Abstract

The linear characteristics of a vertically stacked multiring resonator (VMR) that can support a photonic bandgap with a defect located at the middle of the structure are investigated numerically. Initially, the spectral transfer characteristics of the uniform structure are studied. Then, the transmission properties of the VMR structure possessing a defect are investigated. The defect is realized by varying the waveguide width of one of the rings in the VMR chain. Finally, the existence of defect modes in the linear periodic array is numerically demonstrated by solving the corresponding coupled wave equations. Numerical results predict a high quality factor (Q) of up to 1.6×105 for this microcavity. We also show that our microcavity has a good insensitivity of quality factor to geometric imperfections.

© 2009 Optical Society of America

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2007 (4)

2006 (1)

H. Tazawa and W. H. Steier, “Analysis of ring resonator-based traveling-wave modulators,” IEEE Photon. Technol. Lett. 18, 211-213 (2006).

2005 (5)

2004 (7)

2003 (1)

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

2002 (2)

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670-684 (2002).

2001 (2)

2000 (4)

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344-346 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near infrared wavelengths,” Science 289, 604-606 (2000).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323-325 (2000).

1999 (2)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

1998 (1)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149(1997).
[CrossRef]

1990 (1)

J. Capmany and M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

1982 (1)

1972 (1)

Absil, P. P.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

V. Van, P. P. Absil, J. V. Hryniewicz, and P. T. Ho, “Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model,” J. Lightwave Technol. 19, 1734-1739(2001).
[CrossRef]

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344-346 (2000).
[CrossRef]

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202-1214 (2005).
[CrossRef]

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202-1214 (2005).
[CrossRef]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Barlow, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Bartal, G.

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Blanco, A.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Bolivar, P. H.

Boyd, R. W.

Brambilla, G.

Bruce, A. J.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

Buljan, H.

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Busch, K.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

Capmany, J.

J. Capmany and M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Cappuzzo, M. A.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

Chak, P.

Charvolin, T.

Chin, M. K.

Chodorow, M.

Chu, S. T.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323-325 (2000).

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344-346 (2000).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near infrared wavelengths,” Science 289, 604-606 (2000).
[CrossRef]

Cohen, O.

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

Deubel, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Efremidis, N. K.

Eggleton, B. J.

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Enkrich, C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149(1997).
[CrossRef]

Fleischer, J. W.

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Freedman, B.

Gill, D.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

Gomez, L. T.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

Grover, R.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Hadji, E.

Hanic, S. T.

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

Heebner, J. E.

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Henschel, W.

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Ho, P. T.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

V. Van, P. P. Absil, J. V. Hryniewicz, and P. T. Ho, “Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model,” J. Lightwave Technol. 19, 1734-1739(2001).
[CrossRef]

Hryniewicz, J. V.

Huang, Y.

Hugonin, J. P.

Ibrahim, T. A.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149(1997).
[CrossRef]

Johnson, F. G.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Kawata, S.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697-698(2001).

King, O.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

Koch, W.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Kokubun, Y.

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323-325 (2000).

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Kurz, H.

Lalanne, P.

Lalanne, Ph.

Landobasa, Y. M.

Lee, I.-Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Lenz, G.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

Li, C.

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Little, B. E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323-325 (2000).

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344-346 (2000).
[CrossRef]

Lou, J.

Ma, N.

Madsen, C. K.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

Manela, O.

Marder, S. R.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Mazur, E.

McCord-Maughon, D.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Meisel, D. C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Mias, S.

Miklyaev, Y. V.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Mookherjea, S.

Muriel, M. A.

J. Capmany and M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Niehusmann, J.

Noda, S.

S. T. Hanic, C. M. d. Sterke, M. J. Steel, B. J. Eggleton, Y. Tanaka, and S. Noda, “High-Q. cavities in multilayer photonic crystal slabs,” Opt. Express 15, 17248 (2007).
[CrossRef]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202-1214 (2005).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near infrared wavelengths,” Science 289, 604-606 (2000).
[CrossRef]

Painter, O.

