Abstract

Although nonlinear methods can provide only the amplitude and the phase of an isolated ultrashort pulse, linear techniques can yield such measurements with a much better sensitivity and reliability when a reference pulse is available. We demonstrate two such methods, dual-quadrature spectral interferometry and Fourier-transform spectral interferometry. These techniques are simple to implement, very sensitive, and provide a complete measurement of the complex electric field, E(ω), as a continuous function of frequency.

© 1995 Optical Society of America

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Adamietz, F.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

Albrecht, T. F.

T. F. Albrecht, K. Seibert, and H. Kurz, Opt. Commun. 84, 223 (1991).
[CrossRef]

Anderson, K. K.

M. J. LaGasse, K. K. Anderson, H. A. Hasue, and J. G. Fujimoto, Appl. Phys. Lett. 54, 2068 (1989).
[CrossRef]

Antonetti, A.

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

Arnaud, J. A.

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

Audebert, P.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Banyai, W. C.

N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 6, 675 (1989).
[CrossRef]

Barthelemy, A.

F. Reynaud, F. Salin, and A. Barthelemy, Opt. Lett. 14, 275 (1989).
[CrossRef] [PubMed]

Becker, P. C.

C.-H. Brito-Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, IEEE J. Quantum Electron. 24, 261 (1988).
[CrossRef]

Bigot, J.-Y.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schafer, Phys. Rev. B 50, 8439 (1994).
[CrossRef]

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Bott, K.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Brabec, T.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

Brito-Cruz, C.-H.

C.-H. Brito-Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, IEEE J. Quantum Electron. 24, 261 (1988).
[CrossRef]

Calatroni, J.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 111,632 (1994).
[CrossRef]

Canioni, L.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Chambaret, J.-P.

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

Ché riaux, G.

L. Lepetit, M. Joffre, G. Ché riaux, A. Migus and D. Hulin, in Quantum Electronics and Laser Science, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper QWG1.

Chemla, D. S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schafer, Phys. Rev. B 50, 8439 (1994).
[CrossRef]

Chilla, J. L. A.

J. L. A. Chilla and O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Colombeau, B.

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Ducasse, A.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

Duchesne, C.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 111,632 (1994).
[CrossRef]

Falliès, F.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Fargin, E.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

Finlayson, N.

N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 6, 675 (1989).
[CrossRef]

Flem, G. Le

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Fluegel, B.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

Foing, J.-P.

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

Fork, R. L.

C.-H. Brito-Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, IEEE J. Quantum Electron. 24, 261 (1988).
[CrossRef]

Froehly, C.

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. (Paris) 4, 183 (1973).

Fujimoto, J. G.

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993); J. Paye, IEEE J. Quantum Electron. 30, 2693 (1994).
[CrossRef] [PubMed]

M. J. LaGasse, K. K. Anderson, H. A. Hasue, and J. G. Fujimoto, Appl. Phys. Lett. 54, 2068 (1989).
[CrossRef]

Gauthier, J. C.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Geindre, J.-P.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Gordon, J. P.

C.-H. Brito-Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, IEEE J. Quantum Electron. 24, 261 (1988).
[CrossRef]

Griffiths, P. R.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry, Vol. 83 of Chemical Analysis Series (Wiley, New York, 1986), p. 369.

Guillaume, C. Benoit à la

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

Hamoniaux, G.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Haseth, J. A. de

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry, Vol. 83 of Chemical Analysis Series (Wiley, New York, 1986), p. 369.

Hasue, H. A.

M. J. LaGasse, K. K. Anderson, H. A. Hasue, and J. G. Fujimoto, Appl. Phys. Lett. 54, 2068 (1989).
[CrossRef]

Heuckeroth, V.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Hey, R.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Hulin, D.

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

L. Lepetit, M. Joffre, G. Ché riaux, A. Migus and D. Hulin, in Quantum Electronics and Laser Science, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper QWG1.

Ippen, E. P.

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993); J. Paye, IEEE J. Quantum Electron. 30, 2693 (1994).
[CrossRef] [PubMed]

Joffre, M.

L. Lepetit, M. Joffre, G. Ché riaux, A. Migus and D. Hulin, in Quantum Electronics and Laser Science, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper QWG1.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 111,632 (1994).
[CrossRef]

Juncar, P.

P. Juncar and J. Pinard, Rev. Sci. Instrum. 53, 939 (1982).
[CrossRef]

Kane, D. J.

