Abstract

An analysis of the passively mode locked regime in semiconductor lasers is presented, leading to an explicit expression relating the timing jitter diffusion constant to the optical linewidths in these devices. Experimental results for single section quantum-dash based lasers validating the theoretical analysis are presented for the first time. Timing jitter of mode locked lasers at rates of up to 130 GHz has been experimentally estimated from the optical spectra without requiring fast photodetection.

© 2012 OSA

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  1. D. Von der Linde, “Characterization of noise in continuously operating mode-locked lasers,” Appl. Phys., B Photophys. Laser Chem. 39(4), 201–217 (1986).
    [CrossRef]
  2. D. Eliyahu, R. A. Salvatore, and A. Yariv, “Effect of noise on the power spectrum of passively mode-locked lasers,” J. Opt. Soc. Am. B 14(1), 167–174 (1997).
    [CrossRef]
  3. L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
    [CrossRef]
  4. F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).
  5. T. Habruseva, S. O’Donoghue, N. Rebrova, F. Kéfélian, S. P. Hegarty, and G. Huyet, “Optical linewidth of a passively mode-locked semiconductor laser,” Opt. Lett. 34(21), 3307–3309 (2009).
    [CrossRef] [PubMed]
  6. M. J. Ablowitz, B. Ilan, and S. T. Cundiff, “Noise-induced linewidth in frequency combs,” Opt. Lett. 31(12), 1875–1877 (2006).
    [CrossRef] [PubMed]
  7. R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
    [CrossRef]
  8. R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
    [CrossRef]
  9. J. K. Wahlstrand, J. T. Willits, C. R. Menyuk, and S. T. Cundiff, “The quantum-limited comb lineshape of a mode-locked laser: Fundamental limits on frequency uncertainty,” Opt. Express 16(23), 18624–18630 (2008).
    [CrossRef] [PubMed]
  10. Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
    [CrossRef]
  11. H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
    [CrossRef]
  12. R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
    [CrossRef]
  13. F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
    [CrossRef]
  14. K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
    [CrossRef]
  15. J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
    [CrossRef] [PubMed]
  16. R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
    [CrossRef]
  17. F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
    [CrossRef]
  18. A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circ. Syst. I  47, 655–674 (2000).
  19. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
    [CrossRef]
  20. “The control of jitter and wander within digital networks which are based on the synchronous digital hierarchy (SDH),” Recommendation G.825, ITU-T, (2001).

2011 (1)

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

2009 (2)

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

T. Habruseva, S. O’Donoghue, N. Rebrova, F. Kéfélian, S. P. Hegarty, and G. Huyet, “Optical linewidth of a passively mode-locked semiconductor laser,” Opt. Lett. 34(21), 3307–3309 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (1)

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

2006 (2)

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

M. J. Ablowitz, B. Ilan, and S. T. Cundiff, “Noise-induced linewidth in frequency combs,” Opt. Lett. 31(12), 1875–1877 (2006).
[CrossRef] [PubMed]

2004 (4)

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[CrossRef]

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
[CrossRef]

2002 (1)

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

2000 (1)

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circ. Syst. I  47, 655–674 (2000).

1997 (1)

1993 (1)

H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[CrossRef]

1986 (1)

D. Von der Linde, “Characterization of noise in continuously operating mode-locked lasers,” Appl. Phys., B Photophys. Laser Chem. 39(4), 201–217 (1986).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Ablowitz, M. J.

Accard, A.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Akrout, A.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

Aubin, G.

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

Brenot, R.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Cundiff, S. T.

Dagens, B.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Demir, A.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circ. Syst. I  47, 655–674 (2000).

Derouin, E.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Drisse, O.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Duan, G.

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

Duan, G. H.

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Eliyahu, D.

Ell, R.

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Fujimoto, J. G.

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Grein, M. E.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Habruseva, T.

Haus, H.

H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[CrossRef]

Haus, H. A.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Hegarty, S. P.

Huyet, G.

