Abstract

TM-polarized nonlinear modes supported by a symmetric five-layer dielectric structure consisting of a nonlinear medium of thickness θ (characterized by the diagonal dielectric tensor 11 = 220, 33 = 0 + α|E3|2, where E3 is the TE-field component) sandwiched between two linear films of thickness β (with dielectric constant 1), which are bounded from the free ends by the same nonlinear medium, are analyzed. Dispersion relations and the expressions for the power flow, derived for the symmetric and antisymmetric modes, show that for a sufficiently large value of β/λ, where λ is the wavelength, these modes should show bistable behavior, provided that power flow is the control parameter.

© 1987 Optical Society of America

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  1. N. N. Ahmediev, Sov. Phys. JETP 56, 299 (1982).
  2. D. Michalache, preprint IC/85/40 (International Center for Theoretical Physics, 1985).
  3. C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).
  4. C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
    [CrossRef]
  5. H. Vach, G. I. Stegeman, C. T. Seaton, I. C. Choo, Opt. Lett. 9, 238 (1984).
    [CrossRef] [PubMed]
  6. I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
    [CrossRef]
  7. G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
    [CrossRef]
  8. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  9. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  10. L. F. Mollenauer, R. H. Stolen, M. N. Islam, Opt. Lett. 10, 229 (1985).
    [CrossRef] [PubMed]
  11. A. Kumar, S. N. Sarkar, A. K. Ghatak, Opt. Lett. 11, 321 (1986).
    [CrossRef] [PubMed]
  12. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  13. D. Anderson, M. Lisak, Opt. Lett. 9, 468 (1984).
    [CrossRef] [PubMed]
  14. K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
    [CrossRef]
  15. R. K. Varshney, M. A. Nehme, R. Srivastava, R. V. Ramaswami, preprint (University of Florida, Gainesville, Fla., 1986).
  16. G. I. Stegeman, Appl. Phys. Lett. 44, 830 (1984).
    [CrossRef]
  17. D. Michalache, D. Mazilu, H. Potia, Phys. Scr. 30, 335 (1984).
    [CrossRef]

1986 (1)

1985 (4)

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

C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, M. N. Islam, Opt. Lett. 10, 229 (1985).
[CrossRef] [PubMed]

1984 (4)

1982 (3)

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

N. N. Ahmediev, Sov. Phys. JETP 56, 299 (1982).

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[CrossRef]

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1973 (2)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Ahmediev, N. N.

N. N. Ahmediev, Sov. Phys. JETP 56, 299 (1982).

Anderson, D.

Bennion, I.

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

Blow, K. J.

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

Chilwell, J. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

Choo, I. C.

Doran, N. J.

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

Ghatak, A. K.

Goodwin, M. J.

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

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Islam, M. N.

Kumar, A.

Lisak, M.

Mai, X.

C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).

Mazilu, D.

D. Michalache, D. Mazilu, H. Potia, Phys. Scr. 30, 335 (1984).
[CrossRef]

Michalache, D.

D. Michalache, D. Mazilu, H. Potia, Phys. Scr. 30, 335 (1984).
[CrossRef]

D. Michalache, preprint IC/85/40 (International Center for Theoretical Physics, 1985).

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, M. N. Islam, Opt. Lett. 10, 229 (1985).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Nehme, M. A.

R. K. Varshney, M. A. Nehme, R. Srivastava, R. V. Ramaswami, preprint (University of Florida, Gainesville, Fla., 1986).

Potia, H.

D. Michalache, D. Mazilu, H. Potia, Phys. Scr. 30, 335 (1984).
[CrossRef]

Ramaswami, R. V.

R. K. Varshney, M. A. Nehme, R. Srivastava, R. V. Ramaswami, preprint (University of Florida, Gainesville, Fla., 1986).

Sarkar, S. N.

Seaton, C. T.

C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

H. Vach, G. I. Stegeman, C. T. Seaton, I. C. Choo, Opt. Lett. 9, 238 (1984).
[CrossRef] [PubMed]

Shoemaker, R. L.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

Smith, S. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

Srivastava, R.

R. K. Varshney, M. A. Nehme, R. Srivastava, R. V. Ramaswami, preprint (University of Florida, Gainesville, Fla., 1986).

Stegeman, G. I.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).

