Abstract

We evaluate ways to analyze optical-heterodyne measurements of frequency chirp in pulsed, single-longitudinal-mode output from lasers (or other coherent light sources) that operate on nanosecond time scales. The instantaneous frequency is extracted from the beat signal generated between a continuous-wave reference beam and the output of the pulsed source. Three analysis techniques are tested: Fourier-transform, direct curve fitting, and electronic mixing. We use synthetic beat waveforms based on actual experimental parameters to evaluate the three methods and apply these chirp-measurement techniques to an injection-seeded optical parametric oscillator system.

© 2004 Optical Society of America

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References

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  1. M. S. Fee, K. Danzmann, and S. Chu, “Optical heterodyne measurement of pulsed lasers: toward high-precision pulsed spectroscopy,” Phys. Rev. A 45, 4911–4924 (1992).
    [CrossRef] [PubMed]
  2. S. Gangopadhyay, N. Melikechi, and E. E. Eyler, “Optical phase perturbations in nanosecond pulsed amplification and second-harmonic generation,” J. Opt. Soc. Am. B 11, 231–241 (1994).
    [CrossRef]
  3. N. Melikechi, S. Gangopadhyay, and E. E. Eyler, “Phase dynamics in nanosecond pulsed dye laser amplification,” J. Opt. Soc. Am. B 11, 2402–2411 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
    [CrossRef]
  7. I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
    [CrossRef]
  11. R. T. White, Y. He, B. J. Orr, M. Kono, and K. G. H. Baldwin, “Pulsed injection-seeded optical parametric oscillator with low frequency chirp for high-resolution spectroscopy,” Opt. Lett. 28, 1248–1250 (2003).
    [CrossRef] [PubMed]
  12. R. T. White, Y. He, B. J. Orr, M. Kono, and K. G. H. Baldwin, “Control of frequency chirp in nanosecond-pulsed laser spectroscopy. 2. A long-pulse optical parametric oscillator for narrow optical bandwidth,” J. Opt. Soc. Am. B 21, 1586–1594 (2004).
    [CrossRef]
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2004 (1)

2003 (1)

2000 (1)

1999 (1)

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

1998 (1)

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

1996 (3)

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Precision measurements in helium at 58 nm: ground state Lamb shift and the 1 1S–2 1P transition isotope shift,” Phys. Rev. Lett. 76, 1216–1219 (1996).
[CrossRef] [PubMed]

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
[CrossRef]

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

1995 (1)

1994 (2)

1992 (1)

M. S. Fee, K. Danzmann, and S. Chu, “Optical heterodyne measurement of pulsed lasers: toward high-precision pulsed spectroscopy,” Phys. Rev. A 45, 4911–4924 (1992).
[CrossRef] [PubMed]

1978 (1)

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

Balakrishnan, A.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Baldwin, K. G. H.

R. T. White, Y. He, B. J. Orr, M. Kono, and K. G. H. Baldwin, “Control of frequency chirp in nanosecond-pulsed laser spectroscopy. 2. A long-pulse optical parametric oscillator for narrow optical bandwidth,” J. Opt. Soc. Am. B 21, 1586–1594 (2004).
[CrossRef]

R. T. White, Y. He, B. J. Orr, M. Kono, and K. G. H. Baldwin, “Pulsed injection-seeded optical parametric oscillator with low frequency chirp for high-resolution spectroscopy,” Opt. Lett. 28, 1248–1250 (2003).
[CrossRef] [PubMed]

S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Bergeson, S. D.

S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Bowers, M. S.

Cheng, C. H.

S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Chu, S.

M. S. Fee, K. Danzmann, and S. Chu, “Optical heterodyne measurement of pulsed lasers: toward high-precision pulsed spectroscopy,” Phys. Rev. A 45, 4911–4924 (1992).
[CrossRef] [PubMed]

Danzmann, K.

M. S. Fee, K. Danzmann, and S. Chu, “Optical heterodyne measurement of pulsed lasers: toward high-precision pulsed spectroscopy,” Phys. Rev. A 45, 4911–4924 (1992).
[CrossRef] [PubMed]

Eikema, K. S. E.

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
[CrossRef]

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Precision measurements in helium at 58 nm: ground state Lamb shift and the 1 1S–2 1P transition isotope shift,” Phys. Rev. Lett. 76, 1216–1219 (1996).
[CrossRef] [PubMed]

Eyler, E. E.

