Abstract

We introduce a self-reference method of parabolic temporal lensing and aberration-free spectrotemporal imaging for the direct measurements of femtosecond waveforms, with the goal of designing an ultrafast optical oscilloscope. Our method is based on dispersive stretching of the signal pulse and afterwards cancellation of the dispersion-induced phase in a quadratic nonlinear process by adding a reference parabolic phase (instead of Kerr lensing of traditional spectral compression). We have implemented the method through sum-frequency generation using the self-shaped nonlinear-dispersive similariton as a reference pulse and have demonstrated it experimentally for the direct measurements of amplitude- and phase-modulated pulses on a femtosecond time scale.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  5. P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  21. L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
    [CrossRef]
  22. A. V. Zohrabyan, A. A. Kutuzian, V. Zh. Ninoyan, and L. Kh. Mouradian, “Spectral compression of picosecond pulses by means of cross phase modulation,” AIP Conf. Proc. 406, 395-401 (1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  29. L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.
  30. A. A. Kutuzyan, T. G. Mansuryan, A. A. Kirakosyan, and L. K. Mouradian, “Self-forming of temporal dark soliton in spectral compressor,” Proc. SPIE 5135, 156-160 (2003).
    [CrossRef]
  31. F. Louradour, E. Lopez-Lago, V. Couderc, V. Messager, and A. Barthélémy, “Dispersive-scan measurement of the fast component of the third-order nonlinearity of bulk materials and waveguides,” Opt. Lett. 24, 1361-1363 (1999).
    [CrossRef]
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    [CrossRef]
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  34. L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.
  35. G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.
  36. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).
  37. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

2005 (1)

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Time-to-frequency conversion of optical waveforms using a single time lens system,” Phys. Scr. T118, 115-117 (2005).
[CrossRef]

2004 (4)

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Spectro-temporal imaging of optical pulses with a single time lens,” IEEE Photon. Technol. Lett. 16, 882-884 (2004).
[CrossRef]

P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29, 775 (2004).
[CrossRef] [PubMed]

B. Xu, J. M. Gunn, M. Dela Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B 23, 750-759 (2004).
[CrossRef]

2003 (4)

2001 (1)

2000 (2)

B. R. Washburn, J. A. Buck, and S. E. Ralph, “Transform-limited spectral compression due to self-phase modulation in fibers,” Opt. Lett. 25, 445-447 (2000).
[CrossRef]

L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795-801 (2000).
[CrossRef]

1999 (2)

1998 (2)

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792-794 (1998).
[CrossRef]

1997 (3)

1995 (2)

N. L. Markaryan and L. Kh. Muradyan, “Determination of the temporal profiles of ultrashort pulses by a fibre-optic compression technique,” Quantum Electron. 25, 668-670 (1995).
[CrossRef]

A. V. Zohrabian and L. Kh. Mouradian, “Compression of the spectrum of picosecond pulses,” Quantum Electron. 25, 695-697 (1995).
[CrossRef]

1994 (2)

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664-666 (1994).
[CrossRef] [PubMed]

1993 (2)

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]

M. Oberthaler and R. A. Hopfel, “Special narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63, 1017-1019 (1993).
[CrossRef]

1991 (1)

N. L. Margaryan, L. Kh. Mouradian, and T. A. Papazyan, “Spectral compression of ultrashort laser pulses,” Sov. J. Quantum Electron. 21, 783-785 (1991).
[CrossRef]

1986 (1)

M. Vampouille, J. Marty, and C. Froehly, “Optical frequency intermodulation between two picosecond laser pulses,” IEEE J. Quantum Electron. 22, 192-194 (1986).
[CrossRef]

1984 (1)

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, “Observation et applications des modulations de fréquence dans les fibers unimodales,” J. Opt. (Paris) 15, 385-390 (1984).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Akturk, S.

Arons, E.

Azana, J.

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Time-to-frequency conversion of optical waveforms using a single time lens system,” Phys. Scr. T118, 115-117 (2005).
[CrossRef]

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Spectro-temporal imaging of optical pulses with a single time lens,” IEEE Photon. Technol. Lett. 16, 882-884 (2004).
[CrossRef]

J. Azana, “Time-to-frequency conversion using a single time lens,” Opt. Commun. 217, 205-209 (2003).
[CrossRef]

Banyai, W. C.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

Barthélémy, A.