D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993); R. Trebino and D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
[CrossRef] [PubMed]

Kobayashi, T.

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 16, 1683 (1991).
[CrossRef] [PubMed]

E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 18, 370 (1993).
[CrossRef] [PubMed]

Koch, S. W.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Krausz, F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

Kuhl, J.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Kurz, H.

T. F. Albrecht, K. Seibert, and H. Kurz, Opt. Commun. 84, 223 (1991).
[CrossRef]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. (Paris) 4, 183 (1973).

LaGasse, M. J.

M. J. LaGasse, K. K. Anderson, H. A. Hasue, and J. G. Fujimoto, Appl. Phys. Lett. 54, 2068 (1989).
[CrossRef]

Lepetit, L.

L. Lepetit, M. Joffre, G. Ché riaux, A. Migus and D. Hulin, in Quantum Electronics and Laser Science, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper QWG1.

Likforman, J.-P.

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

Lindberg, M.

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

Martinez, O. E.

J. L. A. Chilla and O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[CrossRef]

Matro, 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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Mayer, E. J.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Meier, T.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Migus, A.

J. Paye and A. Migus, J. Opt. Soc. Am. B 12, 1480 (1995)
[CrossRef]

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

L. Lepetit, M. Joffre, G. Ché riaux, A. Migus and D. Hulin, in Quantum Electronics and Laser Science, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper QWG1.

Minoshima, K.

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 16, 1683 (1991).
[CrossRef] [PubMed]

Mogi, K.

K. Naganuma, K. Mogi, and H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Mycek, M.-A.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schafer, Phys. Rev. B 50, 8439 (1994).
[CrossRef]

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Mysyrowicz, A.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Naganuma, K.

K. Naganuma, K. Mogi, and H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Olazcuaga, R.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

Olbright, G.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

Paye, J.

J. Paye and A. Migus, J. Opt. Soc. Am. B 12, 1480 (1995)
[CrossRef]

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993); J. Paye, IEEE J. Quantum Electron. 30, 2693 (1994).
[CrossRef] [PubMed]

Peyghambarian, N.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

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J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

Pinard, J.

P. Juncar and J. Pinard, Rev. Sci. Instrum. 53, 939 (1982).
[CrossRef]

Ploog, K.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Ramaswamy, M.

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993); J. Paye, IEEE J. Quantum Electron. 30, 2693 (1994).
[CrossRef] [PubMed]

Reynaud, F.

F. Reynaud, F. Salin, and A. Barthelemy, Opt. Lett. 14, 275 (1989).
[CrossRef] [PubMed]

Rice, S. 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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Romero-Rochin, V.

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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Rousse, A.

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Ruggiero, A. 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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 111,632 (1994).
[CrossRef]

Salin, F.

F. Reynaud, F. Salin, and A. Barthelemy, Opt. Lett. 14, 275 (1989).
[CrossRef] [PubMed]

Santos, A. Dos

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

Sarger, L.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

Schafer, W.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schafer, Phys. Rev. B 50, 8439 (1994).
[CrossRef]

Scherer, N. F.

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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

Schmitt-Rink, S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

Schulze, A.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

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N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 6, 675 (1989).
[CrossRef]

Segonds, P.

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

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T. F. Albrecht, K. Seibert, and H. Kurz, Opt. Commun. 84, 223 (1991).
[CrossRef]

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C.-H. Brito-Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, IEEE J. Quantum Electron. 24, 261 (1988).
[CrossRef]

Smith, G. O.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

Spielmann, Ch.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

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N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 6, 675 (1989).
[CrossRef]

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K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 16, 1683 (1991).
[CrossRef] [PubMed]

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E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 18, 370 (1993).
[CrossRef] [PubMed]

Thomas, P.

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

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E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 18, 370 (1993).
[CrossRef] [PubMed]

Trebino, R.

D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993); R. Trebino and D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
[CrossRef] [PubMed]

Vampouille, M.

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. (Paris) 4, 183 (1973).

Walmsley, I. A.

V. Wong and I. A. Walmsley, Opt. Lett. 19, 287 (1994); J. Opt. Soc. Am. B 12, 1491 (1995).
[CrossRef] [PubMed]

Weiss, S.

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[CrossRef] [PubMed]

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schafer, Phys. Rev. B 50, 8439 (1994).
[CrossRef]

Wong, V.

