Abstract

The amplitude and envelope phase noise of a modelocked laser are shown to depend directly on the pump laser amplitude stability. We characterize the sensitivity of this process by a noise transfer function which represents the complex amplitude-to-amplitude modulation (AM-AM) and amplitude-to-phase modulation (AM-PM) conversion gain of the pump-induced amplitude and phase noise, respectively. We find that a linearized laser model extrapolated from relaxation oscillation theory, combined with a thermal model, adequately describe the principal features of the response from <1 Hz to 10 MHz.

© 2007 Optical Society of America

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References

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  1. S. A. Diddams, L. Hollberg, L.-S. Ma, and L. Robertsson, "Femtosecond-laser-based optical clockwork with instability ≤ 6.3×10−16 in 1 s," Opt. Lett. 27, 58-60 (2002).
    [CrossRef]
  2. B. Ilan, M. J. Ablowitz, and S. T. Cundiff, "Quantum-noise limit on the linewidth of frequency combs," in Proceedings of the Conference on Lasers and Electro-Optics (CLEO 2007) (Optical Society of America, 2007), paper CTuJ2.
    [CrossRef]
  3. B. Willke, S. Brozek, K. Danzmann, V. Quetschke, and S. Gossler, "Frequency stabilization of a monolithic Nd:YAG ring laser by controlling the power of the laser-diode pump source," Opt. Lett. 25, 1019-1021 (2000).
    [CrossRef]
  4. B. R. Washburn, W. C. Swann, and N. R. Newbury, "Response dynamics of the frequency comb output from a femtosecond fiber laser," Opt. Express 13, 10622-10633 (2005).
    [CrossRef] [PubMed]
  5. L. Matos, O. D. Mucke, C. Jian, and F. X. Kartner, "Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers," Opt. Express 14, 2497-2511 (2006).
    [CrossRef] [PubMed]
  6. 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 (CLEO 2003) (Optical Society of America, 2003), paper CFB2.
  7. B. H. Kolner, R. P. Scott, and C. Langrock, "Laser phase noise degradation from thermal effects due to pump power fluctuations," in Proceedings of the 2003 IEEE/LEOS Summer Topical Meeting on Photonic Time/Frequency Measurement and Control (IEEE, 2003), paper TuC3.3.
  8. F. W. Helbing, G. Steinmeyer, U. Keller, R. S. Windeler, J. Stenger, and H. R. Telle, "Carrier-envelope offset dynamics of modelocked lasers," Opt. Lett. 27, 194-196 (2002).
    [CrossRef]
  9. 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]
  10. A. E. Siegman, Lasers (University Science Books, 1986).
  11. H. G. Danielmeyer and F. W. Ostermayer, Jr., "Diode-pump-modulated Nd:YAG laser," J. Appl. Phys. 43, 2911- 2913 (1972).
    [CrossRef]
  12. H. A. Haus and A. Mecozzi, "Noise of mode-locked lasers," IEEE J. Quantum Electron. 29, 983-996 (1993).
    [CrossRef]
  13. 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]
  14. A. K. Cousins, "Temperature and thermal stress in finite-Length end-Pumped laser rods," IEEE J. Quantum Electron. 28, 1057-1069 (1992).
    [CrossRef]
  15. T. D. Mulder, R. P. Scott, K. A. Baker, and B. H. Kolner, "Characterization of the complex noise transfer function of a modelocked Ti:sapphire laser," in Proceedings of the Conference on Lasers and Electro-Optics (CLEO 2007) (Optical Society of America, 2007), paper JThD38.
    [CrossRef]

2007 (1)

2006 (1)

2005 (1)

2002 (2)

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 (1)

1993 (1)

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

1992 (1)

A. K. Cousins, "Temperature and thermal stress in finite-Length end-Pumped laser rods," IEEE J. Quantum Electron. 28, 1057-1069 (1992).
[CrossRef]

1972 (1)

H. G. Danielmeyer and F. W. Ostermayer, Jr., "Diode-pump-modulated Nd:YAG laser," J. Appl. Phys. 43, 2911- 2913 (1972).
[CrossRef]

Brozek, S.

Cousins, A. K.

A. K. Cousins, "Temperature and thermal stress in finite-Length end-Pumped laser rods," IEEE J. Quantum Electron. 28, 1057-1069 (1992).
[CrossRef]

Cundiff, S. T.