V. Messager, F. Louradour, C. Froehly, and A. Barthélémy, “Coherent measurement of short laser pulses based on spectral interferometry resolved in time,” Opt. Lett. 28, 743-745 (2003).
[CrossRef] [PubMed]

L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795-801 (2000).
[CrossRef]

F. Louradour, E. Lopez-Lago, V. Couderc, V. Messager, and A. Barthélémy, “Dispersive-scan measurement of the fast component of the third-order nonlinearity of bulk materials and waveguides,” Opt. Lett. 24, 1361-1363 (1999).
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, “Observation et applications des modulations de fréquence dans les fibers unimodales,” J. Opt. (Paris) 15, 385-390 (1984).
[CrossRef]

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

L. Kh. Mouradian, F. Louradour, C. Froehly, and A. Barthélémy, “Self- and cross-phase modulation of chirped pulses: spectral imaging of femtosecond pulses,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of OSA Technical Digest Series (Optical Society of America, 1998), paper NFC4.

L. Kh. Mouradian, A. V. Zohrabian, C. Froehly, F. Louradour, and A. Barthélémy, “Spectral imaging of pulses temoral profile,” in Conference on Lasers and Electro-Optics (CLEO/Europe), OSA Technical Digest Series (Optical Society of America, 1998), paper CMA5.
[CrossRef]

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Bennett, C. V.

Berger, N. K.

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Time-to-frequency conversion of optical waveforms using a single time lens system,” Phys. Scr. T118, 115-117 (2005).
[CrossRef]

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Spectro-temporal imaging of optical pulses with a single time lens,” IEEE Photon. Technol. Lett. 16, 882-884 (2004).
[CrossRef]

Bloom, D. M.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

Buck, J. A.

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Chiu, T. H.

Clark, S. W.

Colombeau, B.

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, “Observation et applications des modulations de fréquence dans les fibers unimodales,” J. Opt. (Paris) 15, 385-390 (1984).
[CrossRef]

Couderc, V.

Dantus, M.

Dela Cruz, M.

Emplit, P.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

Emplit, Ph.

P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

Fainman, Y.

Fischer, B.

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Time-to-frequency conversion of optical waveforms using a single time lens system,” Phys. Scr. T118, 115-117 (2005).
[CrossRef]

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Spectro-temporal imaging of optical pulses with a single time lens,” IEEE Photon. Technol. Lett. 16, 882-884 (2004).
[CrossRef]

Froehly, C.

P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

V. Messager, F. Louradour, C. Froehly, and A. Barthélémy, “Coherent measurement of short laser pulses based on spectral interferometry resolved in time,” Opt. Lett. 28, 743-745 (2003).
[CrossRef] [PubMed]

L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795-801 (2000).
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

M. Vampouille, J. Marty, and C. Froehly, “Optical frequency intermodulation between two picosecond laser pulses,” IEEE J. Quantum Electron. 22, 192-194 (1986).
[CrossRef]

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, “Observation et applications des modulations de fréquence dans les fibers unimodales,” J. Opt. (Paris) 15, 385-390 (1984).
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabian, C. Froehly, F. Louradour, and A. Barthélémy, “Spectral imaging of pulses temoral profile,” in Conference on Lasers and Electro-Optics (CLEO/Europe), OSA Technical Digest Series (Optical Society of America, 1998), paper CMA5.
[CrossRef]

L. Kh. Mouradian, F. Louradour, C. Froehly, and A. Barthélémy, “Self- and cross-phase modulation of chirped pulses: spectral imaging of femtosecond pulses,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of OSA Technical Digest Series (Optical Society of America, 1998), paper NFC4.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Godil, A. A.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

Gunn, J. M.

Haelterman, M.

P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

Hopfel, R. A.

M. Oberthaler and R. A. Hopfel, “Special narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63, 1017-1019 (1993).
[CrossRef]

Iaconis, C.

Ilday, F. Ö.

Kalashyan, M.

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

Kane, D. J.

Kauffman, M. T.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

Kimmel, M.

Kirakosyan, A. A.

A. A. Kutuzyan, T. G. Mansuryan, A. A. Kirakosyan, and L. K. Mouradian, “Self-forming of temporal dark soliton in spectral compressor,” Proc. SPIE 5135, 156-160 (2003).
[CrossRef]

Kockaert, P.

P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

Kolner, B. H.

Kutuzian, A. A.

