Abstract

We present a high-spectral-resolution and experimentally simple version of spectral interferometry using optical fibers and crossed beams, which we call SEA TADPOLE. Rather than using collinear unknown and reference pulses separated in time to yield spectral fringes—and reduced spectral resolution—as in current versions, we use time-coincident pulses crossed at a small angle to generate spatial fringes. This allows the extraction of the spectral phase with the full spectrometer resolution, which allows the measurement of much longer and more complex pulses. In fact, SEA TADPOLE achieves spectral super-resolution, yielding the pulse spectrum with even better resolution. Avoiding collinear beams and using fiber coupling also vastly simplify alignment. We demonstrate SEA TADPOLE by measuring a chirped pulse, a double pulse separated by 14 ps, and a complex pulse comprising two trains of pulses with a timebandwidth product of ~400.

© 2006 Optical Society of America

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  1. Cl. Froehly, A. Lacourt, and J. Ch. Viénot, "Time Impulse Responce and time Frequency Responce of Optical Pupils," Nouv. Rev. Opt. Appl. 4, 183-196 (1973).
    [CrossRef]
  2. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, "Measurement of the Intensity and Phase of Ultraweak, Ultrashort Laser Pulse," Opt. Lett. 21, 884-886 (1996).
    [CrossRef] [PubMed]
  3. L. Lepetit, G. Chériaux, and M. Joffre, "Linear Techniques of Phase Measurement by Femtosecond Spectral Interferometry for Applications in Spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995).
    [CrossRef]
  4. T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari, "Accurate pulse shaping with feedback control in amplitude and phase for amplified femtosecond pulses," in Conference on Lasers and Electro-Optics (CLEO), (Baltimore, MD., 2003), p. 2.
  5. R. Levis, Gerahun Menkir, Herschel Rabitz, "Selective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses," Science 292, 709 (2001).
    [CrossRef] [PubMed]
  6. T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
    [CrossRef]
  7. D. J. Kane, and R. Trebino, "Characterization of Arbitrary Femtosecond Pulses Using Frequency Resolved Optical Gating," IEEE J. Quantum Electron. 29, 571-579 (1993).
    [CrossRef]
  8. C. Iaconis, and I. A. Walmsley, "Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
    [CrossRef]
  9. JonathonR. Birge, Richard Ell, Franz X. Kaertner, "Two-dimensional spectral shearing interferometry for few-cycle pulse characterization " Opt. Lett. 31, 2063-2065 (2006).
    [CrossRef] [PubMed]
  10. A. Vakhtin, Kristen Peterson, Willian Wood, Daniel Kane, "Differental Spectral interferometry: an imaging technique for biomedical applications," Opt. Lett. 28, (2003).
    [CrossRef] [PubMed]
  11. A. P. Kovaecs, K. Osvay, Zs. Bor, "Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry," Opt. Lett. 20, 788-791 (1995).
    [CrossRef]
  12. A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
    [CrossRef]
  13. D. Meshulach, D. Yelin and Y. Silberberg, "Real-time spatial-spectral interference measurements of ultrashort optical pulses," J. Opt. Soc. of Am. B 14, 2095-2099 (1997).
    [CrossRef]
  14. E. M. Kosik, A. S. Radunsky, I. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30326-328 (2005).
    [CrossRef] [PubMed]

2006 (1)

2005 (2)

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

E. M. Kosik, A. S. Radunsky, I. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30326-328 (2005).
[CrossRef] [PubMed]

2004 (1)

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

2003 (1)

A. Vakhtin, Kristen Peterson, Willian Wood, Daniel Kane, "Differental Spectral interferometry: an imaging technique for biomedical applications," Opt. Lett. 28, (2003).
[CrossRef] [PubMed]

2001 (1)

R. Levis, Gerahun Menkir, Herschel Rabitz, "Selective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses," Science 292, 709 (2001).
[CrossRef] [PubMed]

1999 (1)

C. Iaconis, and I. A. Walmsley, "Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

1997 (1)

D. Meshulach, D. Yelin and Y. Silberberg, "Real-time spatial-spectral interference measurements of ultrashort optical pulses," J. Opt. Soc. of Am. B 14, 2095-2099 (1997).
[CrossRef]

1996 (1)

1995 (2)

1993 (1)

D. J. Kane, and R. Trebino, "Characterization of Arbitrary Femtosecond Pulses Using Frequency Resolved Optical Gating," IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

1973 (1)

Cl. Froehly, A. Lacourt, and J. Ch. Viénot, "Time Impulse Responce and time Frequency Responce of Optical Pupils," Nouv. Rev. Opt. Appl. 4, 183-196 (1973).
[CrossRef]

Bor, Z.

