Abstract

Low phase-noise microwave generation has previously been demonstrated using self-referenced frequency combs to divide down a low noise optical reference. We demonstrate an approach based on a fs Er-fiber laser that avoids the complexity of self-referenced stabilization of the offset frequency. Instead, the repetition rate of the femtosecond Er-fiber laser is phase locked to two cavity-stabilized cw fiber lasers that span 3.74 THz by use of an intracavity electro-optic modulator with over 2 MHz feedback bandwidth. The fs fiber laser effectively divides the 3.74 THz difference signal to produce microwave signals at harmonics of the repetition rate. Through comparison of two identical dividers, we measure a residual phase noise on a 1.5 GHz carrier of −120 dBc/Hz at 1 Hz offset.

© 2011 OSA

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2011 (5)

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(7), 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(1), 140–151 (2011).
[CrossRef]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

D. R. Leibrandt, M. J. Thorpe, M. Notcutt, R. E. Drullinger, T. Rosenband, and J. C. Bergquist, “Spherical reference cavities for frequency stabilization of lasers in non-laboratory environments,” Opt. Express 19(4), 3471–3482 (2011).
[CrossRef] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[CrossRef] [PubMed]

2010 (5)

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010).
[CrossRef] [PubMed]

M. J. Thorpe, D. R. Leibrandt, T. M. Fortier, and T. Rosenband, “Measurement and real-time cancellation of vibration-induced phase noise in a cavity-stabilized laser,” Opt. Express 18(18), 18744–18751 (2010).
[CrossRef] [PubMed]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330(6007), 1081–1084 (2010).
[CrossRef] [PubMed]

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
[CrossRef]

2009 (3)

2008 (2)

S. Xiao, L. Hollberg, N. R. Newbury, and S. A. Diddams, “Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator,” Opt. Express 16(12), 8498–8508 (2008).
[CrossRef] [PubMed]

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301-1–0513011-2 (2008).

2007 (1)

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43(5), 378–384 (2007).
[CrossRef]

2006 (4)

2005 (4)

2004 (2)

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78(3–4), 321–324 (2004).
[CrossRef]

J. Kim, F. X. Kärtner, and M. H. Perrott, “Femtosecond synchronization of radio frequency signals with optical pulse trains,” Opt. Lett. 29(17), 2076–2078 (2004).
[CrossRef] [PubMed]

2003 (1)

E. Ivanov, S. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1059–1065 (2003).
[CrossRef]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

1999 (1)

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

1998 (1)

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Microwave interferometry: application to precision measurements and noise reduction techniques,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45(6), 1526–1536 (1998).
[CrossRef] [PubMed]

1997 (1)

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997).
[CrossRef]

1983 (1)

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Abgrall, M.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Avino, S.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330(6007), 1081–1084 (2010).
[CrossRef] [PubMed]

Bartels, A.

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[CrossRef] [PubMed]

Baumann, E.

Bergquist, J. C.

Bize, S.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Boudot, R.

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[CrossRef] [PubMed]

Bourgeois, P. Y.

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[CrossRef] [PubMed]

Clairon, A.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Coddington, I.

Coq, Y. L.

Cundiff, S. T.

D. D. Hudson, K. W. Holman, R. J. Jones, S. T. Cundiff, J. Ye, and D. J. Jones, “Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator,” Opt. Lett. 30(21), 2948–2950 (2005).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

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(1), 140–151 (2011).
[CrossRef]

De Natale, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330(6007), 1081–1084 (2010).
[CrossRef] [PubMed]

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(1), 140–151 (2011).
[CrossRef]

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

E. Ivanov, S. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1059–1065 (2003).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. (to be published).

Diddams, S. A.

Drever, R.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Drullinger, R. E.

Dunlop, A.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

English, E.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Fallnich, C.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78(3–4), 321–324 (2004).
[CrossRef]

Feder, K. S.

Fejer, M. M.

