Abstract

We address the trade-offs among delay, loss, and bandwidth in the design of coupled-resonator optical waveguide (CROW) delay lines. We begin by showing the convergence of the transfer matrix, tight-binding, and time domain formalisms in the theoretical analysis of CROWs. From the analytical formalisms we obtain simple, analytical expressions for the achievable delay, loss, bandwidth, and a figure of merit to be used to compare delay line performance. We compare CROW delay lines composed of ring resonators, toroid resonators, Fabry–Perot resonators, and photonic crystal defect cavities based on recent experimental results reported in the literature.

© 2004 Optical Society of America

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2004 (3)

2003 (13)

G. T. Paloczi, Y. Huang, A. Yariv, and S. Mookherjea, “Polymeric Mach–Zehnder interferometer using serially coupled microresonators,” Opt. Express 11, 2666–2671 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

A. Melloni and F. Morichetti, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).
[CrossRef]

O. J. Painter, K. Srinivasan, and P. E. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photonics Technol. Lett. 15, 1255–1257 (2003).
[CrossRef]

Y. Yanagase, S. Yamagata, and Y. Kokubun, “Wavelength tunable polymer microring resonator filter with 9.4 nm tuning range,” Electron. Lett. 39, 922–924 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, T. Handley, and L. Maleki, “Second-order filter response with series-coupled silica microresonators,” IEEE Photonics Technol. Lett. 15, 543–544 (2003).
[CrossRef]

2002 (12)

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “High-Q channel-dropping filters using ring resonators with integrated SOAs,” IEEE Photonics Technol. Lett. 14, 1442–1444 (2002).
[CrossRef]

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
[CrossRef]

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, and T. F. Krauss, “Planar photonic crystal coupled cavity waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[CrossRef]

M. Strassner, C. Luber, A. Tarraf, and N. Chitica, “Widely tunable-constant bandwidth monolithic Fabry–Perot filter with a stable cavity design for WDM systems,” IEEE Photonics Technol. Lett. 14, 1548–1550 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
[CrossRef]

S. Lan, S. Nishikawa, H. Ishikawa, and O. Wada, “Engineering photonic crystal impurity bands for waveguides, all-optical switches and optical delay lines,” IEICE Trans. Electron. E85C, 181–189 (2002).

S. Mookherjea and A. Yariv, “Pulse propagation in a coupled-resonator optical waveguide to all orders of dispersion,” Phys. Rev. E 65, 056601 (2002).
[CrossRef]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

D. N. Christodoulides and N. K. Efremidis, “Discrete temporal solitons along a chain of nonlinear coupled microcavities embedded in photonic crystals,” Opt. Lett. 27, 568–570 (2002).
[CrossRef]

S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects,” Opt. Lett. 27, 2079–2081 (2002).
[CrossRef]

P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters and modulators,” J. Lightwave Technol. 20, 1968–1975 (2002).
[CrossRef]

2001 (7)

S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, and U. Osterle, “Miniband transmission in a photonic crystal waveguide coupled-resonator optical waveguide,” Opt. Lett. 26, 1019–1051 (2001).
[CrossRef]

S. Mookherjea and A. Yariv, “Optical pulse propagation in the tight-binding approximation,” Opt. Express 9, 91–96 (2001), http://www.opticsexpress
[CrossRef] [PubMed]

H. F. Taylor, “Design of multireflector resonant bandpass filters for guided wave optics,” J. Lightwave Technol. 19, 866–871 (2001).
[CrossRef]

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525–532 (2001).
[CrossRef]

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
[CrossRef]

S. Mookherjea and A. Yariv, “Optical pulse propagation and holographic storage in a coupled-resonator optical waveguide,” Phys. Rev. E 64, 066602 (2001).
[CrossRef]

M. Bayindir, S. Tanriseven, and E. Ozbay, “Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures,” Appl. Phys. A: Solids Surf. 72, 117–119 (2001).
[CrossRef]

2000 (3)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320–322 (2000).
[CrossRef]

C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18, 860–868 (2000).
[CrossRef]

1999 (4)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
[CrossRef]

R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
[CrossRef]

S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
[CrossRef]

1998 (1)

N. Stefanou and A. Modinos, Impurity bands in photonic insulators, Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

1997 (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

1995 (1)

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

1991 (1)

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

Absil, P. P.

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320–322 (2000).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

Armani, D. K.

A. L. Martin, D. K. Armani, L. Yang, and K. J. Vahala, “Replica-molded high-Q polymer microresonators,” Opt. Lett. 29, 533–535 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Asakawa, K.

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

Barclay, P. E.

