ˙ 1 =iω p 1 i μ 2 E(t) ( N 2 N 1 ),
p ˙ 2 =iω p 2 +i μ 2 E(t) ( N 2 N 1 ),
N 1 = c 1 * c 1 ,
N 2 = c 2 * c 2 .
P ˙ =ωQ,
Q ˙ =ωP+ 2ρ μ 2 E(t)( N 2 N 1 ),
N ˙ 1 = EQ ρ ,
N ˙ 2 = EQ ρ .
1 τ p = 1 2 ( 1 τ 2 + 1 τ 3 ),
P ˙ =ωQP/ τ p ,
Q ˙ =ωP+ 2ρ μ 2 E(t)( N 2 N 1 )Q/ τ p ,
N ˙ 1 = EQ ρ R N 1 τ p + N 2 τ 1 + N 3 τ p + R N 4 τ 1 ,
N ˙ 2 = EQ ρ ( 1 τ 1 + R τ 1 + R τ p ) N 2 + N 4 τ p ,
N ˙ 3 = R N 1 τ p + R N 2 τ 1 N 3 τ p + R 2 N 4 τ 1 ,
N ˙ 4 =( 1 τ p + R τ 1 + R 2 τ 1 ) N 4 + R N 2 τ p .
E= 1 2 [ eexp( iΩt )+ e * exp( iΩt ) ],
P= 1 2 [ pexp( iΩt )+ p * exp( iΩt ) ],
Q= 1 2 [ qexp( iΩt )+ q * exp( iΩt ) ],
N= n ¯ + 1 2 [ nexp( 2iΩt )+ n * exp( 2iΩt ) ],
p ˙ +iΩp=ωqp/ τ p ,
q ˙ +iΩq=ωp+ ω p 2 ω [ e( n ¯ 2 n ¯ 1 )+ e * 2 ( n 2 n 1 ) ]q/ τ p ,
n ¯ ˙ 1 =ω( e q * + e * q ) R n ¯ 1 τ p + n ¯ 2 τ 1 + n ¯ 3 τ p + R n ¯ 4 τ 1 ,
n ˙ 1 +2iΩ n 1 =2ωeq R n 1 τ p + n 2 τ 1 + n 3 τ p + R n 4 τ 1 ,
n ¯ ˙ 2 =ω( e q * + e * q )( 1 τ 1 + R τ 1 + R τ p ) n ¯ 2 + n ¯ 4 τ p ,
n ˙ 2 +2iΩ n 2 =2ωeq( 1 τ 1 + R τ 1 + R τ p ) n 2 + n 4 τ p ,
n ¯ ˙ 3 = R n ¯ 1 τ p + R n ¯ 2 τ 1 n ¯ 3 τ p + R 2 n ¯ 4 τ 1 ,
n ˙ 3 +2iΩ n 3 = R n 1 τ p + R n 2 τ 1 n 3 τ p + R 2 n 4 τ 1 ,
n ¯ ˙ 4 =( 1 τ p + R τ 1 + R 2 τ 1 ) n ¯ 4 + R n ¯ 2 τ p ,
n ˙ 4 +2iΩ n 4 =( 1 τ p + R τ 1 + R 2 τ 1 ) n 4 + R n 2 τ p ,

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