Abstract

The optical fiber used as a microwave delay line exhibits high stability and low noise and makes accessible a long delay (100μs) in a wide bandwidth (40GHz, limited by the optronic components). Hence, it finds applications as the frequency reference in microwave oscillators and as the reference discriminator for the measurement of phase noise. The fiber is suitable to measure the oscillator stability with a sensitivity of parts in 1012. Enhanced sensitivity is obtained with two independent delay lines, after correlating and averaging. Short-term stability of parts in 1012 is achieved inserting the delay line in an oscillator. The frequency can be set in steps multiple of the inverse delay, which is in the 10100kHz region. We add to the available references a considerable amount of engineering and practical knowledge, the understanding of 1f noise, calibration, the analysis of the cross-spectrum technique to reduce the instrument background, the phase-noise model of the oscillator, and the experimental test of the oscillator model.

© 2008 Optical Society of America

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References

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2007 (2)

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

E. Rubiola and R. Boudot, “The effect of AM noise on correlation phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 926-932 (2007).
[CrossRef] [PubMed]

2006 (1)

E. Rubiola, E. Salik, N. Yu, and L. Maleki, “Flicker noise in high-speed p-i-n photodiodes,” IEEE Trans. Microwave Theory Tech. 54, 816-820 (2006).
[CrossRef]

2005 (3)

W. Shieh and L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474-476 (2005).
[CrossRef]

E. Rubiola, E. Salik, S. Huang, and L. Maleki, “Photonic delay technique for phase noise measurement of microwave oscillators,” J. Opt. Soc. Am. B 22, 987-997 (2005).
[CrossRef]

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

2004 (3)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

E. Rubiola and F. Lardet-Vieudrin, “Low flicker-noise amplifier for 50 Ω sources,” Rev. Sci. Instrum. 75, 1323-1326 (2004).
[CrossRef]

2003 (4)

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

D. J. Jones, K. W. Holman, M. Notcutt, J. Ye, J. Chandalia, L. A. Jiang, E. P. Ippen, and H. Yokoyama, “Ultralow-jitter, 1550-nm mode-locked semiconductor laser synchronized to a visible optical frequency standard,” Opt. Lett. 28, 813-815 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

2002 (2)

E. Rubiola and V. Giordano, “Advanced interferometric phase and amplitude noise measurements,” Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, “AM noise impact on low level phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

2000 (2)

1999 (1)

E. Rubiola, V. Giordano, and J. Groslambert, “Very high frequency and microwave interferometric PM and AM noise measurements,” Rev. Sci. Instrum. 70, 220-225 (1999).
[CrossRef]

1997 (1)

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, “Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef] [PubMed]

1996 (1)

1978 (1)

J. Rutman, “Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress,” Proc. IEEE 66, 1048-1075 (1978).
[CrossRef]

1977 (1)

R. Brendel, G. Marianneau, and J. Ubersfeld, “Phase and amplitude modulation effects in a phase detector using an incorrectly balanced mixer,” IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

1944 (1)

H. T. Friis, “Noise figure of radio receivers,” Proc. IRE 32, 419-422 (1944).
[CrossRef]

Abeles, J.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Audoin, C.

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, 1989).
[CrossRef]

Barnes, J. A.

D. Halford, A. E. Wainwright, and J. A. Barnes, “Flicker noise of phase in RF amplifiers: characterization, cause, and cure,” (Abstract) in Proceedings of Freqency Control Symposium (1968), pp. 340-341.

Bazin, N.

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

Boubekeur, N.

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

Boudot, R.

E. Rubiola and R. Boudot, “The effect of AM noise on correlation phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 926-932 (2007).
[CrossRef] [PubMed]

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

E. Rubiola and R. Boudot, “1/f noise of RF and microwave amplifiers,” available soon on http://arxiv.org.

R. Boudot, “Oscillateurs micro-onde à haute pureté spectrale,” Ph.D. dissertation (Université de Franche Comté, 2006).

Bourgeois, P.-Y.

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

Braun, A.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Brendel, R.