K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
[CrossRef]

O. J. Painter, K. Srinivasan, and P. E. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Bayindir, M.

M. Bayindir, S. Tanriseven, and E. Ozbay, “Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures,” Appl. Phys. A: Solids Surf. 72, 117–119 (2001).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Benisty, H.

Benyattou, T.

R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
[CrossRef]

Blondeau, R.

R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
[CrossRef]

Brown, D. H.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, and T. F. Krauss, “Planar photonic crystal coupled cavity waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Calhoun, L. C.

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
[CrossRef]

Chen, J.

K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
[CrossRef]

Chitica, N.

M. Strassner, C. Luber, A. Tarraf, and N. Chitica, “Widely tunable-constant bandwidth monolithic Fabry–Perot filter with a stable cavity design for WDM systems,” IEEE Photonics Technol. Lett. 14, 1548–1550 (2002).
[CrossRef]

Cho, A. Y.

K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
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Chu, S. T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
[CrossRef]

S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
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B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

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R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
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A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
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T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
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B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
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T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
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K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
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T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
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H. Haciwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16, 135–137 (2004).
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S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
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D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “High-Q channel-dropping filters using ring resonators with integrated SOAs,” IEEE Photonics Technol. Lett. 14, 1442–1444 (2002).
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A. A. Savchenkov, V. S. Ilchenko, T. Handley, and L. Maleki, “Second-order filter response with series-coupled silica microresonators,” IEEE Photonics Technol. Lett. 15, 543–544 (2003).
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T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
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B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
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D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “High-Q channel-dropping filters using ring resonators with integrated SOAs,” IEEE Photonics Technol. Lett. 14, 1442–1444 (2002).
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R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
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S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
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Hryniewicz, J. V.

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
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J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320–322 (2000).
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R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
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A. A. Savchenkov, V. S. Ilchenko, T. Handley, and L. Maleki, “Second-order filter response with series-coupled silica microresonators,” IEEE Photonics Technol. Lett. 15, 543–544 (2003).
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B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
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S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects,” Opt. Lett. 27, 2079–2081 (2002).
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R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
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T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
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B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
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S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
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D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
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H. Haciwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16, 135–137 (2004).
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B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
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S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
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Krauss, T. F.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, and T. F. Krauss, “Planar photonic crystal coupled cavity waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
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A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
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B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
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S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects,” Opt. Lett. 27, 2079–2081 (2002).
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S. Lan, S. Nishikawa, H. Ishikawa, and O. Wada, “Engineering photonic crystal impurity bands for waveguides, all-optical switches and optical delay lines,” IEICE Trans. Electron. E85C, 181–189 (2002).

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R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
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A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
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G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525–532 (2001).
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Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
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J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320–322 (2000).
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B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
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S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
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B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
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C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18, 860–868 (2000).
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A. A. Savchenkov, V. S. Ilchenko, T. Handley, and L. Maleki, “Second-order filter response with series-coupled silica microresonators,” IEEE Photonics Technol. Lett. 15, 543–544 (2003).
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H. Haciwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16, 135–137 (2004).
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S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects,” Opt. Lett. 27, 2079–2081 (2002).
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Pan, W.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
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S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
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S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
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A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
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B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
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A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
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S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
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G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525–532 (2001).
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Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
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D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
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S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
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R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
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K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
[CrossRef]

O. J. Painter, K. Srinivasan, and P. E. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Steer, M.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, and T. F. Krauss, “Planar photonic crystal coupled cavity waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Stefanou, N.

N. Stefanou and A. Modinos, Impurity bands in photonic insulators, Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Steier, W. H.

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photonics Technol. Lett. 15, 1255–1257 (2003).
[CrossRef]

P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters and modulators,” J. Lightwave Technol. 20, 1968–1975 (2002).
[CrossRef]

Strassner, M.

M. Strassner, C. Luber, A. Tarraf, and N. Chitica, “Widely tunable-constant bandwidth monolithic Fabry–Perot filter with a stable cavity design for WDM systems,” IEEE Photonics Technol. Lett. 14, 1548–1550 (2002).
[CrossRef]

Sugimoto, Y.

Taflove, A.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

Takato, N.

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

Tanriseven, S.

M. Bayindir, S. Tanriseven, and E. Ozbay, “Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures,” Appl. Phys. A: Solids Surf. 72, 117–119 (2001).
[CrossRef]

Tarraf, A.

M. Strassner, C. Luber, A. Tarraf, and N. Chitica, “Widely tunable-constant bandwidth monolithic Fabry–Perot filter with a stable cavity design for WDM systems,” IEEE Photonics Technol. Lett. 14, 1548–1550 (2002).
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Tascone, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Taylor, H. F.