S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

S. Gangopadhyay, N. Melikechi, and E. E. Eyler, “Optical phase perturbations in nanosecond pulsed amplification and second-harmonic generation,” J. Opt. Soc. Am. B 11, 231–241 (1994).
[CrossRef]

N. Melikechi, S. Gangopadhyay, and E. E. Eyler, “Phase dynamics in nanosecond pulsed dye laser amplification,” J. Opt. Soc. Am. B 11, 2402–2411 (1994).
[CrossRef]

Fee, M. S.

M. S. Fee, K. Danzmann, and S. Chu, “Optical heterodyne measurement of pulsed lasers: toward high-precision pulsed spectroscopy,” Phys. Rev. A 45, 4911–4924 (1992).
[CrossRef] [PubMed]

Fischer von Weikersthal, B.

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

Gabrysch, M.

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

Gangopadhyay, S.

Harris, F. J.

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

He, Y.

Hogervorst, W.

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Precision measurements in helium at 58 nm: ground state Lamb shift and the 1 1S–2 1P transition isotope shift,” Phys. Rev. Lett. 76, 1216–1219 (1996).
[CrossRef] [PubMed]

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
[CrossRef]

Jungmann, K.

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

Kono, M.

Lucatorto, T. B.

S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Marangos, J. P.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

McIlrath, T. J.

S. D. Bergeson, K. G. H. Baldwin, T. B. Lucatorto, T. J. McIlrath, C. H. Cheng, and E. E. Eyler, “Doppler-free two-photon spectroscopy in the vacuum ultraviolet: helium 1 1S–2 1S transition,” J. Opt. Soc. Am. B 17, 1599–1606 (2000).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Melikechi, N.

O’Brian, T. R.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Orr, B. J.

Reinhard, I.

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

Rolston, S. L.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Sansonetti, C. J.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Smith, A. V.

Ubachs, W.

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
[CrossRef]

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Precision measurements in helium at 58 nm: ground state Lamb shift and the 1 1S–2 1P transition isotope shift,” Phys. Rev. Lett. 76, 1216–1219 (1996).
[CrossRef] [PubMed]

Vassen, W.

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Precision measurements in helium at 58 nm: ground state Lamb shift and the 1 1S–2 1P transition isotope shift,” Phys. Rev. Lett. 76, 1216–1219 (1996).
[CrossRef] [PubMed]

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
[CrossRef]

Wen, J.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, C. H. Cheng, and E. E. Eyler, “Precision spectroscopy in He as a test of QED,” Phys. Scr. T83, 76–82 (1999).
[CrossRef]

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

Westbrook, N.

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

White, R. T.

zu Pulitz, G.

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

Appl. Phys. B: Lasers Opt. (1)

I. Reinhard, M. Gabrysch, B. Fischer von Weikersthal, K. Jungmann, and G. zu Pulitz, “Measurement and compensation of frequency chirping in pulsed dye laser amplifiers,” Appl. Phys. B: Lasers Opt. 63, 467–472 (1996).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Lett. (1)

Phys. Rev. A (2)

K. S. E. Eikema, W. Ubachs, W. Vassen, and W. Hogervorst, “Lamb shift measurement in the 1 1S ground state of helium,” Phys. Rev. A 55, 1866–1884 (1996).
[CrossRef]

M. S. Fee, K. Danzmann, and S. Chu, “Optical heterodyne measurement of pulsed lasers: toward high-precision pulsed spectroscopy,” Phys. Rev. A 45, 4911–4924 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

S. D. Bergeson, A. Balakrishnan, K. G. H. Baldwin, T. B. Lucatorto, J. P. Marangos, T. J. McIlrath, T. R. O’Brian, S. L. Rolston, C. J. Sansonetti, J. Wen, N. Westbrook, C. H. Cheng, and E. E. Eyler, “Measurement of the He ground state Lamb shift via the two-photon 1 1S–2 1S transition,” Phys. Rev. Lett. 80, 3475–3478 (1998).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematic of the (OH) technique used to measure the optical phase evolution of pulses from a coherent light source. The AOM is driven at angular frequency ωm. Inset, unchirped synthetic beat waveform and its optically delayed pulse intensity profile.

Fig. 2
Fig. 2

Power spectrum of the beat waveform in Fig. 1 (solid curve) and the three filter functions superimposed: Blackman (dashed curve), first-order Blackman (dashed–dotted curve), and Tukey (r=0.75; dotted curve).

Fig. 3
Fig. 3

FT algorithm applied to the synthetic 8-ns pulse with a linear chirp rate of +1 MHz ns-1. Bottom, calculated finst(t). Top, residual deviation of finst(t) from the input chirp profile. Results are shown for three filter functions: Tukey (solid curve; r=0.75, δ=0.8), first-order Blackman (dashed curve; δ=0.9), and Blackman (dashed–dotted curve; δ=1.1). The dotted line (bottom) is the input chirp profile, and the vertical dashed lines define the 10%-intensity interval for the input pulse.

