Abstract

The first integral of the complete set of Maxwell’s equations coupled through intrinsic nonlinearities in Kerr-type media has been found. The application of this result to wave propagation along a nonlinear optical waveguide leads to a general dispersion relation for nonlinear surface and guided waves of arbitrary polarization, i.e., hybrid TE–TM waves.

© 1989 Optical Society of America

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References

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  1. C. T. Seaton, G. I. Stegeman, H. G. Winful, Opt. Eng. 24, 593 (1985).
  2. G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
    [CrossRef]
  3. A. D. Boardman, P. Egan, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 3–77; G. I. Stegeman, C. T. Seaton, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 309–363.
  4. P. D. Maker, R. Terhune, Phys. Rev. 137, A801 (1964).
    [CrossRef]
  5. H. Vach, C. T. Seaton, G. I. Stegeman, I. C. Khoo, Opt. Lett. 9, 238 (1984).
    [CrossRef] [PubMed]
  6. I. Bennion, M. J. Goodwin, W. J. Stewart, Electron. Lett. 21, 41 (1985).
    [CrossRef]
  7. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef] [PubMed]
  8. A. A. Maradudin, Z. Phys. B 41, 341 (1981).
    [CrossRef]
  9. V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Pis’ma Zh. Eksp. Teor. Fiz. 32, 532 (1980) [JETP Lett. 32, 512 (1980)].
  10. C. T. Seaton, J. D. Valera, B. Svenson, G. I. Stegeman, Opt. Lett. 10, 149 (1985).
    [CrossRef] [PubMed]
  11. N. N. Akhmediev, Zh. Eksp. Teor. Fiz. 84, 1907 (1983) [Sov. Phys. JETP 57, 1111 (1983)].
  12. A. G. Litvak, G. M. Fraiman, Zh. Eksp. Teor. Fiz. 68, 1288 (1975) [Sov. Phys. JETP 41, 640 (1975)].
  13. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
    [CrossRef] [PubMed]
  14. D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, T. Twardowski, Opt. Lett. 12, 187 (1987).
    [CrossRef] [PubMed]
  15. R. I. Joseph, D. N. Christodoulides, Opt. Lett. 12, 826 (1987).
    [CrossRef] [PubMed]
  16. A. L. Berkhoer, V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].
  17. G. I. Stegeman, J. D. Valera, C. T. Seaton, Solid State Commun. 52, 293 (1984).
    [CrossRef]
  18. F. Lederer, D. Mihalache, Solid State Commun. 59, 151 (1986).
    [CrossRef]
  19. D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986).
    [CrossRef]

1987 (3)

1986 (2)

F. Lederer, D. Mihalache, Solid State Commun. 59, 151 (1986).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986).
[CrossRef]

1985 (4)

C. T. Seaton, J. D. Valera, B. Svenson, G. I. Stegeman, Opt. Lett. 10, 149 (1985).
[CrossRef] [PubMed]

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

G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[CrossRef]

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

1984 (2)

G. I. Stegeman, J. D. Valera, C. T. Seaton, Solid State Commun. 52, 293 (1984).
[CrossRef]

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

1983 (1)

N. N. Akhmediev, Zh. Eksp. Teor. Fiz. 84, 1907 (1983) [Sov. Phys. JETP 57, 1111 (1983)].

1981 (1)

A. A. Maradudin, Z. Phys. B 41, 341 (1981).
[CrossRef]

1980 (2)

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Pis’ma Zh. Eksp. Teor. Fiz. 32, 532 (1980) [JETP Lett. 32, 512 (1980)].

W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
[CrossRef] [PubMed]

1975 (1)

A. G. Litvak, G. M. Fraiman, Zh. Eksp. Teor. Fiz. 68, 1288 (1975) [Sov. Phys. JETP 41, 640 (1975)].

1970 (1)

A. L. Berkhoer, V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

1964 (1)

P. D. Maker, R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Pis’ma Zh. Eksp. Teor. Fiz. 32, 532 (1980) [JETP Lett. 32, 512 (1980)].

