Abstract

We introduce a simple all-inline variation of a balanced optical cross-correlator (BOC) that allows to measure the arrival time difference (ATD), over the full Nyquist bandwidth, with increased common-mode rejection and long-term stability. An FPGA-based signal processing unit allows for real-time signal normalization and enables locking to any setpoint with an unprecedented accuracy of 0.07 % within an increased ATD range of more than 400 fs, resulting in attosecond resolution locking. The setup precision is verified with an out-of-loop measurement to be less than 80 as residual jitter paving the way for highly demanding applications such as parametric waveform synthesizers.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

3 April 2017: Corrections were made to the Figs. 1–5 and the body text.


OSA Recommended Articles
Ultra-precise timing and synchronization for large-scale scientific instruments

Ming Xin, Kemal Şafak, and Franz X. Kärtner
Optica 5(12) 1564-1578 (2018)

Remote two-color optical-to-optical synchronization between two passively mode-locked lasers

H. Li, L.-J. Chen, H. P. H. Cheng, J. E. May, S. Smith, K. Muehlig, A. Uttamadoss, J. C. Frisch, A. R. Fry, F. X. Kärtner, and P. H. Bucksbaum
Opt. Lett. 39(18) 5325-5328 (2014)

One-femtosecond, long-term stable remote laser synchronization over a 3.5-km fiber link

Ming Xin, Kemal Şafak, Michael Y. Peng, Patrick T. Callahan, and Franz X. Kärtner
Opt. Express 22(12) 14904-14912 (2014)

References

  • View by:
  • |
  • |
  • |

  1. K. Ono, A. Nakamura, and B. Maess, “Keeping an Eye on the Conductor: Neural Correlates of Visuo-Motor Synchronization and Musical Experience,” Frontiers Human Neurosci. 9, 154 (2015)
    [Crossref]
  2. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012)
    [Crossref] [PubMed]
  3. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008)
    [Crossref]
  4. S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
    [Crossref] [PubMed]
  5. M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
    [Crossref]
  6. N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
    [Crossref]
  7. R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
    [Crossref] [PubMed]
  8. S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
    [Crossref]
  9. O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
    [Crossref]
  10. C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
    [Crossref]
  11. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003)
    [Crossref] [PubMed]
  12. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32, 1044–1046 (2007)
    [Crossref] [PubMed]
  13. D. Li, U. Demirbas, A. Benedick, A. Sennaroglu, J. G. Fujimoto, and F. X. Kärtner, “Attosecond timing jitter pulse trains from semiconductor saturable absorber mode-locked Cr:LiSAF lasers,” Opt. Express 20, 23422–23435 (2012)
    [Crossref] [PubMed]
  14. S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.
  15. S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
    [Crossref]
  16. D. Brida, C. Manzoni, and G. Cerullo, “Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line,” Opt. Lett. 37, 3027–3029 (2012)
    [Crossref] [PubMed]
  17. G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998)
    [Crossref]
  18. C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
    [Crossref] [PubMed]
  19. C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hänsch, “Carrier envelope phase noise in stabilized amplifier systems,” Opt. Lett. 30, 2487–2489 (2005)
    [Crossref] [PubMed]

2017 (1)

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

2016 (1)

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

2015 (4)

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

K. Ono, A. Nakamura, and B. Maess, “Keeping an Eye on the Conductor: Neural Correlates of Visuo-Motor Synchronization and Musical Experience,” Frontiers Human Neurosci. 9, 154 (2015)
[Crossref]

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

2014 (2)

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

2012 (4)

2011 (1)

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

2008 (1)

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

2007 (1)

2005 (1)

2003 (1)

1998 (1)

Apolonski, A.

Behrens, C.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Benedick, A.

Bhardwaj, S.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Bionta, M. R.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Birge, J. R.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Bostedt, C.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Bozek, J.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Brida, D.

Bromberger, H.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Carron, S.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Castagna, J.-C.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Cavalieri, A. L.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Cerullo, G.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

D. Brida, C. Manzoni, and G. Cerullo, “Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line,” Opt. Lett. 37, 3027–3029 (2012)
[Crossref] [PubMed]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Chang, Z.

Chen, J.

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

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

Chen, L.-J.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Chia, S.-H.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Chini, M.

Cirmi, G.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Coffee, R. N.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Costello, J. T.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Cox, J. A.

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

Czwalinna, M. K.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

De Silvestri, S.

Demirbas, U.

Eggleton, B. J.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Fang, S.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Farinello, P.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

Felber, M.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Ferguson, K. R.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Feurer, T.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Fry, A. R.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Fuji, T.

Fujimoto, J. G.

Fung, R.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Galler, A.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Glownia, J. M.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Gohle, C.

Gopinath, J. T.