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M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
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Toba, H.

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
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Trinchero, D.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Troppenz, U.

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “High-Q channel-dropping filters using ring resonators with integrated SOAs,” IEEE Photonics Technol. Lett. 14, 1442–1444 (2002).
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Vahala, K. J.

A. L. Martin, D. K. Armani, L. Yang, and K. J. Vahala, “Replica-molded high-Q polymer microresonators,” Opt. Lett. 29, 533–535 (2004).
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S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
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K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
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Van, V.

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
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Viktorovitch, P.

R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
[CrossRef]

Wada, O.

S. Lan, S. Nishikawa, H. Ishikawa, and O. Wada, “Engineering photonic crystal impurity bands for waveguides, all-optical switches and optical delay lines,” IEICE Trans. Electron. E85C, 181–189 (2002).

Weisbuch, C.

Wilson, R.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, and T. F. Krauss, “Planar photonic crystal coupled cavity waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320–322 (2000).
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Y. Yanagase, S. Yamagata, and Y. Kokubun, “Wavelength tunable polymer microring resonator filter with 9.4 nm tuning range,” Electron. Lett. 39, 922–924 (2003).
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Y. Yanagase, S. Yamagata, and Y. Kokubun, “Wavelength tunable polymer microring resonator filter with 9.4 nm tuning range,” Electron. Lett. 39, 922–924 (2003).
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J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004), http://www.opticsexpress.org.
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G. T. Paloczi, Y. Huang, A. Yariv, and S. Mookherjea, “Polymeric Mach–Zehnder interferometer using serially coupled microresonators,” Opt. Express 11, 2666–2671 (2003), http://www.opticsexpress.org.
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S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Pulse propagation in a coupled-resonator optical waveguide to all orders of dispersion,” Phys. Rev. E 65, 056601 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
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S. Mookherjea and A. Yariv, “Optical pulse propagation in the tight-binding approximation,” Opt. Express 9, 91–96 (2001), http://www.opticsexpress
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S. Mookherjea and A. Yariv, “Optical pulse propagation and holographic storage in a coupled-resonator optical waveguide,” Phys. Rev. E 64, 066602 (2001).
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A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

Zhang, C.

Appl. Phys. A: Solids Surf. (1)

M. Bayindir, S. Tanriseven, and E. Ozbay, “Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures,” Appl. Phys. A: Solids Surf. 72, 117–119 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

K. Srinivasan, P. E. Barclay, O. J. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003).
[CrossRef]

T. D. Happ, M. Kamp, A. Forchel, J. L. Gentner, and L. Goldstein, “Two-dimensional photonic crystal coupled-defect laser diode,” Appl. Phys. Lett. 82, 4–6 (2003).
[CrossRef]

Electron. Lett. (1)

Y. Yanagase, S. Yamagata, and Y. Kokubun, “Wavelength tunable polymer microring resonator filter with 9.4 nm tuning range,” Electron. Lett. 39, 922–924 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525–532 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

R. L. Dantec, T. Benyattou, G. Guillot, A. Spisser, C. Seassal, J. L. Leclercq, P. Viktorovitch, D. Rondi, and R. Blondeau, “Tunable microcavity based on InP-air Bragg mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 111–114 (1999).
[CrossRef]

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, and T. F. Krauss, “Planar photonic crystal coupled cavity waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (9)

M. Strassner, C. Luber, A. Tarraf, and N. Chitica, “Widely tunable-constant bandwidth monolithic Fabry–Perot filter with a stable cavity design for WDM systems,” IEEE Photonics Technol. Lett. 14, 1548–1550 (2002).
[CrossRef]

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photonics Technol. Lett. 15, 1255–1257 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, T. Handley, and L. Maleki, “Second-order filter response with series-coupled silica microresonators,” IEEE Photonics Technol. Lett. 15, 543–544 (2003).
[CrossRef]

D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “High-Q channel-dropping filters using ring resonators with integrated SOAs,” IEEE Photonics Technol. Lett. 14, 1442–1444 (2002).
[CrossRef]

S. T. Chu, W. Pan, S. Sato, T. Kaneko, B. E. Little, and Y. Kokubun, “Wavelength trimming of a microring resonator filter by means of a UV sensitive polymer overlay,” IEEE Photonics Technol. Lett. 11, 688–690 (1999).
[CrossRef]

H. Haciwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16, 135–137 (2004).
[CrossRef]

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photonics Technol. Lett. 11, 215–217 (1999).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photonics Technol. Lett. 12, 320–322 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. I. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860–1867 (2001).
[CrossRef]

IEICE Trans. Electron. (1)

S. Lan, S. Nishikawa, H. Ishikawa, and O. Wada, “Engineering photonic crystal impurity bands for waveguides, all-optical switches and optical delay lines,” IEICE Trans. Electron. E85C, 181–189 (2002).

