Abstract

We present the results of the spectral analysis of intense ultrashort laser pulses propagating through nonlinear transparent media. We discuss the spectral features characteristic of the self-phase-modulation process, which is the most prominent process during nonguided propagation in the weakly nonlinear regime. We describe an application of automatic pulse phase retrieval based on the Kerr-like nonlinearity.

© 1996 Optical Society of America

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1995 (5)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak power femtosecond laser pulses in air,” Opt. Lett. 20, 73 (1995).
[CrossRef] [PubMed]

B. Kohler, J. L. Krause, F. Raksi, K. R. Wilson, V. V. Yakovlev, R. M. Whitnell, and Y. J. Yan, “Controlling the future of matter,” Acc. Chem. Res. 28, 133 (1995).
[CrossRef]

B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. Wilson, N. Schwentner, R. M. Whitnell, and Y. J. Yan, “Quantum control of wave packet evolution with tailored femtosecond pulses,” Phys. Rev. Lett. 74, 3360 (1995).
[CrossRef] [PubMed]

A. Sullivan and W. E. White, “Phase control for production of high-fidelity optical pulses for chirped-pulse amplification,” Opt. Lett. 20, 192 (1995).
[CrossRef] [PubMed]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

1994 (29)

V. Wong and I. A. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 19, 287 (1994).
[CrossRef] [PubMed]

S. P. LeBlanc and R. Sauerbrey, “Ultrashort pulse characterization using plasma-induced cross-phase modulation,” Opt. Commun. 111, 297 (1994).
[CrossRef]

C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, “Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses,” Opt. Lett. 19, 737 (1994).
[CrossRef] [PubMed]

J. Paye, “How to measure the amplitude and phase of an ultrashort light pulse with an autocorrelator and a spectrometer,” IEEE J. Quantum Electron. 30, 2693 (1994).
[CrossRef]

K. W. DeLong and R. Trebino, “Improved ultrashort pulse-retrieval algorithm for frequency-resolved optical gating,” J. Opt. Soc. Am. A 11, 2429 (1994).
[CrossRef]

K. W. DeLong, R. Trebino, and D. J. Kane, “Comparison of ultrashort pulse frequency-resolved optical gating traces for three common beam geometries,” J. Opt. Soc. Am. B 11, 1595 (1994).
[CrossRef]

K. W. DeLong, R. Trebino, D. J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206 (1994).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, “Pulse retrieval in frequency-resolved optical gating based on the method of generalized projections,” Opt. Lett. 19, 2152 (1994).
[CrossRef] [PubMed]

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827 (1994).
[CrossRef]

B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

I. Brener, P. C. M. Planken, M. C. Nuss, M. S. C. Luo, S. L. Chuang, L. Pfeiffer, D. E. Leaird, and A. M. Weiner, “Coherent control of terahertz emission and carrier populations in semiconductor heterostructures,” J. Opt. Soc. Am. B 11, 2457 (1994).
[CrossRef]

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultra-broadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Pulse evolution in a broad-bandwidth Ti:sapphire laser,” Opt. Lett. 19, 1149 (1994).
[CrossRef] [PubMed]

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, 2834 (1994).
[CrossRef]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692 (1994).
[CrossRef] [PubMed]

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, “Temporal aberrations due to misalignments of a stretcher–compressor system and compensation,” IEEE J. Quantum Electron. 30, 1662 (1994).
[CrossRef]

J. R. Houliston, M. H. Key, and I. N. Ross, “Modelling of saturated chirped pulse amplification and recompression,” Opt. Commun. 108, 111 (1994).
[CrossRef]

J. Zhou, C.-P. Huang, C. Shi, M. M. Murnane, and H. C. Kapteyn, “Generation of 21-fs millijoule-energy pulses by use of Ti:sapphire,” Opt. Lett. 19, 126 (1994).
[CrossRef] [PubMed]

C. P. J. Barty, C. L. Gordon, and B. E. Lemoff, “Multi-terawatt 30-fs Ti:sapphire laser system,” Opt. Lett. 19, 1442 (1994).
[CrossRef] [PubMed]