R. Brendel, G. Marianneau, and J. Ubersfeld, “Phase and amplitude modulation effects in a phase detector using an incorrectly balanced mixer,” IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

Chandalia, J.

Chembo, Y. K.

Y. K. Chembo, K. Volyanskiy, L. Larger, E. Rubiola, and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillators: a phase diffusion approach,” J. Quantum Electron. (to be published).

Cibiel, G.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, “AM noise impact on low level phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Colet, P.

Y. K. Chembo, K. Volyanskiy, L. Larger, E. Rubiola, and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillators: a phase diffusion approach,” J. Quantum Electron. (to be published).

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Cussey, J.

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Davis, L.

Delfyett, P. J.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Depriest, C. M.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Eliyahu, D.

D. Eliyahu and L. Maleki, “Low phase noise and spurious level in multi-loop opto-electronic oscillators,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2003), pp. 405-410.

Ferre-Pikal, E. S.

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, “Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef] [PubMed]

Friis, H. T.

H. T. Friis, “Noise figure of radio receivers,” Proc. IRE 32, 419-422 (1944).
[CrossRef]

Giordano, V.

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

E. Rubiola and V. Giordano, “Advanced interferometric phase and amplitude noise measurements,” Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

E. Rubiola and V. Giordano, “Correlation-based phase noise measurements,” Rev. Sci. Instrum. 71, 3085-3091 (2000).
[CrossRef]

E. Rubiola, V. Giordano, and J. Groslambert, “Very high frequency and microwave interferometric PM and AM noise measurements,” Rev. Sci. Instrum. 70, 220-225 (1999).
[CrossRef]

Groslambert, J.

E. Rubiola, V. Giordano, and J. Groslambert, “Very high frequency and microwave interferometric PM and AM noise measurements,” Rev. Sci. Instrum. 70, 220-225 (1999).
[CrossRef]

Gruson, Y.

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

Halford, D.

D. Halford, A. E. Wainwright, and J. A. Barnes, “Flicker noise of phase in RF amplifiers: characterization, cause, and cure,” (Abstract) in Proceedings of Freqency Control Symposium (1968), pp. 340-341.

Hati, A.

A. Hati, D. Howe, D. Walker, and F. Walls, “Noise figure vs. PM noise measurements: a study at microwave frequencies,” in Proceedings of the European Freqency Time Forum and Freqency Control Symposium Joint Meeting (2003).

Holman, K. W.

Howe, D.

A. Hati, D. Howe, D. Walker, and F. Walls, “Noise figure vs. PM noise measurements: a study at microwave frequencies,” in Proceedings of the European Freqency Time Forum and Freqency Control Symposium Joint Meeting (2003).

Huang, S.

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

Ippen, E. P.

Jefferts, S. R.

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, “Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef] [PubMed]

Jiang, L. A.

Jones, D. J.

Jouvenceau, X.

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Kersalé, Y.

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Lardet-Vieudrin, F.

E. Rubiola and F. Lardet-Vieudrin, “Low flicker-noise amplifier for 50 Ω sources,” Rev. Sci. Instrum. 75, 1323-1326 (2004).
[CrossRef]

Larger, L.

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Y. K. Chembo, K. Volyanskiy, L. Larger, E. Rubiola, and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillators: a phase diffusion approach,” J. Quantum Electron. (to be published).

K. Volyanskiy and L. Larger, Quadrature Stabilization in the Opto-Electronic Phase-Noise Measurement System by Laser Tuning, FEMTO-ST internal report (FEMTO-ST, 2008), personal communication.

Llopis, O.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, “AM noise impact on low level phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Lutes, G.

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, “Phase-noise characterization of optoelectronic components by carrier suppression techniques,” in Proceedings of the Optical Fiber Communication (OFC) Conference (1998), pp. 263-264.