Fig. 4
Fig. 4

Percent error in the output of the FT algorithm normalized to the input chirp applied to a range of synthetic pulses (8-ns FWHM duration) with linear chirp rates that range from -10 to +10 MHz ns-1. The error is plotted against the total chirp within the 10%-intensity window (14 ns). Circles and crosses, Δfinst and linear-fit definitions of the chirp, respectively. Results are shown for Blackman, first-order Blackman, and Tukey (r=0.75) filter functions, with the filter’s width parameter δ set at δopt. The error bars in the linear-fit data show the percent of standard deviation of the linear fit from the finst(t) curve compared with the total chirp, within the 10%-intensity interval.

Fig. 5
Fig. 5

Direct-fit method applied to the synthetic 8-ns pulse with a linear chirp rate of +1 MHz ns-1. (a) Input beat-waveform data points (dots) and model fit within the 10%-intensity interval, plus reconstructed intensity profile. (b) Normalized phase term (dots) and least-squares fit with polynomial phase, within the 10%-intensity interval (solid curve). (c) Calculated beat frequency for a moving window that is ∼2 oscillation periods wide. (d) Residual deviation of finst(t) from the input chirp profile.

Fig. 6
Fig. 6

Percent error in the output of the direct-fit algorithm applied to a range of synthetic pulses (8-ns FWHM duration) with linear chirp rates that range from -10 to +10 MHz ns-1. The error is plotted against the total chirp within the 10%-intensity window (14 ns). Crosses, linear-fit definition only; error bars, percent of standard deviation (∼0.5 MHz) of moving-window linear fits (over2 oscillation periods) from the input chirp profiles compared with the total chirp.

Fig. 7
Fig. 7

Schematic of electronic mixing: PD, photodetector; RF, rf driver for the AOM; R, L, I, rf signal input, local oscillator (AOM) input, and intermodulation output of electronic mixers, respectively; D, digitizing oscilloscope; HPF, high-pass filter; LPF, low-pass filter; S1, S2, rf power splitters.

Fig. 8
Fig. 8

Mixer simulation applied to the synthetic 8-ns pulse (linear chirp rate, +1 MHz ns-1). (a) Simulated intermodulation quadrature outputs VIS and VIC. (b) Bottom, calculated finst(t); top, residual frequency difference from a linear fit to finst(t). The frequency of the local oscillator input is 730 MHz. Vertical dashed lines define the 10%-intensity interval.

Fig. 9
Fig. 9

Percent error in the output of the mixer method applied to a range of synthetic pulses (8-ns FWHM duration) with linear chirp rates that range from -10 to +10 MHz ns-1. Crosses, linear fit; circles, Δfinst. Error bars show the percent of standard deviation of the residuals between the linear fit and the calculated finst(t) values compared with the total chirp. The frequency of the local oscillator input was 730 MHz.

Fig. 10
Fig. 10

Mixer dispersion data showing phase delay β (triangles) and the arctangent of amplitude ratio R (circles) as functions of intermodulation frequency (centered at ∼730 MHz).

Fig. 11
Fig. 11

Instantaneous beat-frequency evolution for output from a pulsed PPKTP OPO, shown over the 10%-intensity interval for the FT (heavier solid curve), direct-fit (dotted curve), and mixer (finer solid curve) methods. Vertical dashed lines define the 50%-intensity interval.

Tables (1)

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Table 1 Characteristics of the Filter Functions Used for Chirp Analysis by the FT Methoda

Equations (10)

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(0.44/Δt)<fbeats<fdet.
Ecw(t)=Ecw0 exp[i(ω0-ωm)t)]+c.c.,
Ep(t)=Ep0(t)exp[iωt+iϕ(t)]+c.c.,
finst(t)=(2π)-1dϕ(t)/dt.
VPD|Ecw(t)+Ep(t)|2=|Ecw0|2+|Ep0(t)|2+Ecw0Ep0(t){exp[i(ω+ωm-ω0)t+iϕ(t)]+c.c.}.
|Δfinst|=(finst)max-(finst)min.
VIS=CSμ(t)|Ep0(t)|sin[ϕ(t)+(ω0-ω)t],
VIC=CCμ(t)|Ep0(t)|cos[ϕ(t)+(ω0-ω)t],
VIC=(RVIC-VIS  cos β)/sin β,
VIS=VIS,

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