Danielmeyer, H. G.

H. G. Danielmeyer and F. W. Ostermayer, Jr., "Diode-pump-modulated Nd:YAG laser," J. Appl. Phys. 43, 2911- 2913 (1972).
[CrossRef]

Danzmann, K.

Diddams, S. A.

Gossler, S.

Haus, H. A.

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

Helbing, F. W.

Hollberg, L.

Jian, C.

Kartner, F. X.

Keller, U.

Kolner, B. H.

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]

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]

Ma, L.-S.

Matos, L.

Mecozzi, A.

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

Menyuk, C. R.

Mucke, O. D.

Newbury, N. R.

Ostermayer, F. W.

H. G. Danielmeyer and F. W. Ostermayer, Jr., "Diode-pump-modulated Nd:YAG laser," J. Appl. Phys. 43, 2911- 2913 (1972).
[CrossRef]

Quetschke, V.

Robertsson, L.

Schibli, T.

Scott, R. P.

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.

Steinmeyer, G.

Stenger, J.

Swann, W. C.

Telle, H. R.

Wahlstrand, J. K.

Washburn, B. R.

Willits, J.

Willke, B.

Windeler, R. S.

IEEE J. Quantum Electron. (2)

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

A. K. Cousins, "Temperature and thermal stress in finite-Length end-Pumped laser rods," IEEE J. Quantum Electron. 28, 1057-1069 (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. G. Danielmeyer and F. W. Ostermayer, Jr., "Diode-pump-modulated Nd:YAG laser," J. Appl. Phys. 43, 2911- 2913 (1972).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Other (5)

B. Ilan, M. J. Ablowitz, and S. T. Cundiff, "Quantum-noise limit on the linewidth of frequency combs," in Proceedings of the Conference on Lasers and Electro-Optics (CLEO 2007) (Optical Society of America, 2007), paper CTuJ2.
[CrossRef]

A. E. Siegman, Lasers (University Science Books, 1986).

T. D. Mulder, R. P. Scott, K. A. Baker, and B. H. Kolner, "Characterization of the complex noise transfer function of a modelocked Ti:sapphire laser," in Proceedings of the Conference on Lasers and Electro-Optics (CLEO 2007) (Optical Society of America, 2007), paper JThD38.
[CrossRef]

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 (CLEO 2003) (Optical Society of America, 2003), paper CFB2.

B. H. Kolner, R. P. Scott, and C. Langrock, "Laser phase noise degradation from thermal effects due to pump power fluctuations," in Proceedings of the 2003 IEEE/LEOS Summer Topical Meeting on Photonic Time/Frequency Measurement and Control (IEEE, 2003), paper TuC3.3.

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Figures (3)

Fig. 1.
Fig. 1.

Simplified block diagram of the setup used to measure 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 photoreceivers; PM1, high-frequency photoreceiver.

Fig. 2.
Fig. 2.

Magnitude (a) and phase (b) of the measured and theoretical complex AM NTF response. Parameters: γc = 1.28 × 107 s-1, ωsp = 2π × 700 kHz, γsp = 5×106 s-1.

Fig. 3.
Fig. 3.

Magnitude (a) and phase (b) of the measured and theoretical complex PM NTF response. Independent “spot” measurements of the magnitude are shown as triangles.

Equations (6)

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P ( t ) = P o n A ( t τ co [ n + β ˜ ( ω m ) 2 π cos ( ω m t + ϕ ( ω m ) ) ] )
R P ( t ) = R P 0 + R P 1 cos ω m t
n ( t ) = n ss + Re { ñ 1 e i ω m t } , N ( t ) = N th + Re { Ñ 1 e i ω m t } , T ( t ) = T o + Re { T ˜ 1 e i ω m t }
ñ 1 = ω sp 2 R P 1 γ c ω sp 2 ω m 2 + i 2 γ sp ω m
Ñ 1 = i ω m R P 1 ω sp 2 ω m 2 + i 2 γ sp ω m
T ˜ 1 = 2 k R P 1 R P 0 l = 1 J 0 ( β l r b ) β l 2 J 1 2 ( β l ) 1 1 + i ω m b 2 k β l 2

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