OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 10, Iss. 5 — May. 1, 1993
  • pp: 1101–1111

Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating

Rick Trebino and Daniel J. Kane  »View Author Affiliations

JOSA A, Vol. 10, Issue 5, pp. 1101-1111 (1993)

View Full Text Article

Enhanced HTML    Acrobat PDF (1529 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We recently introduced a new technique, frequency-resolved optical gating (FROG), for directly determining the full intensity I(t) and phase φ(t) of a single femtosecond pulse. By using almost any instantaneous nonlinear-optical interaction of two replicas of the ultrashort pulse to be measured, FROG involves measuring the spectrum of the signal pulse as a function of the delay between the replicas. The resulting trace of intensity versus frequency and delay yields an intuitive display of the pulse that is similar to the pulse spectrogram, except that the gate is a function of the pulse to be measured. The problem of inverting the FROG trace to obtain the pulse intensity and phase can also be considered a complex two-dimensional phase-retrieval problem. As a result, the FROG trace yields, in principle, an essentially unique pulse intensity and phase. We show that this is also the case in practice. We present an iterative-Fourier-transform algorithm for inverting the FROG trace. The algorithm is unusual in its use of a novel constraint: the mathematical form of the signal field. Without the use of a support constraint, the algorithm performs quite well in practice, even for pulses with serious phase distortions and for experimental data with noise, although it occasionally stagnates when pulses with large intensity fluctuations are used.

© 1993 Optical Society of America

Original Manuscript: September 16, 1992
Revised Manuscript: December 1, 1992
Manuscript Accepted: October 9, 1992
Published: May 1, 1993

