Abstract

The amplitude and envelope phase noise of a modelocked Ti:sapphire laser are predicted based on the power spectral density of the pump laser and the noise transfer process. Pump laser noise is found to transfer directly to the modelocked laser’s amplitude and phase noise power spectra through the noise transfer function (NTF) which is independently measured. We find good agreement between the shapes and absolute values of the predicted and measured Ti:sapphire AM and PM noise spectra except in regions where additional environmental influences affect the Ti:sapphire laser. The experiments were conducted with both a single-mode and a multi-mode diode-pumped solid-state pump laser.

© 2008 Optical Society of America

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  1. R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
    [CrossRef] [PubMed]
  2. 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]
  3. A. L. Schawlow and C. H. Townes, "Infrared and Optical Masers," Phys. Rev. 112, 1940-1949 (1958).
    [CrossRef]
  4. H. Haken, "Analogy Between Higher Instabilities in Fluids and Lasers," Phys. Lett. 53A, 77-78 (1975).
  5. E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
    [CrossRef]
  6. H. Haken, Light; Laser Light Dynamics (North-Holland, Amsterdam, 1985) Vol. 2.
    [PubMed]
  7. C. O. Weiss and R. Vilaseca, Dynamics of Lasers (Weinheim, New York, 1991).
  8. H. A. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049-3058 (1975).
    [CrossRef]
  9. O. E. Martinez, R. L. Fork, and J. P. Gordon, "Theory of passively mode-locked lasers for the case of a nonlinear complex-propagation coefficient," J. Opt. Soc. Am. B 2, 753-760 (1985).
    [CrossRef]
  10. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 28, 2086-2096 (1992).
    [CrossRef]
  11. T. Kapitula, J. N. Kutz, and B. Sandstede, "Stability of pulses in the master mode-locking equation," J. Opt. Soc. Am. B 19, 740-746 (2002).
    [CrossRef]
  12. C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. Schibli, and S. T. Cundiff, "Pulse dynamics in modelocked lasers: relaxation oscillations and frequency pulling," Opt. Express 15, 6677-6689 (2007).
    [CrossRef] [PubMed]
  13. R. P. Scott, T. D. Mulder, K. A. Baker, and B. H. Kolner, "Amplitude and phase noise sensitivity of modelocked Ti:sapphire lasers in terms of a complex noise transfer function," Opt. Express 15, 9090-9095 (2007).
    [CrossRef] [PubMed]
  14. R. P. Scott, C. Langrock, and B. H. Kolner, "High dynamic range laser amplitude and phase noise measurement techniques," IEEE J. Sel. Top. Quantum Electron. 7, 641-655 (2001).
    [CrossRef]
  15. L. Matos, O. D. M¨ucke, C. Jian, and F. X. K¨artner, "Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers," Opt. Express 14, 2497-2511 (2006).
    [CrossRef] [PubMed]
  16. R. P. Scott, B. H. Kolner, C. Langrock, R. L. Byer, and M. M. Fejer, "Ti:sapphire laser pump-noise transfer function," in Proceedings of the Conference on Lasers and Electro-optics, Paper CFB2 (Baltimore, MD, 2003).

2007 (2)

2006 (1)

2002 (1)

2001 (1)

R. P. Scott, C. Langrock, and B. H. Kolner, "High dynamic range laser amplitude and phase noise measurement techniques," IEEE J. Sel. Top. Quantum Electron. 7, 641-655 (2001).
[CrossRef]

2000 (2)

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

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]

1992 (1)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

1985 (1)

1975 (2)

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

H. Haken, "Analogy Between Higher Instabilities in Fluids and Lasers," Phys. Lett. 53A, 77-78 (1975).

1963 (1)

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
[CrossRef]

1958 (1)

A. L. Schawlow and C. H. Townes, "Infrared and Optical Masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Baker, K. A.

Cundiff, S. T.

C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. Schibli, and S. T. Cundiff, "Pulse dynamics in modelocked lasers: relaxation oscillations and frequency pulling," Opt. Express 15, 6677-6689 (2007).
[CrossRef] [PubMed]

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]

Diddams, S. A.

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]

Fork, R. L.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

Gordon, J. P.

H¨ansch, T. W.

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Haken, H.

H. Haken, "Analogy Between Higher Instabilities in Fluids and Lasers," Phys. Lett. 53A, 77-78 (1975).

Hall, J. L.

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]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

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

Holzwarth, R.

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

Jian, C.

Jones, D. J.

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]

K¨artner, F. X.

Kapitula, T.

Knight, J. C.

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Kolner, B. H.

