## Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback

Optics Express, Vol. 13, Issue 7, pp. 2707-2715 (2005)

http://dx.doi.org/10.1364/OPEX.13.002707

Acrobat PDF (187 KB)

### Abstract

We investigate experimentally the polarization dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback operating in the long-cavity regime. By means of an analysis of the correlation properties in the time domain and in the frequency domain a connection between a drift phenomenon and frequency components that deviate from the harmonics of the external cavity round-trip frequency is revealed. The latter frequency components are shown to result from an interaction of external cavity dynamics and relaxation oscillations. An analogy to the carrier-envelope effect in mode-locked lasers is drawn. Similar drift phenomena are observed also for other laser systems with delay.

© 2005 Optical Society of America

## 1. Introduction

1. K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Selec. Top. Quantum Electron. **1**, 480–489 (1995). [CrossRef]

2. G. H. M. v. Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” J. Opt. B: Quantum Semiclass. Opt. **7**, 87–143 (1995). [CrossRef]

4. F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. **33**, 2231–2238 (1997). [CrossRef]

5. M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Effects of Optical Feedback on Vertical-Cavity Surface-Emitting Lasers: Experiment and Model,” J. Opt. Soc. Am. B **16**, 2114–2123 (1999). [CrossRef]

6. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical Feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. **28(17)**, 1543–1545 (2003). [CrossRef]

7. M. Sondermann, H. Bohnet, and T. Ackemann, “Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback,” Phys. Rev. A **67**, 021,802 (2003). [CrossRef]

8. G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A **67**, 053,809 (2003). [CrossRef]

9. A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A **68**, 033,805 (2003). [CrossRef]

4. F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. **33**, 2231–2238 (1997). [CrossRef]

5. M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Effects of Optical Feedback on Vertical-Cavity Surface-Emitting Lasers: Experiment and Model,” J. Opt. Soc. Am. B **16**, 2114–2123 (1999). [CrossRef]

6. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical Feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. **28(17)**, 1543–1545 (2003). [CrossRef]

7. M. Sondermann, H. Bohnet, and T. Ackemann, “Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback,” Phys. Rev. A **67**, 021,802 (2003). [CrossRef]

8. G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A **67**, 053,809 (2003). [CrossRef]

9. A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A **68**, 033,805 (2003). [CrossRef]

8. G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A **67**, 053,809 (2003). [CrossRef]

**67**, 053,809 (2003). [CrossRef]

11. F. T. Arecchi, G. Giacomelli, A. Lapucci, and R. Meucci, “Two-dimensional representation of a delayed dynamical system,” Phys. Rev. A **45**, 4225–4228 (1992). [CrossRef] [PubMed]

12. G. Giacomelli, M. Giudici, S. Balle, and J. R. Tredicce, “Experimental evidence of coherence resonance in an optical system,” Phys. Rev. Lett. **84**, 3298–3301 (2000). [CrossRef] [PubMed]

## 2. Experimental results

*ν*

_{ext}=1/

*τ*

_{ext}≈300 MHz. The VCSEL output is split into its linear polarization components by use of a half-wave-plate and a Wollaston prism. The temporal dynamics of each polarization component is recorded simultaneously with avalanche photo diodes (1.8 GHz analogue bandwidth) and a digital oscilloscope (sampling interval 125 ps, 1 GHz analogue bandwidth). In some of the experiments an oscilloscope with 6 GHz bandwidth and a sampling interval of 50 ps was available. This oscilloscope was also used in combination with fast photo diodes of 10 GHz bandwidth but poor sensitivity. Therefore, the photo diode signals were amplified by 20 dB by the cost of cutting off frequency components below 10 MHz. Unintended back reflections into the laser are prevented by optical isolators that are located in each of the two beam paths that emerge from the Wollaston prism.

