Abstract

We report, what is to the best of our knowledge, the narrowest instantaneous linewidth measurement of the beat frequency between two phase locked heterodyned 1.319 μm Nd:YAG lasers. At both 65 kHz and 31.7 GHz beat frequencies, we measured the instantaneous 3 dB linewidth of the optically-generated microwave tones to be < 22.8 μHz, limited only by the minimum instrument resolution. Allan deviation measurements indicate that the laser system follows a 5 MHz quartz reference oscillator to stability levels of σy (1s) = 8.4 × 10−12. At 10.24 GHz, the laser system follows a sapphire loaded cavity oscillator to stability levels of σy (1s) = 1.6 × 10−11. For these measurements, the optical beat note closely follows the linewidth and stability of the driving microwave frequency reference.

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2017 (1)

2016 (4)

A. Bercy, O. Lopez, P. E. Pottie, and A. Amy-Klein, “Ultrastable optical frequency dissemination on a multi-access fibre network,” Appl. Phys. B 122(7) 189 (2016).
[Crossref]

D. B. Leeson, “Oscillator phase noise: a 50-year review,” IEEE Trans. on Ultrason., Ferroelectr., Freq. Control. 63(8), 1208–1225 (2016).
[Crossref]

D. A. Tulchinsky, A. S. Hastings, and K. J. Williams, “Characteristics and performance of offset phase locked single frequency heterodyned laser systems,” Rev. Sci. Instrum. 87(5), 053107 (2016).
[Crossref] [PubMed]

V. Giordano, S. Grop, C. Fluhr, B. Dubois, Y. Kersale, and E. Rubiola, “The autonomous cryocooled sapphire oscillator: a reference for frequency stability and phase noise measurements,” Journal of Physics: Conference Series 723(1), 012030 (2016).

2015 (1)

L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
[Crossref] [PubMed]

2014 (2)

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, “Electro-optical frequency division and stable microwave synthesis,” Science 345(6194), 309–313 (2014).
[Crossref] [PubMed]

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

2013 (4)

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hansch, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111(11), 110801 (2013).
[Crossref] [PubMed]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nature Photonics 7(6), 434–438 (2013).
[Crossref]

A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. DeSalvo, A. Ludlow, S. A. Addams, and D. A. Howe, “State-of-the-art RF Signal Generation from optical frequency division,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 60(9), 1796–1803 (2013).
[Crossref]

G. J. Schneider, J. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radio frequency signal-generation system with over seven octaves of continuous tuning,” Nature Photonics 7(2), 118–122 (2013).
[Crossref]

2011 (2)

2010 (1)

2009 (2)

B. Bernhardt, T. W. Hansch, and R. Holzwarth, “Implementation and characterization of a stable optical frequency distribution system,” Opt. Express 17(9), 16849–16860 (2009).
[Crossref] [PubMed]

R. E. Bartolo, A. Tveten, and C. K. Kirkendal, “The quest for inexpensive, compact, low phase noise laser sources for fiber optic sensing applications,” Proc. SPIE 7503, 750370 (2009).
[Crossref]

2008 (1)

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing sychronization of remote optical and microwave sources,” Nature Photonics 2(12) 733–736 (2008).
[Crossref]

2006 (1)

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Systems 26(1), 19–26 (2006).
[Crossref]

2005 (1)

D. A. Tulchinsky and K. J. Williams, “Excess amplitude and excess phase noise of RF photodiodes operated in compression,” IEEE Photon. Tech. Lett. 17(3), 654–656 (2005).
[Crossref]

2004 (1)

2002 (1)

G. Brida, “High resolution frequency stability measurement system,” Rev. Sci. Instrum. 73(5), 2171–2174 (2002).
[Crossref]

2001 (2)

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

D. A. Tulchinsky and P. J. Matthews, “Ultrawide-band fiber-optic control of a millimeter-wave transmit beamformer,” IEEE Trans. Microwave Theory Tech. 49(7), 1248–1253 (2001).
[Crossref]

1999 (1)

1998 (1)

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photon. Technol. Lett. 10(5), 719–721 (1998).
[Crossref]

1996 (1)

1993 (1)

J. R. Vig, “Military applications of high accuracy frequency standards and clocks,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 40(5), 522–527 (1993).
[Crossref]

