Abstract

Disorder in coupled-resonator optical waveguides (CROWs) is modeled by exploiting the concept of the characteristic impedance of a periodic slow-light waveguide. Every imperfection in the CROW structure is modeled as an impedance discontinuity, and the related backreflection is evaluated by using well-known reflection rules. We demonstrate that backreflections induced by disorder scale with the square of the slowing factor and the square of the disorder parameter, both independently of the specific structure. The method is simple and accurate, holds even when the slowing factor of the CROW is modified by disorder, and can be applied to any slow-light structure where the characteristic impedance can be defined. Theoretical and numerical results are supported by an experimental investigation showing the effects of increasing disorder on both frequency and time domain responses of a ring resonator CROW. Pulse envelope distortions due to distributed backreflections along the disordered CROW arise as one of the main limiting factors for applications based on CROWs.

© 2009 Optical Society of America

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  1. E. Parra and J. R. Lowell, “Toward applications of slow light technology,” Opt. Photonics News 18, 40-45 (2007).
    [Crossref]
  2. A. Melloni, F. Morichetti, and M. Martinelli, “Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides,” J. Opt. Soc. Am. B 25, C87-C97 (2008).
    [Crossref]
  3. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219-226 (2007).
    [Crossref] [PubMed]
  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]
  5. A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. 33, 2389-2391 (2008).
    [Crossref] [PubMed]
  6. A. L. Reynolds, U. Peschel, F. Lederer, P. J. Roberts, T. F. Krauss, and P. J. L. de Maagt, “Coupled defects in photonic crystals,” IEEE Trans. Microwave Theory Tech. 49, 1860-1867 (2001).
    [Crossref]
  7. D. O'Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15, 1228-1233 (2007).
    [Crossref] [PubMed]
  8. L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15, 13129-13138 (2007).
    [Crossref] [PubMed]
  9. S. Mookherjea and A. Oh, “Effect of disorder on slow light velocity in optical slow-wave structures,” Opt. Lett. 32, 289-291 (2007).
    [Crossref] [PubMed]
  10. S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
    [Crossref]
  11. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
    [Crossref] [PubMed]
  12. S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
    [Crossref]
  13. D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29, 1897-1899 (2004).
    [Crossref] [PubMed]
  14. E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
    [Crossref]
  15. R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
    [Crossref] [PubMed]
  16. A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296 (2002).
    [Crossref]
  17. R. M. Fano, Research Laboratory Electronics, “Theoretical limitations on the broadband matching of arbitrary impedances,” Massachusetts Institute of Technology Technical Report 41, (MIT, 1948).
  18. S. Boscolo, M. Midrio, and T. F. Krauss, “Y junctions in photonic crystal channel waveguides: high transmission and impedance matching,” Opt. Lett. 27, 1001-1003 (2002).
    [Crossref]
  19. F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
    [PubMed]
  20. R. E. Collins, Field Theory of Guided Waves, IEEE Press Series on Electromagnetic Wave Theory (IEEE, 1991), pp. 605-641.
  21. A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slowwave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
    [Crossref]
  22. J. R. Brews, “Characteristic impedance of microstrip lines,” IEEE Trans. Microwave Theory Tech. MTT-35, 30-34 (1987).
    [Crossref]
  23. P. Velha, J. P. Hugonin, and P. Lalanne, “Compact and efficient injection of light into band-edge slow-modes,” Opt. Express 15, 6102-6112 (2007).
    [Crossref] [PubMed]
  24. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16, 8395-8405 (2008).
    [Crossref] [PubMed]
  25. C. G. Montgomery, in Principles of Microwave Circuits, C.G.Montgomery, R.H.Dicke, and E.M.Purcell, eds., Vol. 8 in MIT Radiation Laboratory Series, L.N.Ridenour and G.B.Collins, eds. (McGraw-Hill, 1948), Chap. 3.
  26. S. A. Schelkunoff, “Impedance concept in waveguides,” Q. Appl. Math. 2, 1 (1944).
  27. H. Kogelnik and H. P. Weber, “Rays, stored energy, and power flow in dielectric waveguides,” J. Opt. Soc. Am. 64, 174-185 (1974).
    [Crossref]