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

A. V. Zohrabyan, A. A. Kutuzian, V. Zh. Ninoyan, and L. Kh. Mouradian, “Spectral compression of picosecond pulses by means of cross phase modulation,” AIP Conf. Proc. 406, 395-401 (1997).

Kutuzyan, A. A.

A. A. Kutuzyan, T. G. Mansuryan, A. A. Kirakosyan, and L. K. Mouradian, “Self-forming of temporal dark soliton in spectral compressor,” Proc. SPIE 5135, 156-160 (2003).
[CrossRef]

Leith, E. N.

Levit, B.

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Time-to-frequency conversion of optical waveforms using a single time lens system,” Phys. Scr. T118, 115-117 (2005).
[CrossRef]

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Spectro-temporal imaging of optical pulses with a single time lens,” IEEE Photon. Technol. Lett. 16, 882-884 (2004).
[CrossRef]

Li, M.

Lopez-Lago, E.

Louradour, F.

V. Messager, F. Louradour, C. Froehly, and A. Barthélémy, “Coherent measurement of short laser pulses based on spectral interferometry resolved in time,” Opt. Lett. 28, 743-745 (2003).
[CrossRef] [PubMed]

L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795-801 (2000).
[CrossRef]

F. Louradour, E. Lopez-Lago, V. Couderc, V. Messager, and A. Barthélémy, “Dispersive-scan measurement of the fast component of the third-order nonlinearity of bulk materials and waveguides,” Opt. Lett. 24, 1361-1363 (1999).
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

L. Kh. Mouradian, F. Louradour, C. Froehly, and A. Barthélémy, “Self- and cross-phase modulation of chirped pulses: spectral imaging of femtosecond pulses,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of OSA Technical Digest Series (Optical Society of America, 1998), paper NFC4.

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

L. Kh. Mouradian, A. V. Zohrabian, C. Froehly, F. Louradour, and A. Barthélémy, “Spectral imaging of pulses temoral profile,” in Conference on Lasers and Electro-Optics (CLEO/Europe), OSA Technical Digest Series (Optical Society of America, 1998), paper CMA5.
[CrossRef]

Lozovoy, V. V.

Mansuryan, T.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

Mansuryan, T. G.

A. A. Kutuzyan, T. G. Mansuryan, A. A. Kirakosyan, and L. K. Mouradian, “Self-forming of temporal dark soliton in spectral compressor,” Proc. SPIE 5135, 156-160 (2003).
[CrossRef]

Margaryan, N. L.

N. L. Margaryan, L. Kh. Mouradian, and T. A. Papazyan, “Spectral compression of ultrashort laser pulses,” Sov. J. Quantum Electron. 21, 783-785 (1991).
[CrossRef]

Markaryan, N. L.

N. L. Markaryan and L. Kh. Muradyan, “Determination of the temporal profiles of ultrashort pulses by a fibre-optic compression technique,” Quantum Electron. 25, 668-670 (1995).
[CrossRef]

L. Kh. Muradyan, N. L. Markaryan, T. A. Papazyan, and A. A. Ohanyan, “Self-action of chirped pulses: spectral compression,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, 1990), paper CTUH32.

Marty, J.

M. Vampouille, J. Marty, and C. Froehly, “Optical frequency intermodulation between two picosecond laser pulses,” IEEE J. Quantum Electron. 22, 192-194 (1986).
[CrossRef]

Mazurenko, Y. T.

Messager, V.

Mouradian, L.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

Mouradian, L. K.

A. A. Kutuzyan, T. G. Mansuryan, A. A. Kirakosyan, and L. K. Mouradian, “Self-forming of temporal dark soliton in spectral compressor,” Proc. SPIE 5135, 156-160 (2003).
[CrossRef]

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

Mouradian, L. Kh.

L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795-801 (2000).
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

A. V. Zohrabyan, A. A. Kutuzian, V. Zh. Ninoyan, and L. Kh. Mouradian, “Spectral compression of picosecond pulses by means of cross phase modulation,” AIP Conf. Proc. 406, 395-401 (1997).

A. V. Zohrabian and L. Kh. Mouradian, “Compression of the spectrum of picosecond pulses,” Quantum Electron. 25, 695-697 (1995).
[CrossRef]

N. L. Margaryan, L. Kh. Mouradian, and T. A. Papazyan, “Spectral compression of ultrashort laser pulses,” Sov. J. Quantum Electron. 21, 783-785 (1991).
[CrossRef]

L. Kh. Mouradian, F. Louradour, C. Froehly, and A. Barthélémy, “Self- and cross-phase modulation of chirped pulses: spectral imaging of femtosecond pulses,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of OSA Technical Digest Series (Optical Society of America, 1998), paper NFC4.