Rick Trebino and Daniel J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101-1111 (1993)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987). [CrossRef] [PubMed]
  2. H. L. Fragnito, J.-Y. Bigot, P. C. Becker, C. V. Shank, “Evolution of the vibronic absorption spectrum in a molecule following impulsive excitation with a six fsec optical pulse,” Chem. Phys. Lett. 160, 101–104 (1989). [CrossRef]
  3. J. H. Glownia, J. A. Misewich, P. P. Sorokin, “Femtosecond transition-state absorption spectroscopy of Bi atoms produced by photodissociation of gaseous Bi2molecules,”J. Chem. Phys. 92, 3335–3347 (1990). [CrossRef]
  4. E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses—Picosecond Techniques and Applications, S. L. Shapiro, ed. (Springer-Verlag, Berlin, 1977), p. 83. [CrossRef]
  5. J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967). [CrossRef]
  6. N. G. Basov, V. É. Pozhar, V. I. Pustovoit, “Measurement of the duration of high-power ultrashort optical pulses,” So. J. Quantum Electron. 15, 1429–1431 (1985). [CrossRef]
  7. J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond pulses,” Appl. Opt. 24, 1270–1282 (1985). [CrossRef] [PubMed]
  8. R. Trebino, C. C. Hayden, A. M. Johnson, W. M. Simpson, A. M. Levine, “Chirp and self-phase modulation in induced-grating autocorrelation measurements of ultrashort pulses,” Opt. Lett. 15, 1079–1081 (1990). [CrossRef] [PubMed]
  9. J. T. Manassah, “Direct and second-harmonic interferometric determination of chirped pulse parameters,” Appl. Opt. 26, 2941–2942 (1987). [CrossRef]
  10. C. Yan, J. C. Diels, “Amplitude and phase recording of ultrashort pulses,” J. Opt. Soc. Am. B 8, 1259–1263 (1991). [CrossRef]
  11. K. Naganuma, K. Mogi, H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989). [CrossRef]
  12. T. Kobayashi, F.-C Guo, A. Morimoto, T. Sueta, Y. Cho, “Novel method of waveform evaluation of ultrashort optical pulses,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 93–95. [CrossRef]
  13. K. Naganuma, K. Mogi, H. Yamada, “Time direction determination of asymmetric ultrashort optical pulses from second-harmonic generation autocorrelation signals,” Appl. Phys. Lett. 54, 1201–1202 (1989). [CrossRef]
  14. J. Jansky, G. Corradi, “Full intensity profile analysis of ultrashort laser pulses using four-wave mixing or third-harmonic generation,” Opt. Commun. 60, 251–256 (1986). [CrossRef]
  15. N. G. Paulter, A. K. Majumdar, “A new triple correlator design for the measurement of ultrashort pulses,” Opt. Commun. 81, 96–100 (1991). [CrossRef]
  16. A. S. L. Gomes, V. L. da Silva, J. R. Taylor, “Direct measurement of nonlinear frequency chirp of Raman radiation in single-mode optical fibers using a spectral window method,” J. Opt. Soc. Am. B 5, 373–379 (1988). [CrossRef]
  17. G. Szabo, A. Müller, Z. Bor, “A sensitive single-shot method to determine duration and chirp of ultrashort pulses with a streak camera,” Opt. Commun. 82, 56–62 (1991). [CrossRef]
  18. J. E. Rothenberg, D. Grischkowsky, “Measurement of optical phase with subpicosecond resolution by time-domain interferometry,” Opt. Lett. 12, 99–101 (1987). [CrossRef]
  19. T. F. Albrecht, K. Seibert, H. Kurz, “Chirp measurement of large-bandwidth femtosecond optical pulses using two-photon absorption,” Opt. Commun. 84, 223–227 (1991). [CrossRef]
  20. K. W. DeLong, J. Yumoto, “Chirped light and its characterization using the cross-correlation technique,” J. Opt. Soc. Am. B 9, 1593–1604 (1992). [CrossRef]
  21. J. L. A. Chilla, O. E. Martinez, “Direct determination of the amplitude and the phase of femtosecond light pulses,” Opt. Lett. 16, 39–41 (1991). [CrossRef] [PubMed]
  22. J. L. A. Chilla, O. E. Martinez, “Frequency-domain phase measurement of ultrashort light pulses. Effect of noise,” Opt. Commun. 89, 434–440 (1992). [CrossRef]
  23. J. L. A. Chilla, O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. 27, 1228–1235 (1991). [CrossRef]
  24. A. Brun, P. Georges, G. Le Saux, F. Salin, “Single-shot characterization of ultrashort light pulses,” Rev. Sci. Instrum. 27, 1225–1233 (1992).
  25. E. P. Ippen, C. V. Shank, “Dynamic spectroscopy and subpicosecond pulse compression,” Appl. Phys. Lett. 27, 488–490 (1975). [CrossRef]
  26. J. P. Heritage, A. M. Weiner, R. N. Thurston, “Fourier-transform picosecond pulse shaping and spectral-phase measurement in a grating pulse compressor,” in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), pp. 34–37. [CrossRef]
  27. A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990). [CrossRef] [PubMed]
  28. J. P. Foing, L. P. Likforman, M. Joffre, “Femtosecond pulse phase measurement by spectrally resolved up-conversion,” in Ultrafast Phenomena VIII, J. L. Martin, A. Migus, eds. (Springer-Verlag, to be published).
  29. D. J. Kane, R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” J. Quantum Electron. 29, 571–579 (1993). This paper also contains the proof of uniqueness of the FROG-trace inversion, but for the nonlinear-optical interaction of self-diffraction. [CrossRef]
  30. D. J. Kane, R. Trebino, “Single-shot measurement of the intensity and phase of a femtosecond pulse,” in Ultrafast Phenomena IX, J. L. Martin, A. Migus, eds. (Springer-Verlag, to be published).
  31. D. J. Kane, R. Trebino, “Single-shot measurement of the intensity and phase of an arbitrary femtosecond pulse using frequency-resolved optical gating,” Opt. Lett. (to be published).
  32. W. Koenig, H. K. Dunn, L. Y. Lacy, “The sound spectrograph,”J. Acoust. Soc. Am. 18, 19–49 (1946). [CrossRef]
  33. S. H. Nawab, T. F. Quatieri, J. S. Lim, “Signal reconstruction from short-time Fourier transform magnitude,”IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 986–998 (1983). [CrossRef]
  34. R. A. Altes, “Detection, estimation, and classification with spectrograms,”J. Acoust. Soc. Am. 67, 1232–1246 (1980). [CrossRef]
  35. L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77, 941–981 (1989). [CrossRef]
  36. We note here, as in Ref. 29, that the spectrogram is not considered to be the ideal time- and frequency-resolved quantity. The Wigner distribution and wavelet transform, for example, are much more popular at the moment. [See, e.g., C. E. Heil, D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev. 31, 628–666 (1989).] In our opinion, however, it is the spectrogram, or more precisely the FROG trace, that is the most easily experimentally measured time-and frequency-resolved quantity for ultrashort pulses. The above-mentioned alternative measures require such quantities as a time-reversed replica of the pulse or a variable-frequency and simultaneously variable-length window. Such quantities are quite difficult to obtain optically. On the other hand, the spectrogram’s main inadequacy is that its fixed-length window cannot simultaneously provide good measurements of both long-term and short-term variations. This is not a problem for ultrashort-pulse measurement, in which the variations of interest are all short term. It may also be the case that, because in FROG the gate has exactly those time scales as the pulse, FROG may actually avoid the above problem in general, but we have not investigated this issue as yet. [CrossRef]
  37. E. J. Akutowicz, “On the determination of the phase of a Fourier signal. I,” Trans. Am. Math. Soc. 83, 234–239 (1956).
  38. H. Stark, Image Recovery: Theory and Application (Academic, Orlando, Fla., 1987).
  39. R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990). [CrossRef]
  40. R. Barakat, G. Newsam, “Necessary conditions for a unique solution to two-dimensional phase recovery,”J. Math. Phys. 25, 3190–3193 (1984). [CrossRef]
  41. R. G. Lane, W. R. Fright, R. H. T. Bates, “Direct phase retrieval,”IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520–525 (1987). [CrossRef]
  42. D. Israelevitz, J. S. Lim, “A new direct algorithm for image reconstruction from Fourier transform magnitude,”IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 511–519 (1987). [CrossRef]
  43. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987). [CrossRef]
  44. J. H. Seldin, J. R. Fienup, “Iterative blind deconvolution algorithm applied to phase retrieval,” J. Opt. Soc. Am. A 7, 428–433 (1990). [CrossRef]
  45. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  46. R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38, 1797–1813 (1991). [CrossRef]
  47. R. H. T. Bates, D. G. H. Tan, “Fourier phase retrieval when the image is complex,” in Inverse Optics II, A. J. Devaney, R. H. T. Bates, eds., Proc. Soc. Photo-Opt. Instrum. Eng.558, 54–59 (1985). [CrossRef]
  48. A. M. Johnson, C. V. Shank, “Pulse compression in single-mode fibers—picoseconds to femtoseconds,” in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989). pp. 399–450. [CrossRef]
  49. Y. R. Shen, G.-Z. Yang, “Theory of self-phase modulation and spectral broadening,” in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), pp. 1–32. [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited