Abstract

We introduce a novel method for retrieving the phase from a spectral shearing interferogram, based on wavelet-transform technique. We demonstrate with both theoretical and experimental data that this technique provides an alternative and reliable technique for phase retrieval, particularly for highly structured pulse spectra.

© 2005 Optical Society of America

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References

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  1. K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.
  2. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  3. C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses”, IEEE J. Quantum Electron. 35, 501–509 (1999).
    [Crossref]
  4. M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
    [Crossref]
  5. S. Jensen and M. E. Anderson, “Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction,” Appl. Opt. 43, 883–893 (2004).
    [Crossref] [PubMed]
  6. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
    [Crossref] [PubMed]
  7. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
    [Crossref]
  8. K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
    [Crossref] [PubMed]
  9. C. K. Chui ed., An introduction to wavelets (Academic Press, Boston, 1992).
  10. B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
    [Crossref]
  11. Y. Morimoto and Y. Imamoto, “Application of wavelet transform to displacement and strain measurement by grid method,” in Proc. of 1995 SEM Spring Conf. on Exp. Mech. (Society for Experimental Mechanics, MI, 1995), 898–903.
  12. L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
    [Crossref]
  13. Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).
  14. J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
    [Crossref]
  15. D. J. Kane and R. Trebino “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).
    [Crossref] [PubMed]
  16. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
    [Crossref]

2004 (3)

S. Jensen and M. E. Anderson, “Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction,” Appl. Opt. 43, 883–893 (2004).
[Crossref] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
[Crossref]

2003 (2)

2000 (1)

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

1999 (2)

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[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]

1994 (1)

1993 (1)

1992 (1)

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

1982 (1)

Anderson, M. E.

S. Jensen and M. E. Anderson, “Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction,” Appl. Opt. 43, 883–893 (2004).
[Crossref] [PubMed]

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

Barnes, T. H.

Biegert, J.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
[Crossref] [PubMed]

Chen, J. L.

Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).

Couairon, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

de Araujo, L. E. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

De Silvestri, S.

DeLong, K. W.

Deng, Y. Q.

Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

Hong, J. -C.

J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
[Crossref]

Hunter, J.

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]

Imamoto, Y.

Y. Morimoto and Y. Imamoto, “Application of wavelet transform to displacement and strain measurement by grid method,” in Proc. of 1995 SEM Spring Conf. on Exp. Mech. (Society for Experimental Mechanics, MI, 1995), 898–903.

Ina, H.

Jensen, S.

Ji, X. H.

Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).

Kane, D. J.

Keller, U.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
[Crossref] [PubMed]

Kim, Y. Y.

J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
[Crossref]

Kito, T.

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.

Kobayashi, S.

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

Kosik, E. M.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

Morimoto, Y.

Y. Morimoto and Y. Imamoto, “Application of wavelet transform to displacement and strain measurement by grid method,” in Proc. of 1995 SEM Spring Conf. on Exp. Mech. (Society for Experimental Mechanics, MI, 1995), 898–903.

Morita, R.

K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
[Crossref] [PubMed]

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.

Mysyrowicz, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

Nisoli, M.

Oka, K.

Qin, Y. W.

Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).

Sansone, G.

Schenkel, B.

Stagira, S.

Suguro, A.

Svelto, O.

Szu, H. H.

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

Takeda, M.

Tan, S. M.

Telfer, B.

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

Trebino, R.

Vozzi, C.

Walmsley, I. A.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[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]

Watkins, L. R.

White, W. E.

Yamane, K.

K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
[Crossref] [PubMed]

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.

Yamashita, M.

K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
[Crossref] [PubMed]

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. B (2)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

IEEE J. Quantum Electron. (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]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

Opt. Lett. (4)

Society for Exp. Mech. (1)

J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
[Crossref]

Other (4)

Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).

Y. Morimoto and Y. Imamoto, “Application of wavelet transform to displacement and strain measurement by grid method,” in Proc. of 1995 SEM Spring Conf. on Exp. Mech. (Society for Experimental Mechanics, MI, 1995), 898–903.

C. K. Chui ed., An introduction to wavelets (Academic Press, Boston, 1992).

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.

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Figures (5)

Fig. 1.
Fig. 1.

WT graphics for zero phases: (a) magnitude topography. (b) phase topography.

Fig. 2.
Fig. 2.

WT graphics for high order phases.

Fig. 3.
Fig. 3.

Measured spectral shearing interferogram.

Fig. 4.
Fig. 4.

Results of WT: (a) Magnitude topography. (b) Phase topography. (The pink colored curve represents the maximum value of the magnitude.)

Fig. 5.
Fig. 5.

(a) Spectrum and reconstructed phase with WT and FT techniques. (b) Reconstructed pulse profiles in comparison with the transform-limited pulses.

Equations (4)

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W ( Δ ω , ω ) = 1 Δ ω + f ( ω ' ) ψ * ( ω ω Δ ω ) d ω
t = 2 π Δ ω
W ( t , ω ) = t 2 π + f ( ω ' ) ψ * [ ( ω ' ω ) · t 2 π ] d ω '
ψ ( ω ' ) = e ( ω ' 2 2 σ 2 + i 2 π ω ' ) ( σ 2 π ) 1 4

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