L. Kh. Mouradian, A. V. Zohrabian, C. Froehly, F. Louradour, and A. Barthélémy, “Spectral imaging of pulses temoral profile,” in Conference on Lasers and Electro-Optics (CLEO/Europe), OSA Technical Digest Series (Optical Society of America, 1998), paper CMA5.
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Muradyan, L. Kh.

N. L. Markaryan and L. Kh. Muradyan, “Determination of the temporal profiles of ultrashort pulses by a fibre-optic compression technique,” Quantum Electron. 25, 668-670 (1995).
[CrossRef]

L. Kh. Muradyan, N. L. Markaryan, T. A. Papazyan, and A. A. Ohanyan, “Self-action of chirped pulses: spectral compression,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, 1990), paper CTUH32.

Ninoyan, V. J.

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

Ninoyan, V. Zh.

A. V. Zohrabyan, A. A. Kutuzian, V. Zh. Ninoyan, and L. Kh. Mouradian, “Spectral compression of picosecond pulses by means of cross phase modulation,” AIP Conf. Proc. 406, 395-401 (1997).

Nuss, M. C.

Oberthaler, M.

M. Oberthaler and R. A. Hopfel, “Special narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63, 1017-1019 (1993).
[CrossRef]

Ohanyan, A. A.

L. Kh. Muradyan, N. L. Markaryan, T. A. Papazyan, and A. A. Ohanyan, “Self-action of chirped pulses: spectral compression,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, 1990), paper CTUH32.

O'Shea, P.

Palanjyan, K.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

Papazyan, T. A.

N. L. Margaryan, L. Kh. Mouradian, and T. A. Papazyan, “Spectral compression of ultrashort laser pulses,” Sov. J. Quantum Electron. 21, 783-785 (1991).
[CrossRef]

L. Kh. Muradyan, N. L. Markaryan, T. A. Papazyan, and A. A. Ohanyan, “Self-action of chirped pulses: spectral compression,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, 1990), paper CTUH32.

Partovi, A.

Pastirk, I.

Piche, M.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Ralph, S. E.

Rousseau, G.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Sun, P. C.

Tien, A.

Trebino, R.

Vampouille, M.

M. Vampouille, J. Marty, and C. Froehly, “Optical frequency intermodulation between two picosecond laser pulses,” IEEE J. Quantum Electron. 22, 192-194 (1986).
[CrossRef]

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, “Observation et applications des modulations de fréquence dans les fibers unimodales,” J. Opt. (Paris) 15, 385-390 (1984).
[CrossRef]

Villeneuve, A.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Wagner, R.

Walmsley, I. A.

Washburn, B. R.

Weiner, A. M.

Wise, F. W.

Xu, B.

Yavrian, A.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

Yesayan, G.

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

Zeytunyan, A.

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

Zohrabian, A. V.

A. V. Zohrabian and L. Kh. Mouradian, “Compression of the spectrum of picosecond pulses,” Quantum Electron. 25, 695-697 (1995).
[CrossRef]

L. Kh. Mouradian, A. V. Zohrabian, C. Froehly, F. Louradour, and A. Barthélémy, “Spectral imaging of pulses temoral profile,” in Conference on Lasers and Electro-Optics (CLEO/Europe), OSA Technical Digest Series (Optical Society of America, 1998), paper CMA5.
[CrossRef]

Zohrabyan, A. V.

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

A. V. Zohrabyan, A. A. Kutuzian, V. Zh. Ninoyan, and L. Kh. Mouradian, “Spectral compression of picosecond pulses by means of cross phase modulation,” AIP Conf. Proc. 406, 395-401 (1997).