Paloczi, G. T.

Pan, W.

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323-325 (2000).

Pereira, S.

Perry, J. W.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Peyrade, D.

Picard, E.

Poon, A. W.

Poon, J.

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Rockel, H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Rodier, J. C.

Rumi, M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Scheuer, J.

Schwartz, T.

Scotti, R. E.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

Segev, M.

Seiferth, F.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photon. 1, 65-71 (2007).
[CrossRef]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

Shaw, H. J.

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Sipe, J. E.

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Snyder, A. W.

Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Song, B.-S.

Srinivasan, K.

Steel, M. J.

Steier, W. H.

H. Tazawa and W. H. Steier, “Analysis of ring resonator-based traveling-wave modulators,” IEEE Photon. Technol. Lett. 18, 211-213 (2006).

Sterke, C. M. d.

Stokes, L. F.

Sumetsky, M.

Sun, H.-B.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697-698(2001).

Takada, K.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697-698(2001).

Tanaka, T.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697-698(2001).

Tanaka, Y.

Tazawa, H.

H. Tazawa and W. H. Steier, “Analysis of ring resonator-based traveling-wave modulators,” IEEE Photon. Technol. Lett. 18, 211-213 (2006).

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near infrared wavelengths,” Science 289, 604-606 (2000).
[CrossRef]

Tong, L.

Trakalo, M.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

Van, V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

V. Van, P. P. Absil, J. V. Hryniewicz, and P. T. Ho, “Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model,” J. Lightwave Technol. 19, 1734-1739(2001).
[CrossRef]

Velha, P.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149(1997).
[CrossRef]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photon. 1, 65-71 (2007).
[CrossRef]

von Freymann, G.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Vörckel, A.

Wahlbrink, T.

Wegener, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Wu, X.-Li

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photon. 1, 65-71 (2007).
[CrossRef]

Xu, F.

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near infrared wavelengths,” Science 289, 604-606 (2000).
[CrossRef]

Yariv, A.

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

Appl. Phys. Lett. (1)

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography:fabrication, optical characterization and band-structure calculations,” Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P. T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

H. Tazawa and W. H. Steier, “Analysis of ring resonator-based traveling-wave modulators,” IEEE Photon. Technol. Lett. 18, 211-213 (2006).

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323-325 (2000).

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

J. Lightwave Technol. (2)

V. Van, P. P. Absil, J. V. Hryniewicz, and P. T. Ho, “Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model,” J. Lightwave Technol. 19, 1734-1739(2001).
[CrossRef]

J. Capmany and M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Mater. (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Nat. Photon. (1)

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photon. 1, 65-71 (2007).
[CrossRef]

Nature (5)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149(1997).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53-56(2000).

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251-253(1998).

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-Li Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for 3D optical data storage and microfabrication,” Nature 398, 51-54 (1999).

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697-698(2001).

Opt. Express (10)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202-1214 (2005).
[CrossRef]

S. T. Hanic, C. M. d. Sterke, M. J. Steel, B. J. Eggleton, Y. Tanaka, and S. Noda, “High-Q. cavities in multilayer photonic crystal slabs,” Opt. Express 15, 17248 (2007).
[CrossRef]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670-684 (2002).

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025-1035 (2004).
[CrossRef]

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780-1796 (2005).
[CrossRef]

P. Velha, E. Picard, T. Charvolin, E. Hadji, J. C. Rodier, P. Lalanne, and D. Peyrade, “Ultra-high Q/V Fabry-Perot microcavity on SOI substrate,” Opt. Express 15, 16090 (2007).
[CrossRef]

Ph. Lalanne, S. Mias, and J. P. Hugonin, “Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities,” Opt. Express 12, 458-567(2004).
[CrossRef]

Y. M. Landobasa and M. K. Chin, “Defect modes in microring resonator arrays,” Opt. Express 13, 7800-7815 (2005).
[CrossRef]