Grguras, I.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Grünert, J.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Hanna, A. M.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Hänsch, T. W.

Hartmann, N.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Hauri, C. P.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Helml, W.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Hoffmann, M. C.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Hong, K.-H.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Huang, S.-W.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Ilchen, M.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Ippen, E. P

Kaertner, F. X.

Kalaydzhyan, A.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

Kane, D. J.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Kärtner, F. X.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

D. Li, U. Demirbas, A. Benedick, A. Sennaroglu, J. G. Fujimoto, and F. X. Kärtner, “Attosecond timing jitter pulse trains from semiconductor saturable absorber mode-locked Cr:LiSAF lasers,” Opt. Express 20, 23422–23435 (2012)
[Crossref] [PubMed]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

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

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

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Kim, J.

Kolodziejski, L. A.

Krausz, F.

Kuzucu, O.

Li, D.

Li, E.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Liu, H. Y.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Loehl, F.

Maess, B.

K. Ono, A. Nakamura, and B. Maess, “Keeping an Eye on the Conductor: Neural Correlates of Visuo-Motor Synchronization and Musical Experience,” Frontiers Human Neurosci. 9, 154 (2015)
[Crossref]

Mainz, R. E.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Manzoni, C.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

D. Brida, C. Manzoni, and G. Cerullo, “Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line,” Opt. Lett. 37, 3027–3029 (2012)
[Crossref] [PubMed]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Mazza, T.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Meyer, M.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Molodtsov, S. L.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Moses, J.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Mücke, O. D.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Nakamura, A.

K. Ono, A. Nakamura, and B. Maess, “Keeping an Eye on the Conductor: Neural Correlates of Visuo-Motor Synchronization and Musical Experience,” Frontiers Human Neurosci. 9, 154 (2015)
[Crossref]

Nisoli, M.

Ono, K.

K. Ono, A. Nakamura, and B. Maess, “Keeping an Eye on the Conductor: Neural Correlates of Visuo-Motor Synchronization and Musical Experience,” Frontiers Human Neurosci. 9, 154 (2015)
[Crossref]

Ourmazd, A.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Peng, M. Y.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

Petrich, G. S.

Pfeiffer, S.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Predki, P.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Ramakrishna, S.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Rauschenberger, J.

Rossi, G. M.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

S.-H. Chia, G. Cirmi, S. Fang, G. M. Rossi, O. D. Mücke, and F. X. Kärtner, “Two-octave-spanning dispersioncontrolled precision optics for sub-optical-cycle waveform synthesizers,” Optica 1, 315–322 (2014)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Safak, K.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

Santra, R.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Schefer, S.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Schibli, T. R.

Schlarb, H.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

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

Schmidt, C.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Schorb, S.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Schulz, S.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Seideman, T.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Sennaroglu, A.

Stagira, S.

Swiggers, M. L.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Tandon, S. N.

Udem, T.

Vendrell, O.

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Wang, W.-T.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

Wang, X.

Wegner, U.

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

White, W. E.

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

Wong, F. N. C.

Wu, Y.

Xin, M.

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

Yang, Y.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

Ye, H.

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

Zhang, Q.

Zhang, Z.

Zhao, K.

Frontiers Human Neurosci. (1)

K. Ono, A. Nakamura, and B. Maess, “Keeping an Eye on the Conductor: Neural Correlates of Visuo-Motor Synchronization and Musical Experience,” Frontiers Human Neurosci. 9, 154 (2015)
[Crossref]

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

O. D. Mücke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. E. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kärtner, “Toward Waveform Nonlinear Optics Using Multimillijoule Sub-Cycle Waveform Synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015)
[Crossref]

Laser Photonics Rev. (1)

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S.-W. Huang, K.-H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9, 129–171 (2015)
[Crossref]

Light: Sci. Appl. (1)

M. Xin, K. Safak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 5, 16187 (2017)
[Crossref]

Nat. Commun. (1)

S. Schulz, I. Grguras, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Predki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, and A. L. Cavalieri, “Femtosecond all-optical synchronization of an X-ray free-electron laser,” Nat. Commun. 6, 5938 (2015)
[Crossref] [PubMed]

Nat. Photonics (3)

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

N. Hartmann, W. Helml, A. Galler, M. R. Bionta, J. Grünert, S. L. Molodtsov, K. R. Ferguson, S. Schorb, M. L. Swiggers, S. Carron, C. Bostedt, J.-C. Castagna, J. Bozek, J. M. Glownia, D. J. Kane, A. R. Fry, W. E. White, C. P. Hauri, T. Feurer, and R. N. Coffee, “Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers,” Nat. Photonics 8, 706–709 (2014)
[Crossref]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011)
[Crossref]

Nature (1)

R. Fung, A. M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, “Dynamics from noisy data with extreme timing uncertainty,” Nature 532, 471–475 (2016)
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (7)