Maleki, L.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, “Flicker noise in high-speed p-i-n photodiodes,” IEEE Trans. Microwave Theory Tech. 54, 816-820 (2006).
[CrossRef]

W. Shieh and L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474-476 (2005).
[CrossRef]

E. Rubiola, E. Salik, S. Huang, and L. Maleki, “Photonic delay technique for phase noise measurement of microwave oscillators,” J. Opt. Soc. Am. B 22, 987-997 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

X. S. Yao, L. Davis, and L. Maleki, “Coupled optoelectronic oscillators for generating both RF signal and optical pulses,” J. Lightwave Technol. 18, 73-78 (2000).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725-1735 (1996).
[CrossRef]

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, “Phase-noise characterization of optoelectronic components by carrier suppression techniques,” in Proceedings of the Optical Fiber Communication (OFC) Conference (1998), pp. 263-264.

D. Eliyahu and L. Maleki, “Low phase noise and spurious level in multi-loop opto-electronic oscillators,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2003), pp. 405-410.

E. Salik, N. Yu, L. Maleki, and E. Rubiola, “Dual photonic-delay-line cross correlation method for the measurement of microwave oscillator phase noise,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2004), pp. 303-306.

Marianneau, G.

R. Brendel, G. Marianneau, and J. Ubersfeld, “Phase and amplitude modulation effects in a phase detector using an incorrectly balanced mixer,” IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

Mohageg, M.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

Notcutt, M.

Régis, M.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, “AM noise impact on low level phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Rubiola, E.

E. Rubiola and R. Boudot, “The effect of AM noise on correlation phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 926-932 (2007).
[CrossRef] [PubMed]

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

E. Rubiola, E. Salik, N. Yu, and L. Maleki, “Flicker noise in high-speed p-i-n photodiodes,” IEEE Trans. Microwave Theory Tech. 54, 816-820 (2006).
[CrossRef]

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

E. Rubiola, E. Salik, S. Huang, and L. Maleki, “Photonic delay technique for phase noise measurement of microwave oscillators,” J. Opt. Soc. Am. B 22, 987-997 (2005).
[CrossRef]

E. Rubiola and F. Lardet-Vieudrin, “Low flicker-noise amplifier for 50 Ω sources,” Rev. Sci. Instrum. 75, 1323-1326 (2004).
[CrossRef]

E. Rubiola and V. Giordano, “Advanced interferometric phase and amplitude noise measurements,” Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

E. Rubiola and V. Giordano, “Correlation-based phase noise measurements,” Rev. Sci. Instrum. 71, 3085-3091 (2000).
[CrossRef]

E. Rubiola, V. Giordano, and J. Groslambert, “Very high frequency and microwave interferometric PM and AM noise measurements,” Rev. Sci. Instrum. 70, 220-225 (1999).
[CrossRef]

E. Rubiola and R. Boudot, “1/f noise of RF and microwave amplifiers,” available soon on http://arxiv.org.

E. Salik, N. Yu, L. Maleki, and E. Rubiola, “Dual photonic-delay-line cross correlation method for the measurement of microwave oscillator phase noise,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2004), pp. 303-306.

E. Rubiola, “The Leeson effect,” arXiv:physics/0502143v1, web site arxiv.org (2005). Abridged draft version of .

E. Rubiola, Phase Noise and Frequency Stability in Oscillators (Cambridge U. Press, 2008).
[CrossRef]

Y. K. Chembo, K. Volyanskiy, L. Larger, E. Rubiola, and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillators: a phase diffusion approach,” J. Quantum Electron. (to be published).

Rutman, J.

J. Rutman, “Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress,” Proc. IEEE 66, 1048-1075 (1978).
[CrossRef]

Salik, E.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, “Flicker noise in high-speed p-i-n photodiodes,” IEEE Trans. Microwave Theory Tech. 54, 816-820 (2006).
[CrossRef]

E. Rubiola, E. Salik, S. Huang, and L. Maleki, “Photonic delay technique for phase noise measurement of microwave oscillators,” J. Opt. Soc. Am. B 22, 987-997 (2005).
[CrossRef]

E. Salik, N. Yu, L. Maleki, and E. Rubiola, “Dual photonic-delay-line cross correlation method for the measurement of microwave oscillator phase noise,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2004), pp. 303-306.

Salzenstein, P.

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Sauvage, G.

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

Shieh, W.

