Abstract

In this paper we propose analyse the apodisation or windowing of the coupling coefficients in the unit cells of coupled resonator waveguide devices (CROWs) as a means to reduce the level of secondary sidelobes in the bandpass characteristic of their transfer functions. This technique is regularly employed in the design of digital filters and has been applied as well in the design of other photonic devices such as corrugated waveguide filters and fiber Bragg gratings. The apodisation of both Type-I and Type-II structures is discussed for several windowing functions.

© 2007 Optical Society of America

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  1. T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, and M. Yasu, “Ring resonators composed of GeO2-doped silica waveguides,” J. Lightwave Technol. 12, 1781–1788 (1992).
    [CrossRef]
  2. A. Melloni, R. Costa, P. Monguzzi, and M. Martinelli, “Ring-resonator filters in silicon oxynitride technology for dense wavelength-division multiplexing systems,” Opt. Lett. 28, 1567–1569 (2003)
    [CrossRef] [PubMed]
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    [CrossRef]
  4. 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]
  5. P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.
  6. 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]
  7. 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]
  8. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photon 1, 65–71 (2007).
    [CrossRef]
  9. H. Tazawa and W. H. Steier, “Analysis of ring resonator-based traveling-wave modulators,” IEEE Photon. Technol. Lett. 18, 211–213 (2006).
    [CrossRef]
  10. 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)
    [CrossRef]
  11. 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)
    [CrossRef]
  12. K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846, (2003)
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. Y. Landobasa, S. Darmawan, and M. Chin, “Matrix Analysis of 2-D Microresonator Lattice Optical Filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005)
    [CrossRef]
  16. D. L. MacFarlane and E. M. Dowling, “Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures,” J. Opt. Soc. Am. 11, 236–245, (1994).
    [CrossRef]
  17. A. Yariv, “Universal relations for coupling of optical power between micro resonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000)
    [CrossRef]
  18. Y. Landobasa and M. Chin, “Defect modes in micro-ring resonator arrays,” Opt. Express 13, 7800–7815 (2005).
    [CrossRef] [PubMed]
  19. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing. Prentice-Hall (1999)
  20. P. S. Cross and H. Kogelnik, “Sidelobe suppression in corrugated-waveguide filters,” Opt. Lett. 1, 43–45 (1977)
    [CrossRef] [PubMed]
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    [CrossRef]
  22. A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech: Norwood, MA, 2000).
  23. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
    [CrossRef] [PubMed]
  24. L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
    [CrossRef]
  25. K. Okamoto. Fundamentals of Optical Waveguides. (Academic Press, 2nd ed, 2005).
  26. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. Optoel. 140, 177–188 (1993).
    [CrossRef]

2007 (1)

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

2006 (2)

2005 (2)

Y. Landobasa, S. Darmawan, and M. Chin, “Matrix Analysis of 2-D Microresonator Lattice Optical Filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005)
[CrossRef]

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

2004 (2)

2003 (2)

2002 (2)

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]

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]

2001 (1)

2000 (2)

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)
[CrossRef]

A. Yariv, “Universal relations for coupling of optical power between micro resonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000)
[CrossRef]

1999 (1)

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)
[CrossRef]

1996 (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodised linearly chirped fiber gratings for dispersioncompensation,” J. Light. Technol. 14, 2581–2588 (1996)
[CrossRef]

1995 (1)

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

1994 (1)

D. L. MacFarlane and E. M. Dowling, “Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures,” J. Opt. Soc. Am. 11, 236–245, (1994).
[CrossRef]

1993 (1)

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. Optoel. 140, 177–188 (1993).
[CrossRef]

1992 (1)

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, and M. Yasu, “Ring resonators composed of GeO2-doped silica waveguides,” J. Lightwave Technol. 12, 1781–1788 (1992).
[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]

1977 (1)

Absil, P. P.

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]

R. Grover, P. P. Absil, V. Van, J. V. Hryniewicz, B. E. Little, O. King, L. C. Calhoun, F. G. Johnson, and P. -T. Ho, “Vertically coupled GaInAsP InP microring resonators,” Opt. Lett. 26, 506–508 (2001)
[CrossRef]

Baets, R.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Beckx, S.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Bermel, P.

Bogaerts, W.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Boyd, R. W.

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)
[CrossRef]

Buck, J. R.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing. Prentice-Hall (1999)

Burr, G.

Calhoun, L. C.

Capmany, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodised linearly chirped fiber gratings for dispersioncompensation,” J. Light. Technol. 14, 2581–2588 (1996)
[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]

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)
[CrossRef]

Chak, P.

Chin, M.

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

Y. Landobasa, S. Darmawan, and M. Chin, “Matrix Analysis of 2-D Microresonator Lattice Optical Filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005)
[CrossRef]

Christiaens, I.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Chu, S. T.

