Abstract

We argue that the planar optical waveguide is the geometry of choice for observing electromagnetic Stark ladders.

© 1991 Optical Society of America

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References

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  1. G. Monsivais, M. del Castillo-Mussot, F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
    [Crossref] [PubMed]
  2. G. H. Wannier, Elements of Solid State Theory (Cambridge U. Press, London, 1959), pp. 190–193.
  3. D. Emin, C. F Hart, Phys. Rev. B 36, 7353 (1987).
    [Crossref]
  4. F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
    [Crossref]
  5. J. Agler, R. Froese, Commun. Math. Phys. 100, 161 (1985).
    [Crossref]
  6. E. E. Mendez, F. Agulló-Rueda, J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988).
    [Crossref] [PubMed]
  7. J. M. Combes, P. D. Hislop, J. Phys. A 23, 1501 (1990).
    [Crossref]
  8. See, e.g., L. D. Landau, E. M. Lifshitz, L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984), p. 291.
  9. H. Kogelnik, in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), pp. 7-87.
    [Crossref]
  10. P. K. Tien, Rev. Mod. Phys. 49, 361 (1977).
    [Crossref]
  11. M. J. Beesley, J. G. Castledine, Appl. Opt. 4, 2720 (1970).
    [Crossref]
  12. D. Vincent, J.W. Y. Lit, Can. J. Phys. 57, 45 (1979).
    [Crossref]
  13. D. Vincent, R. Tremblay, J.W.Y. Lit, J. Opt. Soc. Am. 70, 964 (1979).
  14. E. Popov, L. Mashev, Opt. Acta 32, 265 (1985).
    [Crossref]
  15. L. A. Weller-Brophy, D.G. Hall, J. Opt. Soc. Am. A 2, 863 (1985).
    [Crossref]

1990 (2)

G. Monsivais, M. del Castillo-Mussot, F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[Crossref] [PubMed]

J. M. Combes, P. D. Hislop, J. Phys. A 23, 1501 (1990).
[Crossref]

1988 (1)

E. E. Mendez, F. Agulló-Rueda, J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988).
[Crossref] [PubMed]

1987 (1)

D. Emin, C. F Hart, Phys. Rev. B 36, 7353 (1987).
[Crossref]

1985 (3)

J. Agler, R. Froese, Commun. Math. Phys. 100, 161 (1985).
[Crossref]

E. Popov, L. Mashev, Opt. Acta 32, 265 (1985).
[Crossref]

L. A. Weller-Brophy, D.G. Hall, J. Opt. Soc. Am. A 2, 863 (1985).
[Crossref]

1983 (1)

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

1979 (2)

D. Vincent, J.W. Y. Lit, Can. J. Phys. 57, 45 (1979).
[Crossref]

D. Vincent, R. Tremblay, J.W.Y. Lit, J. Opt. Soc. Am. 70, 964 (1979).

1977 (1)

P. K. Tien, Rev. Mod. Phys. 49, 361 (1977).
[Crossref]

1970 (1)

M. J. Beesley, J. G. Castledine, Appl. Opt. 4, 2720 (1970).
[Crossref]

Agler, J.

J. Agler, R. Froese, Commun. Math. Phys. 100, 161 (1985).
[Crossref]

Agulló-Rueda, F.

E. E. Mendez, F. Agulló-Rueda, J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988).
[Crossref] [PubMed]

Beesley, M. J.

M. J. Beesley, J. G. Castledine, Appl. Opt. 4, 2720 (1970).
[Crossref]

Bentosela, F.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

Carmona, R.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

Castledine, J. G.

M. J. Beesley, J. G. Castledine, Appl. Opt. 4, 2720 (1970).
[Crossref]

Claro, F.

G. Monsivais, M. del Castillo-Mussot, F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[Crossref] [PubMed]

Combes, J. M.

J. M. Combes, P. D. Hislop, J. Phys. A 23, 1501 (1990).
[Crossref]

del Castillo-Mussot, M.

G. Monsivais, M. del Castillo-Mussot, F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[Crossref] [PubMed]

Duclos, P.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

Emin, D.

D. Emin, C. F Hart, Phys. Rev. B 36, 7353 (1987).
[Crossref]

Froese, R.

J. Agler, R. Froese, Commun. Math. Phys. 100, 161 (1985).
[Crossref]

Hall, D.G.

Hart, C. F

D. Emin, C. F Hart, Phys. Rev. B 36, 7353 (1987).
[Crossref]

Hislop, P. D.

J. M. Combes, P. D. Hislop, J. Phys. A 23, 1501 (1990).
[Crossref]

Hong, J. M.

E. E. Mendez, F. Agulló-Rueda, J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988).
[Crossref] [PubMed]

Kogelnik, H.

H. Kogelnik, in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), pp. 7-87.
[Crossref]

Landau, L. D.

See, e.g., L. D. Landau, E. M. Lifshitz, L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984), p. 291.

