Abstract

We demonstrate a simple, all-optical, fiber-based method for characterizing the spectral amplitude and phase of ultrafast pulses using a differential tomographic measurement realized via four-wave mixing. The technique is applied to subpicosecond pulses in the C-band of the telecommunication spectrum. Characterization of amplified pulses and propagation through dispersive media is demonstrated and compared with autocorrelation mea surements and calculated predictions. We show how our approach can be extended to larger bandwidths in similar systems, extending tomographic reconstruction of coherent fields to nearly an octave of bandwidth while maintaining a robust, waveguide-based geometry.

© 2011 Optical Society of America

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R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

2007

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D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Azaña, J.

Barry, L. P.

Broaddus, D. H.

Bromage, J.

Chen, X.

Dorrer, C.

Dudley, J. M.

Dulkeith, E.

Foster, M. A.

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, Opt. Express 18, 1904 (2010).
[CrossRef] [PubMed]

D. H. Broaddus, M. A. Foster, O. Kuzucu, A. C. Turner-Foster, K. W. Koch, M. Lipson, and A. L. Gaeta, Opt. Express 18, 14262 (2010).
[CrossRef] [PubMed]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

Gaeta, A. L.

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, Opt. Express 18, 1904 (2010).
[CrossRef] [PubMed]

D. H. Broaddus, M. A. Foster, O. Kuzucu, A. C. Turner-Foster, K. W. Koch, M. Lipson, and A. L. Gaeta, Opt. Express 18, 14262 (2010).
[CrossRef] [PubMed]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

Geraghty, D.

R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

Harvey, J. D.

Iaconis, C.

Kane, D. J.

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Kang, I.

Koch, K. W.

Kuzucu, O.

Li, F.

Lipson, M.

D. H. Broaddus, M. A. Foster, O. Kuzucu, A. C. Turner-Foster, K. W. Koch, M. Lipson, and A. L. Gaeta, Opt. Express 18, 14262 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, Opt. Express 18, 1904 (2010).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

Osgood, R. M.

Panoiu, N. C.

Park, Y.

Salem, R.

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, Opt. Express 18, 1904 (2010).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, Opt. Express 18, 1904 (2010).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner-Foster, D. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photon. 2, 35 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, Nature 456, 81 (2008).
[CrossRef] [PubMed]

Vlasov, Y. A.

Walmsley, I. A.

Wong, V.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for all-optical simplified tomography. The output from a femtosecond oscillator is split into two spectral components to produce the pump and signal fields. The polarization of the pump is rotated and the pump field is dispersed, amplified, and filtered. The signal passes through a selected amount of dispersion before it is recombined with the pump on a 50 / 50 beam splitter. The copropagating fields are then mixed in highly nonlinear fiber, and the output spectrum is measured.

Fig. 2
Fig. 2

Comparison of signal field temporal measurements. The measured autocorrelation (black solid curve) is in good agreement with the reconstructed autocorrelation (red circles), in contrast with the reconstructed autocorrelation of a pulse with the same spectrum but a flat phase (blue diamonds).

Fig. 3
Fig. 3

Reconstruction of a 3.04 rad phase jump. The spectrum (solid curve) shows a dip due to scattering from the 0 π / 2 interface of the phase plate. The measured phase profile without the plate (not shown) is subtracted from the measurement with the plate (dotted red curve), revealing a measured phase jump of 3.17 rad (dashed blue curve).

Fig. 4
Fig. 4

Reconstructed induced dispersion and output autocorrelation FWHM for various lengths of SMF. Tomographic dispersion reconstruction is compared to calculation and then used to predict the measured autocorrelation FWHM.

Equations (2)

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I θ = I ( ω ) I θ ( ω ) δ θ ,
E i ( t ) E p ( t ) 2 | E s * ( t ) | e i [ ( 2 ω p ω s ) t + β τ ( 2 ) τ 2 ϕ s ( t ) ] ,

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