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)
[CrossRef]

Costa, R.

Cross, P. S.

Dalton, L. R.

Darmawan, S.

Y. Landobasa, S. Darmawan, and M. Chin, “Matrix Analysis of 2-D Microresonator Lattice Optical Filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005)
[CrossRef]

Demeester, P.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

Dowling, E. M.

D. L. MacFarlane and E. M. Dowling, “Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures,” J. Opt. Soc. Am. 11, 236–245, (1994).
[CrossRef]

Dumon, P.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Farjadpour, A.

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)
[CrossRef]

Groen, F. H.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

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]

R. Grover, P. P. Absil, V. Van, J. V. Hryniewicz, B. E. Little, O. King, L. C. Calhoun, F. G. Johnson, and P. -T. Ho, “Vertically coupled GaInAsP InP microring resonators,” Opt. Lett. 26, 506–508 (2001)
[CrossRef]

Hagness, S.C.

A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech: Norwood, MA, 2000).

Heebner, J. E.

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]

Ho, P. -T.

Hryniewicz, J. V.

Huang, Y.

Ibanescu, M.

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.

Johnson, F. G.

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]

R. Grover, P. P. Absil, V. Van, J. V. Hryniewicz, B. E. Little, O. King, L. C. Calhoun, F. G. Johnson, and P. -T. Ho, “Vertically coupled GaInAsP InP microring resonators,” Opt. Lett. 26, 506–508 (2001)
[CrossRef]

Johnson, S. G.

King, O.

Kogelnik, H.

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)
[CrossRef]

Kominato, T.

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, and M. Yasu, “Ring resonators composed of GeO2-doped silica waveguides,” J. Lightwave Technol. 12, 1781–1788 (1992).
[CrossRef]

Landobasa, Y.

Y. Landobasa, S. Darmawan, and M. Chin, “Matrix Analysis of 2-D Microresonator Lattice Optical Filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005)
[CrossRef]

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

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)
[CrossRef]

Little, B. E.

Love, J. D.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. Optoel. 140, 177–188 (1993).
[CrossRef]

MacFarlane, D. L.

D. L. MacFarlane and E. M. Dowling, “Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures,” J. Opt. Soc. Am. 11, 236–245, (1994).
[CrossRef]

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)
[CrossRef]

Marti, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodised linearly chirped fiber gratings for dispersioncompensation,” J. Light. Technol. 14, 2581–2588 (1996)
[CrossRef]

Martinelli, M.

Melloni, A.

Metaal, E. G.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

Monguzzi, P.

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]

Oei, Y. S.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

Ohmori, Y.

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, and M. Yasu, “Ring resonators composed of GeO2-doped silica waveguides,” J. Lightwave Technol. 12, 1781–1788 (1992).
[CrossRef]

Okamoto, K.

K. Okamoto. Fundamentals of Optical Waveguides. (Academic Press, 2nd ed, 2005).

Okazaki, H.

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, and M. Yasu, “Ring resonators composed of GeO2-doped silica waveguides,” J. Lightwave Technol. 12, 1781–1788 (1992).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing. Prentice-Hall (1999)

Ortega, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodised linearly chirped fiber gratings for dispersioncompensation,” J. Light. Technol. 14, 2581–2588 (1996)
[CrossRef]

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)
[CrossRef]

Pastor, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodised linearly chirped fiber gratings for dispersioncompensation,” J. Light. Technol. 14, 2581–2588 (1996)
[CrossRef]

Pereira, S.

Poon, J.

Rabiei, P.

Rodriguez, A.

Roundy, D.

Rowland, D. R.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. Optoel. 140, 177–188 (1993).
[CrossRef]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing. Prentice-Hall (1999)

Scheuer, J.

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)
[CrossRef]

Sekaric, L.

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

Sipe, J. E.

Smit, M. K.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

Spiekman, L. H.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: the corner mirrors of the future?,” IEE Proc. Optoel 142,61–65 (1995).
[CrossRef]

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).
[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]

Taflove, A.

A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech: Norwood, MA, 2000).

Takato, N.

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, and M. Yasu, “Ring resonators composed of GeO2-doped silica waveguides,” J. Lightwave Technol. 12, 1781–1788 (1992).
[CrossRef]

Tatay, V.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodised linearly chirped fiber gratings for dispersioncompensation,” J. Light. Technol. 14, 2581–2588 (1996)
[CrossRef]

Tazawa, H.

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

Vahala, K. J.

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

Van, V.

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]

R. Grover, P. P. Absil, V. Van, J. V. Hryniewicz, B. E. Little, O. King, L. C. Calhoun, F. G. Johnson, and P. -T. Ho, “Vertically coupled GaInAsP InP microring resonators,” Opt. Lett. 26, 506–508 (2001)
[CrossRef]

Van Thourhout, D.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Vlasov, Y.

