Abstract

It is known that slow light propagation in disordered photonic crystal channel waveguides leads to backscattering and localization phenomena. The knowledge of the reflection of a slow light mode at a single disorder defect of the periodical structure can help to estimate the backscattering intensity and the localization length. Here, this Bloch-mode reflection is calculated in a simplified slow light waveguide using an eigenmode-expansion approach. We show that by properly engineering the waveguide, backscattering can be significantly reduced while maintaining the same low group velocity. A strong effect of the mode’s anticrossing taking place in photonic crystal line-defects is demonstrated on backscattering. The localization length of slow light waveguides is estimated, which provides fundamental limits for the applicability of slow light waveguides.

© 2009 Optical Society of America

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2009 (3)

2008 (7)

2007 (7)

2006 (1)

2005 (9)

J. B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis," J. Opt. Soc. Am. B 22, 1062-1074 (2005).
[CrossRef]

D. Gerace and L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Express 13, 4939-4951 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-4939
[CrossRef] [PubMed]

M. Lipson, "Guiding, modulating, and emitting light on silicon-challenges and opportunities," J. Lightwave Technol. 23, 4222-4238 (2005).
[CrossRef]

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

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[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]

A. Y. Petrov and M. Eich, "Dispersion compensation with photonic crystal line-defect waveguides," IEEE J. Sel. Areas Commun. 23, 1396-1401 (2005).
[CrossRef]

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[CrossRef]

2004 (4)

L. C. Andreani, D. Gerace, and M. Agio, "Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs," Photonics Nanostruct. Fundam. Appl. 2, 103-110 (2004).
[CrossRef]

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

M. F. Yanik and S. H. Fan, "Stopping light all optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

D. Gerace and L. C. Andreani, "Disorder-induced losses in photonic crystal waveguides with line defects," Opt. Lett. 29, 1897-1899 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (3)

M. Soljacic, S. G. Johnson, S. H. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19, 2052-2059 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

K. Hosomi and T. Katsuyama, "A dispersion compensator using coupled defects in a photonic crystal," IEEE J. Quantum Electron. 38, 825-829 (2002).
[CrossRef]

2001 (2)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

2000 (1)

T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys. Rev. B 61, 15688-15696 (2000).
[CrossRef]

1999 (1)

1995 (1)

Z. Q. Zhang, "Light amplification and localization in randomly layered media with gain," Phys. Rev. B 52, 7960-7964 (1995).
[CrossRef]

Adachi, J.

Agio, M.

L. C. Andreani, D. Gerace, and M. Agio, "Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs," Photonics Nanostruct. Fundam. Appl. 2, 103-110 (2004).
[CrossRef]

Andreani, L. C.

Baba, T.

R. J. Engelen, D. Mori, T. Baba, and L. Kuipers, "Two regimes of slow-light losses revealed by adiabatic reduction of group velocity," Phys. Rev. B 101, 103901 (2008).
[CrossRef]

T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, "Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide," Opt. Express 16, 9245-9253 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-9245
[CrossRef] [PubMed]

T. Baba, "Slow light in photonic crystals," Nat. Photonics 2, 465 (2008).
[CrossRef]

Baets, R.

J. Jagerska, N. Le Thomas, V. Zabelin, R. Houdre, W. Bogaerts, P. Dumon, and R. Baets, "Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides," Opt. Lett. 34, 359-361 (2009).
[CrossRef] [PubMed]

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

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.

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Bogaerts, W.

Brosi, J. M.

Chen, R. T.

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Chen, X. N.

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Dridi, K. H.

T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys. Rev. B 61, 15688-15696 (2000).
[CrossRef]

Dumon, P.

Eich, M.

J. H. Wülbern, A. Petrov, and M. Eich, "Electro-optical modulator in a polymerinfiltrated silicon slotted photonic crystal waveguide heterostructure resonator," Opt. Express 17, 304-313 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-1-304
[CrossRef] [PubMed]

A. Y. Petrov and M. Eich, "Dispersion compensation with photonic crystal line-defect waveguides," IEEE J. Sel. Areas Commun. 23, 1396-1401 (2005).
[CrossRef]

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Engelen, R. J.

R. J. Engelen, D. Mori, T. Baba, and L. Kuipers, "Two regimes of slow-light losses revealed by adiabatic reduction of group velocity," Phys. Rev. B 101, 103901 (2008).
[CrossRef]

Fan, S. H.

Ferrari, C.

C. Ferrari, F. Morichetti, and A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Am. A 26, pp. 858-866 (2009).
[CrossRef]

Freude, W.

Gerace, D.

