Abstract

We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately π/k0, where k0 is the longitudinal wave vector for which the group velocity is zero.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
  2. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
    [CrossRef] [PubMed]
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    [CrossRef]
  4. J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, Opt. Lett. 27, 1785 (2002).
    [CrossRef]
  9. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
    [CrossRef] [PubMed]
  10. K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  15. V. A. Mandelshtam and H. Taylor, J. Chem. Phys. 107, 6756 (1997).

2004 (1)

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

2003 (4)

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, Opt. Lett. 28, 516 (2003).
[CrossRef]

J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

2000 (2)

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, Phys. Rev. E 65, 016608 (2000).
[CrossRef]

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

1997 (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

V. A. Mandelshtam and H. Taylor, J. Chem. Phys. 107, 6756 (1997).

1960 (1)

P. J. B. Clarricoats and R. A. Waldron, J. Electron. Control 8, 455 (1960).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Benisty, H.

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Clarricoats, P. J. B.

P. J. B. Clarricoats and R. A. Waldron, J. Electron. Control 8, 455 (1960).
[CrossRef]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Fan, S.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Fink, Y.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, Opt. Lett. 28, 516 (2003).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech, Norwood, Mass., 2000).

Haus, H. A.

Houdre, R.

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Ibanescu, M.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, Opt. Lett. 28, 516 (2003).
[CrossRef]

Ilegems, M.

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, Opt. Lett. 28, 516 (2003).
[CrossRef]

M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, Opt. Lett. 27, 1785 (2002).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, Opt. Lett. 28, 516 (2003).
[CrossRef]

M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, Opt. Lett. 27, 1785 (2002).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Krauss, T. F.

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, Phys. Rev. E 65, 016608 (2000).
[CrossRef]

Luo, C.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, Phys. Rev. E 65, 016608 (2000).
[CrossRef]

Mandelshtam, V. A.

V. A. Mandelshtam and H. Taylor, J. Chem. Phys. 107, 6756 (1997).

Mekis, A.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Ochoa, D.

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Painter, O.

K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Roundy, D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, Phys. Rev. E 65, 016608 (2000).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Smith, C. J. M.

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Soljacic, M.

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Srinivasan, K.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech, Norwood, Mass., 2000).

Taylor, H.

V. A. Mandelshtam and H. Taylor, J. Chem. Phys. 107, 6756 (1997).

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Vuckovic, J.

J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, Phys. Rev. E 65, 016608 (2000).
[CrossRef]

Waldron, R. A.

P. J. B. Clarricoats and R. A. Waldron, J. Electron. Control 8, 455 (1960).
[CrossRef]

Watts, M. R.

Yamamoto, Y.

J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

J. Chem. Phys. (1)

V. A. Mandelshtam and H. Taylor, J. Chem. Phys. 107, 6756 (1997).

J. Electron. Control (1)

P. J. B. Clarricoats and R. A. Waldron, J. Electron. Control 8, 455 (1960).
[CrossRef]

Nature (3)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

D. Ochoa, R. Houdre, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith, Phys. Rev. B 61, 4806 (2000).
[CrossRef]

Phys. Rev. E (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, Phys. Rev. E 65, 016608 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, Phys. Rev. Lett. 92, 063903 (2004).
[CrossRef]

Science (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, Science 284, 1819 (1999).
[CrossRef] [PubMed]

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech, Norwood, Mass., 2000).

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Figures (3)

Fig. 1
Fig. 1

Band structure of the axially uniform dielectric-loaded metal waveguide (inset) showing the lowest two modes. The lower mode is anomalous with a nontrivial point of zero group velocity at k0=0.146 2π/a, ω0=0.1656 2πc/a.

Fig. 2
Fig. 2

(a) A piece of the waveguide of length L in Fig. 1 can form a high-Q cavity. (b) Resonant mode in a cavity of length L=3.9a. In an axial cross section we show the electric field component perpendicular to the plane, with the red and blue regions corresponding to positive and negative values, respectively. The metal cladding is shown in black. Note that the finite-difference time-domain computational cell is actually larger than the rectangular box shown here. (c) Resonant mode for L=13.9a. (d) Q is plotted as a function of cavity length L. The red circles are the results of finite-difference time-domain simulations, and the dashed vertical lines correspond to multiples of Λ/2. Also shown as a blue dashed line is the QL curve for a cavity based on a modified waveguide that does not have vg=0 at k0.

Fig. 3
Fig. 3

(a) Cylindrical all-dielectric cavity. (b) Axial cross section of the cavity structure: on top of a substrate with refractive index nsub, we have a central rod with index n1 followed by a region with index n0 and surrounded by a Bragg mirror that confines light to the core region. The electric field component perpendicular to the plane is shown in a color plot.

Tables (1)

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Table 1 Conservation of Round-Trip Phase Shift

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