Abstract

We show stable modes (stationary self-trapped beams) of elliptic cross section in an elliptic-core nonlinear fiber. These stable modes can be tapered in the presence of absorption or gain. Ellipticity of the beam can be controlled by induced tapering. Another interesting feature is the possibility of conversion of an elliptic Gaussian laser beam into a circular Gaussian laser beam. A stationary self-trapped beam plus an elliptic-core nonlinear fiber form an elliptic-core linear fiber for a low-power signal beam, and hence one can induce an elliptic-core linear fiber of optically tunable parameters for a low-power signal beam.

© 1995 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. K. 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 by another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fibre 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. M. S. Sodha, S. Medhekar, S. Konar, A. Saxena, M. Rajkamal, Opt. Lett. 19, 1110 (1994).
    [CrossRef]
  6. A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
    [CrossRef]
  7. G. Keiser, in Optical Fiber Communications (McGraw-Hill, New York, 1983), pp. 39–40.
  8. S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, Sov. Phys. Usp. 10, 609 (1968).
    [CrossRef]
  9. M. S. Sodha, A. K. Ghatak, V. K. Triphati, Prog. Opt. 13, 169 (1976).
    [CrossRef]
  10. S. Medhekar, A. Saxena, Rajkamal, Ind. J. Pure Appl. Phys. 31, 609 (1993).

1994 (1)

1993 (1)

S. Medhekar, A. Saxena, Rajkamal, Ind. J. Pure Appl. Phys. 31, 609 (1993).

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. K. 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 by another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fibre Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

1990 (1)

A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
[CrossRef]

1976 (1)

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

1968 (1)

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

Aitchison, J. S.

Akhmanov, S. A.

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

Barthelemy, A.

Chen, Y.

A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
[CrossRef]

de la Fuente, R.

Froehly, C.

Ghatak, A. K.

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

Jackel, J. K.

Keiser, G.

G. Keiser, in Optical Fiber Communications (McGraw-Hill, New York, 1983), pp. 39–40.

Khokhlov, R. V.

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

Konar, S.

Leaird, D. E.

Medhekar, S.

M. S. Sodha, S. Medhekar, S. Konar, A. Saxena, M. Rajkamal, Opt. Lett. 19, 1110 (1994).
[CrossRef]

S. Medhekar, A. Saxena, Rajkamal, Ind. J. Pure Appl. Phys. 31, 609 (1993).

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 by another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fibre Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
[CrossRef]

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 by another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fibre Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
[CrossRef]

Rajkamal,

S. Medhekar, A. Saxena, Rajkamal, Ind. J. Pure Appl. Phys. 31, 609 (1993).

Rajkamal, M.

Saxena, A.

M. S. Sodha, S. Medhekar, S. Konar, A. Saxena, M. Rajkamal, Opt. Lett. 19, 1110 (1994).
[CrossRef]

S. Medhekar, A. Saxena, Rajkamal, Ind. J. Pure Appl. Phys. 31, 609 (1993).

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 by another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fibre Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
[CrossRef]

Sodha, M. S.

Sukhorukov, A. P.

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

Triphati, V. K.

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

Weiner, A. M.

Electron. Lett. (1)

A. W. Snyder, Y. Chen, L. Poladian, D. J. Mitchell, Electron. Lett. 26, 643 (1990).
[CrossRef]

Ind. J. Pure Appl. Phys. (1)

S. Medhekar, A. Saxena, Rajkamal, Ind. J. Pure Appl. Phys. 31, 609 (1993).

Opt. Commun. (1)

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 by another beam,” presented at the Fifteenth Annual Meeting of the Australian Conference on Optical Fibre Technology, Sydney, Australia, December 2–6, 1990; T. Thawaites, New Sci. 1751, 14 (1991).

Opt. Lett. (4)

Prog. Opt. (1)

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

Sov. Phys. Usp. (1)

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

Other (1)

G. Keiser, in Optical Fiber Communications (McGraw-Hill, New York, 1983), pp. 39–40.

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Figures (4)

Fig. 1
Fig. 1

Variation of a and b with αE02 for ∂2a/∂ξ2 = 0 and ∂2b/∂ξ2 = 0.

Fig. 2
Fig. 2

Variation of a and b with ξ calculated by Eqs. (4) for αE02 = 1.5 × 10−8, a = 0.067, and b = 0.080 calculated from Eq. (5). Constant a and b indicate a stable mode.

Fig. 3
Fig. 3

Variation of a and b with ξ in regions A, B, and C. The beam tapers in absorbing region B and propagates as a circular Gaussian beam in region C.

Fig. 4
Fig. 4

Variation of a and b with ξ in regions A, B, and C. The beam tapers in gain region B and propagates as a circular Gaussian beam in region C.

Equations (6)

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E E * z = 0 = E 0 2 a ( 0 ) b ( 0 ) exp ( - { [ x / r 0 a ( 0 ) ] 2 + [ y / r 0 b ( 0 ) ] 2 } ) ,
ɛ ( E E * ) = ɛ 0 + i ɛ i + ϕ ( E E * ) - ɛ 21 x 2 - ɛ 22 y 2 ,
ɛ 21 = N c 0 2 r 0 2 ( N c 0 2 - N cl 1 2 N cl 1 2 ) , ɛ 22 = N c 0 2 r 0 2 ( N c 0 2 - N cl 2 2 N cl 2 2 ) ,
2 a ξ 2 = ω 2 c 2 k r 2 a 3 - ( ω r 0 c ) 4 ɛ 21 a k r 2 - ω 4 r 0 2 α E 0 2 γ ɛ s c 4 k r 2 a 2 b [ 1 + ( α E o 2 γ / a b ) ] 2 , 2 b ξ 2 = ω 2 c 2 k r 2 b 3 - ( ω r 0 c ) 4 ɛ 22 b k r 2 - ω 4 r 0 2 α E 0 2 γ ɛ s c 4 k r 2 b 2 a [ 1 + ( α E o 2 γ / a b ) ] 2 ,
ɛ 0 ( a , b ) = ɛ 0 + i ɛ i + ϕ ( E 0 2 a b γ ) , γ = [ k ( 0 ) k * ( 0 ) k ( a , b ) k * ( a , b ) ] × exp { i [ k ( a , b ) - k * ( a , b ) ] d z } , k ( 0 ) = k [ a ( 0 ) , b ( 0 ) ] .
ω 2 r 0 4 ɛ 21 a 4 c 2 + ω 2 r 0 2 α E 0 2 a ɛ s c 2 b [ 1 + ( α E 0 2 / a b ) ] 2 = 1 , ω 2 r 0 4 ɛ 22 b 4 c 2 + ω 2 r 0 2 α E 0 2 b ɛ s c 2 a [ 1 + ( α E 0 2 / a b ) ] 2 = 1.

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