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

Wiaux, V.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Wouters, J.

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout, and R. Baets, “Microring resonators on Silicon-on-Insulator,” in Proc. of European Conf. on Integrated Optics, 2005.

Xia, F.

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

Yariv, A.

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Figures (11)

Fig. 1.
Fig. 1.

Type I CROW structure layout.

Fig. 2.
Fig. 2.

Type-I CROW unit cell and closing cell.

Fig. 3.
Fig. 3.

Type-I CROWreflection transfer function for Gauss window apodisation (parameter G=0, 3 and 4) on (a) one bus and (b) two buses

Fig. 4.
Fig. 4.

Type-I CROW reflection transfer function for Hamming window apodisation (parameter H=0, 0.15 and 0.3) on (a) one bus and (b) two buses

Fig. 5.
Fig. 5.

Type-I CROWreflection transfer function for Kaiser window apodisation (parameter βk =0, 0.15 and 0.3) on (a) one bus and (b) two buses

Fig. 6.
Fig. 6.

Type-I CROW reflection transfer comparison for Gauss, Hamming and Kaiser window apodisation (effective number of rings 6.9), on (a) one bus and (b) two buses

Fig. 7.
Fig. 7.

Type-I CROWreflection normalised delay for Gauss and Kaiser window apodisation

Fig. 8.
Fig. 8.

Type II CROW structure layout.

Fig. 9.
Fig. 9.

Type-II CROW unit cell, opening and closing sections.

Fig. 10.
Fig. 10.

Type-II CROW transmission transfer function for (a) Hamming, (b) Gauss, (c) Kaiser window apodisation (window parameters as in Figs. 35) and (d) comparison for an effective number of rings 6.6.

Fig. 11.
Fig. 11.

Type-II CROW FDTD analysis, (a) power coupling coefficient K vs distance for an InP w=0.3 microns deep-etched waveguide, and (b) model vs FDTD simulation for a 6 ring CROW with Hamming windowing, H=0.12.

Equations (34)

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M UCi = 1 R 2 i ( ( R 1 i R 2 i T 1 i T 2 i ) e j Δ T 2 i e T 1 i e j Δ e j Δ )
M CN = 1 R 2 N ( R 1 N R 2 N T 1 N T 2 N T 2 N T 1 N 1 )
R 1 i = t 1 i t 2 i * ( t 1 i 2 + κ 1 i 2 ) τ i e j δ 1 τ i t 1 i * t 2 i * e j δ
R 2 i = t 2 i t 1 i * ( t 2 i 2 + κ 2 i 2 ) τ i e j δ 1 τ i t 1 i * t 2 i * e j δ
T 1 i = κ 1 i * κ 2 i τ i e j δ 2 1 τ i t 1 i * t 2 i * e j δ
T 2 i = κ 2 i * κ 1 i τ i e j δ 2 1 τ i t 1 i * t 2 i * e j δ
δ = β L c
τ = exp ( α L c )
Δ = β L b
( E N + E N ) = ( T 11 T 12 T 21 T 22 ) ( E 1 + E 1 )
M T = ( T 11 T 12 T 21 T 22 ) = M CN i = N 1 1 M UCi
T = E N + E 1 + E N = 0 = 1 T 22
R = E 1 E 1 + E N = 0 = T 21 T 22
t = 1 K
κ = j K
w ( i ) = exp ( G ( i N 2 N ) 2 )
i = 0 , 1 , , N 1
K = 0 . 1
G = 0 , 3 , 4
w ( i ) = 1 + H cos ( 2 π n ) 1 + H
i = 0 , 1 , , N 1
K = 0.1
H = 0 , 0.15 , 0.3
w ( i ) = β k sinh ( β k ) I 0 ( β k 1 4 n 2 )
i = 0 , 1 , , N 1
n = ( i N 2 ) N
K = 0.1
β k = 1 , 2 , 3
N eff = N Σ i = 0 N 1 i w ( i ) Σ i = 0 N 1 i
τ d T c = ϕ ( δ ) δ
M UCi = 1 κ i ( τ i 1 2 ( κ i 2 + t i 2 ) e j δ 2 t i * t i τ i 1 2 e j δ 2 )
M OS = 1 κ 0 ( ( κ 0 2 + t 0 2 ) τ 0 1 4 e j δ 4 t 0 * τ 0 1 4 e j δ 4 t 0 τ 0 1 4 e j δ 4 τ i 1 4 e j δ 4 )
M CS = 1 κ N ( ( κ N 2 + t N 2 ) τ N 1 4 e j δ 4 t N * τ N 1 4 e j δ 4 t N τ N 1 4 e j δ 4 τ i 1 4 e j δ 4 )
M T = M CS [ i = N 1 1 M UCi ] M OS

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