Abstract

The transmittance, the absorptance, and the phase shift on transmission and on reflection of a nonlinear, absorbing dielectric film are studied numerically for various model nonlinearities. The solution of the coupled nonlinear differential equations is straightforward.

© 1996 Optical Society of America

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References

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  1. W. Chen, D. L. Mills, Phys. Rev. B 35, 524 (1986).
    [CrossRef]
  2. K. M. Leung, Phys. Rev. B 39, 3590 (1989).
    [CrossRef]
  3. T. Peschel, F. J. Lederer, J. Opt. Soc. Am. B 5, 29 (1988).
    [CrossRef]
  4. H. W. Schürmann, R. Schmoldt, Z. Phys. B 92, 179 (1993).
    [CrossRef]
  5. K. L. Stokes, A. Puri, Opt. Lett. 15, 986 (1990).
    [CrossRef] [PubMed]
  6. We used the NDSolve routine of Mathematica 2.2:S. Wolfram, A System for doing Mathematics by Computers (Addison-Wesley, Redwood City, Calif., 1991).
  7. F. Henneberger, Phys. Status Solidi B 37, 371 (1986).
    [CrossRef]
  8. L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
    [CrossRef]
  9. R. Rosman, G. Gibson, K. Boyer, H. Jara, T. S. Luk, I. A. McIntyre, A. McPherson, J. C. Solem, C. K. Rhodes, J. Opt. Soc. Am. B 5, 1237 (1988).
    [CrossRef]
  10. A. N. An, V. T. Kovalev, Sov. J. Quantum Electron. 17, 1075 (1987).
    [CrossRef]
  11. D. Mihalache, D. Mazilu, M. Bertolotti, C. Sibilia, J. Opt. Soc. Am. B 5, 565 (1988).
    [CrossRef]
  12. J. A. Hermann, J. Mod. Opt. 36, 445 (1989).
    [CrossRef]

1993 (1)

H. W. Schürmann, R. Schmoldt, Z. Phys. B 92, 179 (1993).
[CrossRef]

1990 (1)

1989 (2)

K. M. Leung, Phys. Rev. B 39, 3590 (1989).
[CrossRef]

J. A. Hermann, J. Mod. Opt. 36, 445 (1989).
[CrossRef]

1988 (4)

1987 (1)

A. N. An, V. T. Kovalev, Sov. J. Quantum Electron. 17, 1075 (1987).
[CrossRef]

1986 (2)

W. Chen, D. L. Mills, Phys. Rev. B 35, 524 (1986).
[CrossRef]

F. Henneberger, Phys. Status Solidi B 37, 371 (1986).
[CrossRef]

Acioli, L. H.

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

An, A. N.

A. N. An, V. T. Kovalev, Sov. J. Quantum Electron. 17, 1075 (1987).
[CrossRef]

Bertolotti, M.

Boyer, K.

Chen, W.

W. Chen, D. L. Mills, Phys. Rev. B 35, 524 (1986).
[CrossRef]

Gibson, G.

Gomes, A. S. L.

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Henneberger, F.

F. Henneberger, Phys. Status Solidi B 37, 371 (1986).
[CrossRef]

Hermann, J. A.

J. A. Hermann, J. Mod. Opt. 36, 445 (1989).
[CrossRef]

Jara, H.

Kovalev, V. T.

A. N. An, V. T. Kovalev, Sov. J. Quantum Electron. 17, 1075 (1987).
[CrossRef]

Lederer, F. J.

Leung, K. M.

K. M. Leung, Phys. Rev. B 39, 3590 (1989).
[CrossRef]

Luk, T. S.

Mazilu, D.

McIntyre, I. A.

McPherson, A.

Mihalache, D.

Mills, D. L.

W. Chen, D. L. Mills, Phys. Rev. B 35, 524 (1986).
[CrossRef]

Peschel, T.

Puri, A.

Rhodes, C. K.

Rios Leite, J. R.

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

Rosman, R.

Schmoldt, R.

H. W. Schürmann, R. Schmoldt, Z. Phys. B 92, 179 (1993).
[CrossRef]

Schürmann, H. W.

H. W. Schürmann, R. Schmoldt, Z. Phys. B 92, 179 (1993).
[CrossRef]

Sibilia, C.

Solem, J. C.

Stokes, K. L.

Wolfram, S.

We used the NDSolve routine of Mathematica 2.2:S. Wolfram, A System for doing Mathematics by Computers (Addison-Wesley, Redwood City, Calif., 1991).