D. Brida, C. Manzoni, and G. Cerullo, “Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line,” Opt. Lett. 37, 3027–3029 (2012)
[Crossref] [PubMed]

G. Cerullo, M. Nisoli, S. Stagira, and S. De Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998)
[Crossref]

C. Manzoni, S.-W. Huang, G. Cirmi, P. Farinello, J. Moses, F. X. Kärtner, and G. Cerullo, “Coherent synthesis of ultra-broadband optical parametric amplifiers,” Opt. Lett. 37, 1880–1882 (2012)
[Crossref] [PubMed]

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hänsch, “Carrier envelope phase noise in stabilized amplifier systems,” Opt. Lett. 30, 2487–2489 (2005)
[Crossref] [PubMed]

K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012)
[Crossref] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003)
[Crossref] [PubMed]

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

Optica (1)

Other (1)

S. Fang, R. E. Mainz, G. M. Rossi, Y. Yang, G. Cirmi, S.-H. Chia, C. Manzoni, G. Cerullo, O. D. Mücke, and F. X. Kärtner, “Sub-cycle timing lock in a multi-mJ parametric waveform synthesizer,” in CLEO Europe 2015 (2015), paper CG_P_4,.

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 (11)

Fig. 1
Fig. 1 Scheme of the RAM setup: two laser pulses (1 and 2), whose spectra are centered at different wavelengths, are overlapped with the beam combiner BC. A leakage from the BC is directed to the RAM setup. The dispersive element DRAM1 is used to apply a significantly larger chirp on pulse 2 with respect to pulse 1. Signal S1 is generated in the nonlinear crystal NLC1 by SFG or DFG. A second dispersive element DRAM2 is used to adjust the time relation between the two pulses. A second signal S2 is generated in NLC2 at a wavelength different from S1. The two signals are separated spectrally and directed to two photodetectors (PD1 & PD2). An FPGA-based signal processing unit (SPU) performs the normalized difference between PD1 and PD2 (see Eq. (9)) to extract the arrival-time difference (ATD), that can then be used to actively stabilize the ATD by moving a piezoelectric actuator (PZT). The main output of the BC will experience the dispersion Dmain, after which the two pulses can be temporally overlapped and compressed. In order to match the group-delay (GD) difference between the main output and the leakage, a birefringent plate (BP) can be used before DRAM1.
Fig. 2
Fig. 2 Optical scheme of RAM: (a) The left-hand side of each rows shows the two pulses after being combined with an ATD = T. In the main arm the pulses are compressed and overlapped in time (ATD = 0) after Dmain. In the I-crystal RAM setup, DRAM stretches the ω2 pulse such that τ2RAMτ1RAM. The two signals S1 and S2 can be obtained by spectral filtering the broad (and chirped) sum frequency generated by NLC. In the II-crystal RAM setup, DRAM1 modifies the durations of the two pulses such that τ2RAMτ1RAM, then NLC1, phase-matched for ω2B + ω1, generates the first sum frequency S1. DRAM2 delays slightly one pulse with respect to the other, without affecting significantly the durations. NLC2 generates the second sum frequency S2 of ω2A + ω1. In the top-right corner, the corresponding position on the S-curve is marked in red. (b) Same scheme as in panel (a), when the ATD is reduced by δT: the signal S1 decreases, while signal S2 increases.
Fig. 3
Fig. 3 Stabilization of the ATD using the I-crystal RAM scheme: a portion of the pulses generated by a Ti:sapphire laser (150fs, 800nm, 20mJ, 1kHz) is split and sent to drive a white-light-seeded visible NOPA. The other part is sent to two piezo-actuated mirrors (PZT1 & PZT2), and recombined with the VIS-NOPA output with a dichroic beam combiner (DBC). A leakage from the DBC is sent to the two RAM setups. The first RAM setup is used inside the feedback loop acting back on PZT2 in order to stabilize the ATD. The out-of-loop RAM is used to verify the achieved accuracy of the measurement. All experimental data are acquired by a computer. In order to characterize the transfer function of the active stabilization, PZT1 can be driven by an arbitrary waveform.
Fig. 4
Fig. 4 (a) Spectral evolution of the VIS-NOPA due to depletion from the SFG, during a triangular ATD scan. (b) Corresponding spectral evolution of the SFG. The shaded areas indicate the spectral regions that were blocked by the filter, while the integral over frequency of each of the bright areas corresponds to the S1 and S2 signals.
Fig. 5
Fig. 5 Influence of spectral filtering on S-curve. Blue curve: S-curve from I-crystal RAM obtained by splitting the SFG spectrum in two with a narrow spectral gap in between. Red curve: same as blue curve, but for a larger spectral gap. Green curve: S-curve from II-crystal RAM setup with narrowband interference filters. The measurement range and thus the temporal resolution can be tuned simply by applying different spectral filters. All S-curves here were obtained by measuring and averaging over few tens of curves.
Fig. 6
Fig. 6 ATD rms for the cases of plain subtraction (black) and normalized difference (red) according to Eq. (9). Data extracted from n = 326 S-curve scans (hence a higher residual noise than for an active lock). The normalized difference allows for low detection noise over a much wider measurement range.
Fig. 7
Fig. 7 (a) Single-shot ATD measurement of an open/closed active stabilization loop over 50 seconds. (b) Zoomed-in portion of the ATD trace with 287 as residual jitter rms. (c) Jitter spectral density and integrated jitter with activated stabilization loop.
Fig. 8
Fig. 8 The outputs of the individual detectors of the IL and OOL RAM setups (IL: PD1/PD2 (A1/B1) on top red/blue, OOL: PD3/PD4 (A2/B2) on bottom red/blue with inverted sign) are plotted versus ATD (left vertical scale, n = 326 scans superimposed). The two corresponding normalized S-curves are plotted in green and violet (right vertical scale, the sign of the violet S-curve has been inverted for sake of clarity).
Fig. 9
Fig. 9 ATD spectral density of the IL RAM (grey) and of the difference between the IL RAM and OOL RAM (dark grey). Integrated ATD rms jitter of the IL and OOL RAM (red, blue) and of the difference between IL and OOL (green). Each jitter spectrum is integrated both starting from DC and starting from Nyquist frequency (integration direction is indicated by colored arrows).
Fig. 10
Fig. 10 An in-loop and an out-of-loop RAM setup measure the ATD between two pulses from our benchmark laser system. A gated integrator determines the energy of the RAM signals separately, an ADC with 24-bit resolution (ENOB ≈ 17bits) digitizes the signals. The normalized difference as well as a PI controller and a custom finite-impulse-response (FIR) filter are implemented inside an FPGA, which generates a feedback signal to actively stabilize the ATD with piezo actuator PZT2. A monitor attached to the FPGA produces realtime data plots allowing for an intuitive system optimization. A microcontroller provides an interface between the FPGA and a computer via Ethernet for streaming data and controlling all the system parameters. Furthermore, a function generator is implemented to introduce artificial noise on the second piezo actuator PZT1.
Fig. 11
Fig. 11 Characterization of the frequency response of the RAM setup with and without an active PI lock: a sinusoidal 13.3 fs (4.7fsrms) peak-to-peak ATD is introduced with PZT1, while PZT2 is used in the feedback loop to lock the ATD. The frequency-dependent damping of such active locking exhibits a corner frequency of 80 Hz (−3 dB point), when optimized for high feedback bandwidth. The performance of the PI lock is compared with the theoretically achievable performance calculated considering a 0 dB proportional component and a latency of two laser pulses (2 ms).