T. Habruseva, S. O’Donoghue, N. Rebrova, F. Kéfélian, S. P. Hegarty, and G. Huyet, “Optical linewidth of a passively mode-locked semiconductor laser,” Opt. Lett. 34(21), 3307–3309 (2009).
[CrossRef] [PubMed]

F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
[CrossRef]

Ilan, B.

Ippen, E. P.

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Jiang, L. A.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Kartner, F. X.

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Kéfélian, F.

T. Habruseva, S. O’Donoghue, N. Rebrova, F. Kéfélian, S. P. Hegarty, and G. Huyet, “Optical linewidth of a passively mode-locked semiconductor laser,” Opt. Lett. 34(21), 3307–3309 (2009).
[CrossRef] [PubMed]

F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
[CrossRef]

Keller, U.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Landreau, J.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Le Gouezigou, O.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Lelarge, F.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Make, D.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Martinez, A.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

McInerney, J. G.

F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
[CrossRef]

Mecozzi, A.

H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[CrossRef]

Mehrotra, A.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circ. Syst. I  47, 655–674 (2000).

Menyuk, C. R.

Merghem, K.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

Morgner, U.

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

O’Donoghue, S.

T. Habruseva, S. O’Donoghue, N. Rebrova, F. Kéfélian, S. P. Hegarty, and G. Huyet, “Optical linewidth of a passively mode-locked semiconductor laser,” Opt. Lett. 34(21), 3307–3309 (2009).
[CrossRef] [PubMed]

F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Paschotta, R.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
[CrossRef]

Poingt, F.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Pommereau, F.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Provost, J. G.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Ramdane, A.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

Rebrova, N.

Renaudier, J.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Rosales, R.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

Rousseau, B.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Roychowdhury, J.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circ. Syst. I  47, 655–674 (2000).

Salvatore, R. A.

Schibli, T.

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Schlatter, A.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

Shen, A.

Sotobayashi, H.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

Takushima, Y.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

Telle, H. R.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

Todaro, M. T.

F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
[CrossRef]

Tourrenc, J. P.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

J. P. Tourrenc, A. Akrout, K. Merghem, A. Martinez, F. Lelarge, A. Shen, G. H. Duan, and A. Ramdane, “Experimental investigation of the timing jitter in self-pulsating quantum-dash lasers operating at 1.55 µm,” Opt. Express 16(22), 17706–17713 (2008).
[CrossRef] [PubMed]

van Dijk, F.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

Von der Linde, D.

D. Von der Linde, “Characterization of noise in continuously operating mode-locked lasers,” Appl. Phys., B Photophys. Laser Chem. 39(4), 201–217 (1986).
[CrossRef]

Wahlstrand, J. K.

Willits, J. T.

Wong, S. T.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Yariv, A.

Zeller, S. C.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

Appl. Phys. B (3)

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[CrossRef]

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

K. Merghem, A. Akrout, A. Martinez, G. Aubin, A. Ramdane, F. Lelarge, and G. Duan, “Pulse generation at 346 GHz using a passively mode locked quantum-dash-based laser at 1.55 μm,” Appl. Phys. Lett. 94(2), 021107 (2009).
[CrossRef]

Appl. Phys., B Photophys. Laser Chem. (1)

D. Von der Linde, “Characterization of noise in continuously operating mode-locked lasers,” Appl. Phys., B Photophys. Laser Chem. 39(4), 201–217 (1986).
[CrossRef]

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

IEEE J. Quantum Electron. (2)

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J. P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode locked lasers for 1.55 μm applications,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1292–1301 (2011).
[CrossRef]

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J. G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G. H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

F. Kéfélian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photon. Technol. Lett. 20(16), 1405–1407 (2008).
[CrossRef]

IEEE Trans. Circ. Syst. (1)

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: a unifying theory and numerical methods for characterization,” IEEE Trans. Circ. Syst. I  47, 655–674 (2000).

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (1)

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” Proc. SPIE 5595, 213–227 (2004).
[CrossRef]

Top. Appl. Phys. (1)

F. X. Kartner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Few-cycle pulses directly from a laser,” Top. Appl. Phys. 95, 73 (2004).

Other (1)

“The control of jitter and wander within digital networks which are based on the synchronous digital hierarchy (SDH),” Recommendation G.825, ITU-T, (2001).