1989 (1)

K. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett. 25(18), 1242–1243 (1989).
[Crossref]

1985 (1)

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proceedings of the IEEE 66(1), 51–83 (1978).
[Crossref]

1975 (1)

F. L. Walls and A. DeMarchi, “RF spectrum of a signal after frequency multiplication; measurement and comparison with a simple calculation,” IEEE Trans. Instrum. and Meas. 24(3), 210–217 (1975).
[Crossref]

1971 (1)

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

1966 (1)

D. B. Leeson and G. F. Johnson, “Short-term stability for a Doppler radar: requirements, measurements, and techniques,” Proceedings of the IEEE 54(2), 244–246 (1966).
[Crossref]

1958 (1)

R. B. Blackman and J. W. Tukey, “The measurement of power spectra from the point of view of communications engineering – part I,” Bell Syst. Techn. J. 37(1), 185–282 (1958).
[Crossref]

Addams, S. A.

A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. DeSalvo, A. Ludlow, S. A. Addams, and D. A. Howe, “State-of-the-art RF Signal Generation from optical frequency division,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 60(9), 1796–1803 (2013).
[Crossref]

Amy-Klein, A.

A. Bercy, O. Lopez, P. E. Pottie, and A. Amy-Klein, “Ultrastable optical frequency dissemination on a multi-access fibre network,” Appl. Phys. B 122(7) 189 (2016).
[Crossref]

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

Argence, B.

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

Barnes, C.

A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. DeSalvo, A. Ludlow, S. A. Addams, and D. A. Howe, “State-of-the-art RF Signal Generation from optical frequency division,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 60(9), 1796–1803 (2013).
[Crossref]

Barnes, J. A.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

Bartolo, R. E.

R. E. Bartolo, A. Tveten, and C. K. Kirkendal, “The quest for inexpensive, compact, low phase noise laser sources for fiber optic sensing applications,” Proc. SPIE 7503, 750370 (2009).
[Crossref]

Baumann, E.

L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
[Crossref] [PubMed]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nature Photonics 7(6), 434–438 (2013).
[Crossref]

W. C. Swann, E. Baumann, F. R. Girgetta, 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(24), 24387–24395 (2011).
[Crossref] [PubMed]

Berceli, T.

G. Kovacs, P. R. Herczfeld, and T. Berceli, “Phase stability of optical self-heterodyned microwave signals with Nd:YVO4 laser,” in 2010 IEEE Topical Meeting on Microwave Photonics (MWP) (IEEE, 2010), pp. 159–162.
[Crossref]

Bercy, A.

A. Bercy, O. Lopez, P. E. Pottie, and A. Amy-Klein, “Ultrastable optical frequency dissemination on a multi-access fibre network,” Appl. Phys. B 122(7) 189 (2016).
[Crossref]

Bergquist, J. C.

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

Bernhardt, B.

Blackman, R. B.

R. B. Blackman and J. W. Tukey, “The measurement of power spectra from the point of view of communications engineering – part I,” Bell Syst. Techn. J. 37(1), 185–282 (1958).
[Crossref]

Brida, G.

G. Brida, “High resolution frequency stability measurement system,” Rev. Sci. Instrum. 73(5), 2171–2174 (2002).
[Crossref]

Byer, R. L.

Carruthers, T. F.

Carty, T.

Chang, S.

S. Chang, A. G. Mann, and A. N. Luiten, “Cryogenic sapphire oscillator with improved frequency stability,” in 2000 IEEE/EIA International Frequency Control Symposium and Exhibition, (IEEE2000), pp. 475–479.
[Crossref]

Chardonnet, C.

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

Chen, B. W.

Chen, J.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing sychronization of remote optical and microwave sources,” Nature Photonics 2(12) 733–736 (2008).
[Crossref]

Chen, T. J.

Chen, W. Y.

Chi, A. R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[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 Systems 26(1), 19–26 (2006).
[Crossref]

Coddington, I.

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J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing sychronization of remote optical and microwave sources,” Nature Photonics 2(12) 733–736 (2008).
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Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photon. Technol. Lett. 10(5), 719–721 (1998).
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L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
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J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, “Electro-optical frequency division and stable microwave synthesis,” Science 345(6194), 309–313 (2014).
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K. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett. 25(18), 1242–1243 (1989).
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Fluhr, C.