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Bor, Zs.

Bowie, J. L.

Chériaux, G.

DeLong, K. W.

Dorrer, C.

Fittinghoff, D. N.

Froehly, Cl.

Cl. Froehly, A. Lacourt, and J. Ch. Viénot, "Time Impulse Responce and time Frequency Responce of Optical Pupils," Nouv. Rev. Opt. Appl. 4, 183-196 (1973).
[CrossRef]

Görbe, M.

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Iaconis, C.

C. Iaconis, and I. A. Walmsley, "Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

Jennings, R. T.

Joffre, M.

Jonathon,

Kane, D. J.

D. J. Kane, and R. Trebino, "Characterization of Arbitrary Femtosecond Pulses Using Frequency Resolved Optical Gating," IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

Kannari, F.

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

Klenbniczki, J.

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Kosik, E. M.

Kovaecs, A. P.

Kovaecs, A.P.

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Krumbügel, M. A.

Kurdi, G.

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Lacourt, A.

Cl. Froehly, A. Lacourt, and J. Ch. Viénot, "Time Impulse Responce and time Frequency Responce of Optical Pupils," Nouv. Rev. Opt. Appl. 4, 183-196 (1973).
[CrossRef]

Lepetit, L.

Levis, R.

R. Levis, Gerahun Menkir, Herschel Rabitz, "Selective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses," Science 292, 709 (2001).
[CrossRef] [PubMed]

Meshulach, D.

D. Meshulach, D. Yelin and Y. Silberberg, "Real-time spatial-spectral interference measurements of ultrashort optical pulses," J. Opt. Soc. of Am. B 14, 2095-2099 (1997).
[CrossRef]

Ohno, K.

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

Okamoto, T.

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

Osvay, K.

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

A. P. Kovaecs, K. Osvay, Zs. Bor, "Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry," Opt. Lett. 20, 788-791 (1995).
[CrossRef]

Radunsky, A. S.

Silberberg, Y.

D. Meshulach, D. Yelin and Y. Silberberg, "Real-time spatial-spectral interference measurements of ultrashort optical pulses," J. Opt. Soc. of Am. B 14, 2095-2099 (1997).
[CrossRef]

Sweetser, J. N.

Tanabe, T.

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

Trebino, R.

Vakhtin, A.

A. Vakhtin, Kristen Peterson, Willian Wood, Daniel Kane, "Differental Spectral interferometry: an imaging technique for biomedical applications," Opt. Lett. 28, (2003).
[CrossRef] [PubMed]

Viénot, J. Ch.

Cl. Froehly, A. Lacourt, and J. Ch. Viénot, "Time Impulse Responce and time Frequency Responce of Optical Pupils," Nouv. Rev. Opt. Appl. 4, 183-196 (1973).
[CrossRef]

Walmsley, I.

Walmsley, I. A.

Yamanaka, M.

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

Yelin, D.

D. Meshulach, D. Yelin and Y. Silberberg, "Real-time spatial-spectral interference measurements of ultrashort optical pulses," J. Opt. Soc. of Am. B 14, 2095-2099 (1997).
[CrossRef]

Appl. Phys. B (1)

A.P. Kovaecs, K. Osvay, G. Kurdi, M. Görbe, J. Klenbniczki, Z. Bor, "Dispersion Control of a pulse stretcher-compressor system with two-dimensional spectral interferometry," Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. J. Kane, and R. Trebino, "Characterization of Arbitrary Femtosecond Pulses Using Frequency Resolved Optical Gating," IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

