Abstract

We present a frequency domain model of shot noise in the photodetection of ultrashort optical pulse trains using a time-varying analysis. Shot-noise-limited photocurrent power spectral densities, signal-to-noise expressions, and shot-noise spectral correlations are derived that explicitly include the finite response of the photodetector. It is shown that the strength of the spectral correlations in the shot noise depends on the optical pulsewidth, and that these correlations can create orders-of-magnitude imbalance between the shot-noise-limited amplitude and phase noise of photonically generated microwave carriers. It is also shown that only by accounting for spectral correlations can shot noise be equated with the fundamental quantum limit in the detection of optical pulse-to-pulse timing jitter.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955–1982 (2007).
    [CrossRef]
  2. J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
    [CrossRef]
  3. J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy—Maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Syst. Mag. 26(1), 19–26 (2006).
    [CrossRef]
  4. P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
    [CrossRef]
  5. N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
    [CrossRef]
  6. I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wireless Compon. Lett. 15, 226–228 (2005).
    [CrossRef]
  7. J. A. Scheer and J. L. Kurtz, Coherent Radar Performance Estimation (Artech House, 1993).
  8. G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
    [CrossRef]
  9. J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
    [CrossRef]
  10. T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
    [CrossRef]
  11. W. C. Swann, E. Baumann, F. R. Giorgetta, and N. R. Newbury, “Microwave generation with low residual phase noise from a femtosecond fiber laser with an intracavity electro-optic modulator,” Opt. Express 19, 24387–24395 (2011).
    [CrossRef]
  12. Z. Li, Y. Fu, M. Piels, H. P. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385–B390 (2011).
    [CrossRef]
  13. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991), Chap. 17, pp. 675–678.
  14. R. W. Boyd, Radiometry and the Detection of Optical Radiation, Pure and Applied Optics (Wiley, 1983), Chap. 8, pp. 119–127.
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), Chap. 9., pp. 452–458.
  16. N. Campbell, “The study of discontinuous phenomena,” Proc. Cambridge Philos. Soc. 15, 117–136 (1909).
  17. N. Campbell, “Discontinuities in light emission,” Proc. Cambr. Phil. Soc. 15, 310–328 (1910).
  18. S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).
  19. P. J. Winzer, “Shot-noise formula for time-varying photon rates: a general derivation,” J. Opt. Soc. Am. B 14, 2424–2429 (1997).
    [CrossRef]
  20. T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
    [CrossRef]
  21. B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
    [CrossRef]
  22. M. B. Gray, A. J. Stevenson, H. A. Bachor, and D. E. McClelland, “Harmonic demodulation of nonstationary shot noise,” Opt. Lett. 18, 759–761 (1993).
    [CrossRef]
  23. M. Rakhmanov, “Demodulation of intensity and shot noise in the optical heterodyne detection of laser interferometers for gravitational waves,” Appl. Opt. 40, 6596–6605 (2001).
    [CrossRef]
  24. A. N. Bruyevich, “Fluctuations in autooscillators for periodically nonstationary shot noise,” Telecommun. Radio Eng. (Engl. Trans.) Part 2 23, 91–96 (1968).
  25. L. Roschier, T. T. Heikkila, and P. Hakonen, “Cyclostationary shot noise in mesoscopic measurements,” J. Appl. Phys. 96, 5927–5929 (2004).
    [CrossRef]
  26. W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
    [CrossRef]
  27. J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
    [CrossRef]
  28. F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).
  29. R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
    [CrossRef]
  30. J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
    [CrossRef]
  31. W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
    [CrossRef]
  32. D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983).
    [CrossRef]
  33. B. Saleh, Photoelectron Statistics, Springer Series in Optical Sciences (Springer-Verlag, 1978), Chap. 5., vol. 6, pp. 161–164.
  34. W. A. Gardner, Statistical Spectral Analysis: A Nonprobabalistic Theory, Prentice Hall Information and System Sciences Series (Prentice-Hall, 1988), Chap. 1, pp. 3–33.
  35. R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
    [CrossRef]
  36. H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
    [CrossRef]
  37. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE, 1987), Chap. 7, pp. 119–123.
  38. 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]
  39. P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
    [CrossRef]
  40. S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
    [CrossRef]
  41. K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6, 639–641 (1994).
    [CrossRef]
  42. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, 2002), Chap. 3., pp. 114–116.
  43. Characterization of Clocks and Oscillators: NIST Technical Note 1337 (US GPO, Washington, DC, 1990).
  44. 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,” IEEE Electron Device Lett. 41, 650–651 (2005).
  45. 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]
  46. F. Quinlan, S. Gee, S. Ozharar, and P. J. Delfyett, “Ultralow-jitter and amplitude-noise semiconductor-based actively mode-locked laser,” Opt. Lett. 31, 2870–2872 (2006).
    [CrossRef]
  47. 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]
  48. F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
    [CrossRef]
  49. D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
    [CrossRef]
  50. C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
    [CrossRef]
  51. R. E. Slusher and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
    [CrossRef]
  52. A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
    [CrossRef]
  53. J. D. Deschenes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
    [CrossRef]
  54. A. Yariv, “Signal-to-noise considerations in fiber links with periodic or distributed optical amplification,” Opt. Lett. 15, 1064–1066 (1990).
    [CrossRef]
  55. N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
    [CrossRef]
  56. S. Y. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, “Correlation of supermode noise of harmonically mode-locked lasers,” J. Opt. Soc. Am. B 24, 1490–1497 (2007).
    [CrossRef]
  57. G. Cibiel, M. Regis, 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]

