Abstract

We demonstrate that a combination of prisms and diffraction gratings can provide not only quadratic but also cubic phase compensation of ultrashort optical pulses. We obtain compressed pulses as short as 6 fsec.

© 1987 Optical Society of America

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References

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  1. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
    [CrossRef]
  2. J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832 (1984).
    [CrossRef]
  3. J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281 (1984).
    [CrossRef]
  4. W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
    [CrossRef]
  5. E. P. Treacy, IEEE J. Quantum Electron. QE-19, 454 (1969).
    [CrossRef]
  6. I. P. Christov, I. V. Tomov, Opt. Commun. 58, 338 (1986).
    [CrossRef]
  7. C. V. Shank, R. L. Fork, C. H. Brito Cruz, W. H. Knox, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 179.
  8. C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
    [CrossRef]
  9. J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  10. W. H. Knox, M. C. Downer, R. L. Fork, C. V. Shank, Opt. Lett. 9, 552 (1984).
    [CrossRef] [PubMed]
  11. J. C. Diels, E. W. Van Stryland, D. Gold, in Proceedings of the First International Conference on Picosecond Phenomena (Springer-Verlag, Berlin, 1978), p. 117.
  12. E. P. Ippen, C. V. Shank, Ultrashort Light Pulses (Springer-Verlag, Berlin, 1977), p. 83.
  13. R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150 (1984).
    [CrossRef] [PubMed]
  14. D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), p. 6-29.
  15. R. Meinel, Opt. Commun. 47, 343 (1983).
    [CrossRef]
  16. W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
    [CrossRef]

1986 (2)

I. P. Christov, I. V. Tomov, Opt. Commun. 58, 338 (1986).
[CrossRef]

C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
[CrossRef]

1985 (2)

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

1984 (4)

R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150 (1984).
[CrossRef] [PubMed]

W. H. Knox, M. C. Downer, R. L. Fork, C. V. Shank, Opt. Lett. 9, 552 (1984).
[CrossRef] [PubMed]

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832 (1984).
[CrossRef]

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281 (1984).
[CrossRef]

1983 (1)

R. Meinel, Opt. Commun. 47, 343 (1983).
[CrossRef]

1982 (2)

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

1969 (1)

E. P. Treacy, IEEE J. Quantum Electron. QE-19, 454 (1969).
[CrossRef]

Brito Cruz, C. H.

C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
[CrossRef]

C. V. Shank, R. L. Fork, C. H. Brito Cruz, W. H. Knox, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 179.

Christov, I. P.

I. P. Christov, I. V. Tomov, Opt. Commun. 58, 338 (1986).
[CrossRef]

Diels, J. C.

J. C. Diels, E. W. Van Stryland, D. Gold, in Proceedings of the First International Conference on Picosecond Phenomena (Springer-Verlag, Berlin, 1978), p. 117.

Dietel, W.

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Dopel, E.

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Downer, M. C.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, C. V. Shank, Opt. Lett. 9, 552 (1984).
[CrossRef] [PubMed]

Fork, R. L.

C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

W. H. Knox, M. C. Downer, R. L. Fork, C. V. Shank, Opt. Lett. 9, 552 (1984).
[CrossRef] [PubMed]

R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150 (1984).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

C. V. Shank, R. L. Fork, C. H. Brito Cruz, W. H. Knox, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 179.

Fujimoto, J. G.

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832 (1984).
[CrossRef]

Gold, D.

J. C. Diels, E. W. Van Stryland, D. Gold, in Proceedings of the First International Conference on Picosecond Phenomena (Springer-Verlag, Berlin, 1978), p. 117.

Gordon, J. P.

Grischkowsky, D.

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281 (1984).
[CrossRef]

Halbout, J. M.

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281 (1984).
[CrossRef]

Ippen, E. P.

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832 (1984).
[CrossRef]

E. P. Ippen, C. V. Shank, Ultrashort Light Pulses (Springer-Verlag, Berlin, 1977), p. 83.

Knox, W. H.

C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, C. V. Shank, Opt. Lett. 9, 552 (1984).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, C. H. Brito Cruz, W. H. Knox, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 179.

Kuhlke, D.

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Martinez, O. E.

Meinel, R.

R. Meinel, Opt. Commun. 47, 343 (1983).
[CrossRef]

Shank, C. V.

C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, C. V. Shank, Opt. Lett. 9, 552 (1984).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

C. V. Shank, R. L. Fork, C. H. Brito Cruz, W. H. Knox, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 179.

E. P. Ippen, C. V. Shank, Ultrashort Light Pulses (Springer-Verlag, Berlin, 1977), p. 83.

Stolen, R. H.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Tomlinson, W. J.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Tomov, I. V.

I. P. Christov, I. V. Tomov, Opt. Commun. 58, 338 (1986).
[CrossRef]

Treacy, E. P.

E. P. Treacy, IEEE J. Quantum Electron. QE-19, 454 (1969).
[CrossRef]

Valdmanis, J. A.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

Van Stryland, E. W.