7. M. Sondermann, H. Bohnet, and T. Ackemann, “Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback,” Phys. Rev. A **67**, 021,802 (2003). [CrossRef]

9. A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A **68**, 033,805 (2003). [CrossRef]

13. T. Ackemann, M. Sondermann, A. V. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B **77**, 739–746 (2003). [CrossRef]

*I*

_{x,y}(

*t*) by Fourier transformation (denoted in the formula below by a tilde) and use of the relationship

*CSD*(|

*f*|)=

*Ĩ*

_{x}(

*f*)·

*f*)+

*Ĩ*

_{x}(-

*f*)·

*f*). This results in a real number for the CSD at a certain frequency of modulus

*f*with a positive (negative) number indicating correlation (anticorrelation).

**68**, 033,805 (2003). [CrossRef]

**67**, 053,809 (2003). [CrossRef]

*τ*

_{ext}. The shape of these structures changes continuously, if the time delay in the ACFs is increased continuously: For small values of the delay, the structure is predominantly pointing upwards. With increasing delay time, the structure is first transformed such that it resembles the form of a dispersion curve [e.g., about 10 ns in Fig. 1(b)], until at approximately 20 ns the structure is predominantly pointing downwards. If the delay time is increased even further, the process is continued.

*τ*

_{ext}was also observed recently for the dominant polarization mode in the case of polarized feedback [8

**67**, 053,809 (2003). [CrossRef]

11. F. T. Arecchi, G. Giacomelli, A. Lapucci, and R. Meucci, “Two-dimensional representation of a delayed dynamical system,” Phys. Rev. A **45**, 4225–4228 (1992). [CrossRef] [PubMed]

**67**, 053,809 (2003). [CrossRef]

*ν*

_{ext}[cf. Fig. 4(b)].

*ν*

_{ext}is not discernable in the power spectrum. Instead, one weak component at slightly lower frequencies and a strong component at slightly larger frequencies is observed [see Fig. 4(b)]. If the injection current is changed, both peaks move further apart from each other, i.e., the deviation from

*ν*

_{ext}increases [see the inset in Fig. 4(b)]. At the reduced threshold (current value 0.92 in the inset of the figure), only one peak with a centre frequency of approximately

*ν*

_{ext}is discernable.

## 3. Discussion

**67**, 021,802 (2003). [CrossRef]

**68**, 033,805 (2003). [CrossRef]

26. J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. **172**, 59–68 (1999). [CrossRef]

27. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science **288**, 635–639 (2000). [CrossRef] [PubMed]

28. T. Udem, R. Holzwarth, and T. W. Hánsch, “Optical frequency metrology,” Nature **416**, 233–247 (2002). [CrossRef] [PubMed]

*τ*

_{rep}, which is the round-trip time of the pulse in the laser cavity. In the frequency domain, there is a frequency comb with a separation

*ν*

_{rep}=1/

*τ*

_{rep}and an envelope, which is centred at the optical carrier frequency. It turns out that the actual value of the frequency components of the comb is not given by

*m*·ν

_{rep}but by

*ν*

_{CEO}+

*m*·ν

_{rep}, where

*ν*

_{CEO}denotes the so-called carrier-envelope offset frequency. The name originates from the fact that there is a phase slippage between the optical carrier wave and the pulse envelope, if

*ν*

_{CEO}≠=0.

*ν*

_{ext}) is still given by the group velocity of the light in the external cavity, where the frequency of the ‘faster’ pulsing (the RO frequency) is determined by an interplay of carrier and field dynamics. Hence, it is probably not surprising that there is an offset frequency, in general.