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Backsbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

S. Wilks, P. E. Young, J. Hammer, M. Tabak, and W. L. Kruer, “Spreading of intense laser beams due to filamentation,” Phys. Rev. Lett. 73, 2994 (1994).
[CrossRef] [PubMed]

D. Strickland and P. B. Corkum, “Resistance of short pulses to self-focusing,” J. Opt. Soc. Am. B 11, 492 (1994).
[CrossRef]

X. D. Cao, G. P. Agrawal, and C. J. McKinstrie, “Self-focusing of chirped optical pulses in nonlinear dispersive media,” Phys. Rev. A 49, 4085 (1994).
[CrossRef] [PubMed]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

M. Ciarocca, J. P. Marangos, D. D. Burgess, M. H. R. Hutchinson, R. A. Smith, S. C. Rae, and K. Burnett, “Spectral and spatial modifications to an intense 1 mm laser pulse interacting with a dense argon gas,” Opt. Commun. 110, 425 (1994).
[CrossRef]

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell (∼100 Å) and L-shell (∼6 Å) transitions,” Phys. Rev. Lett. 72, 1810 (1994).
[CrossRef] [PubMed]

A. B. Borisov, X. Shi, V. B. Karpov, V. V. Korobkin, J. C. Solem, O. B. Shiryaev, A. McPherson, K. Boyer, and C. K. Rhodes, “Stable self-channeling of intense ultraviolet pulses in underdense plasma, producing channels exceeding 100 Rayleigh lengths,” J. Opt. Soc. Am. B 11, 1941 (1994).
[CrossRef]

A. Sullivan, H. Hamster, S. P. Gordon, R. W. Falcone, and H. Nathel, “Propagation of intense, ultrashort laser pulses in plasmas,” Opt. Lett. 19, 1544 (1994).
[CrossRef] [PubMed]

Q. Z. Wang, Q. D. Liu, D. Liu, P. P. Ho, and R. R. Alfano, “High-resolution spectra of self-phase modulation in optical fibers,” J. Opt. Soc. Am. B 11, 1084 (1994).
[CrossRef]

1993 (16)

C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409 (1993).
[CrossRef] [PubMed]

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
[CrossRef] [PubMed]

J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[CrossRef] [PubMed]

S. P. Le Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. B 10, 1801 (1993).
[CrossRef]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, “Compact and efficient multipass Ti:sapphire system for femtosecond chirped-pulse amplification at the terawatt level,” Opt. Lett. 18, 140 (1993).
[CrossRef]

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

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, 4051 (1993).
[CrossRef] [PubMed]

B. E. Lemoff and C. P. J. Barty, “Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses,” Opt. Lett. 18, 1651 (1993).
[CrossRef] [PubMed]

W. E. White, F. G. Patterson, R. L. Combs, D. F. Price, and R. L. Shepherd, “Compensation of higher-order frequency-dependent phase terms in chirped-pulse amplification systems,” Opt. Lett. 18, 1343 (1993).
[CrossRef] [PubMed]

M. Beck, M. G. Raymer, I. A. Walmsley, and V. Wong, “Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses,” Opt. Lett. 18, 2041 (1993).
[CrossRef] [PubMed]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101 (1993).
[CrossRef]

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, “Measurement of the amplitude and phase of ultrashort light pulses from spectrally resolved autocorrelation,” Opt. Lett. 18, 1946 (1993).
[CrossRef] [PubMed]

Y.-H. Chuang, L. Zheng, and D. D. Meyerhofer, “Propagation of light pulses in a chirped-pulse-amplification laser,” IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

M. M. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032 (1993).
[CrossRef] [PubMed]

1992 (10)

J. S. Melinger, A. Hariharan, S. R. Gandhi, and W. S. Warren, “Generation of narrowband inversion with broadband laser pulses,” Phys. Rev. Lett. 68, 2000 (1992).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum. Electron. 28, 908 (1992).
[CrossRef]