V. Giordano, S. Grop, C. Fluhr, B. Dubois, Y. Kersale, and E. Rubiola, “The autonomous cryocooled sapphire oscillator: a reference for frequency stability and phase noise measurements,” Journal of Physics: Conference Series 723(1), 012030 (2016).

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V. Giordano, S. Grop, C. Fluhr, B. Dubois, Y. Kersale, and E. Rubiola, “The autonomous cryocooled sapphire oscillator: a reference for frequency stability and phase noise measurements,” Journal of Physics: Conference Series 723(1), 012030 (2016).

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Goldberg, L.

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J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing sychronization of remote optical and microwave sources,” Nature Photonics 2(12) 733–736 (2008).
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Kersale, Y.

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L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
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Lee, H.

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, “Electro-optical frequency division and stable microwave synthesis,” Science 345(6194), 309–313 (2014).
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S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
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P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
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[Crossref]

Shi, S.

G. J. Schneider, J. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radio frequency signal-generation system with over seven octaves of continuous tuning,” Nature Photonics 7(2), 118–122 (2013).
[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 Systems 26(1), 19–26 (2006).
[Crossref]

Sinclair, L. C.

L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
[Crossref] [PubMed]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nature Photonics 7(6), 434–438 (2013).
[Crossref]

Smith, W. L.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

Sonderhouse, L.

L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
[Crossref] [PubMed]

Song, S. C.

S. C. Song and Y. S. Hong, “A new approach for evaluating the phase noise requirements of STALO in a Doppler radar,” in The Proceedings of the 4th European Radar Conference, (IEEE, 2007), pp. 198 – 201.

Sow, P. L. T.

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

Stein, S. R.

S. R. Stein, “Frequency and Time – Their Measurement and Characterization,” in Precision Frequency Control, 2, ed. E. A. Gerber and A. Ballato, eds. (Academic, 1985), chap. 12.

Swann, W. C.

L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
[Crossref] [PubMed]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nature Photonics 7(6), 434–438 (2013).
[Crossref]

W. C. Swann, E. Baumann, F. R. Girgetta, 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(24), 24387–24395 (2011).
[Crossref] [PubMed]

Sydnor, R. L.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

G. J. Dick, P. F. Kuhnle, and R. L. Sydnor, “Zero-crossing detector with sub-microsecond jtter and crosstalk,” in 22nd Annual Precise Time and Time Interval (PTTI) Applications Planning Meeting, (PTTI, 1990), pp. 269–282.

Taubman, M. S.

M. S. Taubman, “Optical frequency stabilization and optical phase locked loops: golden threads of precision measurement,” in American Control Conference (ACC), 2013, (IEEE, 2013), pp. 1488–1505.
[Crossref]

J. L. Hall, M. S. Taubman, and J. Ye, “Laser Stabilization,” in Handbook of Optics: II - Design, Fabrication, and Testing; Sources and Detectors; Radiometry and Photometry, 3rd edition, M. Bass, ed. (McGraw-Hill Professional, 2010), Chap. 22.

Tetu, M.

J. Vanier and M. Tetu, “Time domain measurement and frequency stability: a tutorial introduction,” in The Proceedings of the 10th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, (PTTI1978), pp. 247–291.

Thorne, A.

A. Thorne, U. Litzen, and S. Johansson, “The Width and Shape of Spectral Lines – Convolution of Line Profiles: The Voigt Profile,” in Spectrophysics: Principles and Applications, (Springer-Verlag, 1999), Chap. 8.5.

Tobar, M. E.

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Advanced phase noise suppression technique for next generation of ultra low-noise microwave oscillators,” in Proceedings of the 1995 IEEE International Frequency Control Symposium (49th Annual Symposium), (IEEE, 1995), pp. 314–320.
[Crossref]

Tokunaga, S. K.

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

Tukey, J. W.

R. B. Blackman and J. W. Tukey, “The measurement of power spectra from the point of view of communications engineering – part I,” Bell Syst. Techn. J. 37(1), 185–282 (1958).
[Crossref]

Tulchinsky, D. A.

D. A. Tulchinsky, A. S. Hastings, and K. J. Williams, “Characteristics and performance of offset phase locked single frequency heterodyned laser systems,” Rev. Sci. Instrum. 87(5), 053107 (2016).
[Crossref] [PubMed]

D. A. Tulchinsky and K. J. Williams, “Excess amplitude and excess phase noise of RF photodiodes operated in compression,” IEEE Photon. Tech. Lett. 17(3), 654–656 (2005).
[Crossref]

D. A. Tulchinsky and P. J. Matthews, “Ultrawide-band fiber-optic control of a millimeter-wave transmit beamformer,” IEEE Trans. Microwave Theory Tech. 49(7), 1248–1253 (2001).
[Crossref]

Tveten, A.

R. E. Bartolo, A. Tveten, and C. K. Kirkendal, “The quest for inexpensive, compact, low phase noise laser sources for fiber optic sensing applications,” Proc. SPIE 7503, 750370 (2009).
[Crossref]

Udem, Th.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hansch, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111(11), 110801 (2013).
[Crossref] [PubMed]

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

Vahala, K. J.

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, “Electro-optical frequency division and stable microwave synthesis,” Science 345(6194), 309–313 (2014).
[Crossref] [PubMed]

Vanier, J.

J. Vanier and M. Tetu, “Time domain measurement and frequency stability: a tutorial introduction,” in The Proceedings of the 10th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, (PTTI1978), pp. 247–291.

Vessot, R. F. C.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

Vig, J. R.

J. R. Vig, “Military applications of high accuracy frequency standards and clocks,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 40(5), 522–527 (1993).
[Crossref]

Vogel, K. R.

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

Walls, F. L.

F. L. Walls and A. DeMarchi, “RF spectrum of a signal after frequency multiplication; measurement and comparison with a simple calculation,” IEEE Trans. Instrum. and Meas. 24(3), 210–217 (1975).
[Crossref]

Weller, J. F.

K. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett. 25(18), 1242–1243 (1989).
[Crossref]

Williams, K.

K. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett. 25(18), 1242–1243 (1989).
[Crossref]

Williams, K. J.

D. A. Tulchinsky, A. S. Hastings, and K. J. Williams, “Characteristics and performance of offset phase locked single frequency heterodyned laser systems,” Rev. Sci. Instrum. 87(5), 053107 (2016).
[Crossref] [PubMed]

D. A. Tulchinsky and K. J. Williams, “Excess amplitude and excess phase noise of RF photodiodes operated in compression,” IEEE Photon. Tech. Lett. 17(3), 654–656 (2005).
[Crossref]

K. J. Williams, Optical Sciences Division, U.S. Naval Research Laboratory, 4555 Overlook Avenue, S.W., Washington, DC., 20375 (personal communication, 2016).

Wineland, D. J.

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

Winkler, G. M. R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

Woode, R. A.

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Advanced phase noise suppression technique for next generation of ultra low-noise microwave oscillators,” in Proceedings of the 1995 IEEE International Frequency Control Symposium (49th Annual Symposium), (IEEE, 1995), pp. 314–320.
[Crossref]

Yang, Y. P.

Yasuda, M.

Ye, J.

J. Ye and J. L. Hall, “Optical phase locking in the microradian domain: potential applications to NASA spaceborne optical measurements,” Opt. Lett. 24(24), 1838–1840 (1999).
[Crossref]

J. L. Hall, M. S. Taubman, and J. Ye, “Laser Stabilization,” in Handbook of Optics: II - Design, Fabrication, and Testing; Sources and Detectors; Radiometry and Photometry, 3rd edition, M. Bass, ed. (McGraw-Hill Professional, 2010), Chap. 22.

Yi, X.