R. P. Scott, T. D. Mulder, K. A. Baker, and B. H. Kolner, "Amplitude and phase noise sensitivity of modelocked Ti:sapphire lasers in terms of a complex noise transfer function," Opt. Express 15, 9090-9095 (2007).
[CrossRef] [PubMed]

R. P. Scott, C. Langrock, and B. H. Kolner, "High dynamic range laser amplitude and phase noise measurement techniques," IEEE J. Sel. Top. Quantum Electron. 7, 641-655 (2001).
[CrossRef]

Kutz, J. N.

Langrock, C.

R. P. Scott, C. Langrock, and B. H. Kolner, "High dynamic range laser amplitude and phase noise measurement techniques," IEEE J. Sel. Top. Quantum Electron. 7, 641-655 (2001).
[CrossRef]

Lorenz, E. N.

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
[CrossRef]

M¨ucke, O. D.

Martinez, O. E.

Matos, L.

Menyuk, C. R.

Mulder, T. D.

Ranka, J. K.

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]

Russell, P. St. J.

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Sandstede, B.

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, "Infrared and Optical Masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Schibli, T.

Scott, R. P.

R. P. Scott, T. D. Mulder, K. A. Baker, and B. H. Kolner, "Amplitude and phase noise sensitivity of modelocked Ti:sapphire lasers in terms of a complex noise transfer function," Opt. Express 15, 9090-9095 (2007).
[CrossRef] [PubMed]

R. P. Scott, C. Langrock, and B. H. Kolner, "High dynamic range laser amplitude and phase noise measurement techniques," IEEE J. Sel. Top. Quantum Electron. 7, 641-655 (2001).
[CrossRef]

Smith, R. P.

Stentz, A.

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]

Townes, C. H.

A. L. Schawlow and C. H. Townes, "Infrared and Optical Masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Udem, T.

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Wadsworth, W. J.

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Wahlstrand, J. K.

Willits, J.

Windeler, R. S.

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]

IEEE J. Quantum Electron. (1)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. P. Scott, C. Langrock, and B. H. Kolner, "High dynamic range laser amplitude and phase noise measurement techniques," IEEE J. Sel. Top. Quantum Electron. 7, 641-655 (2001).
[CrossRef]

J. Appl. Phys. (1)

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

J. Atmos. Sci. (1)

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (3)

Phys. Lett. (1)

H. Haken, "Analogy Between Higher Instabilities in Fluids and Lasers," Phys. Lett. 53A, 77-78 (1975).

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, "Infrared and Optical Masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Phys. Rev. Lett. (1)

R. Holzwarth, T. Udem, T. W. H¨ansch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

Science (1)

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]

Other (3)

H. Haken, Light; Laser Light Dynamics (North-Holland, Amsterdam, 1985) Vol. 2.
[PubMed]

C. O. Weiss and R. Vilaseca, Dynamics of Lasers (Weinheim, New York, 1991).

R. P. Scott, B. H. Kolner, C. Langrock, R. L. Byer, and M. M. Fejer, "Ti:sapphire laser pump-noise transfer function," in Proceedings of the Conference on Lasers and Electro-optics, Paper CFB2 (Baltimore, MD, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Transfer of pump noise to AM and envelope PM noise of a modelocked Ti:sapphire laser.

Fig. 2.
Fig. 2.

Simplified block diagram of the setup used to measure laser noise and the complex noise transfer function. VSA, Agilent 89410 Vector Signal Analyzer; AOM, acousto-optic modulator; PD, photodiode; PLL, phase-locked loop; VCXO, voltage-controlled crystal oscillator; AM1 and AM2, baseband AM noise photoreceivers (DC-40 MHz); PM1, phase noise RF photoreceiver (80 MHz-120 MHz); LNA, low noise amplifier; Spectrum Analyzer, HP 3561A+HP 3585A.

Fig. 3.
Fig. 3.

(a) Pump laser noise PSD for a single-longitudinal mode DPSS laser (Pump 1) and a multi-longitudinal mode DPSS laser (Pump 2). (b) Magnitudes of AM and PM NTFs of the Ti:sapphire laser using Pump 1 and Pump 2.

Fig. 4.
Fig. 4.

Measured and predicted (a) AM and (b) PM noise of a KLM Ti:sapphire laser pumped with a single-mode DPSS laser (Pump 1). (Note the different scales).

Fig. 5.
Fig. 5.

Measured and predicted (a) AM and (b) PM noise of a KLM Ti:sapphire laser pumped with a multi-mode DPSS laser (Pump 2). (Note the different scales).

Equations (3)

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H AM ( ω m ) m L ( ω m ) m p , H PM ( ω m ) β ( ω m ) m p
S AM ( ω m ) = H AM ( ω m ) 2 S P ( ω m )
S PM SSB ( ω m ) = H PM ( ω m ) 2 2 S P ( ω m )

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