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

AIP Conf. Proc. (1)

A. V. Zohrabyan, A. A. Kutuzian, V. Zh. Ninoyan, and L. Kh. Mouradian, “Spectral compression of picosecond pulses by means of cross phase modulation,” AIP Conf. Proc. 406, 395-401 (1997).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Oberthaler and R. A. Hopfel, “Special narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63, 1017-1019 (1993).
[CrossRef]

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Vampouille, J. Marty, and C. Froehly, “Optical frequency intermodulation between two picosecond laser pulses,” IEEE J. Quantum Electron. 22, 192-194 (1986).
[CrossRef]

L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795-801 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

P. Kockaert, M. Haelterman, Ph. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Spectro-temporal imaging of optical pulses with a single time lens,” IEEE Photon. Technol. Lett. 16, 882-884 (2004).
[CrossRef]

J. Opt. (Paris) (1)

M. Vampouille, A. Barthélémy, B. Colombeau, and C. Froehly, “Observation et applications des modulations de fréquence dans les fibers unimodales,” J. Opt. (Paris) 15, 385-390 (1984).
[CrossRef]

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

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

Opt. Commun. (1)

J. Azana, “Time-to-frequency conversion using a single time lens,” Opt. Commun. 217, 205-209 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (9)

V. Messager, F. Louradour, C. Froehly, and A. Barthélémy, “Coherent measurement of short laser pulses based on spectral interferometry resolved in time,” Opt. Lett. 28, 743-745 (2003).
[CrossRef] [PubMed]

V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29, 775 (2004).
[CrossRef] [PubMed]

S. W. Clark, F. Ö. Ilday, and F. W. Wise, “Fiber delivery of femtosecond pulses from a Ti:sapphire laser,” Opt. Lett. 26, 1320-1322 (2001).
[CrossRef]

B. R. Washburn, J. A. Buck, and S. E. Ralph, “Transform-limited spectral compression due to self-phase modulation in fibers,” Opt. Lett. 25, 445-447 (2000).
[CrossRef]

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]

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664-666 (1994).
[CrossRef] [PubMed]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792-794 (1998).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Upconversion time microscope demonstrating 103× magnification of femtosecond waveforms,” Opt. Lett. 24, 783-785 (1999).
[CrossRef]

F. Louradour, E. Lopez-Lago, V. Couderc, V. Messager, and A. Barthélémy, “Dispersive-scan measurement of the fast component of the third-order nonlinearity of bulk materials and waveguides,” Opt. Lett. 24, 1361-1363 (1999).
[CrossRef]

Phys. Scr. (1)

J. Azana, N. K. Berger, B. Levit, and B. Fischer, “Time-to-frequency conversion of optical waveforms using a single time lens system,” Phys. Scr. T118, 115-117 (2005).
[CrossRef]

Proc. SPIE (2)

L. Kh. Mouradian, A. V. Zohrabyan, V. J. Ninoyan, A. A. Kutuzian, C. Froehly, F. Louradour, and A. Barthélémy, “Characterization of optical signals in fiber-optic Fourier converter,” Proc. SPIE 3418, 78-85 (1998).
[CrossRef]

A. A. Kutuzyan, T. G. Mansuryan, A. A. Kirakosyan, and L. K. Mouradian, “Self-forming of temporal dark soliton in spectral compressor,” Proc. SPIE 5135, 156-160 (2003).
[CrossRef]

Quantum Electron. (2)

N. L. Markaryan and L. Kh. Muradyan, “Determination of the temporal profiles of ultrashort pulses by a fibre-optic compression technique,” Quantum Electron. 25, 668-670 (1995).
[CrossRef]

A. V. Zohrabian and L. Kh. Mouradian, “Compression of the spectrum of picosecond pulses,” Quantum Electron. 25, 695-697 (1995).
[CrossRef]

Sov. J. Quantum Electron. (1)

N. L. Margaryan, L. Kh. Mouradian, and T. A. Papazyan, “Spectral compression of ultrashort laser pulses,” Sov. J. Quantum Electron. 21, 783-785 (1991).
[CrossRef]

Other (9)

L. Kh. Muradyan, N. L. Markaryan, T. A. Papazyan, and A. A. Ohanyan, “Self-action of chirped pulses: spectral compression,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, 1990), paper CTUH32.

L. Kh. Mouradian, A. V. Zohrabian, C. Froehly, F. Louradour, and A. Barthélémy, “Spectral imaging of pulses temoral profile,” in Conference on Lasers and Electro-Optics (CLEO/Europe), OSA Technical Digest Series (Optical Society of America, 1998), paper CMA5.
[CrossRef]

L. Kh. Mouradian, F. Louradour, C. Froehly, and A. Barthélémy, “Self- and cross-phase modulation of chirped pulses: spectral imaging of femtosecond pulses,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of OSA Technical Digest Series (Optical Society of America, 1998), paper NFC4.