D. Gerace and L. C. Andreani, "Light-matter interaction in photonic crystal slabs," Phys. Status Solidi B 244, 3528-3539 (2007).
[CrossRef]

D. Gerace and L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Express 13, 4939-4951 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-4939
[CrossRef] [PubMed]

L. C. Andreani, D. Gerace, and M. Agio, "Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs," Photonics Nanostruct. Fundam. Appl. 2, 103-110 (2004).
[CrossRef]

D. Gerace and L. C. Andreani, "Disorder-induced losses in photonic crystal waveguides with line defects," Opt. Lett. 29, 1897-1899 (2004).
[CrossRef] [PubMed]

Gomez-Iglesias, A.

Gu, L. L.

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Hosomi, K.

K. Hosomi and T. Katsuyama, "A dispersion compensator using coupled defects in a photonic crystal," IEEE J. Quantum Electron. 38, 825-829 (2002).
[CrossRef]

Houdre, R.

Hughes, S.

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]

Ibanescu, M.

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, "Experimental observation of strong photon localization in disordered photonic crystal waveguides," Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Ippen, E.

Jacobs, S.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Jagerska, J.

Jiang, W.

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Jiang, Y. Q.

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

M. Soljacic, S. G. Johnson, S. H. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19, 2052-2059 (2002).
[CrossRef]

Johnson, S. G.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

M. Soljacic, S. G. Johnson, S. H. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19, 2052-2059 (2002).
[CrossRef]

Karalis, A.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Karle, T.

Katsuyama, T.

K. Hosomi and T. Katsuyama, "A dispersion compensator using coupled defects in a photonic crystal," IEEE J. Quantum Electron. 38, 825-829 (2002).
[CrossRef]

Kawaaski, T.

Khurgin, J. B.

Koos, C.

Krauss, T. F.

Kuipers, L.

R. J. Engelen, D. Mori, T. Baba, and L. Kuipers, "Two regimes of slow-light losses revealed by adiabatic reduction of group velocity," Phys. Rev. B 101, 103901 (2008).
[CrossRef]

Kuramochi, E.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, "Nonlinear and adiabatic control of high-Q photonic crystal nanocavities," Opt. Express 15, pp. 17458-17481 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17458
[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]

Le Thomas, N.

Lee, R. K.

Leuthold, J.

Li, J.

Lipson, M.

McMillan, J. E.

McNab, S. J.

Melloni, A.

C. Ferrari, F. Morichetti, and A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Am. A 26, pp. 858-866 (2009).
[CrossRef]

Michaeli, A.

Mitsugi, S.

Moll, N.

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]

S. Mookherjea and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

Mori, D.

Morichetti, F.

C. Ferrari, F. Morichetti, and A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Am. A 26, pp. 858-866 (2009).
[CrossRef]

Morita, M.

Mortensen, N. A.

J. G. Pedersen, S. Xiao, and N. A. Mortensen, "Limits of slow light in photonic crystals," Phys. Rev. B 78, 153101 (2008).
[CrossRef]

Notomi, M.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, "Nonlinear and adiabatic control of high-Q photonic crystal nanocavities," Opt. Express 15, pp. 17458-17481 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17458
[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]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

O'Boyle, M.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

O'Brien, D.

O'Faolain, L.

Oh, A.

Osgood, R. M.

Panoiu, N. C.

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]

Pedersen, J. G.

J. G. Pedersen, S. Xiao, and N. A. Mortensen, "Limits of slow light in photonic crystals," Phys. Rev. B 78, 153101 (2008).
[CrossRef]

Petrov, A.

Petrov, A. Y.

A. Y. Petrov and M. Eich, "Dispersion compensation with photonic crystal line-defect waveguides," IEEE J. Sel. Areas Commun. 23, 1396-1401 (2005).
[CrossRef]

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Povinelli, M. L.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Ramunno, L.

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]

Salib, M.

Sasaki, H.

Scherer, A.

Settle, M. D.

Shinya, A.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, "Nonlinear and adiabatic control of high-Q photonic crystal nanocavities," Opt. Express 15, pp. 17458-17481 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17458
[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]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[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]

Soljacic, M.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

M. Soljacic, S. G. Johnson, S. H. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19, 2052-2059 (2002).
[CrossRef]

Sondergaard, T.

T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys. Rev. B 61, 15688-15696 (2000).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

Tanabe, T.

Taniyama, H.

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, "Experimental observation of strong photon localization in disordered photonic crystal waveguides," Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Vlasov, Y. A.

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, "Experimental observation of strong photon localization in disordered photonic crystal waveguides," Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Waldow, M.

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]

White, T. P.

Wong, C. W.

Wülbern, J. H.

Xiao, S.

J. G. Pedersen, S. Xiao, and N. A. Mortensen, "Limits of slow light in photonic crystals," Phys. Rev. B 78, 153101 (2008).
[CrossRef]

Xu, Y.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

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]

Yang, X. D.