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

P. Brumer and M. Shapiro, “Laser control of molecular processes,” Annu. Rev. Phys. Chem. 43, 257 (1992).
[CrossRef] [PubMed]

S. A. Rice, “New ideas for guiding the evolution of a quantum system,” Science 258, 412 (1992).
[CrossRef] [PubMed]

P. Chernev and V. Petrov, “Self-focusing of light pulses in the presence of normal group-velocity dispersion,” Opt. Lett. 17, 172 (1992).
[CrossRef] [PubMed]

B. M. Penetrante, J. N. Bardsley, W. M. Wood, C. W. Siders, and M. C. Downer, “Ionization-induced frequency shifts in intense femtosecond laser pulses,” J. Opt. Soc. Am. B 9, 2032 (1992).
[CrossRef]

J. K. Crane, M. D. Perry, S. Herman, and R. W. Falcone, “High-field harmonic generation in helium,” Opt. Lett. 17, 1256 (1992).
[CrossRef] [PubMed]

J. D. Kmetec, C. L. Gordon, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV x-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68, 1527 (1992).
[CrossRef] [PubMed]

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

1991 (4)

M. M. Murnane, H. C. Kapteyn, M. D. Rosen, and R. W. Falcone, “Ultrafast x-ray pulses from laser-produced plasmas,” Science 251, 531 (1991).
[CrossRef] [PubMed]

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

C. Yan and J.-C. Diels, “Amplitude and phase recording of ultrashort pulses,” J. Opt. Soc. Am. B 8, 1259 (1991).
[CrossRef]

J. L. A. Chilla and O. E. Martinez, “Direct determination of the amplitude and the phase of femtosecond light pulses,” Opt. Lett. 16, 39 (1991).,
[CrossRef] [PubMed]

1990 (2)

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65, 2355 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317 (1990).
[CrossRef] [PubMed]

1989 (2)

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

P. B. Corkum and C. Rolland, “Femtosecond continua produced in gases,” IEEE J. Quantum Electron. 25, 2634 (1989).
[CrossRef]

1988 (1)

M. Neito-Vesperinas, R. Navarro, and F. J. Fuentes, “Performance of a simulated-annealing algorithm for phase retrieval,” J. Opt. Soc. Am. A. 5, 30 (1988).
[CrossRef]

1987 (1)

1985 (1)

1982 (1)

1981 (1)

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109 (1981).
[CrossRef]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1978 (1)

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 448 (1978).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129 (1976).
[CrossRef]

1975 (2)

Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Agrawal, G. P.

X. D. Cao, G. P. Agrawal, and C. J. McKinstrie, “Self-focusing of chirped optical pulses in nonlinear dispersive media,” Phys. Rev. A 49, 4085 (1994).
[CrossRef] [PubMed]

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109 (1981).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Alfano, R. R.

Antonetti, A.

Auld, B. A.

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827 (1994).
[CrossRef]

Backsbaum, P. H.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Backsbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

Balcou, Ph.

C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
[CrossRef] [PubMed]

Bandrauk, A. D.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65, 2355 (1990).
[CrossRef] [PubMed]

Bardsley, J. N.

Barty, C. P. J.

Batteh, J. H.

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109 (1981).
[CrossRef]

Beck, M.

Becker, P. C.

Blanchot, N.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, “Temporal aberrations due to misalignments of a stretcher–compressor system and compensation,” IEEE J. Quantum Electron. 30, 1662 (1994).
[CrossRef]

Bloom, D. M.

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827 (1994).
[CrossRef]

Borisov, A. B.