2013

J. D. Deschenes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
[CrossRef]

2012

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

2011

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[CrossRef]

W. C. Swann, E. Baumann, F. R. Giorgetta, and N. R. Newbury, “Microwave generation with low residual phase noise from a femtosecond fiber laser with an intracavity electro-optic modulator,” Opt. Express 19, 24387–24395 (2011).
[CrossRef]

Z. Li, Y. Fu, M. Piels, H. P. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385–B390 (2011).
[CrossRef]

2010

J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
[CrossRef]

2009

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef]

2008

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[CrossRef]

2007

2006

F. Quinlan, S. Gee, S. Ozharar, and P. J. Delfyett, “Ultralow-jitter and amplitude-noise semiconductor-based actively mode-locked laser,” Opt. Lett. 31, 2870–2872 (2006).
[CrossRef]

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy—Maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Syst. Mag. 26(1), 19–26 (2006).
[CrossRef]

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
[CrossRef]

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

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[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,” IEEE Electron Device Lett. 41, 650–651 (2005).

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wireless Compon. Lett. 15, 226–228 (2005).
[CrossRef]

2004

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
[CrossRef]

L. Roschier, T. T. Heikkila, and P. Hakonen, “Cyclostationary shot noise in mesoscopic measurements,” J. Appl. Phys. 96, 5927–5929 (2004).
[CrossRef]

2002

G. Cibiel, M. Regis, 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]

2001

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]

M. Rakhmanov, “Demodulation of intensity and shot noise in the optical heterodyne detection of laser interferometers for gravitational waves,” Appl. Opt. 40, 6596–6605 (2001).
[CrossRef]

1999

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
[CrossRef]

1998

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

1997

1996

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

1994

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6, 639–641 (1994).
[CrossRef]

1993

1991

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

1990

R. E. Slusher and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

A. Yariv, “Signal-to-noise considerations in fiber links with periodic or distributed optical amplification,” Opt. Lett. 15, 1064–1066 (1990).
[CrossRef]

1989

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

1986

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

1983

D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983).
[CrossRef]

1968

A. N. Bruyevich, “Fluctuations in autooscillators for periodically nonstationary shot noise,” Telecommun. Radio Eng. (Engl. Trans.) Part 2 23, 91–96 (1968).

1944

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).

1910

N. Campbell, “Discontinuities in light emission,” Proc. Cambr. Phil. Soc. 15, 310–328 (1910).

1909

N. Campbell, “The study of discontinuous phenomena,” Proc. Cambridge Philos. Soc. 15, 117–136 (1909).

Abgrall, M.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, 2002), Chap. 3., pp. 114–116.

Audoin, C.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

Bachor, H. A.

Bartels, A.

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,” IEEE Electron Device Lett. 41, 650–651 (2005).

Baumann, E.

Beling, A.

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

Bize, S.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Bowers, J. E.

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation, Pure and Applied Optics (Wiley, 1983), Chap. 8, pp. 119–127.

Braje, D.

Bruyevich, A. N.