J. C. Diels, E. W. Van Stryland, D. Gold, in Proceedings of the First International Conference on Picosecond Phenomena (Springer-Verlag, Berlin, 1978), p. 117.

Weiner, A. M.

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832 (1984).
[CrossRef]

Wilhelmi, B.

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Appl. Phys. Lett. (4)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

J. G. Fujimoto, A. M. Weiner, E. P. Ippen, Appl. Phys. Lett. 44, 832 (1984).
[CrossRef]

J. M. Halbout, D. Grischkowsky, Appl. Phys. Lett. 45, 1281 (1984).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, J. A. Valdmanis, C. V. Shank, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Chem. Phys. Lett. (1)

C. H. Brito Cruz, R. L. Fork, W. H. Knox, C. V. Shank, Chem. Phys. Lett. 132, 341 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. P. Treacy, IEEE J. Quantum Electron. QE-19, 454 (1969).
[CrossRef]

Opt. Commun. (3)

I. P. Christov, I. V. Tomov, Opt. Commun. 58, 338 (1986).
[CrossRef]

R. Meinel, Opt. Commun. 47, 343 (1983).
[CrossRef]

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Opt. Lett. (3)

Other (4)

J. C. Diels, E. W. Van Stryland, D. Gold, in Proceedings of the First International Conference on Picosecond Phenomena (Springer-Verlag, Berlin, 1978), p. 117.

E. P. Ippen, C. V. Shank, Ultrashort Light Pulses (Springer-Verlag, Berlin, 1977), p. 83.

C. V. Shank, R. L. Fork, C. H. Brito Cruz, W. H. Knox, in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 179.

D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, New York, 1972), p. 6-29.

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Figures (3)

Fig. 1
Fig. 1

Combined grating and prism sequence used to remove both quadratic and cubic phase distortion. The solid line is a reference line. The dashed line is the path of a plane wave that propagates between the gratings at an angle θ with respect to the normal to the grating faces and between the prism pairs at an angle β with respect to a line drawn between the prism apices. The plane LL′ is a plane of symmetry for the grating sequence, and the plane MM′ is a plane of symmetry for the prism sequence.

Fig. 2
Fig. 2

Experimental plots of an upconverted signal for a set of six wavelengths of the fundamental produced by nonlinear mixing of the compressed and uncompressed pulses in KDP versus relative delay between the pulses. The relative delay at which the peak upconverted signal occurs is a direct measure of the relative delay experienced by a given wavelength component of the compressed pulse. These data represent the optimum pulse compression obtained by using only the grating portion of the compression sequence shown in Fig. 1.

Fig. 3
Fig. 3

Experimental interferometric autocorrelation trace for a compressed pulse for lp = 71 cm and lg = 0.5 cm. The interference maxima and minima calculated for the interferometric autocorrelation trace for a hyperbolic-secant-squared pulse of 6-fsec duration are indicated by crosses. The close agreement between experiment and theory demonstrates an absence of significant phase distortion in the compressed pulse.

Tables (2)

Tables Icon

Table 1 Second and Third Derivatives of Phase with Respect to Frequency for a Double Prism Pair, a Double Grating Pair, and Material

Tables Icon

Table 2 Second and Third Derivatives of Phase with Respect to Frequency for the Double Prism Pair and Double Grating Pair Described in the Texta

Equations (11)

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ϕ ( ω ) = ϕ ( ω 0 ) + ( d ϕ d ω ) ω 0 ( ω ω 0 ) + 1 2 ( d 2 ϕ d ω 2 ) ω 0 × ( ω ω 0 ) 2 + 1 6 ( d 3 ϕ d ω 3 ) ω 0 ( ω ω 0 ) 3 ,
d 2 ϕ p d ω 2 = λ 3 2 π 2 c 2 d 2 P d λ 2
d 2 ϕ g d ω 2 = λ 3 l g π c 2 d 2 [ 1 ( λ d sin γ ) 2 ] 3 / 2
d 2 ϕ m d ω 2 = λ 3 l m 2 π c 2 d 2 n m d λ 2
d 3 ϕ p d ω 3 = λ 4 4 π 2 c 3 ( 3 d 2 P d λ 2 + λ d 3 P d λ 3 )
d 3 ϕ g d ω 3 = d 2 ϕ g d ω 2 6 π λ c × ( 1 + λ d sin γ sin 2 γ ) [ 1 ( λ d sin γ ) 2 ]
d 3 ϕ m d ω 3 = λ 4 l m 4 π 2 c 3 ( 3 d 2 n m d λ 2 + λ d 3 n m d λ 3 )
d 2 P d λ 2 = 4 [ d 2 n d λ 2 + ( 2 n n 3 ) ( d n d λ ) 2 ] l p sin β 8 ( d n d λ ) 2 l p cos β
d 3 P d λ 3 = 4 d 3 n d λ 3 l p sin β 24 d n d λ d 2 n d λ 2 l p cos β
d 2 ϕ d ω 2 ( fsec 2 )
d 3 ϕ d ω 3 ( fsec 3 )

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