A. B. Borisov, X. Shi, V. B. Karpov, V. V. Korobkin, J. C. Solem, O. B. Shiryaev, A. McPherson, K. Boyer, and C. K. Rhodes, “Stable self-channeling of intense ultraviolet pulses in underdense plasma, producing channels exceeding 100 Rayleigh lengths,” J. Opt. Soc. Am. B 11, 1941 (1994).
[CrossRef]

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell (∼100 Å) and L-shell (∼6 Å) transitions,” Phys. Rev. Lett. 72, 1810 (1994).
[CrossRef] [PubMed]

Boyer, K.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell (∼100 Å) and L-shell (∼6 Å) transitions,” Phys. Rev. Lett. 72, 1810 (1994).
[CrossRef] [PubMed]

A. B. Borisov, X. Shi, V. B. Karpov, V. V. Korobkin, J. C. Solem, O. B. Shiryaev, A. McPherson, K. Boyer, and C. K. Rhodes, “Stable self-channeling of intense ultraviolet pulses in underdense plasma, producing channels exceeding 100 Rayleigh lengths,” J. Opt. Soc. Am. B 11, 1941 (1994).
[CrossRef]

Brabec, T.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultra-broadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

Braun, A.

Brener, I.

Brito Cruz, C. H.

Broers, B.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Brown, G. S.

J. D. Kmetec, C. L. Gordon, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV x-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68, 1527 (1992).
[CrossRef] [PubMed]

Brumer, P.

P. Brumer and M. Shapiro, “Laser control of molecular processes,” Annu. Rev. Phys. Chem. 43, 257 (1992).
[CrossRef] [PubMed]

Burgess, D. D.

M. Ciarocca, J. P. Marangos, D. D. Burgess, M. H. R. Hutchinson, R. A. Smith, S. C. Rae, and K. Burnett, “Spectral and spatial modifications to an intense 1 mm laser pulse interacting with a dense argon gas,” Opt. Commun. 110, 425 (1994).
[CrossRef]

Burnett, K.

M. Ciarocca, J. P. Marangos, D. D. Burgess, M. H. R. Hutchinson, R. A. Smith, S. C. Rae, and K. Burnett, “Spectral and spatial modifications to an intense 1 mm laser pulse interacting with a dense argon gas,” Opt. Commun. 110, 425 (1994).
[CrossRef]

S. P. Le Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. B 10, 1801 (1993).
[CrossRef]

Cao, X. D.

X. D. Cao, G. P. Agrawal, and C. J. McKinstrie, “Self-focusing of chirped optical pulses in nonlinear dispersive media,” Phys. Rev. A 49, 4085 (1994).
[CrossRef] [PubMed]

Carlson, R. J.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Chambaret, J. P.

Che, J.

B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. Wilson, N. Schwentner, R. M. Whitnell, and Y. J. Yan, “Quantum control of wave packet evolution with tailored femtosecond pulses,” Phys. Rev. Lett. 74, 3360 (1995).
[CrossRef] [PubMed]

Chelkowski, S.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65, 2355 (1990).
[CrossRef] [PubMed]

Chen, X.

A. McPherson, T. S. Luk, B. D. Thompson, A. B. Borisov, O. B. Shiryaev, X. Chen, K. Boyer, and C. K. Rhodes, “Multiphoton induced x-ray emission from Kr clusters on M-shell (∼100 Å) and L-shell (∼6 Å) transitions,” Phys. Rev. Lett. 72, 1810 (1994).
[CrossRef] [PubMed]

Chernev, P.

Chilla, J. L. A.

Christov, I. P.

Chuang, S. L.

Chuang, Y.-H.

Y.-H. Chuang, L. Zheng, and D. D. Meyerhofer, “Propagation of light pulses in a chirped-pulse-amplification laser,” IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

Ciarocca, M.

M. Ciarocca, J. P. Marangos, D. D. Burgess, M. H. R. Hutchinson, R. A. Smith, S. C. Rae, and K. Burnett, “Spectral and spatial modifications to an intense 1 mm laser pulse interacting with a dense argon gas,” Opt. Commun. 110, 425 (1994).
[CrossRef]

Cina, J. A.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Combs, R. L.

Corkum, P. B.

D. Strickland and P. B. Corkum, “Resistance of short pulses to self-focusing,” J. Opt. Soc. Am. B 11, 492 (1994).
[CrossRef]

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65, 2355 (1990).
[CrossRef] [PubMed]

P. B. Corkum and C. Rolland, “Femtosecond continua produced in gases,” IEEE J. Quantum Electron. 25, 2634 (1989).
[CrossRef]

Crane, J. K.

