Abstract

When confronted with a pulse train whose intensity and/or phase versus time varies from pulse to pulse, multi-shot pulse-measurement techniques usually exhibit a coherent artifact (CA), which substantially complicates the interpretation of the measurement. In frequency-resolved optical gating (FROG), such instabilities are indicated by discrepancies between the measured and retrieved FROG traces. Here we consider the simultaneous retrieval of the CA and the average pulse characteristics from a single FROG trace in the limit of significant fluctuations. We use a modified generalized projections algorithm. Two electric fields are simultaneously retrieved, while the data constraint is updated as the algorithm progresses using only the assumption that the trace can be modeled as the sum of two spectrograms, one corresponding to the pulse and the other corresponding to the CA. An additional flat-spectral-phase constraint is added to one of the fields to ensure that it only reacts to the presence of the CA. Using this novel retrieval method, the complete retrieval of the characteristics of pulses in an unstable train from FROG traces is demonstrated.

© 2019 Optical Society of America

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References

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2019 (1)

2017 (2)

2016 (1)

2015 (4)

2014 (1)

2013 (3)

K. G. Wilcox and A. C. Tropper, Laser Photonics Rev. 7, 422 (2013).
[Crossref]

A. F. J. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, Opt. Lett. 38, 4327 (2013).
[Crossref]

M. Rhodes, G. Steinmeyer, J. Ratner, and R. Trebino, Laser Photonics Rev. 7, 557 (2013).
[Crossref]

2010 (1)

1997 (1)

1995 (1)

1994 (1)

1986 (1)

1981 (1)

Z. Vardeny and J. Tauc, Opt. Commun. 39, 396 (1981).
[Crossref]

1975 (1)

C. V. Shank and D. H. Auston, Phys. Rev. Lett. 34, 479 (1975).
[Crossref]

1967 (2)

M. A. Duguay, S. L. Shapiro, and P. M. Rentzepis, Phys. Rev. Lett. 19, 1014 (1967).
[Crossref]

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Appl. Phys. Lett. 11, 216 (1967).
[Crossref]

Aguergaray, C.

Auston, D. H.

C. V. Shank and D. H. Auston, Phys. Rev. Lett. 34, 479 (1975).
[Crossref]

Barillot, T.

Birge, J.

Bourassin-Bouchet, C.

C. Bourassin-Bouchet and M. E. Couprie, Nat. Commun. 6, 1 (2015).
[Crossref]

Broderick, N. G. R.

Clement, T. S.

Couprie, M. E.

C. Bourassin-Bouchet and M. E. Couprie, Nat. Commun. 6, 1 (2015).
[Crossref]

Dantus, M.

DeLong, K. W.

Duguay, M. A.

M. A. Duguay, S. L. Shapiro, and P. M. Rentzepis, Phys. Rev. Lett. 19, 1014 (1967).
[Crossref]

Düsterer, S.

Erkintalo, M.

Escoto, E.

Fittinghoff, D. N.

Giordmaine, J. A.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Appl. Phys. Lett. 11, 216 (1967).
[Crossref]

Greening, D.

Guang, Z.

M. Rhodes, Z. Guang, and R. Trebino, Appl. Sci. 7, 40 (2017).
[Crossref]

Gustafson, E. K.

Hyyti, J.

Jafari, R.

Jiang, Y.

Jones, T.

Kane, D. J.

Kohler, B.

Lozovoy, V. V.

Marangos, J. P.

Matia-Hernando, P.

Moshammer, R.

Mukhopadhyay, M.

Pestov, D.

Pfeifer, T.

Rasskazov, G.

Ratner, J.

M. Rhodes, G. Steinmeyer, J. Ratner, and R. Trebino, Laser Photonics Rev. 7, 557 (2013).
[Crossref]

Rentzepis, P. M.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Appl. Phys. Lett. 11, 216 (1967).
[Crossref]

M. A. Duguay, S. L. Shapiro, and P. M. Rentzepis, Phys. Rev. Lett. 19, 1014 (1967).
[Crossref]

Rhodes, M.

M. Rhodes, Z. Guang, and R. Trebino, Appl. Sci. 7, 40 (2017).
[Crossref]

M. Rhodes, M. Mukhopadhyay, J. Birge, and R. Trebino, J. Opt. Soc. Am. B 32, 1881 (2015).
[Crossref]

M. Rhodes, G. Steinmeyer, and R. Trebino, Appl. Opt. 53, D1 (2014).
[Crossref]

M. Rhodes, G. Steinmeyer, J. Ratner, and R. Trebino, Laser Photonics Rev. 7, 557 (2013).
[Crossref]

Rodriguez, G.