V. Wong and I. A. Walmsley, Opt. Lett. 19, 287 (1994); J. Opt. Soc. Am. B 12, 1491 (1995).
[CrossRef] [PubMed]

Yamada, H.

K. Naganuma, K. Mogi, and H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Other (31)

S. Weiss, M.-A. Mycek, J.-Y. Bigot, S. Schmitt-Rink, and D. S. Chemla, Phys. Rev. Lett. 69, 2685 (1992).
[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, J. Chem. Phys. 95, 1487 (1991).
[CrossRef]

K. Naganuma, K. Mogi, and H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

J. L. A. Chilla and O. E. Martinez, IEEE J. Quantum Electron. 27, 1228 (1991).
[CrossRef]

T. F. Albrecht, K. Seibert, and H. Kurz, Opt. Commun. 84, 223 (1991).
[CrossRef]

J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, IEEE J. Quantum Electron. 28, 2285 (1992).
[CrossRef]

D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993); R. Trebino and D. J. Kane, J. Opt. Soc. Am. A 10, 1101 (1993).
[CrossRef] [PubMed]

J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993); J. Paye, IEEE J. Quantum Electron. 30, 2693 (1994).
[CrossRef] [PubMed]

V. Wong and I. A. Walmsley, Opt. Lett. 19, 287 (1994); J. Opt. Soc. Am. B 12, 1491 (1995).
[CrossRef] [PubMed]

M. J. LaGasse, K. K. Anderson, H. A. Hasue, and J. G. Fujimoto, Appl. Phys. Lett. 54, 2068 (1989).
[CrossRef]

N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 6, 675 (1989).
[CrossRef]

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 16, 1683 (1991).
[CrossRef] [PubMed]

L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, J. Opt. Soc. Am. B 11, 995 (1994).
[CrossRef]

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry, Vol. 83 of Chemical Analysis Series (Wiley, New York, 1986), p. 369.

D. S. Chemla, J.-Y. Bigot, M.-A. Mycek, S. Weiss, and W. Schafer, Phys. Rev. B 50, 8439 (1994).
[CrossRef]

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. (Paris) 4, 183 (1973).

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

F. Reynaud, F. Salin, and A. Barthelemy, Opt. Lett. 14, 275 (1989).
[CrossRef] [PubMed]

E. Tokunaga, A. Terasaki, and T. Kobayashi, Opt. Lett. 18, 370 (1993).
[CrossRef] [PubMed]

J.-P. Geindre, P. Audebert, A. Rousse, F. Falliès, J. C. Gauthier, A. Mysyrowicz, A. Dos Santos, G. Hamoniaux, and A. Antonetti, Opt. Lett. 19, 1997 (1994).
[CrossRef] [PubMed]

P. Juncar and J. Pinard, Rev. Sci. Instrum. 53, 939 (1982).
[CrossRef]

When the state of polarization of the unknown pulse must be measured, one may repeat the experiments for two positions of a linear analyzer placed on the unknown pulse beam.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, Phys. Rev. Lett. 59, 2588 (1987).
[CrossRef] [PubMed]

C.-H. Brito-Cruz, J. P. Gordon, P. C. Becker, R. L. Fork, and C. V. Shank, IEEE J. Quantum Electron. 24, 261 (1988).
[CrossRef]

M. Joffre, D. Hulin, A. Migus, A. Antonetti, C. Benoit à la Guillaume, N. Peyghambarian, M. Lindberg, and S. W. Koch, Opt. Lett. 13, 276 (1988).
[CrossRef] [PubMed]

M. Joffre, D. Hulin, J.-P. Foing, J.-P. Chambaret, A. Migus and A. Antonetti, IEEE J. Quantum Electron. 25, 2505 (1989).
[CrossRef]

J. Paye and A. Migus, J. Opt. Soc. Am. B 12, 1480 (1995)
[CrossRef]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 111,632 (1994).
[CrossRef]

E. J. Mayer, G. O. Smith, V. Heuckeroth, J. Kuhl, K. Bott, A. Schulze, T. Meier, S. W. Koch, P. Thomas, R. Hey, and K. Ploog, Phys. Rev. B 51, 10909 (1995).
[CrossRef]

L. Lepetit, M. Joffre, G. Ché riaux, A. Migus and D. Hulin, in Quantum Electronics and Laser Science, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper QWG1.