29. G. H. M. v. Tartwijk, A. M. Levine, and D. Lenstra, “Sisyphus effect in semiconductor lasers with optical feedback,” IEEE J. Selec. Top. Quantum Electron. **1**, 466–472 (1995). [CrossRef]

*ν*

_{ext}have been predicted for coherent [30

30. J. S. Cohen, R. R. Drenten, and B. H. Verbeek, “The Effect of Optical Feedback on the Relaxation Oscillation in Semiconductor Lasers,” IEEE J. Quantum Electron. **24(10)**, 1989–1995 (1988). [CrossRef]

31. N. A. Loiko and A. M. Samson, “Possible regimes of generation of a semiconductor laser with a delayed opto-electric feedback,” Opt. Commun. **93**, 66–72 (1992). [CrossRef]

32. G. Giacomelli and A. Politi, “Multiple scale analysis of delayed dynamical systems,” Physica D **145**, 26–42 (1998). [CrossRef]

33. M. Bestehorn, E. V. Grigorieva, H. Haken, and S. A. Kaschenko, “Order parameters for class-B lasers with a long time delayed feedback,” Physica D **145**, 110–129 (2000). [CrossRef]

34. E. V. Grigorieva, H. Haken, and S. A. Kaschenko, “Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback,” Opt. Commun. **165**, 279–292 (1999). [CrossRef]

*and*power spectra are discussed.

## Acknowledgments

## References and links

1. | K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Selec. Top. Quantum Electron. |

2. | G. H. M. v. Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” J. Opt. B: Quantum Semiclass. Opt. |

3. | B. Krauskopf and D. Lenstra, eds., |

4. | F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. |

5. | M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Effects of Optical Feedback on Vertical-Cavity Surface-Emitting Lasers: Experiment and Model,” J. Opt. Soc. Am. B |

6. | M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical Feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. |

7. | M. Sondermann, H. Bohnet, and T. Ackemann, “Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback,” Phys. Rev. A |

8. | G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A |

9. | A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A |

10. | M. San Miguel, “Polarization properties of vertical cavity surface emitting lasers,” in |

11. | F. T. Arecchi, G. Giacomelli, A. Lapucci, and R. Meucci, “Two-dimensional representation of a delayed dynamical system,” Phys. Rev. A |

12. | G. Giacomelli, M. Giudici, S. Balle, and J. R. Tredicce, “Experimental evidence of coherence resonance in an optical system,” Phys. Rev. Lett. |

13. | T. Ackemann, M. Sondermann, A. V. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,” Appl. Phys. B |

14. | M. P. v. Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. v. Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. |

15. | M. Giudici, C. Green, G. Nespolo, U. Giacomelli, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E |

16. | M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, “Dynamical behavior of semiconductor lasers with frequency selective optical feedback,” Chaos, Solitons & Fractals |

17. | A. Gavrielides, T. C. Newell, V. Kovanis, R. G. Harrison, N. Swanston, D. Yu, and W. Lu, “Synchronous Sisyphus effect in diode lasers subject to optical feedback,” Phys. Rev. A |

18. | W. H. Press, B. Flannery, S. Teukolsky, and W. Vettering, |

19. | L. A. Coldren and S. W. Corzine, |

20. | J. Mørk, B. Tromborg, and J. Mark, “Chaos in Semiconductor Lasers with Optical Feedback: Theory and Experiment,” IEEE J. Quantum Electron. |

21. | M. Ahmed and M. Yamada, “Influence of Instantaneous Mode Competition on the Dynamics of Semiconductor Lasers,” IEEE J. Quantum Electron. |

22. | I. Leyva, E. Allaria, and R. Meucci, “Transient polarization dynamics in a CO |

23. | M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A |

24. | A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multi-mode semiconductor lasers,” Phys. Rev. A |

25. | T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of Semiconductor Lasers Subject to Delayed Optical Feedback: The Short Cavity Regime,” Phys. Rev. Lett. |

26. | J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. |

27. | D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science |

28. | T. Udem, R. Holzwarth, and T. W. Hánsch, “Optical frequency metrology,” Nature |

29. | G. H. M. v. Tartwijk, A. M. Levine, and D. Lenstra, “Sisyphus effect in semiconductor lasers with optical feedback,” IEEE J. Selec. Top. Quantum Electron. |

30. | J. S. Cohen, R. R. Drenten, and B. H. Verbeek, “The Effect of Optical Feedback on the Relaxation Oscillation in Semiconductor Lasers,” IEEE J. Quantum Electron. |

