Abstract

We report the first theoretical investigation of passive mode-locking in photonic crystal mode-locked lasers. Related work has investigated coupled-resonator-optical-waveguide structures in the regime of active mode-locking [Opt. Express 13, 4539–4553 (2005)]. An extensive numerical investigation of the influence of key parameters of the active sections and the photonic crystal cavity on the laser performance is presented. The results show the possibility of generating stable and high quality pulses in a large parameter region. For optimized dispersion properties of the photonic crystal waveguide cavity, the pulses have sub picosecond widths and are nearly transform limited.

© 2010 OSA

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  1. H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE Journal of Quantum Electronics 29, 983–996 (1993).
    [Crossref]
  2. J. Mulet and J. Mørk, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 42, 249–256 (2006).
    [Crossref]
  3. K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
    [Crossref]
  4. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals”, Nature Materials 3, 211–219 (2004).
    [Crossref] [PubMed]
  5. E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: constructions, experiments, models and applications”, IEE Proceedings - Optoelectronics 147, 251–278 (2000).
    [Crossref]
  6. M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
    [Crossref]
  7. R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
    [Crossref] [PubMed]
  8. J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
    [Crossref] [PubMed]
  9. A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers”, Physical Review A 72(3), 033808 (2005).
    [Crossref]
  10. S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
    [Crossref]
  11. A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser”, IEEE Journal of Quantum Electronics 45, 462–468 (2009).
    [Crossref]
  12. R. G. M. P. Koumans and R. van Roijen, “Theory for passive mode-locking in semiconductor laser structures including the effects of self-phase modulation, dispersion, and pulse collisions”, IEEE Journal of Quantum Electronics 32, 478–492 (1996).
    [Crossref]
  13. J. Mulet, M. Kroh, and J. Mørk, “Pulse properties of external-cavity mode-locked semiconductor lasers”, Optics Express 14, 1119–1124 (2006).
    [Crossref] [PubMed]
  14. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
    [Crossref] [PubMed]
  15. J. S. Bendat and A. G. Piersol, Random Data, Analysis and Measurement Procedures, (John Wiley & Sons, INC., 2000).
  16. M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
    [Crossref]
  17. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, (John Wiley & Sons, Inc., 1995).
  18. L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
    [Crossref] [PubMed]
  19. S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
    [Crossref]
  20. G. P. Agraval, Nonlinear Fiber Optics, (Academic Press, 2007).
  21. J. A. Leegwater, “Theory of mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 32, 1782–1790 (1996).
    [Crossref]
  22. N. Cheng and J. C. Cartledge, “Measurement-based model for MQW electroabsorption modulators”, Journal of Lightwave Technology 23, 4265–4269 (2005).
    [Crossref]

2010 (1)

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

2009 (3)

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser”, IEEE Journal of Quantum Electronics 45, 462–468 (2009).
[Crossref]

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

2008 (1)

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

2007 (1)

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

2006 (4)

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
[Crossref] [PubMed]

J. Mulet and J. Mørk, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 42, 249–256 (2006).
[Crossref]

J. Mulet, M. Kroh, and J. Mørk, “Pulse properties of external-cavity mode-locked semiconductor lasers”, Optics Express 14, 1119–1124 (2006).
[Crossref] [PubMed]

2005 (2)

N. Cheng and J. C. Cartledge, “Measurement-based model for MQW electroabsorption modulators”, Journal of Lightwave Technology 23, 4265–4269 (2005).
[Crossref]

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers”, Physical Review A 72(3), 033808 (2005).
[Crossref]

2004 (2)

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals”, Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

2000 (1)

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: constructions, experiments, models and applications”, IEE Proceedings - Optoelectronics 147, 251–278 (2000).
[Crossref]

1996 (2)

J. A. Leegwater, “Theory of mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 32, 1782–1790 (1996).
[Crossref]

R. G. M. P. Koumans and R. van Roijen, “Theory for passive mode-locking in semiconductor laser structures including the effects of self-phase modulation, dispersion, and pulse collisions”, IEEE Journal of Quantum Electronics 32, 478–492 (1996).
[Crossref]

1995 (1)

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE Journal of Quantum Electronics 29, 983–996 (1993).
[Crossref]

Agraval, G. P.

G. P. Agraval, Nonlinear Fiber Optics, (Academic Press, 2007).

Angelo, C.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Avrutin, E. A.

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: constructions, experiments, models and applications”, IEE Proceedings - Optoelectronics 147, 251–278 (2000).
[Crossref]

Barbarin, Y.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

Beggs, D. M.

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

Bendat, J. S.