Equations (9)

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

GD D RAM 1 ( ω 1 ) GD D RAM 1 ( ω 2 ) GD D main ( ω 1 ) GD D main ( ω 2 ) .
GDD D RAM 1 ( ω 1 ) GDD D main ( ω 1 ) and GDD D RAM 1 ( ω 2 ) GDD D main ( ω 2 ) .
E SFG ( t , T ) E 1 ( t ) E 2 ( t + T ) = A 1 ( t ) A 2 ( t + T ) e i ( ω 1 t + ω 2 ( t + T ) + ω ˙ 1 t 2 / 2 + ω ˙ 2 ( t + T ) 2 / 2 ) A 1 ( t ) A 2 ( T ) e i ( ( ω 1 + ω 2 ) t + ω 2 T + ω ˙ 1 t 2 / 2 + ω ˙ 2 ( t + T ) 2 / 2 ) ,
ω iSFG ( t , T ) = ω 1 + ω 2 + ω ˙ 1 t + ω ˙ 2 ( t + T ) .
ω SFG ( T ) = ω iSFG ( 0 , T ) = ω 1 + ω 2 + ω ˙ 2 T ,
ω iSFG lowest ( Δ T / 2 ) = ω iSFG ( τ 1 RAM / 2 , Δ T / 2 ) = ω 1 + ω 2 ω ˙ 1 ( τ 1 RAM / 2 ) + ω ˙ 2 ( ( τ 1 RAM / 2 ) + ( Δ T / 2 ) ) = 0
Δ T = τ 1 RAM + Ω 1 Ω 2 τ 2 RAM .
L D RAM 1 = c T AB | n g ( ω 2 B ) n g ( ω 2 A ) | and L D RAM 2 = c T shift | n g ( ω 2 B ) n g ( ω 1 ) | ,
ND ( T ) = A ( T ) B ( T ) A ( T ) + B ( T ) ,

Metrics