Fermann, M. E.

Ferraro, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330(6007), 1081–1084 (2010).
[CrossRef] [PubMed]

Ford, G.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Fortier, T.

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. (to be published).

Fortier, T. M.

Foster, S.

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43(5), 378–384 (2007).
[CrossRef]

Fox, R. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

Gagliardi, G.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330(6007), 1081–1084 (2010).
[CrossRef] [PubMed]

Giordano, V.

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

Giorgetta, F. R.

Gray, M. B.

Grop, S.

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

Guena, J.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Hall, J.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Hartl, I.

Hartnett, J. G.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301-1–0513011-2 (2008).

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(1), 140–151 (2011).
[CrossRef]

A. Hati, D. A. Howe, F. L. Walls, and D. K. Walker, “Merits of PM noise measurement over noise figure: a study at microwave frequencies,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(10), 1889–1894 (2006).
[CrossRef] [PubMed]

Haus, H.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997).
[CrossRef]

Haverkamp, N.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78(3–4), 321–324 (2004).
[CrossRef]

Hollberg, L.

S. Xiao, L. Hollberg, N. R. Newbury, and S. A. Diddams, “Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator,” Opt. Express 16(12), 8498–8508 (2008).
[CrossRef] [PubMed]

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[CrossRef] [PubMed]

E. Ivanov, S. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1059–1065 (2003).
[CrossRef]

Holman, K. W.

Hong, F.-L.

Hosaka, K.

Hough, J.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Howe, D. A.

A. Hati, D. A. Howe, F. L. Walls, and D. K. Walker, “Merits of PM noise measurement over noise figure: a study at microwave frequencies,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(10), 1889–1894 (2006).
[CrossRef] [PubMed]

Hudson, D. D.

Hundertmark, H.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78(3–4), 321–324 (2004).
[CrossRef]

Inaba, H.

Ippen, E.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997).
[CrossRef]

Ivanov, E.

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

E. Ivanov, S. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1059–1065 (2003).
[CrossRef]

Ivanov, E. N.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301-1–0513011-2 (2008).

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Microwave interferometry: application to precision measurements and noise reduction techniques,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45(6), 1526–1536 (1998).
[CrossRef] [PubMed]

Jiang, H.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. (to be published).

Jiang, Y.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[CrossRef] [PubMed]

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(7), 425–429 (2011).
[CrossRef]

Jiang, Y. Y.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

Jones, D.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997).
[CrossRef]

Jones, D. J.

D. D. Hudson, K. W. Holman, R. J. Jones, S. T. Cundiff, J. Ye, and D. J. Jones, “Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator,” Opt. Lett. 30(21), 2948–2950 (2005).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Jones, R. J.

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(1), 140–151 (2011).
[CrossRef]

Kärtner, F. X.

Katsuyama, T.

Kawato, S.

Keller, U.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Kersale, Y.

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
[CrossRef]

Kersalé, Y.

Kim, J.

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(7), 425–429 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[CrossRef] [PubMed]

Kobayashi, T.

Kohno, T.

Kowalski, F.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Langrock, C.

Le Coq, Y.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Leibrandt, D. R.

Lemke, N.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[CrossRef] [PubMed]

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(7), 425–429 (2011).
[CrossRef]

Lemke, N. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

Locke, C. R.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301-1–0513011-2 (2008).

Lours, M.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[CrossRef] [PubMed]

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(7), 425–429 (2011).
[CrossRef]

Ludlow, A. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[CrossRef] [PubMed]

Luiten, A. N.

Ma, L. S.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

McClelland, D. E.

McFerran, J.

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

McFerran, J. J.

Millo, J.

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[CrossRef] [PubMed]

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Milnes, M.

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43(5), 378–384 (2007).
[CrossRef]

Minoshima, K.

Munley, A.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Nakajima, Y.

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(1), 140–151 (2011).
[CrossRef]

Nelson, L.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997).
[CrossRef]

Newbury, N. R.