A. N. Bruyevich, “Fluctuations in autooscillators for periodically nonstationary shot noise,” Telecommun. Radio Eng. (Engl. Trans.) Part 2 23, 91–96 (1968).

Campbell, J. C.

Z. Li, Y. Fu, M. Piels, H. P. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385–B390 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Campbell, N.

N. Campbell, “Discontinuities in light emission,” Proc. Cambr. Phil. Soc. 15, 310–328 (1910).

N. Campbell, “The study of discontinuous phenomena,” Proc. Cambridge Philos. Soc. 15, 117–136 (1909).

Cao, J.

Chen, J.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[CrossRef]

Chen, Y. K.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Cibiel, G.

G. Cibiel, M. Regis, 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]

Clairon, A.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

Cliche, J. F.

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy—Maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Syst. Mag. 26(1), 19–26 (2006).
[CrossRef]

Cox, J. A.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[CrossRef]

Dagenais, M.

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6, 639–641 (1994).
[CrossRef]

Danzmann, K.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

Datta, S.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE, 1987), Chap. 7, pp. 119–123.

Delfyett, P. J.

Deschenes, J. D.

J. D. Deschenes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
[CrossRef]

Dick, G. J.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

Diddams, S.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

Diddams, S. A.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[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,” IEEE Electron Device Lett. 41, 650–651 (2005).

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

English, E. M. L.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Esman, R. D.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
[CrossRef]

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6, 639–641 (1994).
[CrossRef]

Fontaine, N. K.

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]

Fortier, T.

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef]

Fortier, T. M.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Frankel, M. Y.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
[CrossRef]

Fu, Y.

Z. Li, Y. Fu, M. Piels, H. P. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385–B390 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Gardner, W. A.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
[CrossRef]

W. A. Gardner, Statistical Spectral Analysis: A Nonprobabalistic Theory, Prentice Hall Information and System Sciences Series (Prentice-Hall, 1988), Chap. 1, pp. 3–33.

Gee, S.

Gee, S. Y.

Genest, J.

J. D. Deschenes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
[CrossRef]

Giorgetta, F. R.

Graffeuil, J.

J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
[CrossRef]

Gray, M. B.

Guena, J.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Haboucha, A.

Hakonen, P.

L. Roschier, T. T. Heikkila, and P. Hakonen, “Cyclostationary shot noise in mesoscopic measurements,” J. Appl. Phys. 96, 5927–5929 (2004).
[CrossRef]

Hati, A.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Haverkamp, N.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Heikkila, T. T.

L. Roschier, T. T. Heikkila, and P. Hakonen, “Cyclostationary shot noise in mesoscopic measurements,” J. Appl. Phys. 96, 5927–5929 (2004).
[CrossRef]

Henry, C. H.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

Heritage, J. P.

Hollberg, L.

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[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,” IEEE Electron Device Lett. 41, 650–651 (2005).

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]

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]

Ivanov, E. N.

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,” IEEE Electron Device Lett. 41, 650–651 (2005).

Jiang, H.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Jiang, H. F.

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

Jiang, W.

Jiang, Y.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

Jiang, Y. Y.

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]

Joshi, A.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

Karalar, A.

Kartner, F. X.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[CrossRef]

Kazarinov, R. F.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

Keller, U.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Kim, J.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[CrossRef]

Kirchner, M.

Kirchner, M. S.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[CrossRef]

Koc, U. V.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Kolner, B. H.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
[CrossRef]

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]

Kondratko, P. K.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Krainer, L.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Kurtz, J. L.

J. A. Scheer and J. L. Kurtz, Coherent Radar Performance Estimation (Artech House, 1993).

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]

Laurent, P.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

Le Coq, Y.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Lee, J.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Lemke, N.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[CrossRef]

Leven, A.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Li, T.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[CrossRef]

Li, Z.

Liman, R. A.

J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
[CrossRef]

Lin, I. S.

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wireless Compon. Lett. 15, 226–228 (2005).
[CrossRef]

Lin, J.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Liu, P.-L.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
[CrossRef]

Llopis, O.

J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
[CrossRef]

G. Cibiel, M. Regis, 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]

Lours, M.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Ludlow, A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

Ludlow, A. D.

Luiten, A. N.

Makdissi, A.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

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]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), Chap. 9., pp. 452–458.

McClelland, D. E.

