Abstract

We theoretically describe a novel configuration of a vertically coupled whispering-gallery-mode resonator waveguide. The waveguide is formed as a chain of doughnut-shaped low-contrast ripples on the surface of a vertical cylinder made from an optically transparent material. One can manipulate the properties of the waveguide by changing the shape of the resonators and the separation distance between them. Application of the structure as an optical delay line is discussed.

© 2005 Optical Society of America

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References

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  1. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]
  2. J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, J. Opt. Soc. Am. B 21, 1818 (2004).
    [CrossRef]
  3. J. B. Khurgin, Phys. Rev. A 62, 013821 (2000).
    [CrossRef]
  4. V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
    [CrossRef]
  5. M. Sumetsky, Opt. Express 13, 4331 (2005).
    [CrossRef] [PubMed]
  6. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
    [CrossRef]

2005 (1)

2004 (2)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, J. Opt. Soc. Am. B 21, 1818 (2004).
[CrossRef]

2000 (2)

J. B. Khurgin, Phys. Rev. A 62, 013821 (2000).
[CrossRef]

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

1999 (1)

Astratov, V. N.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

Boyd, R. W.

Chak, P.

Culshaw, I. S.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

De La Rue, R. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

Heebner, J. E.

Ilchenko, V. S.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Khurgin, J. B.

J. B. Khurgin, Phys. Rev. A 62, 013821 (2000).
[CrossRef]

Krauss, T. F.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

Lee, R. K.

Maleki, L.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Matsko, A. B.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Pereira, S.

Savchenkov, A. A.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Scherer, A.

Sipe, J. E.

Skolnick, M. S.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

Stevenson, R. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

Sumetsky, M.

Whittaker, D. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

Xu, Y.

Yariv, A.

Appl. Phys. Lett. (1)

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, Appl. Phys. Lett. 77, 178 (2000).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

J. B. Khurgin, Phys. Rev. A 62, 013821 (2000).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Resonator waveguide.

Fig. 2
Fig. 2

(a) Distribution of the field in (b) a single low-contrast WGM resonator on a post. The field distribution was obtained by numerical solution of two-dimensional Eq. (2). The angular momentum number of the mode shown is ν = 10 4 .

Fig. 3
Fig. 3

Solution of Eq. (5) for period l = 25 μ m ( l g = 5 μ m ) , wavelength λ = 1.5 μ m , radius a = 0.3 cm , bump height A 0 = 30 μ m , and ϵ 0 = 2.2 . Inset, structure of the first band evaluated by use of Eq. (6).

Fig. 4
Fig. 4

Left, a set of coupled WGM rings placed on a single rod. Right, a map obtained with two-dimensional numerical simulations describing ultraslow propagation of an optical pulse. The group velocity is less than 20 cm s .

Equations (10)

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× ( × E ) k 2 ϵ ( r ) E = 0 ,
2 Ψ r 2 + 2 Ψ z 2 + { k 2 ϵ 0 [ 1 2 A ( z ) a ] ν 2 r 2 } Ψ = 0 ,
2 Ψ z z 2 2 k 2 ϵ 0 A ( z ) a Ψ z = k z 2 Ψ z ,
2 Ψ r r 2 + ( k 2 ϵ 0 k z 2 ν 2 r 2 ) Ψ r = 0 ,
cos ( β l ) = cosh [ l g ( 2 k 2 ϵ 0 A 0 a k z 2 ) 1 2 ] cos [ k z ( l l g ) ] + k 2 ϵ 0 A 0 a k z ( 2 k 2 ϵ 0 A 0 a k z 2 ) 1 2 sinh [ l g ( 2 k 2 ϵ 0 A 0 a k z 2 ) 1 2 ] sin [ k z ( l l g ) ] ,
( ω 2 c 2 ) ϵ 0 = k ν , q 2 + k z 2 .
ω c c ϵ 0 k ν , q + 1 2 k ν , q ( π m l l g ) 2
Δ ω c ϵ 0 4 π 2 m 2 k ν , q 2 ( l l q ) 3 a 2 A 0 exp ( l g k ν , q 2 A 0 a ) .
k ν , q 1 a [ ν + α q ( ν 2 ) 1 3 ϵ 0 ϵ 0 1 ] ,
V g ϵ 0 c Δ ω ϵ 0 l 2 π c = 2 π m 2 l k ν , q 2 ( l l g ) 3 a 2 A 0 exp ( l g k ν , q 2 A 0 a ) .

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