Appl. Phys. Lett. (1)

L. H. Acioli, A. S. L. Gomes, J. R. Rios Leite, Appl. Phys. Lett. 53, 1788 (1988).
[CrossRef]

J. Mod. Opt. (1)

J. A. Hermann, J. Mod. Opt. 36, 445 (1989).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (1)

Phys. Rev. B (2)

W. Chen, D. L. Mills, Phys. Rev. B 35, 524 (1986).
[CrossRef]

K. M. Leung, Phys. Rev. B 39, 3590 (1989).
[CrossRef]

Phys. Status Solidi B (1)

F. Henneberger, Phys. Status Solidi B 37, 371 (1986).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. N. An, V. T. Kovalev, Sov. J. Quantum Electron. 17, 1075 (1987).
[CrossRef]

Z. Phys. B (1)

H. W. Schürmann, R. Schmoldt, Z. Phys. B 92, 179 (1993).
[CrossRef]

Other (1)

We used the NDSolve routine of Mathematica 2.2:S. Wolfram, A System for doing Mathematics by Computers (Addison-Wesley, Redwood City, Calif., 1991).

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Figures (2)

Fig. 1
Fig. 1

Configuration considered in this Letter. A plane wave is incident upon an absorbing NL film.

Fig. 2
Fig. 2

(a) Transmittance (curve I) and absorptance (curve II), (b) phase shift on transmission (curve I) and phase shift on reflection (curve II) for ɛL = 4, β = 0.01, κ = 0.01, and k0d = 2. Curves III indicate the Kerr case as a reference (ɛL = 4, β = 0.01, κ = 0). (a) Curves III and IV denote transmittance and absorptance, respectively; (b) curves III and IV denote phase shift on transmission and on reflection, respectively.

Equations (27)

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E c = 1 2 ( E 0 exp { i [ - k 0 ɛ 1 ( y - d ) - ω 0 t ] + ( E r exp ( i δ r ) exp { i [ k 0 ɛ 1 ( y - d ) - ω 0 t ] } + c . c . ) e z ,
E f = 1 2 { E ( y ) exp [ i q ( y ) ] + c . c . } e z ,
E s = 1 2 { E 3 exp ( i δ t ) exp [ i ( - k 0 ɛ 3 y - ω 0 t ) ] + c . c . ) e z ,
d 2 E f d y 2 + k 0 2 ɛ 2 ( E f 2 ) E f = 0
E - ( q ) 2 E + ɛ R ( E 2 ) E = 0 ,
q E + 2 q E + ɛ I ( E 2 ) E = 0 ,
E ( 0 ) = E 3 ,             E ( 0 ) = 0 ,             q ( 0 ) = - ɛ 3 .
E 0 2 = 1 4 { E 2 ( ξ ) [ 1 - q ( ξ ) ɛ 1 ] 2 + E ( ξ ) 2 ɛ 1 } ξ = k 0 d ,
E r 2 = 1 4 { E 2 ( ξ ) [ 1 + q ( ξ ) ɛ 1 ] 2 + E ( ξ ) 2 ɛ 1 } ξ = k 0 d ,
sin q ( k 0 d ) = - E ( ξ ) 2 ɛ 1 E 0 | ξ = k 0 d .
A = 1 - R - T ,
T = ɛ 3 ɛ 1 E 2 ( 0 ) E 0 2 ,
R = E r 2 E 0 2 .
E 2 ( ξ ) q ( ξ ) = - ɛ 3 E 2 ( 0 ) - 0 ξ d ξ ɛ I [ E 2 ( ξ ) ] E 2 ( ξ ) .
A = 1 ɛ 1 E 0 2 0 k 0 d d ξ ɛ i [ E 2 ( ξ ) ] E 2 ( ξ ) .
sin  δ r = - E ( ξ ) E ( ξ ) 2 ɛ 1 E 0 2 1 - T - A | ξ = k 0 d .
δ t = q ( 0 ) = 0 k 0 d d ξ ɛ 3 E 2 ( 0 ) + ɛ 1 E 0 2 A ( ξ ) E 2 ( ξ ) + arcsin [ - E ( ξ ) 2 ɛ 1 E 0 | ξ = k 0 d ] ,
A ( ξ ) = 1 ɛ 1 E 0 2 0 ξ d ξ ɛ I [ E 2 ( ξ ) ] E 2 ( ξ )
ɛ 2 = ɛ L ( 1 + i β ) + α E f 2 .
E = ( q ) 2 E + ɛ L E ± E 3 = 0 ,
q E + 2 q E + β ɛ L E = 0 ,
ɛ 2 = ɛ L ( 1 + i β ) + α E f 2 1 + α / ɛ s E f 2 ,
E - ( q ) 2 E + ɛ L E ± ɛ s E 3 1 + E 2 = 0 ,
ɛ 2 = ɛ L ( 1 + i β ) + α E f 2 + γ E f 4 ,
E - ( q ) 2 E + ( ɛ L + α E 2 + γ E 4 ) E = 0.
ɛ 2 = ɛ L ( 1 + i β ) + α ( 1 + i κ ) E f 2 ,
q E + 2 q E + ɛ L β E + κ E 3 = 0.

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