C. Iaconis, and I. A. Walmsley, "Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. of Am. B (1)

D. Meshulach, D. Yelin and Y. Silberberg, "Real-time spatial-spectral interference measurements of ultrashort optical pulses," J. Opt. Soc. of Am. B 14, 2095-2099 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari., "Feedback control for accurate shaping of ultrashort opticsal pulses prior to chirped pulse amplification," Jpn. J. Appl. Phys. 43, 1366-1375 (2004).
[CrossRef]

Nouv. Rev. Opt. Appl. (1)

Cl. Froehly, A. Lacourt, and J. Ch. Viénot, "Time Impulse Responce and time Frequency Responce of Optical Pupils," Nouv. Rev. Opt. Appl. 4, 183-196 (1973).
[CrossRef]

Opt. Lett. (5)

Science (1)

R. Levis, Gerahun Menkir, Herschel Rabitz, "Selective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses," Science 292, 709 (2001).
[CrossRef] [PubMed]

Other (1)

T. Tanabe, K. Ohno, T. Okamoto, M. Yamanaka, F. Kannari, "Accurate pulse shaping with feedback control in amplitude and phase for amplified femtosecond pulses," in Conference on Lasers and Electro-Optics (CLEO), (Baltimore, MD., 2003), p. 2.

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Figures (7)

Fig. 1.
Fig. 1.

Phase retrieval in SEA TADPOLE: (a) A typical experimental SEA TADPOLE trace. (b) A 1D-FT of the interferogram with respect to position (showing only the magnitude of the complex data). The side-bands are the interference terms. The phase of either of the sidebands yields the spectral-phase difference between the signal and reference pulses.

Fig. 2.
Fig. 2.

Experimental setup for SEA TADPOLE: The reference and unknown pulses enter the device via equal-length, single-mode optical fibers. In the horizontal dimension, the light is collimated and then spectrally resolved at the camera using the grating and the cylindrical lens. In the vertical dimension, the light emerging from the two fibers crosses at a small angle and makes horizontal spatial fringes at the CCD camera.

Fig. 3.
Fig. 3.

(a) The SEA TADPOLE trace of a chirped pulse. (b) The retrieved spectrum and spectral phase. The red curve is a quadratic fit to the spectral phase, in close agreement with the chirp predicted by the known Sellmeier equations for SF11.

Fig. 4.
Fig. 4.

The reconstructed electric field of a 14-ps double pulse generated by a Michelson interferometer: (a) Spectral intensity and phase of the double pulse. (b) Temporal intensity and phase. Inserts are expanded views of two of the pulses with their phases shown.

Fig. 5.
Fig. 5.

The reconstructed electric field of a double train of pulses generated by a Michelson interferometer and an etalon. (a) Spectral intensity and phase. (b) Temporal intensity and phase. The time between the peaks in the train is about 350 fs, in agreement with the known thickness of the calibrated etalon used to generate the train.

Fig. 6.
Fig. 6.

The measured spectra from Figs. 4a and 5a (the green lines) reconstructed from SEA TADPOLE traces compared with independently measured spectra (the blue lines) using the same spectrometer (simply by blocking the reference beam). (a) The spectrum of the 14 ps double pulse. (b) The spectrum of the double train of pulses. Note the significantly better spectral resolution of the SEA TADPOLE-measured spectra, despite the use of the identical spectrometer for both measurements.

Fig. 7.
Fig. 7.

Convolving the field versus convolving the spectrum when zero crossings are present in the field. (a) The field of the double pulse before (blue) and after (green) convolving it with a (0.4 nm wide) Lorentzian. (b) The precise spectrum of the field (red), the spectrum after the field has been convolved with the Lorentzian (black), the same curve, but normalized to have the same area as the red curve (green), and the spectrum convolved with the Lorentzian (blue). This shows that convolving the field preserves spectral structure better than doing so with its magnitude squared.

Equations (1)

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S ( ω , x ) = S ref ( ω ) + S unk ( ω ) + 2 S ref ( ω ) S unk ( ω ) cos ( 2 k x sin θ + φ unk ( ω ) φ ref ( ω ) )

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