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, 4051 (1993).
[CrossRef] [PubMed]

J. K. Crane, M. D. Perry, S. Herman, and R. W. Falcone, “High-field harmonic generation in helium,” Opt. Lett. 17, 1256 (1992).
[CrossRef] [PubMed]

Curley, P. F.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultra-broadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

Dahleh, M.

W. S. Warren, H. Rabitz, and M. Dahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259, 1581 (1993).
[CrossRef] [PubMed]

DeLong, K. W.

Diels, J.-C.

Diels, J.-C. M.

Downer, M. C.

Du, D.

Du, M.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Durfee, C. G.

C. G. Durfee and H. M. Milchberg, “Light pipe for high intensity laser pulses,” Phys. Rev. Lett. 71, 2409 (1993).
[CrossRef] [PubMed]

Eichmann, H.

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, 2834 (1994).
[CrossRef]

Falcone, R. W.

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129 (1976).
[CrossRef]

Fienup, J. R.

Fiorini, C.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, “Temporal aberrations due to misalignments of a stretcher–compressor system and compensation,” IEEE J. Quantum Electron. 30, 1662 (1994).
[CrossRef]

Fittinghoff, D. N.

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129 (1976).
[CrossRef]

Fleming, G. R.

N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Foing, J.-P.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

Fontaine, J. J.

Fork, R. L.

Franco, M. A.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

M. A. Franco, B. S. Prade, E. T. J. Nibbering, J.-Y. Vinet, and A. Mysyrowicz, “A 3-D numerical code for the propagation of optical pulses in nonlinear media,” in Ultrafast Phenomena IX, Vol. 60 of Springer Series in Chemistry and Physics, P. F. Barbara, W. H. Knox, G. A. Mourou, and A. H. Zewail, eds. (Springer, Berlin, 1994), p. 265.
[CrossRef]

Fuentes, F. J.

M. Neito-Vesperinas, R. Navarro, and F. J. Fuentes, “Performance of a simulated-annealing algorithm for phase retrieval,” J. Opt. Soc. Am. A. 5, 30 (1988).
[CrossRef]

Fujimoto, J. G.

Gandhi, S. R.

J. S. Melinger, A. Hariharan, S. R. Gandhi, and W. S. Warren, “Generation of narrowband inversion with broadband laser pulses,” Phys. Rev. Lett. 68, 2000 (1992).
[CrossRef] [PubMed]

Godil, A. A.

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827 (1994).
[CrossRef]

Gordon, C. L.

C. P. J. Barty, C. L. Gordon, and B. E. Lemoff, “Multi-terawatt 30-fs Ti:sapphire laser system,” Opt. Lett. 19, 1442 (1994).
[CrossRef] [PubMed]

J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[CrossRef] [PubMed]

J. D. Kmetec, C. L. Gordon, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV x-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68, 1527 (1992).
[CrossRef] [PubMed]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Gordon, S. P.

Goswami, D.

Grillon, G.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, “Compact and efficient multipass Ti:sapphire system for femtosecond chirped-pulse amplification at the terawatt level,” Opt. Lett. 18, 140 (1993).
[CrossRef]

Hammer, J.

S. Wilks, P. E. Young, J. Hammer, M. Tabak, and W. L. Kruer, “Spreading of intense laser beams due to filamentation,” Phys. Rev. Lett. 73, 2994 (1994).
[CrossRef] [PubMed]

Hamster, H.

Hariharan, A.

J. S. Melinger, A. Hariharan, S. R. Gandhi, and W. S. Warren, “Generation of narrowband inversion with broadband laser pulses,” Phys. Rev. Lett. 68, 2000 (1992).
[CrossRef] [PubMed]

Harris, S. E.

J. D. Kmetec, C. L. Gordon, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV x-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68, 1527 (1992).
[CrossRef] [PubMed]

Herman, S.