31. | N. A. Loiko and A. M. Samson, “Possible regimes of generation of a semiconductor laser with a delayed opto-electric feedback,” Opt. Commun. |

32. | G. Giacomelli and A. Politi, “Multiple scale analysis of delayed dynamical systems,” Physica D |

33. | M. Bestehorn, E. V. Grigorieva, H. Haken, and S. A. Kaschenko, “Order parameters for class-B lasers with a long time delayed feedback,” Physica D |

34. | E. V. Grigorieva, H. Haken, and S. A. Kaschenko, “Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback,” Opt. Commun. |

**OCIS Codes**

(140.2020) Lasers and laser optics : Diode lasers

(140.3460) Lasers and laser optics : Lasers

(140.4050) Lasers and laser optics : Mode-locked lasers

(140.5960) Lasers and laser optics : Semiconductor lasers

(270.3100) Quantum optics : Instabilities and chaos

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 10, 2005

Revised Manuscript: March 18, 2005

Published: April 4, 2005

**Citation**

Markus Sondermann and Thorsten Ackemann, "Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Express **13**, 2707-2715 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-7-2707

Sort: Journal | Reset

### References

- K. Petermann, �??External optical feedback phenomena in semiconductor lasers,�?? IEEE J. Selec. Top. Quantum Electron. 1, 480�??489 (1995). [CrossRef]
- G. H. M. v. Tartwijk and D. Lenstra, �??Semiconductor lasers with optical injection and feedback,�?? J. Opt. B: Quantum Semiclass. Opt. 7, 87�??143 (1995). [CrossRef]
- B. Krauskopf and D. Lenstra, eds., Fundamental issues of nonlinear laser dynamics, vol. 548 of AIP Conference Proceedings (American Institute of Physics, Melville, 2000).
- F. Robert, P. Besnard, M. L. Chares, and G. M. Stephan, �??Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,�?? IEEE J. Quantum Electron. 33, 2231�??2238 (1997). [CrossRef]
- M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, �??Effects of Optical Feedback on Vertical-Cavity Surface-Emitting Lasers: Experiment and Model,�?? J. Opt. Soc. Am. B 16, 2114�??2123 (1999). [CrossRef]
- M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, �??Optical Feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,�?? Opt. Lett. 28(17), 1543�??1545 (2003). [CrossRef]
- M. Sondermann, H. Bohnet, and T. Ackemann, �??Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback,�?? Phys. Rev. A 67, 021,802 (2003). [CrossRef]
- G. Giacomelli, F. Marin, and M. Romanelli, �??Multi-time-scale dynamics of a laser with polarized optical feedback,�?? Phys. Rev. A 67, 053,809 (2003). [CrossRef]
- A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, �??Description and analysis of low frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,�?? Phys. Rev. A 68, 033,805 (2003). [CrossRef]
- M. San Miguel, �??Polarization properties of vertical cavity surface emitting lasers,�?? in Semiconductor quantum optoelectronics: From quantum physics to smart devices, A. Miller, M. Ebrahimzadeh, and D. M. Finlayson, eds., pp. 339�??366 (SUSSP and Institute of Physics Publishing, Bristol, 1999).
- F. T. Arecchi, G. Giacomelli, A. Lapucci, and R. Meucci, �??Two-dimensional representation of a delayed dynamical system,�?? Phys. Rev. A 45, 4225�??4228 (1992). [CrossRef] [PubMed]
- G. Giacomelli, M. Giudici, S. Balle, and J. R. Tredicce, �??Experimental evidence of coherence resonance in an optical system,�?? Phys. Rev. Lett. 84, 3298�??3301 (2000). [CrossRef] [PubMed]
- T. Ackemann, M. Sondermann, A. V. Naumenko, and N. A. Loiko, �??Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback,�?? Appl. Phys. B 77, 739�??746(2003). [CrossRef]