W. Shieh and L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474-476 (2005).
[CrossRef]

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, “Phase-noise characterization of optoelectronic components by carrier suppression techniques,” in Proceedings of the Optical Fiber Communication (OFC) Conference (1998), pp. 263-264.

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Strekalov, D.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

Tavernier, H.

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Tournier, E.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, “AM noise impact on low level phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Ubersfeld, J.

R. Brendel, G. Marianneau, and J. Ubersfeld, “Phase and amplitude modulation effects in a phase detector using an incorrectly balanced mixer,” IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Vanier, J.

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, 1989).
[CrossRef]

Vig, J. R.

J. R. Vig (chair.), IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology-Random Instabilities IEEE Standard1139-1999 (IEEE, 1999).

Volyanskiy, K.

Y. K. Chembo, K. Volyanskiy, L. Larger, E. Rubiola, and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillators: a phase diffusion approach,” J. Quantum Electron. (to be published).

K. Volyanskiy and L. Larger, Quadrature Stabilization in the Opto-Electronic Phase-Noise Measurement System by Laser Tuning, FEMTO-ST internal report (FEMTO-ST, 2008), personal communication.

Wainwright, A. E.

D. Halford, A. E. Wainwright, and J. A. Barnes, “Flicker noise of phase in RF amplifiers: characterization, cause, and cure,” (Abstract) in Proceedings of Freqency Control Symposium (1968), pp. 340-341.

Walker, D.

A. Hati, D. Howe, D. Walker, and F. Walls, “Noise figure vs. PM noise measurements: a study at microwave frequencies,” in Proceedings of the European Freqency Time Forum and Freqency Control Symposium Joint Meeting (2003).

Walls, F.

A. Hati, D. Howe, D. Walker, and F. Walls, “Noise figure vs. PM noise measurements: a study at microwave frequencies,” in Proceedings of the European Freqency Time Forum and Freqency Control Symposium Joint Meeting (2003).

Walls, F. L.

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, “Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef] [PubMed]

Yao, X. S.

X. S. Yao, L. Davis, and L. Maleki, “Coupled optoelectronic oscillators for generating both RF signal and optical pulses,” J. Lightwave Technol. 18, 73-78 (2000).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725-1735 (1996).
[CrossRef]

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, “Phase-noise characterization of optoelectronic components by carrier suppression techniques,” in Proceedings of the Optical Fiber Communication (OFC) Conference (1998), pp. 263-264.

Ye, J.

Yilmaz, T. A.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Yokoyama, H.

Yu, N.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, “Flicker noise in high-speed p-i-n photodiodes,” IEEE Trans. Microwave Theory Tech. 54, 816-820 (2006).
[CrossRef]

E. Salik, N. Yu, L. Maleki, and E. Rubiola, “Dual photonic-delay-line cross correlation method for the measurement of microwave oscillator phase noise,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2004), pp. 303-306.

Acta Phys. Pol. A (1)

P. Salzenstein, J. Cussey, X. Jouvenceau, H. Tavernier, L. Larger, E. Rubiola, and G. Sauvage, “Realization of a phase noise measurement bench using cross correlation and double optical delay line,” Acta Phys. Pol. A 112, 1107-1111 (2007).

Eur. Phys. J.: Appl. Phys. (1)

V. Giordano, P.-Y. Bourgeois, Y. Gruson, N. Boubekeur, R. Boudot, E. Rubiola, N. Bazin, and Y. Kersalé, “New advances in ultra-stable microwave oscillators,” Eur. Phys. J.: Appl. Phys. 32, 133-141 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, “Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations,” IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Shieh and L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474-476 (2005).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. Brendel, G. Marianneau, and J. Ubersfeld, “Phase and amplitude modulation effects in a phase detector using an incorrectly balanced mixer,” IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

E. Rubiola, E. Salik, N. Yu, and L. Maleki, “Flicker noise in high-speed p-i-n photodiodes,” IEEE Trans. Microwave Theory Tech. 54, 816-820 (2006).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (3)

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, “AM noise impact on low level phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

