Abstract

We present a theoretical investigation of self-focusing in a hollow waveguide filled with noble gas. Our analysis was performed for a laser pulse that was predominantly in the fundamental mode and revealed the physical processes involved in self-focusing in a hollow waveguide. A critical power for self-focusing was obtained that was found to be substantially higher than the critical power for self-focusing in a bulk medium. Useful design criteria for pulse-compression systems are presented. We identify the parameter range for which the transverse variation of the pulse phase introduced by the Kerr nonlinearity is small.

© 1998 Optical Society of America

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References

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  1. H. Nakatsuka, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
    [CrossRef]
  2. A. Baltuska, Z. Wei, M. S. Pshenicknikov, and D. A. Wiersma, Opt. Lett. 22, 102 (1997).
    [CrossRef] [PubMed]
  3. M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997); M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferenz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997); S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 1562 (1997).
    [CrossRef] [PubMed]
  4. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  5. W. Heuer and H. Zacharias, IEEE J. Quantum Electron. QE-24, 2087 (1988).
    [CrossRef]
  6. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  7. E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
    [CrossRef]
  8. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and W. W. Van Stryland, Opt. Eng. 30, 1228 (1984).
    [CrossRef]

1997 (1)

1996 (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997); M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferenz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997); S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 1562 (1997).
[CrossRef] [PubMed]

1988 (1)

W. Heuer and H. Zacharias, IEEE J. Quantum Electron. QE-24, 2087 (1988).
[CrossRef]

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]

1981 (1)

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Agrawal, G. P.

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

Balant, A. C.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Baltuska, A.

De Silvestri, S.

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997); M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferenz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997); S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 1562 (1997).
[CrossRef] [PubMed]

Grischkowsky, D.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

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]

Heuer, W.

W. Heuer and H. Zacharias, IEEE J. Quantum Electron. QE-24, 2087 (1988).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Nisoli, M.

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997); M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferenz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997); S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 1562 (1997).
[CrossRef] [PubMed]

Pshenicknikov, M. S.

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]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

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]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

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]

Svelto, O.

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997); M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferenz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997); S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 1562 (1997).
[CrossRef] [PubMed]

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]

Wei, Z.

Wiersma, D. A.

Zacharias, H.

W. Heuer and H. Zacharias, IEEE J. Quantum Electron. QE-24, 2087 (1988).
[CrossRef]

Appl. Phys. Lett. (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997); M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferenz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997); S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, Ch. Spielmann, and F. Krausz, Opt. Lett. 22, 1562 (1997).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Heuer and H. Zacharias, IEEE J. Quantum Electron. QE-24, 2087 (1988).
[CrossRef]

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. (1)

Phys. Rev. Lett. (1)

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 47, 910 (1981).
[CrossRef]

Other (2)

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

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

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Figures (1)

Fig. 1
Fig. 1

Pulse phase owing to Kerr nonlinearity in a hollow waveguide as a function of the radial and the temporal coordinates for a propagation distance (a) ξ=L2/50 and (b) ξ=29L2. For the other parameters see the text.

Equations (8)

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

××E-1c2t2-tdtn2r, t-tEt=2n2c2t2E2E,
E=12jpVjpr, φAjpz, texpiβjp0z-iω0t+c.c.,
ξ-iLˆ1G1=iγTˆd1G12G1+p>1dp×2G12Gpexp-iΔβp0ξ+G12Gp*expiΔβp0ξ,
ξ-iLˆp+Δβp1τGp=iγdpTˆG12G1expiΔβp0ξ.
G1ξ, τP0Gτexp-α10ξexpiγd1P0Gτ2Le,
Gpξ, τP0γP0dpΔβp0G12G1ξ, τexpiΔβp0ξ-P03/2G2Gτ+Δβp1ξexp-αp0ξ.
κ2=P0/Pcw21,  Pcw=u22-u12λ2/8πn2.
P0p0.3λ2/n¯2.

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