- M. P. v. Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. v. Poel, �??Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,�?? Opt. Commun. 110, 137�??140 (1994). [CrossRef]
- M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, �??Andronov bifurcation and excitability in semiconductor lasers with optical feedback,�?? Phys. Rev. E 55, 6414�??6118 (1997). [CrossRef]
- M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, �??Dynamical behavior of semiconductor lasers with frequency selective optical feedback,�?? Chaos, Solitons & Fractals 10, 811�??818 (1999).
- A. Gavrielides, T. C. Newell, V. Kovanis, R. G. Harrison, N. Swanston, D. Yu, andW. Lu, �??Synchronous Sisyphus effect in diode lasers subject to optical feedback,�?? Phys. Rev. A 60, 1577�??1580 (1999). [CrossRef]
- W. H. Press, B. Flannery, S. Teukolsky, and W. Vettering, Numerical recipes: the art of scientific computing (Cambridge University Press, Cambridge, 1992).
- L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).
- J. Mørk, B. Tromborg, and J. Mark, �??Chaos in Semiconductor Lasers with Optical Feedback: Theory and Experiment,�?? IEEE J. Quantum Electron. 28(1), 93�??108 (1992). [CrossRef]
- M. Ahmed and M. Yamada, �??Influence of Instantaneous Mode Competition on the Dynamics of Semiconductor Lasers,�?? IEEE J. Quantum Electron. 38(6), 682�??693 (2002). [CrossRef]
- I. Leyva, E. Allaria, and R. Meucci, �??Transient polarization dynamics in a CO2 laser,�?? Opt. Commun. 217, 335�??342 (2003). [CrossRef]
- M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, �??Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,�?? Phys. Rev. A 68, 033,822 (2003). [CrossRef]
- A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, �??Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,�?? Phys. Rev. A 64, 023,801 (2001). [CrossRef]
- T. Heil, I. Fischer, W. Els¨a�?er, and A. Gavrielides, �??Dynamics of Semiconductor Lasers Subject to Delayed Optical Feedback: The Short Cavity Regime,�?? Phys. Rev. Lett. 87(24), 243,901 (2001).
- J. Reichert, R. Holzwarth, T. Udem, and T. W. H¨ansch, �??Measuring the frequency of light with mode-locked lasers,�?? Opt. Commun. 172, 59�??68 (1999). [CrossRef]
- D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.Windeler, J. L. Hall, and S. T. Cundiff, �??Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,�?? Science 288, 635�??639 (2000). [CrossRef] [PubMed]
- T. Udem, R. Holzwarth, and T. W. H´ansch, �??Optical frequency metrology,�?? Nature 416, 233�??247 (2002). [CrossRef] [PubMed]
- G. H. M. v. Tartwijk, A. M. Levine, and D. Lenstra, �??Sisyphus effect in semiconductor lasers with optical feedback,�?? IEEE J. Selec. Top. Quantum Electron. 1, 466�??472 (1995). [CrossRef]
- J. S. Cohen, R. R. Drenten, and B. H. Verbeek, �??The Effect of Optical Feedback on the Relaxation Oscillation in Semiconductor Lasers,�?? IEEE J. Quantum Electron. 24(10), 1989�??1995 (1988). [CrossRef]
- N. A. Loiko and A. M. Samson, �??Possible regimes of generation of a semiconductor laser with a delayed optoelectric feedback,�?? Opt. Commun. 93, 66�??72 (1992). [CrossRef]
- G. Giacomelli and A. Politi, �??Multiple scale analysis of delayed dynamical systems,�?? Physica D 145, 26�??42 (1998). [CrossRef]
- M. Bestehorn, E. V. Grigorieva, H. Haken, and S. A. Kaschenko, �??Order parameters for class-B lasers with a long time delayed feedback,�?? Physica D 145, 110�??129 (2000). [CrossRef]
- E. V. Grigorieva, H. Haken, and S. A. Kaschenko, �??Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback,�?? Opt. Commun. 165, 279�??292 (1999). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.