Abstract

We derive exact dispersion relations for transverse magnetic polarized guided waves at an interface between either a linear dielectric or a metal and a nonlinear dielectric. The nonlinearity is taken to be a Kerr-type nonlinearity. Numerical results are presented for the dielectric–metal case.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. E. Kaplan, Sov. Phys. JETP Lett. 24, 114 (1976); Sov. Phys. JETP Lett. 45, 896 (1977).
  2. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef] [PubMed]
  3. A. A. Maradudin, in Optical and Acoustic Waves in Solids—Modern Topics, M. Borissov, ed. (World, Singapore, 1983), p. 72.
  4. V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).
  5. C. T. Seaton, J. D. Valera, B. Svenson, G. I. Stegeman, Opt. Lett. 10, 149 (1985).
    [CrossRef] [PubMed]
  6. N. N. Akhmediev, Sov. Phys. JETP 57, 1111 (1983).
  7. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).
  8. G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
    [CrossRef]
  9. A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).
  10. See, for example, J. R. Reitz, F. J. Milford, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass., 1966).

1985 (1)

1983 (1)

N. N. Akhmediev, Sov. Phys. JETP 57, 1111 (1983).

1982 (1)

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

1981 (1)

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

1980 (1)

1976 (1)

A. E. Kaplan, Sov. Phys. JETP Lett. 24, 114 (1976); Sov. Phys. JETP Lett. 45, 896 (1977).

1970 (1)

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Agranovich, V. M.

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Akhmediev, N. N.

N. N. Akhmediev, Sov. Phys. JETP 57, 1111 (1983).

Babichenko, V. S.

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Berkhoer, A. L.

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Boardman, A. D.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).

Chernyak, V. Ya.

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Kaplan, A. E.

A. E. Kaplan, Sov. Phys. JETP Lett. 24, 114 (1976); Sov. Phys. JETP Lett. 45, 896 (1977).

Maradudin, A. A.

A. A. Maradudin, in Optical and Acoustic Waves in Solids—Modern Topics, M. Borissov, ed. (World, Singapore, 1983), p. 72.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).

Milford, F. J.

See, for example, J. R. Reitz, F. J. Milford, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass., 1966).

Reitz, J. R.

See, for example, J. R. Reitz, F. J. Milford, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass., 1966).

Seaton, C. T.

Stegeman, G. I.

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

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

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).

Svenson, B.

Tomlinson, W. J.

Twardowski, T.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).

Valera, J. D.

Wright, E. M.

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).

Zakharov, V. E.

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

IEEE J. Quantum Electron. (1)

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

Opt. Lett. (2)

Sov. Phys. JETP (2)

N. N. Akhmediev, Sov. Phys. JETP 57, 1111 (1983).

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Sov. Phys. JETP Lett. (2)

A. E. Kaplan, Sov. Phys. JETP Lett. 24, 114 (1976); Sov. Phys. JETP Lett. 45, 896 (1977).

V. M. Agranovich, V. S. Babichenko, V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Other (3)

A. A. Maradudin, in Optical and Acoustic Waves in Solids—Modern Topics, M. Borissov, ed. (World, Singapore, 1983), p. 72.

See, for example, J. R. Reitz, F. J. Milford, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass., 1966).

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, E. M. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A (to be published).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Dispersion curves for parameter values ω = 3.66 × 105 rad, x = z = 2.405, s = −2.5, α1 = 6.4 × 10−12 m2V−2, and (a) α1 = 3α2; (b) α1 = α2

Fig. 2
Fig. 2

Ex versus transverse coordinate z for case (a) of Fig. 1 and (a) β = 9, (b) β = 13, (c) β = 25. The interface is at z = 0.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

d d z E x = 1 β [ z z - β 2 ] E z ,
d d z z z E z = - β x x E x ,
H y = - 0 c β z z E z ,
E ( r , t ) = ½ [ i E x ( z ) x + E z ( z ) y ] exp [ i ( ω t - β x ) ] + c . c .
z z = z + α 1 E z 2 + α 2 E x 2 ,
x x = x + α 1 E x 2 + α 2 E z 2 ,
( d E x d z ) 2 = ( β 2 - z ) E z 2 - x E x 2 - α 2 ( E x E z ) 2 - α 1 2 ( E x 4 + E z 4 ) ,
E x ( z ) = E 0 x exp ( q s z ) ,             z < 0 ,
E z = β ( z z - β 2 ) d d z E x ,
D z = β z z ( z z - β 2 ) d d z E x ,
nl = z + α 1 E 0 z 2 + α 2 E 0 x 2 ,
d E x d z = - ( nl - β 2 ) s q s nl E 0 x = 1 β ( nl - β 2 ) E 0 z ,
E 0 x = - nl q s β s E 0 z = - ( z + α 1 E 0 z 2 + α 2 E 0 x 2 ) q s β s E 0 z .
α 1 2 E 0 x 4 + [ x + ( s q s ) 2 ] E 0 x 2 + ( β s q s E 0 z ) E 0 x - α 1 2 E 0 z 4 = 0.
S = 1 k 0 - d z E × H · x ,
S = 1 2 μ 0 ω β [ 0 z z E z 2 d z + ( nl E 0 z ) 2 2 q s s ] .

Metrics