Lifshitz, E. M.

See, e.g., L. D. Landau, E. M. Lifshitz, L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984), p. 291.

Lit, J.W. Y.

D. Vincent, J.W. Y. Lit, Can. J. Phys. 57, 45 (1979).
[Crossref]

Lit, J.W.Y.

Mashev, L.

E. Popov, L. Mashev, Opt. Acta 32, 265 (1985).
[Crossref]

Mendez, E. E.

E. E. Mendez, F. Agulló-Rueda, J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988).
[Crossref] [PubMed]

Monsivais, G.

G. Monsivais, M. del Castillo-Mussot, F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[Crossref] [PubMed]

Pitaevskii, L. P.

See, e.g., L. D. Landau, E. M. Lifshitz, L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984), p. 291.

Popov, E.

E. Popov, L. Mashev, Opt. Acta 32, 265 (1985).
[Crossref]

Simon, B.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

Souillard, B.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

Tien, P. K.

P. K. Tien, Rev. Mod. Phys. 49, 361 (1977).
[Crossref]

Tremblay, R.

Vincent, D.

D. Vincent, R. Tremblay, J.W.Y. Lit, J. Opt. Soc. Am. 70, 964 (1979).

D. Vincent, J.W. Y. Lit, Can. J. Phys. 57, 45 (1979).
[Crossref]

Wannier, G. H.

G. H. Wannier, Elements of Solid State Theory (Cambridge U. Press, London, 1959), pp. 190–193.

Weder, R.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

Weller-Brophy, L. A.

Appl. Opt. (1)

M. J. Beesley, J. G. Castledine, Appl. Opt. 4, 2720 (1970).
[Crossref]

Can. J. Phys. (1)

D. Vincent, J.W. Y. Lit, Can. J. Phys. 57, 45 (1979).
[Crossref]

Commun. Math. Phys. (2)

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder, Commun. Math. Phys. 88, 387 (1983).
[Crossref]

J. Agler, R. Froese, Commun. Math. Phys. 100, 161 (1985).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. A (1)

J. M. Combes, P. D. Hislop, J. Phys. A 23, 1501 (1990).
[Crossref]

Opt. Acta (1)

E. Popov, L. Mashev, Opt. Acta 32, 265 (1985).
[Crossref]

Phys. Rev. B (1)

D. Emin, C. F Hart, Phys. Rev. B 36, 7353 (1987).
[Crossref]

Phys. Rev. Lett. (2)

E. E. Mendez, F. Agulló-Rueda, J. M. Hong, Phys. Rev. Lett. 60, 2426 (1988).
[Crossref] [PubMed]

G. Monsivais, M. del Castillo-Mussot, F. Claro, Phys. Rev. Lett. 64, 1433 (1990).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

P. K. Tien, Rev. Mod. Phys. 49, 361 (1977).
[Crossref]

Other (3)

See, e.g., L. D. Landau, E. M. Lifshitz, L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984), p. 291.

H. Kogelnik, in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), pp. 7-87.
[Crossref]

G. H. Wannier, Elements of Solid State Theory (Cambridge U. Press, London, 1959), pp. 190–193.

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Figures (3)

Fig. 1
Fig. 1

Top view of the trajectory of a ray in a localized state (dashed curve). The solid and dotted lines indicate local maxima and minima, respectively, in the refractive (effective) index. The light is trapped by two distinct effects to a localization length L: Bragg reflection on the high-index side and TIR on the low-index side. Only a single localized state is shown—others are shifted by an integer number of periods.

Fig. 2
Fig. 2

Schematic of the planar waveguide geometry.

Fig. 3
Fig. 3

Calculated angle-dependent reflectivity for the geometry in Fig. 2. The parameters are nf = 1.64 (photoresist), ns = 1.456 (fused quartz), d = 0.6761 μm, L0 = 1370d, h(z = L0/2) = 0.35 μm, Δh = 5 nm, N(z = 0) = 1.5209, N(z = L0/2) = 1.5672, N(z = L0) = 1.6135, N(z < 0) = N(z = L02), and λ = 0.5145 μm.

Equations (9)

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

( z + M d ) = ( z ) + α M d ,
N ( z ) = N 0 + β z + Δ N sin 2 π d z
h ( z ) = h 0 + γ z + Δ h sin 2 π d z
2 y 2 + 2 z 2 + [ N 0 + d N d h | h = h 0 ( γ z + Δ h sin 2 π d z ) ] 2 × ( ω c ) 2 = 0 ,
k y 2 + k z 2 = ( N 0 + β z ) 2 ω 2 c 2 ,
k y 2 = ( N 0 + β z 1 ) 2 ω 2 c 2 ,
k y 2 + ( π / d ) 2 = ( N 0 + β z 2 ) 2 ω 2 c 2 .
L z 2 z 1 = ( λ 2 d ) 2 1 2 N 0 β ,
Δ θ = α d ( N m 2 N 0 2 ) 1 / 2 .

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