Abstract

The technique of multiform time derivatives of pulse has been shown necessary to achieve various time-space metrology goals with a precision at or beyond the standard quantum limit. However, the efficient generation of the desired time derivatives remains challenging. In this paper, we report on the efficient realization of multiform time derivatives with a programmable 4-f pulse shaping system. The first-order time derivative of the pulse electric field has been achieved with a generation efficiency of 72.12%, which is more than 20 times higher than that of previous methods. Moreover, the first- and second-order time derivatives of the pulse envelope have been achieved with the generation efficiencies being 11.10% and 3.53%, respectively. In comparison, these efficiencies are three times higher than those for previously reported methods. Meanwhile, the measured fidelities of the three time-derived pulses are reasonably high, with values of 99.53%, 98.37% and 97.32% respectively.

© 2017 Optical Society of America

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References

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  1. T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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2015 (1)

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2011 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
[Crossref]

2008 (2)

M. A. Preciado and M. A. Muriel, “Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission,” Opt. Lett. 33(21), 2458–2460 (2008).
[Crossref] [PubMed]

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

2005 (1)

2004 (1)

2001 (2)

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13(4), 301–306 (2001).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412(6845), 417–419 (2001).
[Crossref] [PubMed]

2000 (2)

1998 (1)

1995 (1)

1990 (1)

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247(4948), 1317–1319 (1990).
[Crossref] [PubMed]

1989 (1)

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

1988 (1)

1986 (1)

W. T. Ni, “Quantum-mechanical noise in an interferometer: intrinsic uncertainty vs measurement uncertainty (a),” Phys. Rev. D Part. Fields 3, 3002–3007 (1986).

Andrejco, M. J.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

Azaña, J.

Barrett, M. D.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Belabas, N.

Bloom, B. J.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Campbell, S. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Chériaux, G.

Dantus, M.

Dorrer, C.

Fabre, C.

Feurer, T.

Fouckhardt, H.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412(6845), 417–419 (2001).
[Crossref] [PubMed]

Heritage, J. P.

Hornung, T.

Hutson, R. B.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Jaekel, M. T.

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13(4), 301–306 (2001).
[Crossref]

Jian, P.

Joffre, M.

Labroille, G.

Lamine, B.

Leaird, D. E.

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247(4948), 1317–1319 (1990).
[Crossref] [PubMed]

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

Lepetit, L.

Likforman, J. P.

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412(6845), 417–419 (2001).
[Crossref] [PubMed]

Lozovoy, V. V.

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412(6845), 417–419 (2001).
[Crossref] [PubMed]

Marti, G. E.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

McNally, R. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Muriel, M. A.

Nelson, K.

Nelson, K. A.

J. C. Vaughan, T. Hornung, T. Feurer, and K. A. Nelson, “Diffraction-based femtosecond pulse shaping with a two-dimensional spatial light modulator,” Opt. Lett. 30(3), 323–325 (2005).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247(4948), 1317–1319 (1990).
[Crossref] [PubMed]

Ni, W. T.

W. T. Ni, “Quantum-mechanical noise in an interferometer: intrinsic uncertainty vs measurement uncertainty (a),” Phys. Rev. D Part. Fields 3, 3002–3007 (1986).

Nicholson, T. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Park, Y.

Pastirk, I.

Pinel, O.

Preciado, M. A.

Reynaud, S.

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13(4), 301–306 (2001).
[Crossref]

Safronova, M. S.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Saifi, M. A.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

Salehi, J. A.

Salin, F.

Silberberg, Y.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

Slavík, R.

Smith, P. W.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

Stone, K.

Strouse, G. F.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Tew, W. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Treps, N.

Vaughan, J.

Vaughan, J. C.

Weiner, A. M.

A. M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
[Crossref]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247(4948), 1317–1319 (1990).
[Crossref] [PubMed]

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

A. M. Weiner, J. P. Heritage, and J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13(4), 300–302 (1988).
[Crossref] [PubMed]

Wiederrecht, G. P.

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247(4948), 1317–1319 (1990).
[Crossref] [PubMed]

Ye, J.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Zhang, W.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Europhys. Lett. (1)

M. T. Jaekel and S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13(4), 301–306 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, and P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25(12), 2648–2655 (1989).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Commun. (1)

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10-18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

Nature (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced positioning and clock synchronization,” Nature 412(6845), 417–419 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

A. M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. D Part. Fields (1)

W. T. Ni, “Quantum-mechanical noise in an interferometer: intrinsic uncertainty vs measurement uncertainty (a),” Phys. Rev. D Part. Fields 3, 3002–3007 (1986).

Phys. Rev. Lett. (1)

B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. 101(12), 123601 (2008).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

Science (1)

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247(4948), 1317–1319 (1990).
[Crossref] [PubMed]

Other (1)

Hamamastu Photonics handbook, “Liquid crystal on silicon-spatial light modulator,” (Hamamastu Photonics, 2016), http://www.hamamatsu.com/resources/pdf/ssd/x10468_series_etc_kacc1172e.pdf .

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. Laser: femtosecond fusion laser; L: lens; HWP: half-wave plate; M: high reflective mirror; D-M: D-shaped mirror; G: grating; C-Lens: cylindrical lens; SLM: spatial light modulator; PBS: polarization beam splitter; SM: spectrometer.

Fig. 2
Fig. 2

(a) Pulse duration and (b) phase of the pulse electric filed. The blue dotted lines denote the results before compensation and the red solid lines after compensation, respectively.

Fig. 3
Fig. 3

Phase and intensity modulation functions for (a) the first-order electric field derivative of the pulse, (b) first-order envelope derivative of the pulse, and (c) second-order envelope derivative of the pulse. The red solid lines and the black solid lines denote the phase modulation functions with and without dispersion compensation included, respectively. The blue dotted lines denote the intensity modulation functions.

Fig. 4
Fig. 4

Measured ratio of the field amplitudes, (a) |E 1 ( λ ) |/|E 0 ( λ )| , (b) |E e1 ( λ ) |/|E 0 ( λ )| , (c) |E e2 ( λ ) |/|E 0 ( λ )| . The blue solid lines denote the experimental results, and the red dashed lines denote the theoretical results.

Fig. 5
Fig. 5

Spectral phases retrieved from FTSI for (a) the first-order time derivative of the pulse electric field, (b) the first-order time derivative of the pulse envelope, and (c) the second-order time derivative of the pulse envelope.

Equations (6)

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

E 1 (t)= dE(t) dt ,
E e1 (t)= dA(t) dt exp(i ω 0 t),
E e2 (t)=( d 2 A(t) d t 2 -1 )exp(i ω 0 t).
E 1 (ω)=iωE(ω),
E e1 (ω)= i(ω ω 0 ) Δω E(ω),
E e2 (ω)=i 1 2 ( (ω ω 0 ) 2 Δ ω 2 -1 )E(ω).

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