Abstract

A simple analysis is presented for calculating the change in the effective index of a guided mode in an optical fiber with reduced cladding surrounded by an optically nonlinear medium. Using first-order perturbation theory, the optical power required to alter the phase-matched condition in a fiber directional coupler incorporating a nonlinear medium is therefore calculated. This may then be applied to an optically controlled switch, the output of which may be transferred from one port to another by application of a high-intensity pulse. This method may be applied to other fiber components, for example, fiber gratings and polarizers.

© 1986 Optical Society of America

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References

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  1. C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
    [CrossRef]
  2. R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973).
    [CrossRef]
  3. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [CrossRef]
  4. K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
    [CrossRef]
  5. D. J. Robbins, Opt. Commun. 47, 309 (1983).
    [CrossRef]
  6. I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
    [CrossRef]
  7. D. Sarid, G. I. Stegeman, Appl. Phys. 52, 5439 (1981).
  8. S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-30, 1568 (1982).
    [CrossRef]
  9. R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
    [CrossRef]
  10. F. J. Liao, J. T. Boyd, Appl. Opt. 21, 2731 (1981).
    [CrossRef]
  11. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  12. M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).
  13. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
    [CrossRef]
  14. M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
    [CrossRef]

1986 (1)

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

1985 (2)

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
[CrossRef]

1983 (2)

D. J. Robbins, Opt. Commun. 47, 309 (1983).
[CrossRef]

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

1982 (1)

S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-30, 1568 (1982).
[CrossRef]

1981 (3)

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

D. Sarid, G. I. Stegeman, Appl. Phys. 52, 5439 (1981).

F. J. Liao, J. T. Boyd, Appl. Opt. 21, 2731 (1981).
[CrossRef]

1975 (1)

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

1973 (1)

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

1971 (1)

1969 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[CrossRef]

Bennion, I.

I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
[CrossRef]

Boyd, J. T.

F. J. Liao, J. T. Boyd, Appl. Opt. 21, 2731 (1981).
[CrossRef]

Chrostowski, J.

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

Combemale, Y.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Cutler, C. C.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).

Gloge, D.

Goodman, J. W.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Goodwin, M. J.

I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
[CrossRef]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Hoffe, R.

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

Ippen, E. P.

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

Jackson, K. P.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Jensen, S. M.

S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-30, 1568 (1982).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Liao, F. J.

F. J. Liao, J. T. Boyd, Appl. Opt. 21, 2731 (1981).
[CrossRef]

Mathieu, X.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Moslehi, B.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Newton, S. A.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Ostrowsky, D. B.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Papuchon, M.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Prise, M. E.

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

Reiber, L.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Robbins, D. J.

D. J. Robbins, Opt. Commun. 47, 309 (1983).
[CrossRef]

Roy, A. M.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Sarid, D.

D. Sarid, G. I. Stegeman, Appl. Phys. 52, 5439 (1981).

Seaton, C. T.

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

Seyourne, B.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Shaw, H. J.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Smith, S. D.

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

Snyder, A. W.

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[CrossRef]

Sodha, M. S.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).

Stegeman, G. I.

D. Sarid, G. I. Stegeman, Appl. Phys. 52, 5439 (1981).

Stewart, W. J.

I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
[CrossRef]

Stolen, R. H.

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

Taghizadeh, M. R.

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

Tooley, F. A. P.

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

Tur, M.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

Werner, M.