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Figures (7)

Fig. 1
Fig. 1

Light-current characteristics of the three QDash lasers with cavity lengths (a) 330 μm (b) 1000 μm and (c) 3800 μm.

Fig. 2
Fig. 2

(a) Optical spectrum and (b) RF spectrum of the 29 consecutive mode beatings (m = 1) of the 1000 μm long laser under ML operation when biased at 150 mA.

Fig. 3
Fig. 3

(a) Self-mode beating spectra with lorentzian fits for modes 11, 16, 21 and 26. (b) Measured mode linewidths as a function of mode number and parabolic fit for the 1000 μm long laser under ML operation when biased at 150 mA.

Fig. 4
Fig. 4

(a) RF spectrum for m = 1 to 4 and corresponding lorentzian fits. Inset: full span RF spectrum. (b) Measured RF linewidths as a function of m with parabolic fit for the laser with cavity length 3800 μm when biased at 200 mA.

Fig. 5
Fig. 5

Measured L(f) for the laser with cavity length 3800 μm when biased at 200 mA and −20 dB/dec fit.

Fig. 6
Fig. 6

(a) Intensity autocorrelation, (b) optical spectrum, and (c) measured mode linewidths for the laser with cavity length 330 μm when biased at 300 mA.

Fig. 7
Fig. 7

Relative error as a function of number of measured modes for the 1000 μm long laser.

Equations (19)

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E( t )=[ n=1 N E n e j[ ω n t+ θ n ( t )+ ϕ n ] ]+c.c
d dt [ ( 2 ω n+1 ω n ω n+2 )t+2 θ n+1 ( t ) θ n ( t ) θ n+2 ( t )+2 ϕ n+1 ϕ n ϕ n+2 ]=0
θ n+1 ( t ) θ n ( t )=Δθ( t )
ω n+1 ω n = ω r
θ n ( t )= θ c ( t )+( n n c )Δθ( t )
E( t )=[ n=1 N E n e j[ ω n t+ θ c ( t )+( n n c )Δθ( t )+ ϕ n ] ]+c.c
I(t) | E( t ) | 2 = m=1 N1 l=1 Nm 2 E m+l E l cos [ m ω r t+mΔθ( t )+( ϕ m+l ϕ l ) ] + m=1 N E m 2 = m=1 N1 l=1 Nm 2 E m+l E l cos [ m ω r ( t+Δ t r ( t ) )+( ϕ m+l ϕ l ) ] + m=1 N E m 2
E( t )=[ n=1 N E n e j[ ω n t+ θ c ( t )+ ω r ( n n c )Δ t r ( t )+ ϕ n ] ]+c.c
| E( ω ) | 2 = R( τ ) e jωτ dτ= n=1 N E n 2 e j ω n τ e 1 2 [ | θ c ( τ ) | 2 + ω r 2 ( n n c ) 2 D+2 ω r ( n n c ) θ c ( τ )Δ t r ( τ ) ] e jωτ dτ n=1 N { [ 1 2 Δ ω θ c + 1 2 ω r 2 ( n n c ) 2 D+ ω r ( n n c ) γ θ c ,Δ t r ] 2 + ( ω ω n ) 2 } 1
Δ ω n =Δ ω min + ω r 2 ( n n min ) 2 D
Δ ω R F m = m 2 ω r 2 D= m 2 Δ ω R F 1
Δ ω n =Δ ω min + Δ ω R F m m 2 ( n n min ) 2
Δ ω n =Δ ω min +Δ ω R F 1 ( n n min ) 2
σ= | Δ t r ( t ) | 2 = Dt
σ( N )= DN T r
σ= | Δ t r ( t ) | 2 = + S Δ t r ( ω ) dω 2π = + D ω 2 dω 2π
σ pc = ω 1 ω 2 D ω 2 dω 2π = ω 1 ω 2 Δ ω R F 1 ω r 2 ω 2 dω 2π
L( ω ) Δ ω R F 1 2 ω 2
σ pc = T 2π ω 1 ω 2 2L( ω ) dω 2π = T 2π f 1 f 2 2L( f ) df

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