L. Kh. Mouradian, A. V. Zohrabyan, A. Villeneuve, A. Yavrian, G. Rousseau, M. Piche, C. Froehly, F. Louradour, and A. Barthélémy, “Applications of temporal Kerr lensing to signal manipulation and analysis,” in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 39 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), paper CTuH6.

A. Zeytunyan, T. Mansuryan, M. Kalashyan, G. Yesayan, L. K. Mouradian, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging by sum frequency generation: ultrafast optical oscilloscope,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FThD3.

L. K. Mouradian, T. Mansuryan, A. Zeytunyan, M. Kalashyan, G. Yesayan, F. Louradour, and A. Barthélémy, “Spectro-temporal imaging through aberration-free temporal lensing: an ultrafast optical oscilloscope,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper NThB3.

G. Yesayan, K. Palanjyan, T. Mansuryan, A. Zeytunyan, L. Mouradian, P. Kockaert, and P. Emplit, “Nonlinear-spectronic similariton of single-mode fiber without gain,” in Nonlinear Photonics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JWA18.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

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Figures (8)

Fig. 1
Fig. 1

Principle of temporal lensing and STI through SFG.

Fig. 2
Fig. 2

Schematic of the SFG-STI setup.

Fig. 3
Fig. 3

Performance of the temporal lensing through the SFG-spectral compression.

Fig. 4
Fig. 4

Performance of the STI through parabolic temporal lensing in SFG.

Fig. 5
Fig. 5

12.3 × SFG-spectral compression through parabolic temporal lensing: (a) the spectrum of the signal, (b) the relevant SFG spectrum in the absence of the D-line, (c) the SFG-compressed spectrum.

Fig. 6
Fig. 6

2.53 × SFG-spectral compression through parabolic temporal lensing: (a) the SFG spectrum of the signal in the absence of the D-line, (b) the SFG-compressed spectrum.

Fig. 7
Fig. 7

(a) Temporal delay ( Δ t ) between the signal and reference pulses results in frequency shift ( Δ λ ) of the SFG-signal, along with spectral compression. (b) The linear dependence λ ( t ) shows the STI scaling coefficient α ( Δ λ Δ t ) 1 = const .

Fig. 8
Fig. 8

STI of different pulses: (a) pulses stretched in glasses with different thickness; (b), (c), (d), (f) two-peak pulses in the 12 × , 2.5 × , and 1.2 × regimes of spectral compression; (e) a pulse with substructure. On the right, autocorrelation tracks of signal pulses and their images are shown.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

A out ( t ) A d ( t ) × A f ( t ) .
{ D - induced phase of [ A d ( t ) ] + phase of [ A f ( t ) ] } = 0 ,
A f ( t ) = Constant during A d ( t ) ,
S out ( ω ) I in ( t ) .
A d ( t ) = ( i γ d ) 1 2 exp ( i γ d t 2 2 ) FT [ A in ( t ) exp ( i γ d t 2 2 ) ] ω = γ t .
A d ( t ) ( i γ d ) 1 2 exp ( i γ d t 2 2 ) FT [ A in ( t ) ] ω = γ t .
A f ( t ) ( i γ f ) 1 2 exp ( i γ f t 2 2 ) FT [ A f ( t ) ] ω = γ t ,
A out ( t ) FT [ A in ( t ) exp ( i γ d t 2 2 ) ] × FT [ A f ( t ) ] exp [ i ( γ d + γ f ) t 2 2 ] .
γ d + γ f = 0 .
A f ( t ) FT [ A f ( t ) ] ω = γ t = const , for t 2 Δ t d ,
FT [ A f ( t ) ] ω = const , for ω 2 Δ ω o .
A out ( t ) FT [ A in ( t ) exp ( i γ t 2 2 ) ] ω = γ t .
FT [ A out ( t ) ] ω = γ t A in ( t ) exp ( i γ t 2 2 ) ,
S out ( ω ) = FT [ A out ( t ) ω = γ t 2 A in ( t ) 2 = I in ( t ) .
FT [ A out ( t ) ] ω = γ t FT [ A ( t ) ] FT [ B ( t ) ] exp [ i ω 2 ( 2 γ ) ] A in ( t ) exp ( i γ t 2 2 ) r ( t ) ,
A ( t ) FT [ A in ( t ) ] × FT [ B ( t ) ] exp ( i Δ γ t 2 2 ) FT [ A in ( t ) ] × FT [ B ( t ) ] ω γ t
FT [ A ( t ) ] A in ( t ) B ( t ) t = ω γ ,

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