Runge, A. F. J.

Shank, C. V.

C. V. Shank and D. H. Auston, Phys. Rev. Lett. 34, 479 (1975).
[Crossref]

Shapiro, S. L.

M. A. Duguay, S. L. Shapiro, and P. M. Rentzepis, Phys. Rev. Lett. 19, 1014 (1967).
[Crossref]

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Appl. Phys. Lett. 11, 216 (1967).
[Crossref]

Siegman, A. E.

Steinmeyer, G.

Tauc, J.

Z. Vardeny and J. Tauc, Opt. Commun. 39, 396 (1981).
[Crossref]

Taylor, A. J.

Tisch, J. W. G.

Trebino, R.

Tropper, A. C.

K. G. Wilcox and A. C. Tropper, Laser Photonics Rev. 7, 422 (2013).
[Crossref]

Ullrich, J.

Vardeny, Z.

Z. Vardeny and J. Tauc, Opt. Commun. 39, 396 (1981).
[Crossref]

Walke, D.

Wecht, K. W.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Appl. Phys. Lett. 11, 216 (1967).
[Crossref]

White, W. E.

Wilcox, K. G.

K. G. Wilcox and A. C. Tropper, Laser Photonics Rev. 7, 422 (2013).
[Crossref]

Wilson, K.

Witting, T.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Appl. Phys. Lett. 11, 216 (1967).
[Crossref]

Appl. Sci. (1)

M. Rhodes, Z. Guang, and R. Trebino, Appl. Sci. 7, 40 (2017).
[Crossref]

J. Opt. Soc. Am. B (4)

Laser Photonics Rev. (2)

M. Rhodes, G. Steinmeyer, J. Ratner, and R. Trebino, Laser Photonics Rev. 7, 557 (2013).
[Crossref]

K. G. Wilcox and A. C. Tropper, Laser Photonics Rev. 7, 422 (2013).
[Crossref]

Nat. Commun. (1)

C. Bourassin-Bouchet and M. E. Couprie, Nat. Commun. 6, 1 (2015).
[Crossref]

Opt. Commun. (1)

Z. Vardeny and J. Tauc, Opt. Commun. 39, 396 (1981).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

M. A. Duguay, S. L. Shapiro, and P. M. Rentzepis, Phys. Rev. Lett. 19, 1014 (1967).
[Crossref]

C. V. Shank and D. H. Auston, Phys. Rev. Lett. 34, 479 (1975).
[Crossref]

Other (1)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, 2002).

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Figures (6)

Fig. 1.
Fig. 1. Intensities of the pulses in spectral and temporal domains, for a time envelope with FWHM=192δt.
Fig. 2.
Fig. 2. Measured and retrieved FROG traces, along with the two traces corresponding to the CA and the average pulse. Top row, 59δt; middle row, 126δt; and bottom row, 192δt. These can be directly compared with the results in Ref. [6].
Fig. 3.
Fig. 3. Retrieved fields for ICA in (a) spectral and (b) temporal domains. (c) and (d) Corresponding average spectrum and pulse shape for the stable component used in constructing the pulse trains. I: 59δt, II: 126δt, and III: 192δt.
Fig. 4.
Fig. 4. Retrieved fields for Iave in (a) spectral and (b) temporal domains. (c) and (d) Corresponding average spectrum and pulse shape for the unstable component used in constructing the pulse trains. I, 59δt; II, 126δt; and III, 192δt.
Fig. 5.
Fig. 5. Measured and retrieved FROG traces from a stable pulse train using the modified GP algorithm.
Fig. 6.
Fig. 6. Measured and retrieved spectra using the RANA approach, along with the autoconvolution coming from the frequency marginal of the trace with 192δt.

Tables (1)

Tables Icon

Table 1. RMS Errors for the Retrieved Intensities in Spectral and Temporal Domains

Equations (4)

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IFROG(ω,τ)1NjN|+Esig,j(t,τ)exp(iωt)dt|2,
IFROG(ω,τ)=aICA(ω,τ)+bIave(ω,τ),
ICA=ICA+β(IFROGbIaveaICA),
Iave=Iave+β(IFROGaICAbIave),

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