Nicholson, J. W.

Notcutt, M.

Oates, C.

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

Oates, C. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (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(7), 425–429 (2011).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[CrossRef] [PubMed]

Onae, A.

Oskay, W. H.

Perrott, M. H.

Quinlan, F.

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(7), 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(1), 140–151 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[CrossRef] [PubMed]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. (to be published).

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Rosenband, T.

Rubiola, E.

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
[CrossRef]

Salza, M.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330(6007), 1081–1084 (2010).
[CrossRef] [PubMed]

Santarelli, G.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[CrossRef] [PubMed]

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Sheard, B. S.

Sherman, J. A.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[CrossRef]

Stanwix, P. L.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301-1–0513011-2 (2008).

Steinmeyer, G.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Stenger, J.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Sutter, D.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Swann, W. C.

Tamura, K.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997).
[CrossRef]

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(1), 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(7), 425–429 (2011).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. (to be published).

Taylor, J. A.

Telle, H.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78(3–4), 321–324 (2004).
[CrossRef]

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[CrossRef]

Thorpe, M. J.

Tikhomirov, A.

S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental thermal noise in distributed feedback fiber lasers,” IEEE J. Quantum Electron. 43(5), 378–384 (2007).
[CrossRef]

Tobar, M.

J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
[CrossRef]

Tobar, M. E.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301-1–0513011-2 (2008).

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Microwave interferometry: application to precision measurements and noise reduction techniques,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45(6), 1526–1536 (1998).
[CrossRef] [PubMed]

Walker, D. K.

A. Hati, D. A. Howe, F. L. Walls, and D. K. Walker, “Merits of PM noise measurement over noise figure: a study at microwave frequencies,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(10), 1889–1894 (2006).
[CrossRef] [PubMed]

Walls, F. L.

A. Hati, D. A. Howe, F. L. Walls, and D. K. Walker, “Merits of PM noise measurement over noise figure: a study at microwave frequencies,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(10), 1889–1894 (2006).
[CrossRef] [PubMed]

Ward, H.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[CrossRef]

Washburn, B. R.

Westbrook, P. S.

Wilpers, G.

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[CrossRef] [PubMed]

J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

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J. Millo, M. Abgrall, M. Lours, E. English, H. Jiang, J. Guena, A. Clairon, M. 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(14), 141105 (2009).
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W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96(21), 211105 (2010).
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Electron. Lett. (2)

S. Grop, P. Y. Bourgeois, R. Boudot, Y. Kersale, E. Rubiola, and V. Giordano, “10 GHz cryocooled sapphire oscillator with extremely low phase noise,” Electron. Lett. 46(6), 420–422 (2010).
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J. McFerran, E. Ivanov, A. Bartels, G. Wilpers, C. Oates, S. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41(11), 650–651 (2005).
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IEEE Photon. J. (2)

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(1), 140–151 (2011).
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H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. Diddams, “Noise floor reduction of an Er:fiber laser-based photonic microwave generator,” IEEE Photon. J. (to be published).

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

E. N. Ivanov, M. E. Tobar, and R. A. Woode, “Microwave interferometry: application to precision measurements and noise reduction techniques,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45(6), 1526–1536 (1998).
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A. Hati, D. A. Howe, F. L. Walls, and D. K. Walker, “Merits of PM noise measurement over noise figure: a study at microwave frequencies,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53(10), 1889–1894 (2006).
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Nat. Photonics (2)

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(7), 425–429 (2011).
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Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
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Science (2)

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Other (3)

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, online first (2011).

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “An optical fibre pulse rate multiplier for ultra-low phase-noise signal generation,” arXiv:1106.5195v1 (2011).

Y. Nakajima, H. Inaba, K. Iwakuni, K. Hosaka, A. Onae, K. Minoshima, and F.-L. Hong, “All-fiber-based frequency comb with an intra-cavity waveguide electro-optic modulator,” in 2010 Conference on Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), (2010).