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, “Electro-optical frequency division and stable microwave synthesis,” Science 345(6194), 309–313 (2014).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

A. Bercy, O. Lopez, P. E. Pottie, and A. Amy-Klein, “Ultrastable optical frequency dissemination on a multi-access fibre network,” Appl. Phys. B 122(7) 189 (2016).
[Crossref]

Appl. Phys. Lett. (1)

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquie, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

Bell Syst. Techn. J. (1)

R. B. Blackman and J. W. Tukey, “The measurement of power spectra from the point of view of communications engineering – part I,” Bell Syst. Techn. J. 37(1), 185–282 (1958).
[Crossref]

Electron. Lett. (1)

K. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett. 25(18), 1242–1243 (1989).
[Crossref]

IEEE Control Systems (1)

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama large millimeter array,” IEEE Control Systems 26(1), 19–26 (2006).
[Crossref]

IEEE Photon. Tech. Lett. (1)

D. A. Tulchinsky and K. J. Williams, “Excess amplitude and excess phase noise of RF photodiodes operated in compression,” IEEE Photon. Tech. Lett. 17(3), 654–656 (2005).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photon. Technol. Lett. 10(5), 719–721 (1998).
[Crossref]

IEEE Trans. Instrum. and Meas. (1)

F. L. Walls and A. DeMarchi, “RF spectrum of a signal after frequency multiplication; measurement and comparison with a simple calculation,” IEEE Trans. Instrum. and Meas. 24(3), 210–217 (1975).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. L. Sydnor, R. F. C. Vessot, and G. M. R. Winkler, “Characterization of Frequency Stability,” IEEE Trans. Instrum. Meas. IM-20(2), 105–120 (1971).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

D. A. Tulchinsky and P. J. Matthews, “Ultrawide-band fiber-optic control of a millimeter-wave transmit beamformer,” IEEE Trans. Microwave Theory Tech. 49(7), 1248–1253 (2001).
[Crossref]

IEEE Trans. on Ultrason., Ferroelectr., Freq. Control. (1)

D. B. Leeson, “Oscillator phase noise: a 50-year review,” IEEE Trans. on Ultrason., Ferroelectr., Freq. Control. 63(8), 1208–1225 (2016).
[Crossref]

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

J. R. Vig, “Military applications of high accuracy frequency standards and clocks,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 40(5), 522–527 (1993).
[Crossref]

A. Hati, C. W. Nelson, C. Barnes, D. Lirette, T. Fortier, F. Quinlan, J. A. DeSalvo, A. Ludlow, S. A. Addams, and D. A. Howe, “State-of-the-art RF Signal Generation from optical frequency division,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 60(9), 1796–1803 (2013).
[Crossref]

Journal of Physics: Conference Series (1)

V. Giordano, S. Grop, C. Fluhr, B. Dubois, Y. Kersale, and E. Rubiola, “The autonomous cryocooled sapphire oscillator: a reference for frequency stability and phase noise measurements,” Journal of Physics: Conference Series 723(1), 012030 (2016).

Nature Photonics (3)

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing sychronization of remote optical and microwave sources,” Nature Photonics 2(12) 733–736 (2008).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nature Photonics 7(6), 434–438 (2013).
[Crossref]

G. J. Schneider, J. Murakowski, C. A. Schuetz, S. Shi, and D. W. Prather, “Radio frequency signal-generation system with over seven octaves of continuous tuning,” Nature Photonics 7(2), 118–122 (2013).
[Crossref]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hansch, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett. 111(11), 110801 (2013).
[Crossref] [PubMed]

Proc. SPIE (1)

R. E. Bartolo, A. Tveten, and C. K. Kirkendal, “The quest for inexpensive, compact, low phase noise laser sources for fiber optic sensing applications,” Proc. SPIE 7503, 750370 (2009).
[Crossref]

Proceedings of the IEEE (2)

D. B. Leeson and G. F. Johnson, “Short-term stability for a Doppler radar: requirements, measurements, and techniques,” Proceedings of the IEEE 54(2), 244–246 (1966).
[Crossref]

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proceedings of the IEEE 66(1), 51–83 (1978).
[Crossref]

Rev. Sci. Instrum. (3)

G. Brida, “High resolution frequency stability measurement system,” Rev. Sci. Instrum. 73(5), 2171–2174 (2002).
[Crossref]

L. C. Sinclair, J. D. Deschenes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86(8), 081301 (2015).
[Crossref] [PubMed]

D. A. Tulchinsky, A. S. Hastings, and K. J. Williams, “Characteristics and performance of offset phase locked single frequency heterodyned laser systems,” Rev. Sci. Instrum. 87(5), 053107 (2016).
[Crossref] [PubMed]

Science (2)

S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001).
[Crossref] [PubMed]

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, “Electro-optical frequency division and stable microwave synthesis,” Science 345(6194), 309–313 (2014).
[Crossref] [PubMed]

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S. R. Stein, “Frequency and Time – Their Measurement and Characterization,” in Precision Frequency Control, 2, ed. E. A. Gerber and A. Ballato, eds. (Academic, 1985), chap. 12.