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,” IEEE Electron Device Lett. 41, 650–651 (2005).

McKinney, J. D.

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wireless Compon. Lett. 15, 226–228 (2005).
[CrossRef]

Meers, B. J.

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

Millo, J.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Muraro, J. L.

J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
[CrossRef]

Napolitano, A.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
[CrossRef]

Nelson, C.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Newbury, N. R.

Niebauer, T. M.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

Oates, C. W.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[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,” IEEE Electron Device Lett. 41, 650–651 (2005).

Okamoto, K.

Olsson, N. A.

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

Ozharar, S.

Pan, H. P.

Paschotta, R.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
[CrossRef]

Paura, L.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
[CrossRef]

Piels, M.

Quinlan, F.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[CrossRef]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

S. Y. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, “Correlation of supermode noise of harmonically mode-locked lasers,” J. Opt. Soc. Am. B 24, 1490–1497 (2007).
[CrossRef]

F. Quinlan, S. Gee, S. Ozharar, and P. J. Delfyett, “Ultralow-jitter and amplitude-noise semiconductor-based actively mode-locked laser,” Opt. Lett. 31, 2870–2872 (2006).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

Rakhmanov, M.

Regis, M.

G. Cibiel, M. Regis, 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]

Rice, S. O.

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE, 1987), Chap. 7, pp. 119–123.

Roschier, L.

L. Roschier, T. T. Heikkila, and P. Hakonen, “Cyclostationary shot noise in mesoscopic measurements,” J. Appl. Phys. 96, 5927–5929 (2004).
[CrossRef]

Rosenband, T.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

Rubiola, 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]

Rudiger, A.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

Rudin, B.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Saleh, B.

B. Saleh, Photoelectron Statistics, Springer Series in Optical Sciences (Springer-Verlag, 1978), Chap. 5., vol. 6, pp. 161–164.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991), Chap. 17, pp. 675–678.

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]

Santarelli, G.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

Scheer, J. A.

J. A. Scheer and J. L. Kurtz, Coherent Radar Performance Estimation (Artech House, 1993).

Schilling, R.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

Schlatter, A.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Scott, R. P.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
[CrossRef]

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]

Seidelin, S.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

Shillue, B.

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy—Maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Syst. Mag. 26(1), 19–26 (2006).
[CrossRef]

Slusher, R. E.

R. E. Slusher and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

Spuhler, G. J.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Stevenson, A. J.

Strain, K. A.

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

Swann, W. C.

Taylor, J.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

Taylor, J. A.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991), Chap. 17, pp. 675–678.

Telle, H. R.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Thorpe, M. J.

Tobar, M. E.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Tournier, E.

G. Cibiel, M. Regis, 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]

Tu, K. Y.

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

Valley, G. C.

von der Linde, D.

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

Walls, D. F.

D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983).
[CrossRef]

Weiner, A. M.

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef]

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wireless Compon. Lett. 15, 226–228 (2005).
[CrossRef]

Williams, K. J.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
[CrossRef]

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6, 639–641 (1994).
[CrossRef]

Wilpers, G.

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,” IEEE Electron Device Lett. 41, 650–651 (2005).

Winkler, W.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

Winzer, P. J.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), Chap. 9., pp. 452–458.

Yariv, A.

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]

Yoo, S. J. B.

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]

Yurke, B.

R. E. Slusher and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

Zeller, S. C.

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Zhang, W.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. B

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
[CrossRef]

R. Paschotta, B. Rudin, A. Schlatter, G. J. Spuhler, L. Krainer, S. C. Zeller, N. Haverkamp, H. R. Telle, and U. Keller, “Relative timing jitter measurements with an indirect phase comparison method,” Appl. Phys. B 80, 185–192 (2005).
[CrossRef]

Appl. Phys. Lett.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guena, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Bell Syst. Tech. J.

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).

IEEE Control Syst. Mag.

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy—Maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Syst. Mag. 26(1), 19–26 (2006).
[CrossRef]

IEEE Electron Device Lett.

J. Graffeuil, R. A. Liman, J. L. Muraro, and O. Llopis, “Cyclostationary shot-noise measurements in RF Schottky-Barrier diode detectors,” IEEE Electron Device Lett. 31, 74–76 (2010).
[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,” IEEE Electron Device Lett. 41, 650–651 (2005).

IEEE J. Sel. Top. Quantum Electron.