2008 (6)

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
[Crossref]

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
[Crossref] [PubMed]

F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
[PubMed]

F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16, 8395-8405 (2008).
[Crossref] [PubMed]

A. Melloni, F. Morichetti, and M. Martinelli, “Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides,” J. Opt. Soc. Am. B 25, C87-C97 (2008).
[Crossref]

A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. 33, 2389-2391 (2008).
[Crossref] [PubMed]

2007 (6)

2005 (2)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

2004 (1)

2003 (2)

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slowwave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
[Crossref]

2002 (2)

2001 (1)

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

1999 (1)

1991 (1)

R. E. Collins, Field Theory of Guided Waves, IEEE Press Series on Electromagnetic Wave Theory (IEEE, 1991), pp. 605-641.

1987 (1)

J. R. Brews, “Characteristic impedance of microstrip lines,” IEEE Trans. Microwave Theory Tech. MTT-35, 30-34 (1987).
[Crossref]

1974 (1)

1948 (2)

C. G. Montgomery, in Principles of Microwave Circuits, C.G.Montgomery, R.H.Dicke, and E.M.Purcell, eds., Vol. 8 in MIT Radiation Laboratory Series, L.N.Ridenour and G.B.Collins, eds. (McGraw-Hill, 1948), Chap. 3.

R. M. Fano, Research Laboratory Electronics, “Theoretical limitations on the broadband matching of arbitrary impedances,” Massachusetts Institute of Technology Technical Report 41, (MIT, 1948).

1944 (1)

S. A. Schelkunoff, “Impedance concept in waveguides,” Q. Appl. Math. 2, 1 (1944).

Andreani, L. C.

Baba, T.

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
[Crossref] [PubMed]

Bandaru, P. R.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
[Crossref]

Bienstman, P.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Boscolo, S.

Botten, L. C.

F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
[PubMed]

Brews, J. R.

J. R. Brews, “Characteristic impedance of microstrip lines,” IEEE Trans. Microwave Theory Tech. MTT-35, 30-34 (1987).
[Crossref]

Collins, R. E.

R. E. Collins, Field Theory of Guided Waves, IEEE Press Series on Electromagnetic Wave Theory (IEEE, 1991), pp. 605-641.

de Maagt, P. J. L.

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

de Sterke, C. M.

F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
[PubMed]

Dossou, K. B.

F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
[PubMed]

Engelen, R. J. P.

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
[Crossref] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219-226 (2007).
[Crossref] [PubMed]

Fano, R. M.

R. M. Fano, Research Laboratory Electronics, “Theoretical limitations on the broadband matching of arbitrary impedances,” Massachusetts Institute of Technology Technical Report 41, (MIT, 1948).

Ferrari, C.

Gerace, D.

Hughes, S.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Hugonin, J. P.

Ibanescu, M.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Johnson, S. G.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Karle, T.

Kogelnik, H.

Krauss, T. F.

Kuipers, L.

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
[Crossref] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219-226 (2007).
[Crossref] [PubMed]

Kuramochi, E.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Lalanne, P.

Lawrence, F.

F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
[PubMed]

Lederer, F.

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

Lee, R. K.

Lidorikis, E.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Lowell, J. R.

E. Parra and J. R. Lowell, “Toward applications of slow light technology,” Opt. Photonics News 18, 40-45 (2007).
[Crossref]

Martinelli, M.

Melloni, A.

Michaeli, A.

Midrio, M.

Montgomery, C. G.

C. G. Montgomery, in Principles of Microwave Circuits, C.G.Montgomery, R.H.Dicke, and E.M.Purcell, eds., Vol. 8 in MIT Radiation Laboratory Series, L.N.Ridenour and G.B.Collins, eds. (McGraw-Hill, 1948), Chap. 3.

Mookherjea, S.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
[Crossref]

S. Mookherjea and A. Oh, “Effect of disorder on slow light velocity in optical slow-wave structures,” Opt. Lett. 32, 289-291 (2007).
[Crossref] [PubMed]

Mori, D.