Akhmediev, N. N.

N. N. Akhmediev, Zh. Eksp. Teor. Fiz. 84, 1907 (1983) [Sov. Phys. JETP 57, 1111 (1983)].

Babichenko, V. S.

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Pis’ma Zh. Eksp. Teor. Fiz. 32, 532 (1980) [JETP Lett. 32, 512 (1980)].

Bennion, I.

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

Berkhoer, A. L.

A. L. Berkhoer, V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Boardman, A. D.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

A. D. Boardman, P. Egan, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 3–77; G. I. Stegeman, C. T. Seaton, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 309–363.

Chernyak, V. Ya.

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Pis’ma Zh. Eksp. Teor. Fiz. 32, 532 (1980) [JETP Lett. 32, 512 (1980)].

Christodoulides, D. N.

Egan, P.

A. D. Boardman, P. Egan, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 3–77; G. I. Stegeman, C. T. Seaton, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 309–363.

Fraiman, G. M.

A. G. Litvak, G. M. Fraiman, Zh. Eksp. Teor. Fiz. 68, 1288 (1975) [Sov. Phys. JETP 41, 640 (1975)].

Goodwin, M. J.

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

Joseph, R. I.

Khoo, I. C.

Lederer, F.

F. Lederer, D. Mihalache, Solid State Commun. 59, 151 (1986).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986).
[CrossRef]

Litvak, A. G.

A. G. Litvak, G. M. Fraiman, Zh. Eksp. Teor. Fiz. 68, 1288 (1975) [Sov. Phys. JETP 41, 640 (1975)].

Maker, P. D.

P. D. Maker, R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Maradudin, A. A.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

A. A. Maradudin, Z. Phys. B 41, 341 (1981).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986).
[CrossRef]

Mihalache, D.

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

F. Lederer, D. Mihalache, Solid State Commun. 59, 151 (1986).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986).
[CrossRef]

Seaton, C. T.

Stegeman, G. I.

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

C. T. Seaton, J. D. Valera, B. Svenson, G. I. Stegeman, Opt. Lett. 10, 149 (1985).
[CrossRef] [PubMed]

G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[CrossRef]

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

G. I. Stegeman, J. D. Valera, C. T. Seaton, Solid State Commun. 52, 293 (1984).
[CrossRef]

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

Stewart, W. J.

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

Svenson, B.

Terhune, R.

P. D. Maker, R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Tomlinson, W. J.

Twardowski, T.

Vach, H.

Valera, J. D.

C. T. Seaton, J. D. Valera, B. Svenson, G. I. Stegeman, Opt. Lett. 10, 149 (1985).
[CrossRef] [PubMed]

G. I. Stegeman, J. D. Valera, C. T. Seaton, Solid State Commun. 52, 293 (1984).
[CrossRef]

Winful, H. G.

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

Wright, E. M.

Zakharov, V. E.

A. L. Berkhoer, V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Zanoni, R.

Electron. Lett. (1)

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

J. Appl. Phys. (1)

G. I. Stegeman, C. T. Seaton, J. Appl. Phys. 58, R57 (1985).
[CrossRef]

Opt. Commun. (1)

D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986).
[CrossRef]

Opt. Eng. (1)

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

Opt. Lett. (5)

Phys. Rev. (1)

P. D. Maker, R. Terhune, Phys. Rev. 137, A801 (1964).
[CrossRef]

Phys. Rev. A (1)

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Pis’ma Zh. Eksp. Teor. Fiz. 32, 532 (1980) [JETP Lett. 32, 512 (1980)].