H. Vach, G. I. Stegeman, C. T. Seaton, I. C. Choo, Opt. Lett. 9, 238 (1984).
[CrossRef] [PubMed]

G. I. Stegeman, Appl. Phys. Lett. 44, 830 (1984).
[CrossRef]

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[CrossRef]

Stewart, W. J.

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

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, M. N. Islam, Opt. Lett. 10, 229 (1985).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Vach, H.

Valera, J. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

Varshney, R. K.

R. K. Varshney, M. A. Nehme, R. Srivastava, R. V. Ramaswami, preprint (University of Florida, Gainesville, Fla., 1986).

Weinful, H. G.

C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).

Appl. Phys. Lett. (3)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

G. I. Stegeman, Appl. Phys. Lett. 44, 830 (1984).
[CrossRef]

Electron. Lett. (1)

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

IEEE J. Quantum Electron. (2)

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[CrossRef]

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, S. D. Smith, IEEE J. Quantum Electron. QE-21, 774 (1985).
[CrossRef]

Opt. Commun. (1)

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

Opt. Eng. (1)

C. T. Seaton, X. Mai, G. I. Stegeman, H. G. Weinful, Opt. Eng. 24, 593 (1985).

Opt. Lett. (4)

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Phys. Scr. (1)

D. Michalache, D. Mazilu, H. Potia, Phys. Scr. 30, 335 (1984).
[CrossRef]

Sov. Phys. JETP (1)

N. N. Ahmediev, Sov. Phys. JETP 56, 299 (1982).

Other (2)

D. Michalache, preprint IC/85/40 (International Center for Theoretical Physics, 1985).

R. K. Varshney, M. A. Nehme, R. Srivastava, R. V. Ramaswami, preprint (University of Florida, Gainesville, Fla., 1986).

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Equations (23)

