Abstract

We discuss the possibility of self-taping and uptapering of a self-guided Gaussian laser beam induced by absorption and gain when the beam propagates in a medium with large saturable nonlinearity. Conditions for self-tapering/uptapering for both the cases, i.e., for absorption and gain, are discussed. The width of the tapered/uptapered beam depends on the rate of absorption and gain and on the length of the absorption and gain regions along the beam-propagation direction.

© 1994 Optical Society of America

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References

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  1. R. de la Fuente, A. Barthelemy, C. Froehly, Opt. Lett. 16, 793 (1991).
    [CrossRef] [PubMed]
  2. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, P. W. E. Smith, Opt. Lett. 16, 15 (1991).
    [CrossRef] [PubMed]
  3. L. Poladian, A. W. Snyder, D. J. Mitchell, Opt. Commun. 84, (1991); A. W. Snyder, L. Poladian, D. J. Mitchell, “Directing one beam of light with another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fiber Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).
  4. A. W. Snyder, L. Poladian, D. J. Mitchell, Opt. Lett. 17, 267 (1992).
    [CrossRef] [PubMed]
  5. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 17, p. 303.
  6. S. A. Akhmanov, A. P. Sukhrukhov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
    [CrossRef]
  7. M. S. Sodha, A. K. Ghatak, V. K. Tripathi, Prog. Opt. 13, 169 (1976).
    [CrossRef]
  8. V. E. Wood, E. D. Evans, R. P. Kenan, Opt. Commun. 69, 156 (1988).
    [CrossRef]

1992 (1)

1991 (3)

R. de la Fuente, A. Barthelemy, C. Froehly, Opt. Lett. 16, 793 (1991).
[CrossRef] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, P. W. E. Smith, Opt. Lett. 16, 15 (1991).
[CrossRef] [PubMed]

L. Poladian, A. W. Snyder, D. J. Mitchell, Opt. Commun. 84, (1991); A. W. Snyder, L. Poladian, D. J. Mitchell, “Directing one beam of light with another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fiber Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

1988 (1)

V. E. Wood, E. D. Evans, R. P. Kenan, Opt. Commun. 69, 156 (1988).
[CrossRef]

1976 (1)

M. S. Sodha, A. K. Ghatak, V. K. Tripathi, Prog. Opt. 13, 169 (1976).
[CrossRef]

1968 (1)

S. A. Akhmanov, A. P. Sukhrukhov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
[CrossRef]

Aitchison, J. S.

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhrukhov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
[CrossRef]

Barthelemy, A.

de la Fuente, R.

Evans, E. D.

V. E. Wood, E. D. Evans, R. P. Kenan, Opt. Commun. 69, 156 (1988).
[CrossRef]

Froehly, C.

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, V. K. Tripathi, Prog. Opt. 13, 169 (1976).
[CrossRef]

Jackel, J. L.

Kenan, R. P.

V. E. Wood, E. D. Evans, R. P. Kenan, Opt. Commun. 69, 156 (1988).
[CrossRef]

Khokhlov, R. V.

S. A. Akhmanov, A. P. Sukhrukhov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
[CrossRef]

Leaird, D. E.

Mitchell, D. J.

A. W. Snyder, L. Poladian, D. J. Mitchell, Opt. Lett. 17, 267 (1992).
[CrossRef] [PubMed]

L. Poladian, A. W. Snyder, D. J. Mitchell, Opt. Commun. 84, (1991); A. W. Snyder, L. Poladian, D. J. Mitchell, “Directing one beam of light with another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fiber Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

Oliver, M. K.

Poladian, L.

A. W. Snyder, L. Poladian, D. J. Mitchell, Opt. Lett. 17, 267 (1992).
[CrossRef] [PubMed]

L. Poladian, A. W. Snyder, D. J. Mitchell, Opt. Commun. 84, (1991); A. W. Snyder, L. Poladian, D. J. Mitchell, “Directing one beam of light with another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fiber Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 17, p. 303.

Silberberg, Y.

Smith, P. W. E.

Snyder, A. W.

A. W. Snyder, L. Poladian, D. J. Mitchell, Opt. Lett. 17, 267 (1992).
[CrossRef] [PubMed]

L. Poladian, A. W. Snyder, D. J. Mitchell, Opt. Commun. 84, (1991); A. W. Snyder, L. Poladian, D. J. Mitchell, “Directing one beam of light with another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fiber Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

Sodha, M. S.

M. S. Sodha, A. K. Ghatak, V. K. Tripathi, Prog. Opt. 13, 169 (1976).
[CrossRef]

Sukhrukhov, A. P.

S. A. Akhmanov, A. P. Sukhrukhov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
[CrossRef]

Tripathi, V. K.

M. S. Sodha, A. K. Ghatak, V. K. Tripathi, Prog. Opt. 13, 169 (1976).
[CrossRef]

Weiner, A. M.

Wood, V. E.

V. E. Wood, E. D. Evans, R. P. Kenan, Opt. Commun. 69, 156 (1988).
[CrossRef]

Opt. Commun. (2)

L. Poladian, A. W. Snyder, D. J. Mitchell, Opt. Commun. 84, (1991); A. W. Snyder, L. Poladian, D. J. Mitchell, “Directing one beam of light with another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fiber Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

V. E. Wood, E. D. Evans, R. P. Kenan, Opt. Commun. 69, 156 (1988).
[CrossRef]

Opt. Lett. (3)

Prog. Opt. (1)

M. S. Sodha, A. K. Ghatak, V. K. Tripathi, Prog. Opt. 13, 169 (1976).
[CrossRef]

Sov. Phys. Usp. (1)

S. A. Akhmanov, A. P. Sukhrukhov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
[CrossRef]

Other (1)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 17, p. 303.

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Figures (2)

Fig. 1
Fig. 1

Variation of f with αE02 for d2 f/dξ2 = 0.

Fig. 2
Fig. 2

Variation of f with ξ in regions A, B, and C. The upper branch shows uptapering by gain (positive ɛi), and the lower branch shows tapering by absorption (negative ɛi)

Equations (6)

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E E * | z = 0 = E 0 2 exp ( - r 2 / r 0 2 ) ,
ɛ ( E E * ) = ɛ 0 + i ɛ i + ϕ ( E E * ) ,
E E * = ( E 0 2 / f 2 ) × exp ( - r 2 / r 0 2 f 2 ) [ K ( 0 ) K * ( 0 ) / K ( f ) K * ( f ) ] 1 / 2 × exp { i [ k ( f ) - K * ( f ) ] d z } ,
d 2 f / d ξ 2 = [ ω 2 / K r 2 ( f ) c 2 f 3 ] - [ ω 4 r 0 2 γ α E 0 2 ɛ s exp ( - γ α E 0 2 / 2 f 2 ) / 2 K r 2 ( f ) c 4 f 3 ] ,
γ = [ K ( 0 ) K * ( 0 ) / K ( f ) K * ( f ) ] 1 / 2 × exp { i [ K ( f ) - K * ( f ) ] d z } .
f 2 = Ω α E 0 2 / 2 log [ 2 c 2 / ( ω 2 Ω α E 0 2 r 0 2 ɛ s ) ] ,

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