Hillegas, C. W.

Ho, P. P.

Höpfel, R. A.

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

Houliston, J. R.

J. R. Houliston, M. H. Key, and I. N. Ross, “Modelling of saturated chirped pulse amplification and recompression,” Opt. Commun. 108, 111 (1994).
[CrossRef]

Huang, C.-P.

Hunter, D. J.

Hutchinson, M. H. R.

M. Ciarocca, J. P. Marangos, D. D. Burgess, M. H. R. Hutchinson, R. A. Smith, S. C. Rae, and K. Burnett, “Spectral and spatial modifications to an intense 1 mm laser pulse interacting with a dense argon gas,” Opt. Commun. 110, 425 (1994).
[CrossRef]

Ippen, E. P.

Joffre, M.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, “Femtosecond pulse phase measurement by spectrally resolved up-conversion: application to continuum compression,” IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

Kane, D. J.

Kapteyn, H. C.

Karpov, V. B.

Key, M. H.

J. R. Houliston, M. H. Key, and I. N. Ross, “Modelling of saturated chirped pulse amplification and recompression,” Opt. Commun. 108, 111 (1994).
[CrossRef]

Kmetec, J. D.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon, “High-order harmonic generation using intense femtosecond pulses,” Phys. Rev. Lett. 70, 766 (1993).
[CrossRef] [PubMed]

J. D. Kmetec, C. L. Gordon, J. J. Macklin, B. E. Lemoff, G. S. Brown, and S. E. Harris, “MeV x-ray generation with a femtosecond laser,” Phys. Rev. Lett. 68, 1527 (1992).
[CrossRef] [PubMed]

Kobayashi, Y.

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C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
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C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
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Taft, G.

Thompson, B. D.

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E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454 (1969).
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B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
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C.-G. Wahlström, J. Larsson, A. Persson, T. Starczewski, S. Svanberg, P. Salières, Ph. Balcou, and A. L’Huillier, “High-order harmonic generation in rare gases with an intense short-pulse laser,” Phys. Rev. A 48, 4709 (1993).
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S. Wilks, P. E. Young, J. Hammer, M. Tabak, and W. L. Kruer, “Spreading of intense laser beams due to filamentation,” Phys. Rev. Lett. 73, 2994 (1994).
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B. Kohler, J. L. Krause, F. Raksi, K. R. Wilson, V. V. Yakovlev, R. M. Whitnell, and Y. J. Yan, “Controlling the future of matter,” Acc. Chem. Res. 28, 133 (1995).
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A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum. Electron. 28, 908 (1992).
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B. Kohler, J. L. Krause, F. Raksi, K. R. Wilson, V. V. Yakovlev, R. M. Whitnell, and Y. J. Yan, “Controlling the future of matter,” Acc. Chem. Res. 28, 133 (1995).
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B. Kohler, J. L. Krause, F. Raksi, K. R. Wilson, V. V. Yakovlev, R. M. Whitnell, and Y. J. Yan, “Controlling the future of matter,” Acc. Chem. Res. 28, 133 (1995).
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S. Wilks, P. E. Young, J. Hammer, M. Tabak, and W. L. Kruer, “Spreading of intense laser beams due to filamentation,” Phys. Rev. Lett. 73, 2994 (1994).
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Acc. Chem. Res. (1)

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M. Ciarocca, J. P. Marangos, D. D. Burgess, M. H. R. Hutchinson, R. A. Smith, S. C. Rae, and K. Burnett, “Spectral and spatial modifications to an intense 1 mm laser pulse interacting with a dense argon gas,” Opt. Commun. 110, 425 (1994).
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B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. Wilson, N. Schwentner, R. M. Whitnell, and Y. J. Yan, “Quantum control of wave packet evolution with tailored femtosecond pulses,” Phys. Rev. Lett. 74, 3360 (1995).
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B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, “Efficient population transfer in a three-level ladder system by frequency-swept ultrashort laser pulses,” Phys. Rev. Lett. 69, 2062 (1992).
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Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

M. A. Franco, B. S. Prade, E. T. J. Nibbering, J.-Y. Vinet, and A. Mysyrowicz, “A 3-D numerical code for the propagation of optical pulses in nonlinear media,” in Ultrafast Phenomena IX, Vol. 60 of Springer Series in Chemistry and Physics, P. F. Barbara, W. H. Knox, G. A. Mourou, and A. H. Zewail, eds. (Springer, Berlin, 1994), p. 265.
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Figures (15)

Fig. 1
Fig. 1

Experimental setup for nonlinear propagation in the weakly nonlinear regime. For details see text.