G. Kovacs, P. R. Herczfeld, and T. Berceli, “Phase stability of optical self-heterodyned microwave signals with Nd:YVO4 laser,” in 2010 IEEE Topical Meeting on Microwave Photonics (MWP) (IEEE, 2010), pp. 159–162.
[Crossref]

J. L. Hall, M. S. Taubman, and J. Ye, “Laser Stabilization,” in Handbook of Optics: II - Design, Fabrication, and Testing; Sources and Detectors; Radiometry and Photometry, 3rd edition, M. Bass, ed. (McGraw-Hill Professional, 2010), Chap. 22.

M. S. Taubman, “Optical frequency stabilization and optical phase locked loops: golden threads of precision measurement,” in American Control Conference (ACC), 2013, (IEEE, 2013), pp. 1488–1505.
[Crossref]

S. C. Song and Y. S. Hong, “A new approach for evaluating the phase noise requirements of STALO in a Doppler radar,” in The Proceedings of the 4th European Radar Conference, (IEEE, 2007), pp. 198 – 201.

A. Thorne, U. Litzen, and S. Johansson, “The Width and Shape of Spectral Lines – Convolution of Line Profiles: The Voigt Profile,” in Spectrophysics: Principles and Applications, (Springer-Verlag, 1999), Chap. 8.5.

“Continuous-Wave (CW) single-frequency IR Laser, NPRO M125/M126 series Lasers.” Data sheet NPRO125126-ds-cl-ae, Lumentum Operations LLC, (2015).

J. Rutman, “Relations between spectral purity and frequency stability,” in “Proceedings of the 28th Annual Symposium on Frequency Control 1974,” (IEEE, 1974), pp. 160–165.

K. J. Williams, Optical Sciences Division, U.S. Naval Research Laboratory, 4555 Overlook Avenue, S.W., Washington, DC., 20375 (personal communication, 2016).

W. J. Riley, NIST special publication 1065: Handbook of Frequency Stability and Analysis (National Institute of Standards and Technology, 1990).

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls (eds.), NIST Technical Note 1337: Characterization of Clocks and Oscillators (National Institute of Standards and Technology, 2008).

J. Vanier and M. Tetu, “Time domain measurement and frequency stability: a tutorial introduction,” in The Proceedings of the 10th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, (PTTI1978), pp. 247–291.

G. J. Dick, P. F. Kuhnle, and R. L. Sydnor, “Zero-crossing detector with sub-microsecond jtter and crosstalk,” in 22nd Annual Precise Time and Time Interval (PTTI) Applications Planning Meeting, (PTTI, 1990), pp. 269–282.

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Advanced phase noise suppression technique for next generation of ultra low-noise microwave oscillators,” in Proceedings of the 1995 IEEE International Frequency Control Symposium (49th Annual Symposium), (IEEE, 1995), pp. 314–320.
[Crossref]