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]

IEEE Microw. Wireless Compon. Lett.

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wireless Compon. Lett. 15, 226–228 (2005).
[CrossRef]

IEEE Photon. J.

H. F. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. 3, 1004–1012 (2011).
[CrossRef]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[CrossRef]

IEEE Photon. Technol. Lett.

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6, 639–641 (1994).
[CrossRef]

P. K. Kondratko, A. Leven, Y. K. Chen, J. Lin, U. V. Koc, K. Y. Tu, and J. Lee, “12.5 GHz optically sampled interference-based photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 17, 2727–2729 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microwave Theory Tech. 47, 1297–1303 (1999).
[CrossRef]

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

G. Cibiel, M. Regis, 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]

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).
[CrossRef]

J. Appl. Phys.

L. Roschier, T. T. Heikkila, and P. Hakonen, “Cyclostationary shot noise in mesoscopic measurements,” J. Appl. Phys. 96, 5927–5929 (2004).
[CrossRef]

J. Lightwave Technol.

R. E. Slusher and B. Yurke, “Squeezed light for coherent communications,” J. Lightwave Technol. 8, 466–477 (1990).
[CrossRef]

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[CrossRef]

Nature

D. F. Walls, “Squeezed states of light,” Nature 306, 141–146 (1983).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. D. Deschenes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
[CrossRef]

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rudiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
[CrossRef]

B. J. Meers and K. A. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef]

Proc. Cambr. Phil. Soc.

N. Campbell, “Discontinuities in light emission,” Proc. Cambr. Phil. Soc. 15, 310–328 (1910).

Proc. Cambridge Philos. Soc.

N. Campbell, “The study of discontinuous phenomena,” Proc. Cambridge Philos. Soc. 15, 117–136 (1909).

Rev. Mod. Phys.

C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics,” Rev. Mod. Phys. 68, 801–853 (1996).
[CrossRef]

Rev. Sci. Instrum.

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]

Signal Process.

W. A. Gardner, A. Napolitano, and L. Paura, “Cyclostationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
[CrossRef]

Telecommun. Radio Eng. (Engl. Trans.) Part 2

A. N. Bruyevich, “Fluctuations in autooscillators for periodically nonstationary shot noise,” Telecommun. Radio Eng. (Engl. Trans.) Part 2 23, 91–96 (1968).

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991), Chap. 17, pp. 675–678.

R. W. Boyd, Radiometry and the Detection of Optical Radiation, Pure and Applied Optics (Wiley, 1983), Chap. 8, pp. 119–127.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), Chap. 9., pp. 452–458.

J. A. Scheer and J. L. Kurtz, Coherent Radar Performance Estimation (Artech House, 1993).

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics7, 290–293 (2013).

B. Saleh, Photoelectron Statistics, Springer Series in Optical Sciences (Springer-Verlag, 1978), Chap. 5., vol. 6, pp. 161–164.

W. A. Gardner, Statistical Spectral Analysis: A Nonprobabalistic Theory, Prentice Hall Information and System Sciences Series (Prentice-Hall, 1988), Chap. 1, pp. 3–33.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, 2002), Chap. 3., pp. 114–116.

Characterization of Clocks and Oscillators: NIST Technical Note 1337 (US GPO, Washington, DC, 1990).

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE, 1987), Chap. 7, pp. 119–123.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Time and frequency domain depictions of optical and photodetected electrical pulse trains. (a) Optical pulse train intensity profile. (b) Photodetected electrical pulse train when the optical pulsewidth is much shorter than the photodetector’s impulse response time. (c) Spectrum of the optical intensity profile. (d) Power spectrum of the photocurrent. Symbols are defined in the text.

Fig. 2.
Fig. 2.

Photodetector saturation modeled as a power-dependent transfer function. (a) Power spectrum of a photodetected train of ultrashort optical pulses under low (red/gray) and high (black) power illumination. Dotted lines represent the rolloff in the response of the photodetector. Shot noise is represented as the shaded regions for low (red/light gray) and high (dark gray) power illumination. In this example, there is a decrease in the photodetector response at high frequencies as the photodetector saturates. This saturation affects the shot-noise spectrum as well as the power in the microwave harmonics. (b) Power in one of the microwave harmonics and shot noise at an adjacent frequency as the average photocurrent is increased. The onset of photodetector saturation leads to a rollover of the power of the microwave harmonic and a decrease in the shot-noise power.

