Abstract

Long-term synchronization between two 10.225 GHz microwave signals at +10 dBm power level, locked to a 44.26 MHz repetition rate passively mode-locked fiber laser, is demonstrated using balanced optical-microwave phase detectors. The out-of-loop measurement result shows 12.8 fs relative timing jitter integrated from 10 Hz to 10 MHz. Long-term timing drift measurement shows 48 fs maximum deviation over one hour, mainly limited by drift of the out-of-loop characterization setup itself. To the best of our knowledge, this is the first time to demonstrate long-term (>1 hour) 3 mrad-level phase stability of a 10.225 GHz microwave signal extracted from a mode-locked laser.

© 2007 Optical Society of America

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References

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  1. J.-F. Cliche and B. Shillue, "Precision timing control for Radio Astronomy," IEEE Control Syst. Mag. 26, 19-26 (2006).
    [CrossRef]
  2. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
    [CrossRef] [PubMed]
  3. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, "Long-term femtosecond timing link stabilization using a single-crystal balanced cross-correlator," Opt. Lett. 32, 1044-1046 (2007).
    [CrossRef] [PubMed]
  4. A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
    [CrossRef] [PubMed]
  5. J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
    [CrossRef]
  6. E. N. Ivanov, S. A. Diddams and L. Hollberg, "Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a Femtosecond Laser," IEEE J. Sel. Top. Quantum Electron. 9, 1059-1065 (2003).
    [CrossRef]
  7. L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
    [CrossRef]
  8. E. N. Ivanov, S. A. Diddams and L. Hollberg, "Noise properties of microwave signals synthesized with Femtosecond Lasers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736-745 (2007).
    [CrossRef] [PubMed]
  9. E. N. Ivanov, S. A. Diddams and L. Hollberg, "Study of the excess noise associated with demodulation of ultrashort infrared pulses," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068-1074 (2005).
    [CrossRef] [PubMed]
  10. J. Kim, F. X. K¨artner, and F. Ludwig, "Balanced optical-microwave phase detectors for optoelectronic phaselocked loops," Opt. Lett. 31, 3659-3661 (2006).
    [CrossRef] [PubMed]
  11. A. E. Siegman, Lasers (University Science Books, 1986).

2007 (4)

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Noise properties of microwave signals synthesized with Femtosecond Lasers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736-745 (2007).
[CrossRef] [PubMed]

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, "Long-term femtosecond timing link stabilization using a single-crystal balanced cross-correlator," Opt. Lett. 32, 1044-1046 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (3)

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
[CrossRef] [PubMed]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Study of the excess noise associated with demodulation of ultrashort infrared pulses," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068-1074 (2005).
[CrossRef] [PubMed]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

2003 (1)

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a Femtosecond Laser," IEEE J. Sel. Top. Quantum Electron. 9, 1059-1065 (2003).
[CrossRef]

Bartels, A.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
[CrossRef] [PubMed]

Bergquist, J. C.

Bi, Z.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

Chen, J.

Cliche, J.-F.

J.-F. Cliche and B. Shillue, "Precision timing control for Radio Astronomy," IEEE Control Syst. Mag. 26, 19-26 (2006).
[CrossRef]

Diddams, S. A.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Noise properties of microwave signals synthesized with Femtosecond Lasers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736-745 (2007).
[CrossRef] [PubMed]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Study of the excess noise associated with demodulation of ultrashort infrared pulses," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068-1074 (2005).
[CrossRef] [PubMed]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
[CrossRef] [PubMed]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a Femtosecond Laser," IEEE J. Sel. Top. Quantum Electron. 9, 1059-1065 (2003).
[CrossRef]

Foreman, S. M.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

Hollberg, L.

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Noise properties of microwave signals synthesized with Femtosecond Lasers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736-745 (2007).
[CrossRef] [PubMed]

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Study of the excess noise associated with demodulation of ultrashort infrared pulses," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068-1074 (2005).
[CrossRef] [PubMed]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
[CrossRef] [PubMed]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a Femtosecond Laser," IEEE J. Sel. Top. Quantum Electron. 9, 1059-1065 (2003).
[CrossRef]

Holman, K. W.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

Hudson, D. D.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

Ivanov, E. N.

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Noise properties of microwave signals synthesized with Femtosecond Lasers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736-745 (2007).
[CrossRef] [PubMed]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Study of the excess noise associated with demodulation of ultrashort infrared pulses," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068-1074 (2005).
[CrossRef] [PubMed]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a Femtosecond Laser," IEEE J. Sel. Top. Quantum Electron. 9, 1059-1065 (2003).
[CrossRef]

Jones, D. J.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

Kärtner, F. X.

Kim, J.

Kim, K.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

Loehl, F.

Ma, L.-S.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

McFerran, J. J.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Oates, C.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

Oates, C. W.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
[CrossRef] [PubMed]

Oskay, W. H.

Robertsson, L.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

Schlarb, H.

Shillue, B.