J. Lightwave Technol. (8)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
[CrossRef]

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

H. F. Taylor, “Design of multireflector resonant bandpass filters for guided wave optics,” J. Lightwave Technol. 19, 866–871 (2001).
[CrossRef]

C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18, 860–868 (2000).
[CrossRef]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters and modulators,” J. Lightwave Technol. 20, 1968–1975 (2002).
[CrossRef]

Nature (London) (3)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

A. Melloni and F. Morichetti, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

Phys. Rev. B (3)

N. Stefanou and A. Modinos, Impurity bands in photonic insulators, Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

O. J. Painter, K. Srinivasan, and P. E. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Phys. Rev. E (4)

S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Optical pulse propagation and holographic storage in a coupled-resonator optical waveguide,” Phys. Rev. E 64, 066602 (2001).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Pulse propagation in a coupled-resonator optical waveguide to all orders of dispersion,” Phys. Rev. E 65, 056601 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

Other (6)

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Paren Oxford U. Press, New York, 1997).

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

For example specifications of the JDS fused coupler, polarization maintaining tap are provided on the JDS Uniphase website: www.jdsu.com/site/images/products/pdf/FFP_021604.pdf.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, P. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order micro-ring resonators,” in Optical Fiber Communication Conference (OFC), Vol. 95 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), paper PDP9.

P. P. Absil, S. T. Chu, D. Gill, J. V. Hryniewicz, F. Johnson, O. King, B. E. Little, F. Seiferth, and V. Van, “Very high order integrated optical filters,” in Optical Fiber Communication Conference (OFC), Vol. 95 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), paper TuL3.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).

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Figures (5)

Fig. 1
Fig. 1

Infinite chain of coupled ring resonators.

Fig. 2
Fig. 2

Traveling wave in a finite chain of ring resonators.

Fig. 3
Fig. 3

Coupled Fabry–Perot cavities. (a) Epitaxilly grown; (b) gratings on a waveguide.

Fig. 4
Fig. 4

Passbands of coupled-resonator structures with identical interresonator coupling |κ| throughout and different waveguide–resonator coupling |κi|. (a) The number of resonators is fixed and the number of coupling constants is varied. (b) The number of coupling constants is fixed and N is varied.

Fig. 5
Fig. 5

Comparing analytical expressions for loss and delay with numerical results by use of the transfer matrices for various propagation losses in the resonators. Solid curves, theoretical results; markers, numerical results. R=100 µm and n=1.54.

Tables (2)

Tables Icon

Table 1 |κ| and the Corresponding |κi| Used in Fig. 5 for N=10

Tables Icon

Table 2 Comparison of CROW Delay Lines Consisting of N=10 Resonators for |κ|=0.1

Equations (25)

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

ω(K)=Ω1-Δα2+γ cos(KΛ),
Δα=d3r[(r)-0(r)]EΩ(r)·EΩ(r),
γ=d3r[0(r-Λzˆ)-(r-Λzˆ)]×EΩ(r)·EΩ(r-Λzˆ).
an+1bn+1=Panbn,P1κ-t1-1t*,
anbn=Qanbn,Q0exp(-iπβR)exp(iπβR)0.
an+1bn+1=PQanbn.
aN+1bN+1ABCDa0b0.
b0a0=-AB,
bN+1a0=C-ADB.
sin(βπR)=±Im(κ)cos(KΛ),
ω(K)=Ω1±|κ|mπcos(KΛ),
2ian sin(βπR)=i|κ|(an+1+an-1).
iωan-iΩan=i|κ|(-1)mΩ2mπ(an+1+an-1).
da˜n(t)dt-iΩa˜n(t)=i(-1)m|κ|Ω2mπ[a˜n+1(t)+a˜n-1(t)].
dAn(t)dt=i(-1)m|κ|Ω2mπ[An+1(t)+An-1(t)].
An(t)=inJntText,
ω(K)Ω=1+(-1)mκ0mπ[sin(KΛ-θ)].
Δωuse|κ|cπnR.
τ=πnRN|κ|c.
Leff=cτn=πRN|κ|,
α=aπRN|κ|=mπN|κ|Qint,
τmax=n/ca.
FOMQint/Qext.
Qext=mπ/|κ|.
FOM=|κ|aπR=Δωuseταtot=τmaxΔωuse.

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