Fig. 3.
Fig. 3.

Correlations in the sidebands about a photonically generated microwave carrier, revealed with a double-sided representation of the photocurrent power spectrum.

Fig. 4.
Fig. 4.

(a) Spectrum of the optical intensity profile of a train of Gaussian-shaped pulses. The pulse duty cycle (τp/Tr) is 0.25. (b) Shot-noise deviation from the long pulse limit for a train of Gaussian pulses.

Fig. 5.
Fig. 5.

(a) Pulse intensity profile spectrum of a train of square pulses with a duty cycle of 0.25. (b) Shot-noise deviation from the long pulse limit for a train of square pulses.

Equations (65)

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

i(t)=kXkh(tkΔt).
h(t)dt=q.
p=ηhνPopt(t)Δtλ(t)Δt,
Popt(t)=P0nf(tnTr),
Si(f)=limT1T|FT{i(t)}|2(A2/Hz),
Si(f)=|H(f)|2[λavg+Sλ(f)],
Pshot(f)=2|Hn(f)|2qIavgRΔf(W).
Sλ(f)=(ηhν)2SP(f),
SP(f)=limT1T|FT{Popt(t)}|2,
Pμ(nfr)=2q2|Hn(nfr)|2Sλ(nfr)RΔf.
SNR(nfr)=Pμ(nfr)2|Hn(nfr)|2qIavgRΔf.
Pμ(nfr)=2Iavg2|Hn(nfr)|2R.
SNR(nfr)=Iavg/(qΔf).
SRIN=2qIavg=2hνηPavg(Hz1).
Si(f,f)=limT1TFT{kXkh(tkΔt)}·FT*{lXlh(tlΔt)}.
Sin(f,f)=H(f)H*(f)limT1T[ΛT(ff)],
|C(nfr+δf,nfrδf)|=|C(nfr+δf,nfr+δf)|=|Sin(nfr+δf,nfr+δf)|[Si(nfr+δf)Si(nfr+δf)]1/2=|P˜opt(2nfr)|P˜opt(0).
[1+a(t)]cos(2πf0t+θ(t))·cos(2πf0t+Φr),
im(t)=[(kXkh(tkΔt))*g(t)]·cos(2πnfrt+Φr),
LAM,PM=qIavg|Hn(nfr)|2RPμ(nfr)[1±|P˜opt(2nfr)|P˜opt(0)·cos(2Φopt(nfr)Φopt(2nfr))](Hz1),
Popt(t)=EpτGπnexp{((tnTr)/τG)2},
LAM,PM=qIavg|Hn(nfr)|2RPμ(nfr)[1±exp{(2πnfrτG)2}].
LAM,PM=qIavg|Hn(nfr)|2RPμ(nfr).
LAM=qIavg=12SRIN
LPM=q2Iavg(2πnfrτG)2.
σt2=1(2πnfr)20fr/22LPM(f)df(s2),
σt2=q2IavgfrτG2=12ηhνEpτG2.
Popt(t)=EpτpnΠ((tnTr)τp),
Π(tτp)={1forτp/2tτp/20otherwise.
LAM,PM=qIavg|Hn(nfr)|2RPμ(nfr)[1±|sinc(2πnτpfr)|·cos(2Φopt(nfr)Φopt(2nfr))].
LPM=q12Iavg(2πnfrτp)2.
Si(f,f)=limT1TFT{kXkh(tkΔt)}×FT*{lXlh(tlΔt)},
FT{x(t)}T/2T/2x(t)ei2πftdtXT(f).
Si(f,f)=limT1TkXkFT{h(tkΔt)}·lXlFT*{h(tlΔt)},
Si(f,f)=limT1TklXkXlHT(f)HT*(f)exp{i2πfkΔt}exp{i2πflΔt},
