Abstract

Power versus effective-index stationary nonlinear surface-wave characteristics are determined for a linear-nonlinear dielectric interface and varying diffusion lengths. The threshold power for the existence of these waves increases linearly with increasing diffusion length. The stability criterion is found to be identical to the diffusion-less limit.

© 1988 Optical Society of America

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References

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  1. D. R. Anderson, Phys. Rev. A 37, 189 (1988).
    [Crossref]
  2. M. Miyagi, S. Nishida, Sci. Rep. Res. Inst. Tohuku Univ. Ser. B 25, 53 (1973).
  3. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [Crossref] [PubMed]
  4. W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, Appl. Opt. 21, 2041 (1982).
    [Crossref] [PubMed]
  5. N. N. Akhmediev, V. I. Korneev, Yu. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).
  6. A. B. Aceves, J. V. Moloney, A. C. Newell, J. Opt. Soc. Am. B 5, 559 (1988).
    [Crossref]
  7. D. J. Hagen, H. A. McKenzie, H. Al Attar, Opt. Lett. 10, 187 (1985).
    [Crossref]
  8. S. Adachi, J. Appl. Phys. 58, R1 (1985).
    [Crossref]
  9. H. B. DeVore, Phys. Rev. 102, 86 (1956).
    [Crossref]
  10. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986), Chap. 16.

1988 (2)

1985 (3)

D. J. Hagen, H. A. McKenzie, H. Al Attar, Opt. Lett. 10, 187 (1985).
[Crossref]

S. Adachi, J. Appl. Phys. 58, R1 (1985).
[Crossref]

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

1982 (1)

1980 (1)

1973 (1)

M. Miyagi, S. Nishida, Sci. Rep. Res. Inst. Tohuku Univ. Ser. B 25, 53 (1973).

1956 (1)

H. B. DeVore, Phys. Rev. 102, 86 (1956).
[Crossref]

Aceves, A. B.

Adachi, S.

S. Adachi, J. Appl. Phys. 58, R1 (1985).
[Crossref]

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Al Attar, H.

Anderson, D. R.

D. R. Anderson, Phys. Rev. A 37, 189 (1988).
[Crossref]

DeVore, H. B.

H. B. DeVore, Phys. Rev. 102, 86 (1956).
[Crossref]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986), Chap. 16.

Gordon, J. P.

Hagen, D. J.

Kaplan, A. E.

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Kuzmenko, Yu. V.

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

McKenzie, H. A.

Miyagi, M.

M. Miyagi, S. Nishida, Sci. Rep. Res. Inst. Tohuku Univ. Ser. B 25, 53 (1973).

Moloney, J. V.

Newell, A. C.

Nishida, S.

M. Miyagi, S. Nishida, Sci. Rep. Res. Inst. Tohuku Univ. Ser. B 25, 53 (1973).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986), Chap. 16.

Smith, P. W.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986), Chap. 16.

Tomlinson, W. J.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986), Chap. 16.

Appl. Opt. (1)

J. Appl. Phys. (1)

S. Adachi, J. Appl. Phys. 58, R1 (1985).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. (1)

H. B. DeVore, Phys. Rev. 102, 86 (1956).
[Crossref]

Phys. Rev. A (1)

D. R. Anderson, Phys. Rev. A 37, 189 (1988).
[Crossref]

Sci. Rep. Res. Inst. Tohuku Univ. Ser. B (1)

M. Miyagi, S. Nishida, Sci. Rep. Res. Inst. Tohuku Univ. Ser. B 25, 53 (1973).

Sov. Phys. JETP (1)

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuzmenko, Sov. Phys. JETP 61, 62 (1985).

Other (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986), Chap. 16.

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Figures (2)

Fig. 1
Fig. 1

Power P versus effective index β characteristics for different values of the scaled diffusion length r. The diffusionless characteristic (r = 0) is included in each figure for comparison. Stable branches of stationary NSW’s are denoted by solid lines, and unstable branches are denoted by dashed lines. In (a) diffusion is allowed across the interface corresponding to the boundary condition given by Eq. (3a); in (b) there is no diffusion across the interface corresponding to the boundary condition given by Eq. (3b). In our computations, the linear-index mismatch Δ = n12n22 = 0.1.

Fig. 2
Fig. 2

Plot of the critical power Pc, corresponding to the minimum in each characteristic in Fig. 1, against qr, the diffusion length scaled to the characteristic NSW width (q−1). The solid curve corresponds to case (a) and the dashed one to case (b).

Equations (8)

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d 2 F d ζ 2 - q 1 2 F = 0 ,             0 ζ > - ,
d 2 F d ζ 2 - q 2 2 F + N F = 0 , N - r 2 d 2 N d ζ 2 = F 2 ,             ζ 0 ,
E ( ζ 0 - ) = E ( ζ 0 + ) ,             d E ( ζ 0 - ) d ζ = d E ( ζ 0 + ) d ζ .
d N d ζ = N 0 r ,             N 0 = n 1 2 - n 2 2 ,
d N d ζ = 0
F = N = d F d ζ = d N d ζ = 0 ,
2 i β F ( ζ , η ) η + 2 F ( ζ , η ) ζ 2 - q i 2 F ( ζ , η ) + N ( ζ , η ) F ( ζ , η ) = 0 ,
N ( ζ , η ) - r 2 2 N ( ζ , η ) ζ 2 = F ( ζ , η ) 2 ,             ζ 0 ,

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