Fig. 2
Fig. 2

Schematic representation of the split-step algorithm for numerical simulation of nonlinear propagation through a dispersive medium. FT, Fourier transform; FT−1, inverse Fourier transform. For details see text.

Fig. 3
Fig. 3

Evolution of the intensity spectrum S(ω, Δz) for 150-fs pulses at 1011 W/cm2 as a function of the distance Δz through silica. One can see the development of significant fringelike structures in the spectra during propagation. The lower plot is identical to the upper one but is represented under a different angle. For details see text.

Fig. 4
Fig. 4

Schematic representation of SPM due to the instantaneous Kerr nonlinearity by means of Gaussian pulses with zero initial phase (transform-limited pulse with a duration of 100 fs FWHM) propagating through a piece of silica with n2 = 3 × 10−16 cm2/W and thickness z = 0.3 cm. The intensity is in the range of 1011 W/cm2, and the maximum value for the B integral is ∼2.5. The reference spectrum is depicted in the lower plot (solid curve), together with the initial phase (dashed line). The propagated spectrum is shown in the middle, and the temporal intensity profile is shown in the upper plot.

Fig. 5
Fig. 5

Same as in Fig. 4, but with an initial (a) positive and (b) negative quadratic phase with a value of ±ϕ2(ω0) = 5.0 × 103 fs2 rad−2.

Fig. 6
Fig. 6

Same as in Fig. 4, but with an initial (a) positive and (b) negative cubic phase with a value of ±ϕ3(ω0) = 8.0 × 105 fs3 rad−3.

Fig. 7
Fig. 7

Same as in Fig. 4, but with an initial (a) positive and (b) negative quartic phase with a value of ±ϕ4(ω0) = 1.3 × 108 fs4 rad−4.

Fig. 8
Fig. 8

Schematic diagram of the automatic phase-retrieval procedure. For details see text.

Fig. 9
Fig. 9

Spectrum of a 150-fs pulse from a Ti:sapphire laser–amplifier chain (lower plot). The corresponding spectrum after transmission through a 3-mm-thick plate of Herasil is shown in the upper plot. The solid curves are experimental spectra, and the open circles are calculated traces. The calculated phase of the optical pulse before transmission through the plate is shown as the dashed curve in the lower plot. The estimate intensity is approximately 1.2 × 1011 W/cm2, and the maximum value of the B integral is equal to 2.

Fig. 10
Fig. 10

Value of the distance error function of Eq. (17) diminishes very rapidly within the first 10–20 iteration rounds, as demonstrated in the upper plot for the experimental case shown in Fig. 9. The lower plot shows that for this case minimization of the distance error function gives a fine adjustment of the pulse energy within 10% accuracy.

Fig. 11
Fig. 11

Same situation as in Fig. 9, except that the compressor has been modified to introduce (a) a negative or (b) a positive chirp to the pulse. Note that the presence of this nearly linear chirp in the pulse is reflected by the calculated quadratic-phase profile. In this case the maximum value of the B integral is equal to ∼1.

Fig. 12
Fig. 12

Results obtained with the same experimental results as in Fig. 9, but with an energy value 50% too high (left) and 50% too low (right) as input in the routine of Fig. 8.

Fig. 13
Fig. 13

Demonstration of the robustness of the numerical procedure of Fig. 8 to the presence of noise. The solid curves represent the numerical reference (lower plot) and the propagated (middle plot) spectra and the initial phase (upper plot). The open circles represent the spectra and the phase retrieved by the numerical procedure. (a) shows the numerical case in which pulses have a substantial amount of cubic phase. (b) is identical, but 10% random noise has been added to the spectra.

