Abstract

Energy-phase coupling inside f-2f nonlinear interferometers poses stringent limits on the tolerable pulse-to-pulse energy fluctuations of phase stable laser systems. Here we report a coupling coefficient of 220±20mrad per 1% energy increase at 800 nm. We also report coefficients from +320 to +820mrad per 1% energy increase in the 1140–1550 nm (signal) range. Finally, we report coefficients from 180 to +30mrad per 1% energy variation in the 1636–1940 nm range.

© 2014 Optical Society of America

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  1. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
    [CrossRef]
  2. T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
    [CrossRef]
  3. T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).
  4. M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
    [CrossRef]
  5. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436–1438 (2001).
    [CrossRef]
  6. A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
    [CrossRef]
  7. A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
    [CrossRef]
  8. C. Li, E. Moon, H. Wang, H. Mashiko, C. M. Nakamura, J. Tackett, and Z. Chang, “Determining the phase-energy coupling coefficient in carrier-envelope phase measurements,” Opt. Lett. 32, 796–798 (2007).
    [CrossRef]
  9. C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, “Mechanism of phase-energy coupling in f-to-2f interferometry,” Appl. Opt. 48, 1303–1307 (2009).
    [CrossRef]
  10. A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
    [CrossRef]

2012 (1)

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

2011 (1)

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

2009 (3)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, “Mechanism of phase-energy coupling in f-to-2f interferometry,” Appl. Opt. 48, 1303–1307 (2009).
[CrossRef]

2007 (1)

2003 (2)

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

2002 (1)

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef]

2001 (1)

Adolph, D.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

Baltuška, A.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef]

Cavalieri, A. L.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Chang, Z.

Chini, M.

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

Fuji, T.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef]

Fujihira, Y.

Gohle, C.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Goulielmakis, E.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

Gu, X.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Hänsch, T. W.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Helml, W.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Hentschel, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Holzwarth, R.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Homma, T.

Horvath, B.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

Johnson, N. G.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

Kakehata, M.

Kienberger, R.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

Kling, M. F.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

Kobayashi, T.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef]

Kobayashi, Y.

Krausz, F.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Kübel, M.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

Li, C.

Mashiko, H.

Möller, M.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

Moon, E.

Nakamura, C. M.

Paulus, G. G.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Rathje, T.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

Sayler, A. M.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

Schätzel, M. G.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Scrinzi, A.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Süßmann, F.

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

Tackett, J.

Takada, H.

Takahashi, H.

Torizuka, K.

Udem, T.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

Uiberacker, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

Wang, H.

Wittmann, T.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Yakovlev, V. S.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[CrossRef]

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

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[CrossRef]

J. Phys. B (1)

T. Rathje, N. G. Johnson, M. Möller, F. Süßmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler, “Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization,” J. Phys. B 45, 074003 (2012).

Nat. Phys. (1)

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[CrossRef]

Nature (1)

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup. For the experiment with the idler (not shown), an additional 250 μm silicon window was used before the iris to filter out the visible light that leaks out of the OPA. About 19 mm of fused silica was also added between the sapphire and the BBO crystal to improve the fringes. In the color version of the figure, black lines are mirrors. Green lines are 60% reflective beam splitters. Blue lines are 98% reflective beam splitters. Light blue rectangles are glass plates, and gray lines are chirped mirrors. Legend: BS, beam splitter; C, compressor; CMs, chirped mirrors; EM, energy meter; F75, concave mirror with F=75mm; F150, concave mirror with F=150mm; G1, glass substrate 1 mm thick; G6, glass substrate 6 mm thick; L, lens with 400 mm focal length; LA, laser amplifier; ND, neutral density filters; OAPM, off-axis parabolic mirror; P, calcite polarizer; PD, InGaAs photodiode for signal and idler and Si photodiode for 800 nm; QPD, quadrant photodiode; S, spectrometer; Sa, sapphire; T, downsizing telescope; VA, variable attenuator.

Fig. 2.
Fig. 2.

Measured (gray squares) and fitted (solid line) phase (left), GD×ω0 (center), and intercept (right) at three different wavelengths: (a) 800 nm (pump), (b) 1250 nm (signal), and (c) 1696 nm (idler).

Fig. 3.
Fig. 3.

Energy-phase coupling at ϵ=1 (Bϕ coefficients).

Tables (1)

Tables Icon

Table 1. Fit Parameters and Statistics for All Datasets

Equations (2)

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

ϕ(ϵ)|ω0=ω0×GD(ϵ)+Intercept(ϵ),
x(ϵ)=Ax+Bx(ϵ1)+Cx2(ϵ1)2x:{ϕ,GDω0,Intercept}.

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