E. Rubiola and R. Boudot, “The effect of AM noise on correlation phase noise measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 926-932 (2007).
[CrossRef] [PubMed]

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, “Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

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

Nature (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode caf2 resonato,” Phys. Rev. Lett. 93, 1-4 (2004).
[CrossRef]

Proc. IEEE (1)

J. Rutman, “Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress,” Proc. IEEE 66, 1048-1075 (1978).
[CrossRef]

Proc. IRE (1)

H. T. Friis, “Noise figure of radio receivers,” Proc. IRE 32, 419-422 (1944).
[CrossRef]

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Rev. Sci. Instrum. (4)

E. Rubiola and V. Giordano, “Correlation-based phase noise measurements,” Rev. Sci. Instrum. 71, 3085-3091 (2000).
[CrossRef]

E. Rubiola and V. Giordano, “Advanced interferometric phase and amplitude noise measurements,” Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

E. Rubiola and F. Lardet-Vieudrin, “Low flicker-noise amplifier for 50 Ω sources,” Rev. Sci. Instrum. 75, 1323-1326 (2004).
[CrossRef]

E. Rubiola, V. Giordano, and J. Groslambert, “Very high frequency and microwave interferometric PM and AM noise measurements,” Rev. Sci. Instrum. 70, 220-225 (1999).
[CrossRef]

Other (18)

K. Volyanskiy and L. Larger, Quadrature Stabilization in the Opto-Electronic Phase-Noise Measurement System by Laser Tuning, FEMTO-ST internal report (FEMTO-ST, 2008), personal communication.

Elisa--Technical Notes of the ESA Cryo Project, Series of FEMTO-ST and ESA internal reports (FEMTO-ST, 2007-2008).

“Analog devices AD9854 DDS,” http://www.analog.com/.

D. Halford, A. E. Wainwright, and J. A. Barnes, “Flicker noise of phase in RF amplifiers: characterization, cause, and cure,” (Abstract) in Proceedings of Freqency Control Symposium (1968), pp. 340-341.

E. Salik, N. Yu, L. Maleki, and E. Rubiola, “Dual photonic-delay-line cross correlation method for the measurement of microwave oscillator phase noise,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2004), pp. 303-306.

A. Hati, D. Howe, D. Walker, and F. Walls, “Noise figure vs. PM noise measurements: a study at microwave frequencies,” in Proceedings of the European Freqency Time Forum and Freqency Control Symposium Joint Meeting (2003).

E. Rubiola and R. Boudot, “1/f noise of RF and microwave amplifiers,” available soon on http://arxiv.org.

R. Boudot, “Oscillateurs micro-onde à haute pureté spectrale,” Ph.D. dissertation (Université de Franche Comté, 2006).

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, “Phase-noise characterization of optoelectronic components by carrier suppression techniques,” in Proceedings of the Optical Fiber Communication (OFC) Conference (1998), pp. 263-264.

W.S. C.Chang, ed., RF Photonic Technology in Optical Fiber Links (Cambridge U. Press2002).
[CrossRef]

H.G.Kimball, ed., Handbook of Selection and Use of Precise Frequency and Time Systems (ITU, 1997).

CCIR Study Group VII, Characterization of Frequency and Phase Noise, Report No. 580-3, in Standard Frequencies and Time Signals, Vol. VII (annex) of Recommendations and Reports of the CCIR (International Telecommunication Union, 1990), pp. 160-171.

J. R. Vig (chair.), IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology-Random Instabilities IEEE Standard1139-1999 (IEEE, 1999).

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, 1989).
[CrossRef]

E. Rubiola, “The Leeson effect,” arXiv:physics/0502143v1, web site arxiv.org (2005). Abridged draft version of .

E. Rubiola, Phase Noise and Frequency Stability in Oscillators (Cambridge U. Press, 2008).
[CrossRef]

Y. K. Chembo, K. Volyanskiy, L. Larger, E. Rubiola, and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillators: a phase diffusion approach,” J. Quantum Electron. (to be published).

D. Eliyahu and L. Maleki, “Low phase noise and spurious level in multi-loop opto-electronic oscillators,” in Proceedings of the European Frequency Time Forum and Frequency Control Symposium Joint Meeting (2003), pp. 405-410.