S. Chang, A. G. Mann, and A. N. Luiten, “Cryogenic sapphire oscillator with improved frequency stability,” in 2000 IEEE/EIA International Frequency Control Symposium and Exhibition, (IEEE2000), pp. 475–479.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Typical free-running beat note between two NPRO 1.319 μm Nd:YAG lasers at a frequency separation of 48 MHz. The full width half maximum is ∼8.0± 0.5 kHz as measured by an Agilent E4888A Series RF spectrum analyzer.
Fig. 2
Fig. 2 Schematic diagram of the optical offset phase locked loop heterodyned laser system.
Fig. 3
Fig. 3 Typical RF spectrum of the optically generated RF beat note of the heterodyned laser system at (a) 65 kHz frequency offset. The beat note from the optical phase locked loop (OPLL) is compared to the RF output of an HP8662A RF source at 65 kHz which is also used to phase lock the laser system. (b) The laser system beat note at 31.7 GHz frequency offset. The beat note from the OPLL is compared to the RF output of an Agilent E8257D RF source at 31.7 GHz, which is also used to phase lock the laser system. The measurements are made with an Agilent 8564E millimeter-wave spectrum analyzer. In both Figs. 3(a) and 3(b), the measured RF beat note line width is limited by the minimum 1 Hz resolution bandwidth of the spectrum analyzer (sweep time 3 s) with 100× averages. In each case, the photocurrent (1mA) and RF oscillator power are set to yield −22 dBm of RF output power. Note: every other (HP8662A)/ every third (OPLL) data point in these Figs. is plotted for clarity.
Fig. 4
Fig. 4 Schematic diagrams of the variations of the measurement systems designed to utilize the maximum measurable frequency (100 kHz) of the HP3562A dynamic signal analyzer. (a) Direct RF source measurement diagram. (b) RF source mixed down to 65 kHz, via a second RF source, measurement diagram. (c) Direct optical phase locked loop laser beat note measurement diagram. (d) Optical phase locked loop laser beat note mixed down to 65 kHz, via a second RF source, measurement diagram.
Fig. 5
Fig. 5 Comparison of the 65 kHz beat note instantaneous linewidth of the optical phase locked loop (OPLL) laser system to that of an HP8662A RF source at 65 kHz. Measured with an HP3562A dynamic signal analyzer. 651 min. per sweep with 4x sweep averaging.
Fig. 6
Fig. 6 Comparison of the 31.7 GHz beat note (mixed down to 65kHz) instantaneous linewidth of the optical phase locked loop (OPLL) laser system to that of a Agilent E8257D RF source at 31.7 GHz + 65 kHz. The 65 kHz difference frequency is measured with an HP3562A dynamic signal analyzer. 651 min. per sweep with 4x sweep averaging.
Fig. 7
Fig. 7 Schematic diagram of the free-running heterodyned two oscillator linewidth measurement system. a) with two separate reference oscillators. b) With the optical phase locked loop laser system inserted between one of the reference oscillators and the heterodyning RF mixer. c) Comparison of the linewidth of the 5 MHz beat note (mixed down to 1.83 Hz) of the optical phase locked loop (OPLL) laser system phase locked to a FTS 1050A OCXO 5 MHz source, and a FEI 1150A OCXO 5 MHz source. The downconverted linewidth of the 5 MHz FTS 1050A and the FEI1150A are shown in the background for reference. In all cases a 10 MHz output of a SRS Rb frequency reference is the 10 MHz reference for the HP3562A dynamic signal analyzer. The 1.83 Hz difference frequency is measured with an HP3562A dynamic signal analyzer. One 651 min. sweep shown.
Fig. 8
Fig. 8 Schematic diagram of the heterodyned two oscillator time interval measurement system. a) with two separate reference oscillators. b) With the optical phase locked loop laser system inserted between one of the reference oscillators and the heterodyning RF mixer.
Fig. 9
Fig. 9 a) Overlapping Allan deviation measurements of the heterodyned laser system in the free-running state, at a 5 MHz frequency offset. b) Overlapping Allan deviation of the heterodyned laser system phase locked to the 5MHz output of an HP8663A RF source (phase locked to a SRS Rb 10 MHz frequency standard). The overlapping Allan deviation of the HP8663A source vs FTS1050A source at 5 MHz is also shown in background. In both cases a FTS 1050A OCXO is the 10 MHz reference for the time and frequency interval counter.
Fig. 10
Fig. 10 Overlapping Allan deviation of the heterodyned laser system phase locked to the 5 MHz output of a SRS Rb frequency reference, a FTS 1050A OCXO 5 MHz source, and a FEI 1150A OCXO 5 MHz source. The overlapping Allan deviation of the SRS Rb vs FTS 1050A and the FEI1150A vs the FTS 1050A are shown in the background for reference. In all cases a FTS 1050A OCXO is the 10 MHz reference for the time and frequency interval counter.
Fig. 11
Fig. 11 Overlapping Allan deviation of the heterodyned laser system phase locked to one of two PSI sapphire loaded cavity oscillator frequency references at 10.24 GHz. Also shown is the overlapping Allan deviation between PSI sapphire oscillator (1) vs PSI sapphire oscillator (2) at 10.24 GHz, for reference. In both cases a FTS 1050A OCXO is the 10 MHz reference for the measurement system.

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