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Appl. Opt. (2)

F. J. Liao, J. T. Boyd, Appl. Opt. 21, 2731 (1981).
[CrossRef]

D. Gloge, Appl. Opt. 10, 2252 (1971).
[CrossRef] [PubMed]

Appl. Phys. (1)

D. Sarid, G. I. Stegeman, Appl. Phys. 52, 5439 (1981).

Appl. Phys. Lett. (3)

C. T. Seaton, S. D. Smith, F. A. P. Tooley, M. E. Prise, M. R. Taghizadeh, Appl. Phys. Lett. 42, 131 (1983).
[CrossRef]

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

M. Papuchon, Y. Combemale, X. Mathieu, D. B. Ostrowsky, L. Reiber, A. M. Roy, B. Seyourne, M. Werner, Appl. Phys. Lett. 27, 289 (1975).
[CrossRef]

Electron. Lett. (1)

I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[CrossRef]

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, IEEE Trans. Microwave Theory Tech. MTT-33, 193 (1985).
[CrossRef]

S. M. Jensen, IEEE Trans. Microwave Theory Tech. MTT-30, 1568 (1982).
[CrossRef]

Opt. Commun. (2)

R. Hoffe, J. Chrostowski, Opt. Commun. 57, 34 (1986).
[CrossRef]

D. J. Robbins, Opt. Commun. 47, 309 (1983).
[CrossRef]

Proc. IEEE (1)

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Other (1)

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).

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Figures (2)

Fig. 1
Fig. 1

The proposed structure.

Fig. 2
Fig. 2

Coupler configuration.

Equations (10)

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E φ = 1 2 E l [ J l ( u r / a ) J l ( u ) K l ( w r / a ) / K l ( w ) ] × [ cos ( l + 1 ) φ + cos ( l - 1 ) φ ] ,             l = 0 , H φ = - 1 2 E l / Z 0 [ n 1 J l ( u r / a ) / J l ( u ) n 2 K l ( w r / a ) / K l ( w ) ] × [ sin ( l + 1 ) φ - sin ( l - 1 ) φ ] ,             l = 0 ,
β ( 1 ) 2 = β ( 0 ) 2 + k 0 2 A Δ E 2 d A / A E 2 d A .
β ( 1 ) 2 = β ( 0 ) 2 + k 0 2 A Δ E l ( d ) 2 K 0 2 [ w ( d ) r / a ] / K 0 2 [ w ( d ) ] d A / A E l ( d ) 2 { J 0 2 ( u r / a ) / J 0 2 ( u ) , r < a K 0 2 ( w r / a ) / K 0 2 ( w ) , r > a d A .
Δ = 2 n 2 n nl E l ( c ) 2 K 0 2 [ w ( c ) r / a ] / K 0 2 [ w ( c ) ] .
n eff ( 0 ) Δ n eff = 2 u ( d ) 2 n 2 n nl E l ( c ) 2 a K 0 2 [ w ( c ) r / a ] K 0 2 [ w ( d ) r / a ] × r d r / K 0 2 [ w ( c ) ] K 1 2 [ w ( d ) ] a 2 v ( d ) 2 .
Δ n eff = π 2 n 2 n nl E l ( c ) 2 u ( d ) 2 a / a exp { - 2 s [ w ( c ) + w ( d ) ] } / s d s / { w ( c ) w ( d ) K 0 2 [ w ( c ) ] K 1 2 [ w ( d ) ] n eff ( 0 ) v ( d ) 2 } .
Δ n eff = π 2 n 2 n nl E l ( c ) 2 u ( d ) 2 ( 2 a / a ) [ w ( c ) + w ( d ) ] exp ( - p ) / p d p / { 2 w ( c ) w ( d ) K 0 2 [ w ( c ) ] K 1 2 [ w ( d ) ] n eff v ( d ) 2 } .
P 1 ( z ) = P 0 cos 2 [ ( Δ β 2 / 4 c 2 + 1 ) 1 / 2 c z ] , P 2 ( z ) = P 0 sin 2 [ ( Δ β 2 / 4 c 2 + 1 ) 1 / 2 c z ] ,
P ( c ) = [ v ( c ) 2 / u ( c ) 2 ] { K 1 2 [ w ( c ) ] / K 0 2 [ w ( c ) ] } × ( π a 2 / 2 ) ( 1 / n 1 Z 0 ) E l ( c ) 2
K l ( x ) = { π / 2 x } exp ( - x ) [ 1 + ( 4 l 2 - 1 ) / 8 x ] .

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