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
[Crossref] [PubMed]

Morichetti, F.

Notomi, M.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

O'Brien, D.

O'Faolain, L.

Oh, A.

Park, J. S.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
[Crossref]

Parra, E.

E. Parra and J. R. Lowell, “Toward applications of slow light technology,” Opt. Photonics News 18, 40-45 (2007).
[Crossref]

Peschel, U.

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

Povinelli, M. L.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Reynolds, A. L.

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

Roberts, P. J.

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

Salib, M.

Schelkunoff, S. A.

S. A. Schelkunoff, “Impedance concept in waveguides,” Q. Appl. Math. 2, 1 (1944).

Scherer, A.

Settle, M. D.

Shinya, A.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Skorobogatiy, M.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Soljacic, M.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

Velha, P.

Watanabe, T.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Weber, H. P.

White, T. P.

Xu, Y.

Yang, S. H.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
[Crossref]

Yariv, A.

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Yuan, X.

IEEE Trans. Microwave Theory Tech. (2)

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

J. R. Brews, “Characteristic impedance of microstrip lines,” IEEE Trans. Microwave Theory Tech. MTT-35, 30-34 (1987).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

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

Nat. Photonics (1)

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90-93 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Opt. Photonics News (1)

E. Parra and J. R. Lowell, “Toward applications of slow light technology,” Opt. Photonics News 18, 40-45 (2007).
[Crossref]

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slowwave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
[Crossref]

Phys. Rev. B (1)

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Phys. Rev. Lett. (2)

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101, 103901 (2008).
[Crossref] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Q. Appl. Math. (1)

S. A. Schelkunoff, “Impedance concept in waveguides,” Q. Appl. Math. 2, 1 (1944).

Other (5)

C. G. Montgomery, in Principles of Microwave Circuits, C.G.Montgomery, R.H.Dicke, and E.M.Purcell, eds., Vol. 8 in MIT Radiation Laboratory Series, L.N.Ridenour and G.B.Collins, eds. (McGraw-Hill, 1948), Chap. 3.

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljacic, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering, and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proceedings of 2003 Fifth International Conference on Transparent Optical Networks (IEEE, 2003) Vol. 1, pp. 103-109.
[Crossref]

F. Lawrence, L. C. Botten, K. B. Dossou, and C. M. de Sterke, “Impedance of photonic crystals,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JTuA127.
[PubMed]

R. E. Collins, Field Theory of Guided Waves, IEEE Press Series on Electromagnetic Wave Theory (IEEE, 1991), pp. 605-641.

R. M. Fano, Research Laboratory Electronics, “Theoretical limitations on the broadband matching of arbitrary impedances,” Massachusetts Institute of Technology Technical Report 41, (MIT, 1948).

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Figures (9)

Fig. 1
Fig. 1

Scheme of a RR-CROW with a discontinuity (a) in the coupling coefficient between adjacent RRs or (b) in the optical lengths, i.e., resonance wavelengths, of the RRs. The field is partially reflected (dashed or dotted arrows) and backpropagates to the through port in the case of both CDB (red) or PDB (blue). (c) Detail of the first perturbed RR in the case of phase disorder. For PDB the impedance mismatch must be calculated at a section shifted by δ L 0 4 with respect to the reference plane located at the center of the RR.

Fig. 2
Fig. 2

Modulus of the normalized impedance Z sw , 0 Z c versus wavelength at the reference planes located in the center of the cavities of a CROW. A structure with a slowing factor S ( λ 0 ) = 6.3 , i.e., finesse F = 10 , has been considered. Z sw is real inside the passband B of the structure (blue solid curve), while it is purely imaginary in the stopband (red dashed curve).

Fig. 3
Fig. 3

Modulus of the normalized impedance of a CROW at the resonance wavelength Z sw ( λ 0 ) Z c versus the direction of propagation z. The black curve shows the impedance in the absence of disorder. The perturbed impedance Z ̂ sw and the subsequent mismatch at the reference plane z = L 4 given by a single defect is reported for both coupling disorder (red curve) and phase disorder (blue curve).

