Abstract

We show that stationary gap solitons are just a limiting case of a wider set of (slowly) moving solitons associated with the photonic stop gap of a periodic nonlinear structure. We give an analytic description of these solitons and provide the prescription for launching such solitons in a realistic waveguide geometry.

© 1989 Optical Society of America

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References

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  1. W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
    [CrossRef] [PubMed]
  2. W. Chen, D. L. Mills, Phys. Rev. B 36, 6269 (1987).
    [CrossRef]
  3. U. Trutchel, F. Lederer, J. Opt. Soc. Am. 5, 2530 (1988).
    [CrossRef]
  4. C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
    [CrossRef] [PubMed]
  5. G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).
  6. S. L. McCall, E. L. Hahn, Phys. Rev. 183, 457 (1969).
    [CrossRef]
  7. C. M. de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
    [CrossRef] [PubMed]
  8. C. M. de Sterke, J. E. Sipe, “Possibilities for the observation of gap solitons in waveguide geometries,” J. Opt. Soc. Am. B (to be published).
  9. H. Kogelnik, Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1979), p. 15.
  10. G. I. Stegeman, Optical Sciences Center, University of Arizona, Tucson, Arizona 85721 (personal communication).
  11. R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
    [CrossRef]
  12. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]

1989

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef] [PubMed]

1988

U. Trutchel, F. Lederer, J. Opt. Soc. Am. 5, 2530 (1988).
[CrossRef]

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[CrossRef] [PubMed]

1987

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

W. Chen, D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1978

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

1969

S. L. McCall, E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Chen, W.

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

W. Chen, D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

de Sterke, C. M.

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef] [PubMed]

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[CrossRef] [PubMed]

C. M. de Sterke, J. E. Sipe, “Possibilities for the observation of gap solitons in waveguide geometries,” J. Opt. Soc. Am. B (to be published).

Hahn, E. L.

S. L. McCall, E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1979), p. 15.

Lamb, G. L.

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

Lederer, F.

U. Trutchel, F. Lederer, J. Opt. Soc. Am. 5, 2530 (1988).
[CrossRef]

Lin, C.

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

McCall, S. L.

S. L. McCall, E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Mills, D. L.

W. Chen, D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Sipe, J. E.

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef] [PubMed]

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[CrossRef] [PubMed]

C. M. de Sterke, J. E. Sipe, “Possibilities for the observation of gap solitons in waveguide geometries,” J. Opt. Soc. Am. B (to be published).

Stegeman, G. I.

G. I. Stegeman, Optical Sciences Center, University of Arizona, Tucson, Arizona 85721 (personal communication).

Stolen, R. H.

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Trutchel, U.

U. Trutchel, F. Lederer, J. Opt. Soc. Am. 5, 2530 (1988).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

U. Trutchel, F. Lederer, J. Opt. Soc. Am. 5, 2530 (1988).
[CrossRef]

Phys. Rev.

S. L. McCall, E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Phys. Rev. A

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 39, 5163 (1989).
[CrossRef] [PubMed]

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[CrossRef] [PubMed]

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Phys. Rev. B

W. Chen, D. L. Mills, Phys. Rev. B 36, 6269 (1987).
[CrossRef]

Phys. Rev. Lett.

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Other

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

C. M. de Sterke, J. E. Sipe, “Possibilities for the observation of gap solitons in waveguide geometries,” J. Opt. Soc. Am. B (to be published).

H. Kogelnik, Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1979), p. 15.

G. I. Stegeman, Optical Sciences Center, University of Arizona, Tucson, Arizona 85721 (personal communication).

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Figures (2)

Fig. 1
Fig. 1

Schematic of the waveguide geometry.

Fig. 2
Fig. 2

Time- and space-averaged electric-field energy densities as a function of position at t = −15 psec (dashed curve), t = 2.5 psec (solid curve), and t = 20 psec (dotted curve).

Equations (5)

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E ( z , t ) = a ( z , t ) φ m ( z ) exp ( i ω m t ) + l Λ l , m d a z φ l ( z ) exp ( i ω m t ) + c . c . ,
i a t + 1 2 ω m 2 a z 2 + α m | a | 2 a = 0 ,
a ( z , t ) = A exp ( i B 2 z ) exp [ i ( δ + Δ ) t ] sech ( B 1 z ℬt ) ,
A = 2 δ / α m , B 1 = 2 δ / ω m , B 2 = + 2 Δ / ω m , = ω m B 1 B 2 ,
E ( z , t ) = A 2 { sech ( t i ) [ C 1 i + C 2 i tanh ( t i ) ] + sech ( t r ) [ C 1 r + C 2 r tanh ( t r ) ] } exp ( i ω c t r ) + c . c . ,

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