J. S. Bendat and A. G. Piersol, Random Data, Analysis and Measurement Procedures, (John Wiley & Sons, INC., 2000).

Bente, E. A. J. M.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

Birkedal, D.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Bischoff, S.

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

Borel, P. I.

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
[Crossref] [PubMed]

Brorson, S. D.

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

Cartledge, J. C.

N. Cheng and J. C. Cartledge, “Measurement-based model for MQW electroabsorption modulators”, Journal of Lightwave Technology 23, 4265–4269 (2005).
[Crossref]

Cassan, E.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Cheng, N.

N. Cheng and J. C. Cartledge, “Measurement-based model for MQW electroabsorption modulators”, Journal of Lightwave Technology 23, 4265–4269 (2005).
[Crossref]

Christiansen, L. J.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Coldren, L. A.

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

Corzine, S. W.

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

Engelen, R. J. P.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Fage-Pedersen, J.

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
[Crossref] [PubMed]

Franck, T.

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

Frandsen, L. H.

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
[Crossref] [PubMed]

Gomez-Iglesias, A.

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

Hanberg, J.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Hao, R.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Haus, H. A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE Journal of Quantum Electronics 29, 983–996 (1993).
[Crossref]

Heck, M. J. R.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

Hvam, J.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Joannopoulos, J. D.

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals”, Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

Koumans, R. G. M. P.

R. G. M. P. Koumans and R. van Roijen, “Theory for passive mode-locking in semiconductor laser structures including the effects of self-phase modulation, dispersion, and pulse collisions”, IEEE Journal of Quantum Electronics 32, 478–492 (1996).
[Crossref]

Krauss, T. F.

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Kroh, M.

J. Mulet, M. Kroh, and J. Mørk, “Pulse properties of external-cavity mode-locked semiconductor lasers”, Optics Express 14, 1119–1124 (2006).
[Crossref] [PubMed]

Kuipers, L.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Kurt, H.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Larsen, A. M.

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

Larsson, D.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Lavrinenko, A. V.

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
[Crossref] [PubMed]

Leegwater, J. A.

J. A. Leegwater, “Theory of mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 32, 1782–1790 (1996).
[Crossref]

Lenstra, D.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

Li, J.

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

Marris-Morini, D.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Marsh, J. H.

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: constructions, experiments, models and applications”, IEE Proceedings - Optoelectronics 147, 251–278 (2000).
[Crossref]

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE Journal of Quantum Electronics 29, 983–996 (1993).
[Crossref]

Michaeli, A.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Mørk, J.

J. Mulet, M. Kroh, and J. Mørk, “Pulse properties of external-cavity mode-locked semiconductor lasers”, Optics Express 14, 1119–1124 (2006).
[Crossref] [PubMed]

J. Mulet and J. Mørk, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 42, 249–256 (2006).
[Crossref]

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

Mulet, J.

J. Mulet, M. Kroh, and J. Mørk, “Pulse properties of external-cavity mode-locked semiconductor lasers”, Optics Express 14, 1119–1124 (2006).
[Crossref] [PubMed]

J. Mulet and J. Mørk, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 42, 249–256 (2006).
[Crossref]

Nielsen, J. M.

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

O’Faolain, L.

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

Oxenlowe, L. K.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Penty, R. V.

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

Piersol, A. G.

J. S. Bendat and A. G. Piersol, Random Data, Analysis and Measurement Procedures, (John Wiley & Sons, INC., 2000).

Pimenov, A. S.

A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser”, IEEE Journal of Quantum Electronics 45, 462–468 (2009).
[Crossref]

Portnoi, E. L.

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: constructions, experiments, models and applications”, IEE Proceedings - Optoelectronics 147, 251–278 (2000).
[Crossref]

Rachinskii, D.

A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser”, IEEE Journal of Quantum Electronics 45, 462–468 (2009).
[Crossref]

Rae, A. R.

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

Roux, X. L.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Salib, M.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Schulz, S.

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

Settle, M. D.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Smit, M. K.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

Soljacic, M.

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals”, Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

Sørensen, M. P.

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

Thompson, M. G.

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

Turaev, D.

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers”, Physical Review A 72(3), 033808 (2005).
[Crossref]

van Roijen, R.

R. G. M. P. Koumans and R. van Roijen, “Theory for passive mode-locking in semiconductor laser structures including the effects of self-phase modulation, dispersion, and pulse collisions”, IEEE Journal of Quantum Electronics 32, 478–492 (1996).
[Crossref]

Vivien, L.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Vladimirov, A. G.

A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser”, IEEE Journal of Quantum Electronics 45, 462–468 (2009).
[Crossref]

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers”, Physical Review A 72(3), 033808 (2005).
[Crossref]

White, I. H.