J.-F. Cliche and B. Shillue, "Precision timing control for Radio Astronomy," IEEE Control Syst. Mag. 26, 19-26 (2006).
[CrossRef]

Wilpers, G.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay and L. Hollberg, "Femtosecondlaser-based synthesis of ultra-stable microwave signals from optical frequency references," Opt. Lett. 30, 667-669 (2005).
[CrossRef] [PubMed]

Windeler, R. S.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

Wong, F. N. C.

Ye, J.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

Zhang, Z.

Zucco, M.

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

Electron. Lett. (1)

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

IEEE Control Syst. Mag. (1)

J.-F. Cliche and B. Shillue, "Precision timing control for Radio Astronomy," IEEE Control Syst. Mag. 26, 19-26 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Frequency uncertainty for optically referenced Femtosecond laser frequency combs," IEEE J. Quantum Electron. 43, 139-146 (2007).
[CrossRef]

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

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a Femtosecond Laser," IEEE J. Sel. Top. Quantum Electron. 9, 1059-1065 (2003).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Noise properties of microwave signals synthesized with Femtosecond Lasers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736-745 (2007).
[CrossRef] [PubMed]

E. N. Ivanov, S. A. Diddams and L. Hollberg, "Study of the excess noise associated with demodulation of ultrashort infrared pulses," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068-1074 (2005).
[CrossRef] [PubMed]

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones and J. Ye, "Remote transfer of ultrastable frequency references via fiber networks," Rev. Sci. Instrum. 78, 021101 (2007).
[CrossRef] [PubMed]

Other (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the optoelectronic phase-locked loop (PLL) using a balanced optical-microwave phase detector. BPF, bandpass filter; VCO, voltage-controlled oscillator. (b) Relative positions of the optical pulse train (blue pulse train), the VCO output signal (red sinusoidal signal), and the reference signal (grey sinusoidal signal). For illustrative simplicity, N is set to N = 1.

Fig. 2.
Fig. 2.

Experimental setup for long-term out-of-loop relative timing jitter measurement between two microwave signals locked to a mode-locked laser. DBM: double-balanced mixer, LPF: low-pass filter, PLL: phase-locked loop, VCO: voltage-controlled oscillator.

Fig. 3.
Fig. 3.

Single-sideband (SSB) phase noise spectra at 10.225 GHz from 10 Hz to 10 MHz: (a) free-running VCO (taken from datasheet); (b) in-loop phase noise of PLL 1; (c) in-loop phase noise of PLL 2; (d) residual phase noise of the out-of-loop characterization setup; (e) out-of-loop relative phase noise between PLL 1 and PLL 2; (f) phase noise level in the ideal condition, when both PLLs are shot-noise limited and there is no excess electronic noise sources. The out-of-loop measurement shows 12.8 fs relative jitter between two extracted microwave signals. The in-loop jitters are 19.2 fs and 18.8 fs for PLL 1 and 2, respectively.

Fig. 4.
Fig. 4.

(a) Long-term background timing drift measurement of the characterization setup. Although the temperature is actively stabilized within 0.41 °C (maximum-minimum) over 10 hours, at certain time frames, up to 41 fs (in 1 hour) and 48 fs (in 4 hours) timing drifts are observed. (b) Long-term out-of-loop drift measurement between two locked VCOs shows that the maximum timing deviation is within 48 fs over one hour. The data was taken at every 5 seconds.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

P in ( t ) = P avg , in T R n = δ ( t n T R ) ,
ϕ ( t ) = Φ 0 sin ( 2 π f 0 t + θ e ) + Φ m sin ( π f R t + Δϕ ) ,
P ( t ) = P avg T R n = sin 2 [ 1 2 Φ 0 sin ( 2 π f 0 t + θ e ) + Φ m sin ( π f R t + Δϕ ) ] δ ( t n T R ) ,
P ( t ) = P avg T R n = [ { Φ 0 2 θ e 2 4 + Φ m 2 2 ( 1 cos ( 2 Δϕ ) ) } + Φ 0 Φ m θ e sin ( π f R t + Δϕ ) ] δ ( t n T R ) .
P ( ± j f R 2 ) = 2 π P avg Φ 0 Φ m sin ( Δϕ ) θ e δ ( f f R 2 ) .
V 2 ( t ) = 2 R G P avg Φ 0 Φ m θ e cos ( π f R t ) .
V 1 ( t ) = V 1 sin ( π f R t + Δϕ ) = V 1 cos ( π f R t ) .
V d = α V 1 ( t ) V 2 ( t ) | f < f R 2 = [ α R G P avg Φ 0 Φ m V 1 ] θ e ,
K d = V d θ e = α R G P avg Φ 0 Φ m V 1 .
P locked = P avg T R n = Φ m 2 δ ( t n T R )
= Φ m 2 P avg .
i ¯ shot 2 = 2 q I 0 = 2 q R Φ m 2 P avg ,
V ¯ d , shot 2 = 1 2 α 2 V 1 2 G 2 i ¯ shot 2
= α 2 V 1 2 q R G 2 Φ m 2 P avg .
S φ , shot = 1 2 · V ¯ d , shot 2 K d 2 = α 2 V 1 2 q R G 2 Φ m 2 P avg 2 ( α R G P avg Φ 0 Φ m V 1 ) 2 = q 2 R P avg Φ 0 2 .

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