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Figures (13)

Fig. 1
Fig. 1

Basic delay-line phase noise measurement.

Fig. 2
Fig. 2

Oscillator phase-noise model.

Fig. 3
Fig. 3

Calculated OEO phase noise.

Fig. 4
Fig. 4

Optical-fiber delay unit.

Fig. 5
Fig. 5

Scheme of the dual-channel instrument.

Fig. 6
Fig. 6

Measured single-channel background noise with zero-length optical fiber.

Fig. 7
Fig. 7

Effect of the laser RIN and the oscillator-under-test AM noise, measured with zero-length fiber.

Fig. 8
Fig. 8

Phase noise of a sapphire oscillator.

Fig. 9
Fig. 9

Measurement of the background noise, including the optical fibers.

Fig. 10
Fig. 10

Background noise, including the optical fibers.

Fig. 11
Fig. 11

Background noise in two-channel mode, measured with zero-length fiber.

Fig. 12
Fig. 12

Scheme of the optoelectronic oscillator.

Fig. 13
Fig. 13

Phase noise of the optoelectronic oscillator.

Equations (26)

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

v ( t ) = [ 1 + α ( t ) ] cos [ 2 π ν 0 t + φ ( t ) ] .
S φ ( f ) = Φ ( j f ) 2 m ( average , m spectra ) ,
S φ ( f ) = n = 4 0 b n f n ( power law ) ,
S y ( f ) = f 2 ν 0 2 S φ ( f ) = n = 2 2 h n f n .
σ y 2 ( τ ) = { h 0 2 τ white frequency noise h 1 2 ln ( 2 ) flicker of frequency . h 2 ( 2 π ) 2 6 τ frequency random walk }
x ( t ) = c ( t ) + a ( t ) ,
y ( t ) = c ( t ) + b ( t ) ,
S y x ( f ) = Y X * m = C C * m + C B * m + A C * m + A B * m = S c ( f ) + O ( 1 m ) ,
S y x ( f ) 1 m S a ( f ) S b ( f ) ( statistical limit ) .
S y x ( f ) [ S c ( f ) ] xtalk , etc. ( hardware limit ) .
S y x ( f ) [ S c ( f ) ] DUT ( DUT measurement ) .
S v ( f ) = k φ 2 H ( j f ) 2 S φ ( f ) ,
H ( j f ) 2 = 4 sin 2 ( π f τ ) .
B ( j f ) = e j 2 π f τ d 1 + j 2 π f τ f .
H ( j f ) = Φ ( j f ) Ψ ( j f ) [ definition of H ( j f ) ] .
H ( j f ) = 1 1 B ( j f ) ,
H ( j f ) 2 = 1 + 4 π 2 f 2 τ f 2 2 2 cos ( 2 π f τ d ) + 4 π 2 f 2 τ f 2 + 2 ω τ f sin ( 2 π f τ d ) .
P λ ( t ) = P ¯ λ [ 1 + m i cos ( 2 π ν 0 t ) ] ,
m i = 2 J 1 ( π V p V π ) ,
P 0 = 1 2 m i 2 R 0 ρ 2 P ¯ λ 2 ( detector output ) ,
N = F k T 0 + 2 q R 0 ρ P ¯ λ ( white noise ) ,
b 0 = 2 m i 2 [ F k T 0 R 0 1 ρ 2 P ¯ λ 2 + 2 q ρ P ¯ λ ] ( white phase noise ) .
P λ = F k T 0 R 0 1 2 ρ q ( threshold power ) .
φ ( t ) = Δ f f m sin 2 π f m t ,
v ( t ) = J 0 ( Δ f f m ) cos 2 π ν 0 t + J 1 ( Δ f f m ) [ cos 2 π ( ν 0 + f m ) t cos 2 π ( ν 0 f m ) t ] ,
v ( t ) = cos 2 π ν 0 t + 1 2 Δ f f m [ cos 2 π ( ν 0 + f m ) t cos 2 π ( ν 0 f m ) t ] .

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