XkXl={λ(kΔt)Δtfork=lλ(kΔt)λ(lΔt)ΔtΔtforkl},
Si(f,f)=H(f)H*(f)limT1Tkλ(kΔt)Δtexp{i2π(ff)kΔt}+kl,lk(kΔt)λ(lΔt)ΔtΔtexp{i2πfkΔt}exp{i2πflΔt}.
Si(f,f)=H(f)H*(f)limT1T[T/2T/2λ(τ)ei2π(ff)τdτ+T/2T/2λ(τ)λ(τ)ei2πfτei2πfτdτdτ]
Si(f,f)=H(f)H*(f)limT1T[ΛT(ff)+ΛT(f)ΛT*(f)].
Si(f)=|H(f)|2[λavg+Sλ(f)](A2/Hz),
λavg=limT1TΛT(0)
Sλ(f)=limT1T|ΛT(f)|2.
Sin(f,f)=H(f)H*(f)limT1T[ΛT(ff)].
Vm(t)=V1[1+a(t)]cos(2πfrt+θ(t))·V2cos(2πfrt+Φr).
Vm(t)=V1V22[1+a(t)].
Vm(t)=V1V22θ(t).
Sm(f)=limT1T|FT{[(kXkh(tkΔt))*g(t)]·cos(2πfrt+Φr)}|2.
Sm(f)=limT1T|kXkFT{[h(tkΔt)*g(t)]·cos(2πfrt+Φr)}|2.
Sm(f)=limT1T|kXk[HT(f)ei2πfkΔtGT(f)]*[12δ(ffr)eiΦr+12δ(f+fr)eiΦr]|2,
14|H(ffr)|2|G(ffr)|2·klXkXl·exp{i2π(ffr)kΔt}exp{i2π(ffr)lΔt},
14|H(f+fr)|2|G(f+fr)|2·klXkXl·exp{i2π(f+fr)kΔt}exp{i2π(f+fr)lΔt},
14H(ffr)H*(f+fr)G(ffr)G*(f+fr)e2iΦr·klXkXlexp{i2π(ffr)kΔt}·exp{i2π(f+fr)lΔt},
14H*(ffr)H(f+fr)G*(ffr)G(f+fr)e2iΦr·klXkXlexp{i2π(ffr)kΔt}·exp{i2π(f+fr)lΔt},
14|H(ffr)|2|G(ffr)|2[limT1TΛT(0)+Sλ(ffr)].
14|H(f+fr)|2|G(f+fr)|2[limT1TΛT(0)+Sλ(f+fr)].
14H(ffr)H*(f+fr)G(ffr)G*(f+fr)e2iΦr·[limT1TT/2T/2λ(τ)ei2π(2fr)τdτ+limT1TT/2T/2λ(τ)λ(τ)ei2π(ffr)τei2π(f+fr)τdτdτ],
14H(ffr)H*(f+fr)G(ffr)G*(f+fr)e2iΦr[limT1TΛT(2fr)+limT1TΛT(ffr)ΛT*(f+fr)].
H(ffr)G(ffr)=H*(f+fr)G*(f+fr).
12|H(ffr)|2|G(ffr)|2[limT1TΛT(0)+Sλ(ffr)].
12|H(ffr)|2|G(ffr)|2Sλ(ffr)·cos(2Φr+2ΦH(ffr)+2ΦG(ffr)+2ΦΛ(ffr))+12|H(ffr)|2|G(ffr)|2limT1T|ΛT(2fr)|·cos(2Φr+2ΦH(ffr)+2ΦG(ffr)ΦΛ(2fr)).
Sm(f)=12|H(ffr)|2|G(ffr)|2[limT1TΛT(0)+limT1T|ΛT(2fr)|·cos(2Φr+2ΦH(ffr)+2ΦG(ffr)ΦΛ(2fr))]+12|H(ffr)|2|G(ffr)|2Sλ(ffr)[1+cos(2Φr+2ΦH(ffr)+2ΦG(ffr)+2ΦΛ(ffr))].
Sm(f)=12|H(ffr)|2|G(ffr)|2[limT1TΛT(0)+limT1T|ΛT(2fr)|·cos(π+2Φopt(fr)Φopt(2fr))],
Sm(f)=12|H(ffr)|2|G(ffr)|2λavg·[1+|P˜opt(2fr)|P˜opt(0)·cos(π+2Φopt(fr)Φopt(2fr))].
Sθ(f)=12λavgSλ(fr)[1+|P˜opt(2fr)|P˜opt(0)·cos(π+2Φopt(fr)Φopt(2fr))].
Sθ(f)=2qIavg|Hn(fr)|2RPμ(fr)[1|P˜opt(2fr)|P˜opt(0)·cos(2Φopt(fr)Φopt(2fr))],

Metrics