Fig. 14
Fig. 14

Demonstration of how the method works for a numerical case of a more complex phase. The solid curves represent the numerical reference (lower plot) and the propagated (middle plot) spectra and the initial phase (upper plot). The open circles show the retrieved data obtained with the algorithm of Fig. 8. Note the change of scale for the trace representing the pulse phase.

Fig. 15
Fig. 15

Self-phase-modulated spectrum after nonlinear propagation of 150-fs pulses through 1-cm BK7 glass for an intensity at 1.2 × 1011 W/cm2 (solid curve). The B integral is equal to ∼3. The upper plot shows the calculated result (open circles) obtained when only a Kerr-like nonlinearity is taken into account. Note that this result is not a stable solution for the numerical procedure of Fig. 8. The lower plot shows the result (open circles) obtained when GVD is included in the calculations. Only the latter result is a stable solution for our numerical procedure. The inset shows the reference spectrum.

Equations (20)

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B ( r , t ) = 2 π λ 0 0 z n 2 I ( r , t ) d z ,
E ( t ) = 1 2 π + F ( ω ) exp ( i ω t ) d ω
F ( ω ) = + E ( t ) exp ( + i ω t ) d t
+ | E ( t ) | 2 d t = 1 2 π + | F ( ω ) | 2 d ω .
E ( x , y , t ) = E ( x , y ) E ( t ) exp ( + ikz i ω t ) ,
W = + + | E ( x , y ) | 2 d x d y + | E ( t ) | 2 d t ,
W = 1 2 π + + | E ( x , y ) | 2 d x d y + | F ( ω ) | 2 d ω .
Ω = Ω 2 π + | F ( ω ) | 2 d ω .
E ( t , 0 ) = 1 2 π exp ( ω 0 t ) + F ( ω , 0 ) × exp [ i ( ω ω 0 ) t ] d ω .
E ( t , Δ z ) = 1 2 π exp ( i ω 0 t ) + F ( ω , 0 ) exp [ i ( ω ω 0 ) t + i β Δ z ] d ω .
F ( ω , Δ z ) = F ( ω , 0 ) exp ( + i β Δ z ) ,
E ( t , Δ z ) = E ( t , 0 ) exp ( + i φ NL ( t , Δ z ) ] .
ϕ ( ω ) = ϕ 2 ( ω 0 ) ( ω ω 0 ) 2 2 + ϕ 3 ( ω 0 ) ( ω ω 0 ) 3 6 + ϕ 4 ( ω 0 ) ( ω ω 0 ) 4 24 + .
ω ( t , Δ z ) = φ ( t , Δ z ) t = 2 π n 2 Δ z λ I ( t , 0 ) t .
F ( ω , Δ z ) = exp ( i ω 0 t ) + E ( t , 0 ) exp [ + i α | E ( t , 0 ) | 2 Δ z i Δ ω t ] d t ,
F ( ω , Δ z ) = j = 1 [ 2 π α | I ( t j , 0 ) | Δ z ] 1 / 2 E ( t j , 0 ) × exp ( + i { α I ( t j , 0 ) Δ z Δ ω t j + ( π / 4 ) sign [ I ( t j , 0 ) ] } ) ,
d [ α I ( t , 0 ) Δ z ] d t + Δ ω = 0 .
E ( t , Δ z ) = E ( t , 0 ) exp [ + i 2 π n 2 λ I ( t , 0 ) Δ z ] ,
E ( t , 0 ) = E ( t , Δ z ) exp [ i 2 π n 2 λ I ( t , 0 ) Δ z ] .
D ( n 2 , W , Δ z ) = { i = 1 N [ S exp , i ( ω , Δ z ) S calc , i ( ω , Δ z ) ] 2 } 1 / 2 i = 1 N S exp , i ( ω , Δ z ) ,

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