Fig. 4
Fig. 4

Average backreflected power in a CROW with N = 50 , B = 0.16 nm , and FSR = 0.8 nm , affected by disorder. Pure coupling (red curve, σ t t = 3.5 % ) and phase (blue curve, σ λ = 2 pm ) disorder backreflection are reported together with the case of mixed disorder (black curve, σ t t = 3.5 % and σ λ = 2 pm ). Analytical results [Eq. (7), dashed curves] agree with TMM 1D numerical simulations (solid curves).

Fig. 5
Fig. 5

Average PDB in two CROWs with different bandwidths ( B 1 = 0.08 pm , B 2 = 0.16 nm ) and the same degree of phase disorder (normal distribution with σ λ = 2 pm ). Both structures are made of 50 RRs with FSR = 0.8 nm . The nominal S ( λ ) of the structures are shown in (a), while the average backreflected power is shown in (b). Both analytical results [Eq. (7), dashed curve] and numerical 1D TMM simulations (solid curve) are reported. Circles and the square show that when S 2 matches S 1 ( λ 0 ) at ± 0.45 B 2 , PDB is the same for the two structures.

Fig. 6
Fig. 6

Average PDB near the band edge ( λ = 40 pm ) in a CROW with N = 50 , B = 0.08 nm , and FSR = 0.8 nm , affected by phase disorder with σ λ = 1 pm . TMM simulations (solid curve) are reported together with the results obtained by using, in the analytical model, the nominal slowing ratio S ( λ ) (dotted curve) or the average slowing ratio S ( λ , σ λ ) altered by disorder (dashed–dotted curve).

Fig. 7
Fig. 7

Top view photograph of an eight-ring CROW in SiON technology. The different shape of the first (last) rings realizes the impedance-matching condition (apodization) between the bus waveguide and the coupled-resonator structure. Gold striplines connect every chromium heater to the contact pads, the latter being wire bonded to the tuning control unit.

Fig. 8
Fig. 8

Average PDB of an eight-ring CROW for different degrees of disorder. The resonance wavelength of each RR is shifted following a normal distribution with standard deviations: (a) σ λ = 12 pm , (b) σ λ = 16 pm , (c) σ λ = 24 pm . Experimental results are reported as solid curves together with TMM numerical simulations (dashed curves).

Fig. 9
Fig. 9

Normalized time traces of light intensity at the through port when 100 ps Gaussian pulses are fed at the in port of a CROW delay line. The average effects of phase disorder are shown for growing (standard deviation) wavelength shifts: σ λ = 0 pm (black), σ λ = 6 pm (blue), σ λ = 12 pm (red). Simulation data are reported as dashed curves, while experimental data are reported as solid curves.

Equations (12)

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Γ sw ( z ) = e ( z ) e + ( z ) = j t exp ( j β L 2 ) exp ( j k L 2 ) 1 t 2 exp ( j k L 2 ) exp ( j 2 k z ) ,
Z sw = Z c 1 + Γ sw 1 Γ sw
Z sw , 0 = 2 Z c S ( λ ) ,
Z sw = Z sw , 0 j tan [ k ( z L 4 ) ] 1 j Z sw , 0 tan [ k ( z L 4 ) ] .
ρ t ( λ ) = Z ̂ sw , 0 Z sw , 0 Z ̂ sw , 0 + Z sw , 0 ,
ρ t ( λ ) = δ S ( λ ) 2 S ( λ ) 1 2 δ t S ( λ ) ,
ρ φ ( λ ) = Z ̂ sw Z sw , 0 Z ̂ sw + Z sw , 0 j π 2 δ L o λ S ( λ )
R D = n = 1 N 4 ρ 2 ( 1 4 ρ 2 ) n 1 γ n ,
R D = γ σ t 2 N S 2 + γ ( π σ L λ ) 2 N S 2 ,
Z c = V 2 ( 2 P ) ,
P = ( W t W z ) c n eff ,
Z c = V 2 2 ( W t W z ) c n eff ,

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