M. Sumetsky, “Vertically-stacked multiring resonator,” Opt. Express 13, 6354-6375 (2005).
[CrossRef]

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupledresonator optical waveguides,” Opt. Express 12, 90-103 (2004).
[CrossRef]

Opt. Lett. (5)

Science (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near infrared wavelengths,” Science 289, 604-606 (2000).
[CrossRef]

Other (1)

A. Yariv, Optical Electronics (Saunders, 1991), Chap. 4.

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Figures (9)

Fig. 1
Fig. 1

Diagram of a typical VMR structure made of N rings wrapped on a rod and two waveguides.

Fig. 2
Fig. 2

Dispersion diagram for an infinite VMR, relating the dimensionless propagation constant B to the dimensionless Bloch wavenumber ξ d .

Fig. 3
Fig. 3

Transmission power, | T ( through ) | 2 , for N = 3 , 5, and 9, calculated making use of Eqs. (3, 5, 8). The shaded region corresponds to the bandgap in the corresponding infinite structure.

Fig. 4
Fig. 4

Effect of the dimensionless coupling parameter K on the thorough transmission spectrum. Parameters include N = 9 , K 0 = 0.8 , and K = 1.2 , 0.9, 0.6, 0.3.

Fig. 5
Fig. 5

Top: through transmission power, | T ( through ) | 2 , of VMR with nine rings and parameters K 0 = K = 0.8 and N = 9 . (a) No defect; the shaded region corresponds to the bandgap in the corresponding infinite structure (Fig. 2). (b) Defect at the fifth ring with δ B defect = 2.2 . The defect mode can be seen as a sharp slit in the bandgap. Bottom: average amplitude distribution | A n | / | A 0 | corresponding to the top panels versus the ring number n. (c) No defect, 0; (d) the above-described defect is introduced.

Fig. 6
Fig. 6

Through transmission power, | T ( through ) | 2 , of VMR with 9 rings and parameters K 0 = K = 0.8 , and N = 9 , for (a)  δ B defect = 1.6 (b)  δ B defect = 1.6 . Average amplitude distribution Re ( A n ) / | A 0 | corresponding to the top panels as a function of the ring number n.

Fig. 7
Fig. 7

Enlarged detail of Fig. 5b around the defect mode.

Fig. 8
Fig. 8

Linewidth broadening of defect mode by approaching the band edge. (a)  Δ B = 0.94 , (b)  Δ B = 1.57 . (c) Other parameters are the same as in Fig. 4.

Fig. 9
Fig. 9

(a) Disorder examples and (b) corresponding Q factor values, the number j = 0 is corresponding to ideal regular structure. The microcavity parameters are the same as in Fig. 5.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

i d A 1 d s + κ 12 A 2 e i ( δ 2 , 1 ) = 0 , i d A n d s + κ n 1 , n A n 1 e i ( δ n 1 , n ) + κ n , n + 1 A n + 1 e i ( δ n + 1 , n ) = 0 , n = 2 , 3 , N 1 , i d A N d s + κ N 1 , N A N 1 e i ( δ N 1 , N ) = 0 ,
A n ( 0 ) = A n ( S n ) exp ( i β S n ) , n = 2 , 3 , , N 1 ,
A 0 ( out ) = cos ( K 0 ) A 0 in + i sin ( K 0 ) A 1 ( S 1 ) , A 1 ( 0 ) = i sin ( K 0 ) A 0 in + cos ( K 0 ) A 1 ( S 1 ) ,
A N + 1 ( out ) = i sin ( K 0 ) A N ( S N ) , A N ( 0 ) = cos ( K 0 ) A N ( S N ) ,
B = 2 π l 2 K cos ( ξ d ) ,
T ( through ) = A 0 ( out ) / A 0 ( in ) ,
T ( drop ) = A N + 1 ( out ) / A 0 ( in ) ,
| T ( drop ) | 2 + | T ( drop ) | 2 = 1

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