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

White, T. P.

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

Wu, H.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Xia, M.

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

Yvind, K.

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Zhang, X.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Zhou, Z.

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

Applied Physics Letters (1)

S. Bischoff, M. P. Sørensen, J. Mørk, S. D. Brorson, T. Franck, J. M. Nielsen, and A. M. Larsen, “Pulse-shaping mechanism in colliding-pulse mode-locked laser diodes”, Applied Physics Letters 67, 3877–3879 (1995).
[Crossref]

IEE Proceedings - Optoelectronics (1)

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: constructions, experiments, models and applications”, IEE Proceedings - Optoelectronics 147, 251–278 (2000).
[Crossref]

IEEE Journal of Quantum Electronics (5)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE Journal of Quantum Electronics 29, 983–996 (1993).
[Crossref]

J. Mulet and J. Mørk, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 42, 249–256 (2006).
[Crossref]

A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser”, IEEE Journal of Quantum Electronics 45, 462–468 (2009).
[Crossref]

R. G. M. P. Koumans and R. van Roijen, “Theory for passive mode-locking in semiconductor laser structures including the effects of self-phase modulation, dispersion, and pulse collisions”, IEEE Journal of Quantum Electronics 32, 478–492 (1996).
[Crossref]

J. A. Leegwater, “Theory of mode-locked semiconductor lasers”, IEEE Journal of Quantum Electronics 32, 1782–1790 (1996).
[Crossref]

IEEE Journal of Selected Topics in Quantum Electronics (2)

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components”, IEEE Journal of Selected Topics in Quantum Electronics 12, 265–276 (2006).
[Crossref]

M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, “InGaAs Quantum-Dot Mode-Locked Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics 15, 661–672 (2009).
[Crossref]

IEEE Photonics Technology Letters (1)

K. Yvind, D. Larsson, L. J. Christiansen, C. Angelo, L. K. Oxenlowe, J. Mørk, D. Birkedal, J. Hvam, and J. Hanberg, “Low-jitter and high-power 40-GHz all-active mode-locked lasers”, IEEE Photonics Technology Letters 16, 975–977 (2004).
[Crossref]

Journal of Lightwave Technology (1)

N. Cheng and J. C. Cartledge, “Measurement-based model for MQW electroabsorption modulators”, Journal of Lightwave Technology 23, 4265–4269 (2005).
[Crossref]

Nature Materials (1)

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals”, Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

Optics Express (5)

R. Hao, E. Cassan, H. Kurt, X. L. Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, “Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion”, Optics Express 18(6), 5942–5950 (2010).
[Crossref] [PubMed]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides”, Optics Express 16(9), 6227–6232 (2008).
[Crossref] [PubMed]

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties”, Optics Express 14, 9444–9450 (2006).
[Crossref] [PubMed]

J. Mulet, M. Kroh, and J. Mørk, “Pulse properties of external-cavity mode-locked semiconductor lasers”, Optics Express 14, 1119–1124 (2006).
[Crossref] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth”, Optics Express 15, 219–226 (2007).
[Crossref] [PubMed]

Physical Review A (1)

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers”, Physical Review A 72(3), 033808 (2005).
[Crossref]

Physical Review B (1)

S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law”, Physical Review B 80, 195305 (2009).
[Crossref]

Other (3)

G. P. Agraval, Nonlinear Fiber Optics, (Academic Press, 2007).

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

J. S. Bendat and A. G. Piersol, Random Data, Analysis and Measurement Procedures, (John Wiley & Sons, INC., 2000).

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Figures (10)

Fig. 1.
Fig. 1.

Illustration of the PC ML laser design. The gain and absorber sections are placed in a line defect cavity, which is created by removing holes of the perfectly periodic PC structure. By altering the shape and position of holes close to the cavity, it is possible to engineer the dispersion properties of the cavity.

Fig. 2.
Fig. 2.

Illustration of the ring cavity model. The pulse circulates in the cavity, passing through each element.

Fig. 3.
Fig. 3.

Left: Phase diagram of possible solution types as a function of the unsaturated gain, g 0, and loss, q 0. The green domain represents ML solutions, red is intensity modulated pulses, blue is irregular solutions with no periodicity, yellow is higher harmonic solutions and orange is CW solutions. Pulse properties of solutions restricted to the black line are shown in Fig. 4. Right: Plots of the different solution types depending on the value of (q 0,g 0). I: (q 0,g 0) = (5,1.5), II: (q 0,g 0) = (5,2.5), III: (q 0,g 0) = (5,4.2), IV: (q 0,g 0) = (5,5).

Fig. 4.
Fig. 4.

