Abstract

Spectral-phase modulation in a zero-dispersion line is a powerful method to compress or temporally shape femtosecond pulses. Results of classical spectral interferometry in characterizing and controlling phase modulators are reported. An improvement of spectral interferometry, polarization spectral interferometry, is analyzed and demonstrated for the control of polarized modulators. Possible errors and limitations are asserted. A new scheme for the real-time control of spectral phase modulation in an amplifier laser system is proposed.

© 1998 Optical Society of America

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References

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  1. A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A 10, 1112–1120 (1993).
    [CrossRef]
  2. 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, 908–919 (1992).
    [CrossRef]
  3. A. Efimov, C. Scaffer, and D. H. Reitze, “Programmable shaping of ultrabroad-bandwidth pulses from a Ti:sapphire laser,” J. Opt. Soc. Am. B 12, 1968–1979 (1995).
    [CrossRef]
  4. A. Efimov and D. H. Reitze, “Spectral adaptive optics: phase compensation for ultrashort chirped pulse amplifier systems,” Proc. SPIE 2701, 190–197 (1996).
    [CrossRef]
  5. Y. Ding, R. M. Brubaker, D. D. Nolte, M. R. Melloch, and A. M. Weiner, “Femtosecond pulse shaping by dynamic holograms in photorefractive multiple quantum wells,” Opt. Lett. 22, 718–720 (1997).
    [CrossRef] [PubMed]
  6. 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, 737–739 (1994).
    [CrossRef] [PubMed]
  7. C. Dorrer, G. Chériaux, J. P. Chambaret, F. Salin, F. Verluise, B. Loiseaux, and J. P. Huignard, “Pulse shaping by a nonpixelized phase modulator,” Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CMC7.
  8. C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183 (1973).
  9. J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. Arnaud, “Nouvelle méthode de mesure de la réponse impulsionnelle des fibres optiques,” Appl. Opt. 19, 3749 (1980).
    [CrossRef] [PubMed]
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  12. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995).
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  15. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–499 (1941).
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1997 (2)

1996 (2)

1995 (2)

1994 (2)

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, 737–739 (1994).
[CrossRef] [PubMed]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Commun. 111, 632–641 (1994).

1993 (1)

1992 (1)

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, 908–919 (1992).
[CrossRef]

1989 (1)

1980 (1)

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183 (1973).

1941 (1)

Arnaud, J.

Barthelemy, A.

Bowie, J. L.

Brubaker, R. M.

Calatroni, J.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Commun. 111, 632–641 (1994).

Chériaux, G.

Colombeau, B.

DeLong, K. W.

Ding, Y.

Efimov, A.

A. Efimov and D. H. Reitze, “Spectral adaptive optics: phase compensation for ultrashort chirped pulse amplifier systems,” Proc. SPIE 2701, 190–197 (1996).
[CrossRef]

A. Efimov, C. Scaffer, and D. H. Reitze, “Programmable shaping of ultrabroad-bandwidth pulses from a Ti:sapphire laser,” J. Opt. Soc. Am. B 12, 1968–1979 (1995).
[CrossRef]

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Commun. 111, 632–641 (1994).

Fittinghoff, D. N.

Froehly, C.

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. Arnaud, “Nouvelle méthode de mesure de la réponse impulsionnelle des fibres optiques,” Appl. Opt. 19, 3749 (1980).
[CrossRef] [PubMed]

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183 (1973).

Goswami, D.

Hillegas, W.

Jennings, R. T.

Joffre, M.

Jones, R. C.

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Commun. 111, 632–641 (1994).

Konoplev, O. A.

Krumbugel, M. A.

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183 (1973).

Leaird, D. E.

A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A 10, 1112–1120 (1993).
[CrossRef]

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, 908–919 (1992).
[CrossRef]

Lepetit, L.

Melloch, M. R.

Meyerhofer, D. D.

Nolte, D. D.

Oudin, S.

Patel, J. S.

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, 908–919 (1992).
[CrossRef]

Piasecki, J.

Reitze, D. H.

Reynaud, F.

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Commun. 111, 632–641 (1994).

Salin, F.

Scaffer, C.

Strickland, D.

Sweetser, J. N.

Trebino, R.

Tull, J. X.

Vampouille, M.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183 (1973).

Walmsley, I. A.

Warren, W. S.

Weiner, A. M.

Wullert, J. R.

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, 908–919 (1992).
[CrossRef]

Zheng, I.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

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, 908–919 (1992).
[CrossRef]

J. Opt. (Paris) (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Notions de réponse impulsionnelle et de fonction de transfert temporelles des pupilles optiques, justifications expérimentales et applications,” J. Opt. (Paris) 4, 183 (1973).

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, “Measurement of phase shifts introduced by nonlinear optical phenomena on subpicosecond pulses,” Opt. Commun. 111, 632–641 (1994).

Opt. Lett. (5)

Proc. SPIE (1)

A. Efimov and D. H. Reitze, “Spectral adaptive optics: phase compensation for ultrashort chirped pulse amplifier systems,” Proc. SPIE 2701, 190–197 (1996).
[CrossRef]

Other (1)

C. Dorrer, G. Chériaux, J. P. Chambaret, F. Salin, F. Verluise, B. Loiseaux, and J. P. Huignard, “Pulse shaping by a nonpixelized phase modulator,” Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CMC7.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for the implementation of classical spectral interferometry in spectral phase modulation.  

Fig. 2
Fig. 2

Retrieval of the dispersion induced by the whole 4f line with an inactive modulator.

Fig. 3
Fig. 3

Principle of polarization spectral interferometry.  

Fig. 4
Fig. 4

Determination of the spatio spectral dependence on the modulator: (a) phase jump induced on the modulator; (b) spatio spectral dependence on the modulator.

Fig. 5
Fig. 5

Example of the convergence of the spectral phase added by the modulator (solid curve) toward an arbitrary phase of order 4 and below (dotted curve).

Fig. 6
Fig. 6

Implementation of a real-time control of spectral phase modulation in an amplifier system using polarization spectral interferometry.

Fig. 7
Fig. 7

(a) Temporal description of the Fourier transform of the signal obtained by spectral interferometry. (b) White noise of level L on the measurement of the spectrum.

Fig. 8
Fig. 8

Error between the actual phase and the retrieved phase for 2 misaligned setup: (a) α1=5°, α2=0°; (b) α1=5°, α2=-5°.

Equations (7)

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cosϕ(ω)2+j sinϕ(ω)2cos(2α)j sinϕ(ω)2sin(2α)j sinϕ(ω)2sin(2α)cosϕ(ω)2-j sinϕ(ω)2cos(2α),
12 11;
12 cos(θ)+sin(θ)cos(θ)-sin(θ).
Eout(ω)=Ein(ω)*[f1* cos(θ)+f2* sin(θ)],
f1=cosϕ1+ϕ22cos2(α1-α2)+cosϕ1-ϕ22sin2(α1-α2)+jsinϕ1+ϕ22sin(α1+α2)cos(α1-α2)+sinϕ1-ϕ22sin(α1-α2)cos(α1+α2),
f2=cosϕ1+ϕ22-cosϕ1-ϕ22sin(α1-α2)cos(α1-α2)+jsinϕ1+ϕ22cos(α1+α2)cos(α1-α2)-sinϕ1-ϕ22sin(α1+α2)sin(α1-α2).
S(ω)=12 |Ein(ω)|2{1-cos[ϕ1(ω)+ϕ2(ω)]}=12 |Ein(ω)|2{1+cos[ϕ1(ω)+ϕ2(ω)+π]},

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