Abstract

We analyze side-coupled standing-wave cavity structures consisting of Fabry–Perot and photonic crystal resonators coupled to two waveguides. We show that optical bright and dark states, analogous to those observed in coherent light–matter interactions, can exist in these systems. These structures may be useful for variable, switchable delay lines.

© 2007 Optical Society of America

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References

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  1. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
    [CrossRef]
  2. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]
  3. J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
    [CrossRef]
  4. J. K. S. Poon, P. Chak, J. M. Choi, and A. Yariv, "Slowing light with Fabry-Perot resonator arrays," (submitted to J. Opt. Soc. Am. B).
  5. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).
  6. S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
    [CrossRef]
  7. J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
    [CrossRef]
  8. E. Peral and A. Yariv, J. Lightwave Technol. 17, 942 (1999).
    [CrossRef]

2002 (2)

1999 (3)

1998 (1)

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

1984 (1)

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Boyd, R. W.

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Chak, P.

S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
[CrossRef]

J. K. S. Poon, P. Chak, J. M. Choi, and A. Yariv, "Slowing light with Fabry-Perot resonator arrays," (submitted to J. Opt. Soc. Am. B).

Choi, J. M.

J. K. S. Poon, P. Chak, J. M. Choi, and A. Yariv, "Slowing light with Fabry-Perot resonator arrays," (submitted to J. Opt. Soc. Am. B).

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Lee, R. K.

Marangos, J. P.

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

Peral, E.

Pereira, S.

Poon, J. K. S.

J. K. S. Poon, P. Chak, J. M. Choi, and A. Yariv, "Slowing light with Fabry-Perot resonator arrays," (submitted to J. Opt. Soc. Am. B).

Scherer, A.

Sipe, J. E.

Xu, Y.

Yariv, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

E. Peral and A. Yariv, J. Lightwave Technol. 17, 942 (1999).
[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

J. K. S. Poon, P. Chak, J. M. Choi, and A. Yariv, "Slowing light with Fabry-Perot resonator arrays," (submitted to J. Opt. Soc. Am. B).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

J. Lightwave Technol. (1)

J. Mod. Opt. (2)

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

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

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Opt. Lett. (1)

Other (2)

J. K. S. Poon, P. Chak, J. M. Choi, and A. Yariv, "Slowing light with Fabry-Perot resonator arrays," (submitted to J. Opt. Soc. Am. B).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

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Figures (6)

Fig. 1
Fig. 1

Schematic of standing-wave resonators side coupled to two waveguides. The light gray regions represent the waveguiding sections and the dark regions represent the high-index regions in the reflectors. (a) FP-SC-CROW structure. (b) Two-channel FP-SCISSOR structure.

Fig. 2
Fig. 2

Dispersion relation of an FP-SC-CROW in the limit of (a) weak waveguide-cavity coupling and (b) no waveguide-cavity coupling.

Fig. 3
Fig. 3

Dispersion relation of an FP-SCISSOR in the limit of (a) weak waveguide-cavity coupling and (b) no waveguide-cavity coupling.

Fig. 4
Fig. 4

(a) TM dispersion relation of a PC-SC-CROW near the resonance frequency of the PC cavity. Inset, unit cell of the structure. The dark rods have n = 3.0 and r = 0.2 a , where a is the lattice constant for the square lattice. The background material has n = 1.0 . (b)–(e) Fields labeled in (a).

Fig. 5
Fig. 5

(a) TM dispersion of a PC-SCISSOR. The PC is identical to Fig. 4. Inset, unit cell of the structure. (b)–(e) Fields labeled in (a).

Fig. 6
Fig. 6

(a) Dispersion relation of an FP-SCISSOR with similar parameters as Fig. 3 but with 40 grating periods separating successive cavities. (b) Group delay in finite FP-SCISSORs consisting of five (solid curve) and eight (dashed curve) cavities.

Equations (3)

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[ e + e ] = [ T R R T ] [ e + e ] ,
[ e + e ] = M [ e + e ] [ T RT 1 R RT 1 T 1 R T 1 ] [ e + e ] ,
d A d z = i κ B , d B d z = i κ A i κ C , d C d z = i κ B ,

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