Solid State Commun. (2)

G. I. Stegeman, J. D. Valera, C. T. Seaton, Solid State Commun. 52, 293 (1984).
[CrossRef]

F. Lederer, D. Mihalache, Solid State Commun. 59, 151 (1986).
[CrossRef]

Z. Phys. B (1)

A. A. Maradudin, Z. Phys. B 41, 341 (1981).
[CrossRef]

Zh. Eksp. Teor. Fiz. (3)

N. N. Akhmediev, Zh. Eksp. Teor. Fiz. 84, 1907 (1983) [Sov. Phys. JETP 57, 1111 (1983)].

A. G. Litvak, G. M. Fraiman, Zh. Eksp. Teor. Fiz. 68, 1288 (1975) [Sov. Phys. JETP 41, 640 (1975)].

A. L. Berkhoer, V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Other (1)

A. D. Boardman, P. Egan, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 3–77; G. I. Stegeman, C. T. Seaton, in Surface Waves in Plasmas and Solids, S. Vukovic, ed. (World Scientific, Singapore, 1986), pp. 309–363.

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Figures (1)

Fig. 1
Fig. 1

Normalized electric-field components: Ey(z = 0) versus Ex(z = 0) of the hybrid TE–TM surface waves that propagate along the interface of the linear dielectric (3 = 2.5) and the nonlinear dielectric with 1 = 2.4025 and α = 6.4 × 10−12 m2V2 (corresponding to 4-methoxybenzulidene-4-n-butylaniline liquid crystal at angular frequency ω = 3.36 × 1015 and rad sec−1) for various values of the refractive index n2.

Equations (11)

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B x = d E y d τ ,             n E y = B z ,             d B x d τ = ( n 2 - y y ) E y ,
d E x d τ = n E z + B y ,             d B y d τ = - x x E x ,             n B y = - z z E z .
( d E y d τ ) 2 = n 2 E y 2 - C 1 2 E y 2 + 2 z z E z 2 - z z 2 E z 2 n 2 - ½ ( 1 E 2 + x x E x 2 + y y E y 2 + z z E z 2 ) + C 2 .
K s 2 E y 2 = n 2 E y 2 + 2 z z E z 2 - z z 2 E z 2 n 2 1 2 [ 1 ( E x 2 + E y 2 + E z 2 ) + x x E x 2 + y y E y 2 + z z E z 2 ] z = - 0 ,
K p 2 z z 2 E z 2 = n 2 E x 2 z = - 0 ,
K S = κ 2 κ 2 tan ( κ 2 τ d ) - κ 3 κ 3 tan ( κ 2 τ d ) + κ 2 , K P = κ 2 2 κ 2 2 - 1 tan ( κ 2 τ d ) - κ 3 3 - 1 κ 3 3 - 1   tan ( κ 2 τ d ) + κ 2 2 - 1 ,
[ 1 + y y + 2 ( K s 2 - n 2 ) ] z z 2 K p 2 E y 2 = [ 2 ( 2 n 2 - z z ) z z - ( 1 + z z ) n 2 - ( 1 + x x ) z z 2 K p 2 ] E x 2 z = - 0 .
n 2 = 3 z z 2 [ ( y y + 1 - 2 3 ) E y 2 + ( x x + 1 - 2 3 ) E x 2 ] ( y y + 1 - 2 3 ) z z 2 E y 2 + [ ( 1 + x x ) z z 2 + ( 1 + z z ) 3 2 - 4 z z 3 2 ] E x 2 | z = - 0 .
[ 2 ( 2 n 2 - z z ) z z - ( 1 + z z ) n 2 - ( 1 + x x ) z z 2 K p 2 ] E x 2 z = - 0 , E y = 0 = 0 ,
n 2 = 3 z z 2 ( x x + 1 - 2 3 ) ( 1 + x x ) z z 2 + ( 1 + z z ) 3 2 - 4 z z 3 2 | z = - 0 , E y = 0 ,
[ z z 2 + ½ 3 ( 1 - 3 z z ) ] E z 2 + ½ 3 [ ( 1 + x x ) E x 2 + ( 1 + y y ) E y 2 ] - 3 2 ( E x 2 + E y 2 ) z = - 0 = 0.

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