Abstract

Optical pulse-compression systems based on bulk materials and hollow waveguides are compared by use of coupled-mode theory. Our analysis reveals an intuitive picture of the temporal and spatial nonlinear processes involved in pulse compression. Further, simple formulas are derived that give an estimate of the spatial distortions and of the self-phase modulation induced by Kerr nonlinearity. Finally, a parameter regime is identified in which self-focusing in bulk media is suppressed, resulting in a substantial improvement in the spatial beam quality of the compressed pulses.

© 2000 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  2. C. Rolland and P. B. Corkum, J. Opt. Soc. Am. B 5, 641 (1988); D. H. Reitze, A. M. Weiner, and D. E. Leaird, Opt. Lett. 16, 1409 (1991).
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    [CrossRef]
  4. S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, F. Krausz, and K. Ferencz, Opt. Lett. 22, 1562 (1997).
    [CrossRef]
  5. A. T. Ryan and G. P. Agrawal, Opt. Lett. 20, 306 (1995).
    [CrossRef] [PubMed]
  6. G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
    [CrossRef]
  7. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
    [CrossRef]
  8. J. K. Ranka and A. L. Gaeta, Opt. Lett. 23, 534 (1998).
    [CrossRef]
  9. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  10. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
    [CrossRef]
  11. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  12. J. U. White, J. Opt. Soc. Am. 32, 285 (1940); J. Opt. Soc. Am. 66, 411 (1976).
  13. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
    [CrossRef]
  14. G. Fibich and A. L. Gaeta, Opt. Lett. 25, 335 (2000).
    [CrossRef]
  15. Some typos in Ref. 8 have to be corrected: In the definition of djp a factor πa2 is missing. Further, in Eq. (6) the factor P03/2 in front of the brace has to be eliminated. Finally, the energy in the higher modes is periodic with 2Lp and not with 4Lp.

2000 (1)

1998 (3)

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

J. K. Ranka and A. L. Gaeta, Opt. Lett. 23, 534 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

1997 (2)

1996 (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

1995 (1)

1988 (1)

1984 (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

1966 (1)

1940 (1)

Agrawal, G. P.

A. T. Ryan and G. P. Agrawal, Opt. Lett. 20, 306 (1995).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Brabec, T.

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
[CrossRef]

Cheng, Z.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, F. Krausz, and K. Ferencz, Opt. Lett. 22, 1562 (1997).
[CrossRef]

Corkum, P. B.

De Silvestri, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Ferencz, K.

Fibich, G.

Gaeta, A. L.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

Kogelnik, H.

Krausz, F.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
[CrossRef]

S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, F. Krausz, and K. Ferencz, Opt. Lett. 22, 1562 (1997).
[CrossRef]

Lenzner, M.

Li, T.

Nisoli, M.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Ranka, J. K.

Rolland, C.

Ryan, A. T.

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

Sartania, S.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

Spielmann, C.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

Spielmann, Ch.

Stagira, S.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

Svelto, O.

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

Tempea, G.

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, F. Krausz, and K. Ferencz, Opt. Lett. 22, 1562 (1997).
[CrossRef]

Van Stryland, W. W.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

White, J. U.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996).
[CrossRef]

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

M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, Z. Cheng, G. Tempea, C. Spielmann, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 4, 414 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng 30, 1228 (1984).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997).
[CrossRef]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Some typos in Ref. 8 have to be corrected: In the definition of djp a factor πa2 is missing. Further, in Eq. (6) the factor P03/2 in front of the brace has to be eliminated. Finally, the energy in the higher modes is periodic with 2Lp and not with 4Lp.

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Figures (1)

Fig. 1
Fig. 1

(a) Schematic of free-space propagation in bulk Kerr nonlinearity with length L much longer than confocal parameter z0. (b) Solid curve; ratio of peak powers Γξ=G1ξ,τ=0/G0ξ,τ=02 in the fundamental TEM00 and in the next-higher TEM01 mode. Note that at the end of the medium nearly all the energy is returned to the fundamental mode, resulting in suppression of self-focusing. Γ is a measure of the strength of self-focusing. Γ=κ2/4 reaches a maximum at ξ0. The peak nonlinear phase shift (dashed curve) reaches a maximum of πκκ=z0/Lnl,  Lnl=1/γP0 for ξ. As κ2/41 must be fulfilled to avoid self-focusing, the maximum nonlinear phase shift is limited to the order of unity. (c) Guided-wave propagation in a gas-filled hollow waveguide with length LL2. We chose optimum input conditions given by w02a/3, so laser pulse evolution in a hollow fiber can be characterized in terms of w0 dependent parameters (L21.1z0, and κ as defined above). (d) Solid curve, ratio of peak powers Γ in the fundamental waveguide mode LP01 and in the next-higher mode LP02. A maximum signal of Γ=κ/π2 is coupled into the higher-order mode at L2. Dashed line, the nonlinear phase shift [ΦnlL2, τ=0=κ, when mode losses are neglected] grows over distances much longer than L2, making the realization of high pulse-compression factors possible.

Equations (11)

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

ξA=iDˆA+i2β0Tˆ-12A+in2β0n0TˆA2A.
A=jpVjpr,φ,ξAjpξ,τ.
Vjp=w0wξ2rwξjLpj2r2w2ξ×exp-r2w2ξ-iβ0r22Rξ+jφ-Φjpξ,
ξ-iDˆG0=iγd0G02G0+iγp12dpG02Gp+dp*G02Gp*,
ξ-iDˆGp=iγdpG02G0.
dpξ=12p1+ξz02 exp2ip arctanξz0.
G0ξ,τP0H0τexpiκH0τ2×arctanξz0-arctanξ0z0,
Gpξ,τP0H0τκH0τ22p+1p+κH0τ2Fξ,τ-Fξ0,τ,
Fξ,τ=exp2ip+κH0τ2arctanξz0,
κ/22=P0/Pcb21,  Pcb=λ02/πn2,
κ/π2=P0/Pcω21,  Pcω=π/2λ02/πn2.

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