Abstract

We show that, when two channel waveguides are coupled by a sequence of periodically spaced microresonators, the group-velocity dispersion is low in the vicinity of the gap associated with the resonant frequency of the resonators. This low dispersion permits the excitation of a gap soliton with much lower energy than in a gap of similar width caused by Bragg reflection.

© 2002 Optical Society of America

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References

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  1. J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity and optical solitons in a resonator-array waveguide,” submitted to Phys. Rev. Lett.
  2. J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B (to be published).
  3. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, Opt. Lett. 25, 344 (2000).
    [Crossref]
  4. A. Melloni, Opt. Lett. 26, 917 (2001).
    [Crossref]
  5. N. A. R. Bhat and J. E. Sipe, Phys. Rev. E 64, 0566-04 (2001).
    [Crossref]
  6. S. Pereira and J. E. Sipe, Phys. Rev. E 62, 5745 (2000).
    [Crossref]
  7. C. M. de Sterke and J. E. Sipe, Opt. Lett. 14, 871 (1989).
    [Crossref] [PubMed]
  8. G. P. Agrawal, Non-Linear Fiber Optics (Academic, San Diego, Calif., 1989).

2001 (2)

N. A. R. Bhat and J. E. Sipe, Phys. Rev. E 64, 0566-04 (2001).
[Crossref]

A. Melloni, Opt. Lett. 26, 917 (2001).
[Crossref]

2000 (2)

1989 (1)

Absil, P. P.

Agrawal, G. P.

G. P. Agrawal, Non-Linear Fiber Optics (Academic, San Diego, Calif., 1989).

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, Phys. Rev. E 64, 0566-04 (2001).
[Crossref]

Boyd, R. W.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity and optical solitons in a resonator-array waveguide,” submitted to Phys. Rev. Lett.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B (to be published).

Chu, S. T.

de Sterke, C. M.

Heebner, J. E.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity and optical solitons in a resonator-array waveguide,” submitted to Phys. Rev. Lett.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B (to be published).

Hryniewicz, J. V.

Little, B. E.

Melloni, A.

Park, Q.-H.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B (to be published).

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity and optical solitons in a resonator-array waveguide,” submitted to Phys. Rev. Lett.

Pereira, S.

S. Pereira and J. E. Sipe, Phys. Rev. E 62, 5745 (2000).
[Crossref]

Sipe, J. E.

N. A. R. Bhat and J. E. Sipe, Phys. Rev. E 64, 0566-04 (2001).
[Crossref]

S. Pereira and J. E. Sipe, Phys. Rev. E 62, 5745 (2000).
[Crossref]

C. M. de Sterke and J. E. Sipe, Opt. Lett. 14, 871 (1989).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. E (2)

N. A. R. Bhat and J. E. Sipe, Phys. Rev. E 64, 0566-04 (2001).
[Crossref]

S. Pereira and J. E. Sipe, Phys. Rev. E 62, 5745 (2000).
[Crossref]

Other (3)

G. P. Agrawal, Non-Linear Fiber Optics (Academic, San Diego, Calif., 1989).

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “Slow light, induced dispersion, enhanced nonlinearity and optical solitons in a resonator-array waveguide,” submitted to Phys. Rev. Lett.

J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B (to be published).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the two-channel SCISSOR. (b) One unit cell of the structure. Filled circles, coupling points at the top and the bottom of the microresonator.

Fig. 2
Fig. 2

Dispersion relation for the two-channel SCISSOR with material parameters given in the text. The gap at ω/c=4.11 µm-1 is associated with the 59th-order resonance of the microresonator. The gap at ω/c=4.075 µm-1 is associated with Bragg reflection. These gaps are at typical communications wavelengths, as indicated by the right-hand axis.

Fig. 3
Fig. 3

Ssol is the ratio of the energy required for forming a gap soliton in a resonator gap to the energy required for forming the same gap soliton in a Bragg gap with the same gap width relative to its center frequency.

Equations (7)

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q0+la+=σbiκbiκbσbq0-la-,
expiνdβbβt-α2-βt expikdα-αexp-iνd-βt expikdl0u0=0,
drΩcelln2rEmk*r·Emkr=δmnδkk,
=gmk¯z,t2dz.
it+iωmk¯zgmk¯z,t=-12ωmk¯2gmk¯z,tz2-Γmk¯gmk¯z,t2gmk¯z,t,
Γmk¯=3ω¯4Aeff 0celldrΩcellχ3rEmk¯r4,
guk¯z,t=A expiB2zexp-iδ+ΔtsechB1z-Ct,

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