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Figures (9)

Fig. 1
Fig. 1

General linear experimental setup: the incident pulse is sent into a linear device and then into a time-integrating detector. The linear device is characterized by its response function, R(t) in the time domain or R(ω) in the frequency domain.

Fig. 2
Fig. 2

Experimental setup for spectral interferometry, based on a Mach–Zehnder interferometer. An unknown electric field, E(ω), is generated in an arbitrary experiment (EXP), either linear or nonlinear. It is set up to interfere in a spectrometer with a reference E0(ω). BS’s, beam splitters; SP, spectrometer; CCD, charge-coupled device array detector.

Fig. 3
Fig. 3

DQSI experimental setup for a phase sensitive measurement of an unknown electric field E(ω): BS’s, beam splitters; LP’s, linear polarizers; QWP, quarter-wave plate; WP, Wollaston prism; SP, spectrometer; CCD, charge-coupled-device array detector.

Fig. 4
Fig. 4

Spectral interferograms obtained from both polarization components, horizontal (solid curve) and vertical (dotted curve), when the unknown pulse is the same as the reference pulse but has undergone a time delay shift τ. The dashed–dotted line shows the phase retrieved from the cosine and the sine parts of the interferogram.

Fig. 5
Fig. 5

Spectral phase (solid curve) obtained when the unknown pulse results from transmission through an interferential filter, either (a) at normal incidence or (b) when the filter is tilted. The dashed–dotted curve shows the spectral intensity.

Fig. 6
Fig. 6

(a) Simulated spectral interferogram between two Gaussian pulses; (b) inverse Fourier transform of the above interferogram, computed in a rotating frame; (c) spectral phase (solid curve) and amplitude (dotted curve) obtained by taking the Fourier transform of the above curve where the points at negative times have been set to 0.

Fig. 7
Fig. 7

(a) Simulated spectral interferogram between a Gaussian pulse and a monoexponential pulse oscillating at a central frequency of 370 THz; (b) inverse Fourier transform of the interferogram; (c) amplitude (dotted curve) and phase (solid curve) of the monoexponential pulse, showing the π phase jump at resonance.

Fig. 8
Fig. 8

(a) Experimental spectral interferogram between femtosecond pulses delayed by a time τ = 500 fs. (b) Amplitude of the inverse Fourier transform of the above interferogram. The direct pulse is centered at 500 fs, while the time-reversed one is centered at −500 fs. (c) Spectral phase obtained from the Fourier transform of the above time-domain response, after multiplication by the Heaviside function, i.e., by the use of FTSI (solid line). Experimental result obtained by DQSI (dotted line) is shifted up for clarity.

Fig. 9
Fig. 9

Simulated spectra that corresponds to the spectral interference between a Gaussian pulse and a monoexponential pulse oscillating at a central frequency of 370 THz. In (b), (c) and (d), the dotted curve shows the actual spectral phase. (a) The two quadratures of the spectral interference, as would be measured in a DQSI setup. Noise was added to the spectra in order to simulate typical experimental conditions. (b) Spectral phase (filled diamonds) as obtained from pointing the fringe maxima in the dotted-line curve of (a). (c) Spectral phase as obtained from DQSI. (d) Spectral phase as obtained from FTSI with only the dotted curve in (a).

Equations (7)

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E ( t ) = R ( t - t ) E ( t ) d t = R ( ω ) E ( ω ) exp ( - i ω t ) d ω 2 π .
S = E ( t ) 2 d t = E ( ω ) 2 d ω 2 π = R ( ω ) 2 E ( ω ) 2 d ω 2 π .
S ( ω ) = E 0 ( ω ) + E ( ω ) 2 = E 0 ( ω ) 2 + E ( ω ) 2 + 2 Re E 0 * ( ω ) E ( ω ) ,
E 0 ( ω ) + E ( ω ) 2 = E 0 ( ω ) 2 + E ( ω ) 2 + 2 Re E 0 * ( ω ) E ( ω ) , i E 0 ( ω ) + E ( ω ) 2 = E 0 ( ω ) 2 + E ( ω ) 2 + 2 Im E 0 * ( ω ) E ( ω ) .
S ( ω ) = 2 Re f ( ω ) exp ( i ω τ ) ,
F - 1 S ( ω ) = f ( t - τ ) + f ( - t - τ ) .
E ( ω ) = F [ Θ ( t ) F - 1 S ( ω ) ] exp ( - i ω τ ) E 0 * ( ω ) .

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