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Figures (6)

Fig. 1
Fig. 1

(a) Concept for microwave generation directly from a fs Er fiber laser. (b) Frequency-domain illustration of the stabilization of the fs laser repetition rate, or tooth spacing, through stabilization of the 3.74 THz (30 nm) wide output comb of the fs fiber laser. PDH: Pound-Drever-Hall lock

Fig. 2
Fig. 2

Schematic of the entire system for generating low phase noise microwaves from a stabilized fs fiber laser. The green table indicates an active vibration-isolation table. A second fs fiber laser is phase locked to the same two cw fiber lasers in a parallel but distinct optical path (not shown) to generate a second microwave signal for measurements of residual phase noise, as shown in the upper left. Brown lines: polarization maintaining fiber, black lines: electrical signals, colored lines: free-space optical beams, BP: bandpass rf filter, PBS: Polarizing beamsplitter, PDH: Pound-Drever-Hall locking electronics, EOM: fiber-coupled waveguide electro-optic phase modulator, AOM: fiber-coupled acousto-optic modulator

Fig. 3
Fig. 3

(a) Residual optical linewidth between the two phase-locked fs fiber lasers with identical repetition rates and 11 MHz difference in offset frequencies, which has been subtracted off. The entire optical bandwidth of the fs lasers contributes to the heterodyne beat. The inset shows a coherent peak with a time-bandwidth limited residual linewidth of 1.2 mHz. (b) The corresponding residual optical phase noise. Ignoring the spike at 2.3 kHz, the integrated phase noise from 1 mHz to 3.5 MHz is 185 mrad and from 1 mHz to 1 MHz is 27 mrad. The corresponding fractional power in the carrier from 1 mHz to 1 MHz is exp(−0.0272) = 99.9%, illustrating the high coherence possible with EOM-based fs fiber lasers [19, 20].

Fig. 4
Fig. 4

(a) In-loop measurement of the rf spectrum for the phase-locked difference signal for fs laser #1 (purple) and #2 (blue) for a 200 kHz span and 10 Hz resolution bandwidth (RBW). The inset is at a 2.5 kHz span and 300 mHz RBW. (b) Corresponding in-loop measurement of the phase noise. The servo bump at 2 MHz on fs laser #1 results from the EOM phase-locked loop (PLL). For fs laser #2, a similar servo bump is observed at 4 MHz (offscale). The integrated phase noise from 1 Hz to 100 kHz is 3.2 mrad and 3.9 mrad for fs lasers #1 and #2, respectively. The group of spurs starting at 60 Hz are harmonics of the 60 Hz power line. The servo bump at 2 kHz on fs laser #2 results from the intracavity PZT. The larger increase at ~80 kHz appears to be related to unsuppressed residual phase noise between the cw lasers and the optical cavity and could be further suppressed by a tighter PDH lock.

Fig. 5
Fig. 5

Residual phase noise at the 1.5 GHz carrier between the output of the two phaselocked fs fiber lasers (black line) along with the measurement noise floor (gray line). The spikes are at harmonics of 60 Hz and appear on both the measured phase noise and the measurement noise floor. The measured phase noise is −120 dBc/Hz at 1 Hz offset.

Fig. 6
Fig. 6

Measured residual phase noise at the 1.5 GHz carrier (black) between the two fs lasers (without the −3 dB correction of Fig. 5) along with the contribution from shot noise (gray), thermal noise (green), the noise on the phase locks (blue and purple) for the two fs fiber lasers. Also shown are the measured RIN (orange and brown) for the two fs fiber lasers, which can be converted to residual phase noise with increasing incident power.

Equations (1)

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L ϕ ( f )= 1 P rf [ q I dc R 4 + NF k B T 2 ]+ α 2 2 RIN( f )+ [ f rf Δ f opt ] 2 L locks ( f )+ L other ( f ),

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