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11 = 22 0 , 33 = 0 + α | E 3 | 2 ,
E 1 , 3 = 1 , 3 ( z ) exp [ i ( ω t k x ) ] , H 2 = 2 ( z ) exp [ i ( ω t k x ) ] ,
d 1 d z i k 3 = i k 0 2 ,
d 2 d z = i k 0 D 1 , k 2 = k 0 D 3 .
d 2 2 A d z 2 q 2 0 [ 0 α k 4 0 k 0 2 q 2 ( 2 A ) 2 ] 2 A = 0 , d 2 2 B d z 2 ( k 2 1 k 0 2 ) 2 B = 0 ,
2 I ( z ) = 2 α f sech [ q ( z z 1 ) ] , 2 II ( z ) = { A 1 cosh [ k 1 ( z z 0 ) ] , n > n 1 A 3 cos [ k 2 ( z z 0 ) ] , n < n 1 , 2 III ( z ) = 2 α f sech [ q ( z z 2 ) ] , 2 IV ( z ) = { A 2 cosh [ k 1 ( z z 0 ) ] , n > n 1 A 4 cos [ k 2 ( z z 0 ) ] , n < n 1 , 2 V ( z ) = 2 α f sech [ q ( z z 3 ) ] ,
q = k 2 0 k 0 2 , n 1 = 1 , f = 0 k 0 q / k 2 , k 1 = k 2 1 k 0 2 , k 2 = k 0 2 1 k 2 .
{ 1 b 1 2 tanh 2 [ k 1 ( β + θ 2 z 0 ) ] } cosh 2 [ k 1 ( θ 2 z 0 ) ] = { 1 b 1 2 tanh 2 [ k 1 ( θ 2 z 0 ) ] } × cosh 2 [ k 1 ( β + θ 2 z 0 ) ] , { 1 b 1 2 tanh 2 [ k 1 ( β + θ 2 + z 0 ) ] } cosh 2 [ k 1 ( θ 2 + z 0 ) ] = { 1 b 1 2 tanh 2 [ k 1 ( θ 2 + z 0 ) ] } × cosh 2 [ k 1 ( β + θ 2 + z 0 ) ] ,
{ 1 b 2 2 tan 2 [ k 2 ( β + θ 2 z 0 ) ] } cos 2 [ k 2 ( θ 2 z 0 ) ] = { 1 b 2 2 tan 2 [ k 2 ( θ 2 z 0 ) ] } × cos 2 [ k 1 ( β + θ 2 z 0 ) ] , { 1 b 2 2 tan 2 [ k 2 ( β + θ 2 + z 0 ) ] } cos 2 [ k 2 ( θ 2 + z 0 ) ] = { 1 b 2 2 tan 2 [ k 2 ( θ 2 + z 0 ) ] } × cos 2 [ k 2 ( β + θ 2 + z 0 ) ] ,
tanh [ q ( β + θ 2 + z 1 ) ] = b 1 tanh [ k 1 ( β + θ 2 + z 0 ) ] , tanh ( q θ / 2 ) = b 1 tanh [ k 1 ( θ 2 + z 0 ) ]
tanh [ q ( β + θ 2 + z 1 ) ] = b 2 tan [ k 2 ( β + θ 2 + z 0 ) ] , tanh ( q θ / 2 ) = b 2 tan [ k 2 ( θ 2 + z 0 ) ]
A 1 2 = A 2 2 = 2 f 2 α cosh 2 [ k 1 ( β + θ 2 + z 0 ) ] × { 1 b 1 2 tanh 2 [ k 1 ( β + θ 2 + z 0 ) ] }
A 3 2 = A 4 2 = 2 f 2 α cos 2 [ k 2 ( β + θ 2 + z 0 ) ] × { 1 b 2 2 tan 2 [ k 2 ( β + θ 2 + z 0 ) ] } .
2 II ( z ) = { B 1 sinh [ k 1 ( z z 0 ) ] , n > n 1 B 3 sin [ k 2 ( z z 0 ) ] , n < n 1 ,
2 IV ( z ) = { B 2 sinh [ k 1 ( z z 0 ) ] , n > n 1 B 4 sin [ k 2 ( z z 0 ) ] , n < n 1 .
tanh [ q ( β + θ 2 + z 1 ) ] = b 1 coth [ k 1 ( β + θ 2 + z 0 ) ] , tanh ( q θ / 2 ) = b 1 coth [ k 1 ( θ 2 + z 0 ) ] ;
tanh [ q ( β + θ 2 + z 1 ) ] = b 2 cot [ k 2 ( β + θ 2 + z 0 ) ] , tanh ( q θ / 2 ) = b 2 cot [ k 2 ( θ 2 + z 0 ) ]
B 1 2 = B 2 2 = 2 f 2 α sinh 2 [ k 1 ( β + θ 2 + z 0 ) ] × { 1 coth 2 [ k 1 ( β + θ 2 + z 0 ) ] } ,
B 3 2 = B 4 2 = 2 f 2 α sin 2 [ k 2 ( β + θ 2 + z 0 ) ] × { 1 b 2 2 cot 2 [ k 2 ( β + θ 2 + z 0 ) ] }
P = c k 8 π k 0 [ 1 0 + 2 2 ( z ) d z α k 2 0 3 k 0 2 + 2 4 d z ] .
P s = P 0 4 f 2 k 0 q ( { 1 2 f 2 k 2 α k 0 2 [ 1 1 3 ( 1 + p 1 + p 1 2 ) ] } × ( 1 p 1 ) + [ 1 2 f 2 k 2 0 k 0 2 ( 1 p 2 2 3 ) p 2 ] ) + p 0 f 2 0 ( 1 p 1 2 ) cosh 2 [ k 1 ( β + θ 2 + z 0 ) ] × [ ( k β 2 + k 4 k 1 { sinh [ 2 k 1 ( β + θ 2 + z 0 ) ] sinh [ 2 k 1 ( θ 2 + z 0 ) ] } ) f 2 k 2 0 k 0 2 cosh 2 [ k 1 ( β + θ 2 + z 0 ) ] ( 1 p 1 2 ) × { 3 K β 2 + k k 1 ( 2 sinh [ k 1 ( β + θ 2 + z 0 ) ] + 1 4 sinh [ 4 k 1 ( β + θ 2 + z 0 ) ] 2 sinh [ 2 k 1 ( θ 2 + z 0 ) ] 1 4 sinh [ 4 k 1 ( θ 2 + z 0 ) ] } )
P 0 = ( c / 8 π α k 0 ) , p 1 = b 1 tanh [ k 1 ( β + θ 2 + z 0 ) ] , p 2 = b 1 tanh [ k 1 ( θ 2 + z 0 ) ] ,
t 1 = f 2 tan [ k 2 ( β + θ 2 + z 0 ) ] , t 2 = f 2 tan [ k 2 ( θ 2 + z 0 ) ] ,

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