Variation of the pulse width (black) and duty cycle (red) for (q 0,g 0) restricted to the line g 0 = 0.65q 0−0.2 in the left plot of Fig. 3.

Fig. 5.
Fig. 5.

(a) A plot of the Taylor expansion (solid black) of the dispersion relation with parameter values from Table 1. The group velocity is constant along the dashed black line. The frequencies on the abscissa are fω 0/2π, were ω 0 is the fast oscillating part of the total field, ( z , t ) = E ( z , t ) e i k 0 z i ω 0 t . (b) Variation of the pulse width in the time (black) and frequency domain (red) with the filter bandwidth, ∆f PCW.

Fig. 6.
Fig. 6.

(a) Variation of the pulse width (black) and the repetition rate, fr , (red) with the length of the PCW, 2L PCW. The dashed blue line shows fr from Eq. (9). (b) Variation of the pulse width (black) and length reduction factor, ρR , (red) as the length of the PCW and the slowdown factor are varied simultaneously, while keeping their product S × 2L PCW = 1200 µm constant.

Fig. 7.
Fig. 7.

Variation of the pulse width (black) and repetition rate (red) as a function of the slowdown factor. The dashed blue line shows fr from Eq. (9).

Fig. 8.
Fig. 8.

Pulse shape for different values of the second and third order expansion coefficients in Eq. (3). The values of ( k ω 0 ( 3 ) , k ω 0 ( 2 ) ) for the different curves are shown in Fig. 9 by the location of the corresponding roman numerals. The dashed red line shows a Gaussian fit to pulse I.

Fig. 9.
Fig. 9.

(a) The dependence of the ratio between the trailing and main pulse peak powers on the second and third order expansion coefficients in Eq. (3). (b) Pulse width as a function of the second and third order expansion coefficients in Eq. (3).

Fig. 10.
Fig. 10.

(a) A phase diagram of solution types found by varying the linewidth enhancement factors. The color code is the same as in Fig. 3. (b) Variation of the pulse width (black) and time-bandwidth product, ∆t FWHMf FWHM, (red) as a function of the linewidth enhancement factors. The values of [ k ω 0 ( 1 ) ] 2 k 0 + k ω 0 ( 2 ) are −4×106 ps2/km (dashed lines) and 2×106 ps2/km (solid lines).

Tables (1)

Tables Icon

Table 1. Parameter values used unless otherwise stated in the figure captions.

Equations (14)

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z E ( z , t ) + 1 ν g b t E ( z , t ) = g r Γ r 2 ( 1 i α r ) [ N r ( z , t ) N r t r ] E ( z , t ) .
F ˜ PCW ( ω ω 0 ) = e i ϕ ( ω ω 0 ) f H ( ω ω 0 ) , F ˜ PCW ( ω ) = + F PCW ( t ) e i ω t
ϕ ( ω ω 0 ) = 2 L PCW 2 k 0 ( [ p = 0 3 1 p ! k ω 0 ( p ) ( ω ω 0 ) p ] 2 k 0 2 ) , k ω 0 ( p ) = d p k ( ω ) d ω P ω = ω 0
f H ( ω ω 0 ) = p = 1 3 a p exp ( b p 2 [ ( ω ω 0 ) 2 c p 2 ] ) .
+ f H ( u ) cos [ ϕ ( u ) ] π ( ω u ) d u = f H ( ω ) sin [ ϕ ( ω ) ] .
d τ G ( τ ) = g 0 Γ G ( τ ) e Q ( τ ) ( e G ( τ ) 1 ) A ( τ ) 2
d τ Q ( τ ) = q 0 Q ( τ ) s ( 1 e Q ( τ ) ) A ( τ ) 2
A ( τ ) = τ F PCW ( τ u ) R ( u T 0 ) A ( u T 0 ) du
R ( τ ) = κ exp [ ( 1 i α g ) G ( τ ) 2 ( 1 i α q ) Q ( τ ) 2 ] .
ζ = γ q ν g b z , τ = γ q ( t z ν g b ) , Γ = γ g γ q , s = g q Γ q g g Γ g
A ( ζ , τ ) = E ( ζ , τ ) ν g b γ q g g Γ g , A ( τ ) = A ( ζ 0 , τ )
G ( τ ) = z g z g + L g g g Γ g [ N g N g t r ] d z Q ( τ ) = z q z q + L q g q Γ q [ N q N q tr ] dz
g 0 = z g z g + L g ( J g γ g N g tr ) g g Γ g γ q dz q 0 = z q z q + L q N q tr g q Γ q dz .
f r = 1 T = [ 1 ν g b ( S × 2 L PCW + 2 L tot ) ] 1 .

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