Yanik, M. F.

M. F. Yanik and S. H. Fan, "Stopping light all optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Yariv, A.

S. Mookherjea and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

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

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

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. D.

Zabelin, V.

Zhang, Z. Q.

Z. Q. Zhang, "Light amplification and localization in randomly layered media with gain," Phys. Rev. B 52, 7960-7964 (1995).
[CrossRef]

Appl. Phys. B (1)

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and R. T. Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Hosomi and T. Katsuyama, "A dispersion compensator using coupled defects in a photonic crystal," IEEE J. Quantum Electron. 38, 825-829 (2002).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

A. Y. Petrov and M. Eich, "Dispersion compensation with photonic crystal line-defect waveguides," IEEE J. Sel. Areas Commun. 23, 1396-1401 (2005).
[CrossRef]

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

S. Mookherjea and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

C. Ferrari, F. Morichetti, and A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Am. A 26, pp. 858-866 (2009).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. D (1)

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D 40, 2666-2670 (2007).
[CrossRef]

Nat. Photonics (2)

T. Baba, "Slow light in photonic crystals," Nat. Photonics 2, 465 (2008).
[CrossRef]

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]

Nature (1)

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Opt. Express (9)

D. Gerace and L. C. Andreani, "Low-loss guided modes in photonic crystal waveguides," Opt. Express 13, 4939-4951 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-4939
[CrossRef] [PubMed]

S. J. McNab, N. Moll, and Y. A. Vlasov, "Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides," Opt. Express 11, 2927-2939 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2927
[CrossRef] [PubMed]

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, "Nonlinear and adiabatic control of high-Q photonic crystal nanocavities," Opt. Express 15, pp. 17458-17481 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17458
[CrossRef] [PubMed]

J. H. Wülbern, A. Petrov, and M. Eich, "Electro-optical modulator in a polymerinfiltrated silicon slotted photonic crystal waveguide heterostructure resonator," Opt. Express 17, 304-313 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-1-304
[CrossRef] [PubMed]

D. O'Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, "Coupled photonic crystal heterostructure nanocavities," Opt. Express 15, pp. 1228-1233 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-3-1228
[CrossRef] [PubMed]

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, "High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide," Opt. Express 16, 4177-4191 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-6-4177
[CrossRef] [PubMed]

T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, "Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide," Opt. Express 16, 9245-9253 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-9245
[CrossRef] [PubMed]

L. O'Faolain, T. P. White, D. O'Brien, X. D. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-13129
[CrossRef] [PubMed]

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, "Systematic design of flat band slow light in photonic crystal waveguides," Opt. Express 16, 6227-6232 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-9-6227
[CrossRef] [PubMed]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Photonics Nanostruct. Fundam. Appl. (1)

L. C. Andreani, D. Gerace, and M. Agio, "Gap maps, diffraction losses, and exciton-polaritons in photonic crystal slabs," Photonics Nanostruct. Fundam. Appl. 2, 103-110 (2004).
[CrossRef]

Phys. Rev. B (5)

J. G. Pedersen, S. Xiao, and N. A. Mortensen, "Limits of slow light in photonic crystals," Phys. Rev. B 78, 153101 (2008).
[CrossRef]

R. J. Engelen, D. Mori, T. Baba, and L. Kuipers, "Two regimes of slow-light losses revealed by adiabatic reduction of group velocity," Phys. Rev. B 101, 103901 (2008).
[CrossRef]

Z. Q. Zhang, "Light amplification and localization in randomly layered media with gain," Phys. Rev. B 52, 7960-7964 (1995).
[CrossRef]

T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys. Rev. B 61, 15688-15696 (2000).
[CrossRef]

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. (4)

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]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 8725, 253902 (2001).
[CrossRef]

M. F. Yanik and S. H. Fan, "Stopping light all optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

J. Topolancik, B. Ilic, and F. Vollmer, "Experimental observation of strong photon localization in disordered photonic crystal waveguides," Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Phys. Status Solidi B (1)

D. Gerace and L. C. Andreani, "Light-matter interaction in photonic crystal slabs," Phys. Status Solidi B 244, 3528-3539 (2007).
[CrossRef]

Other (2)

I. Giuntoni, M. Krause, H. Renner, J. Bruns, A. a. B. E. Gajda, and K. Petermann, "Numerical survey on Bragg reflectors in silicon-on-insulator waveguides," in Proceedings of IEEE 5th International Conference on Group IV Photonics, Sorrento, Italy, 17-19 September (IEEE, 2008) pp. 285-287.

Available at camfr.sourceforge.net.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic representation of the disorder defects in a line-defect waveguide. In our calculations, a single disorder defect is introduced by shifting the holes’ boundary. In this figure several boundaries of the holes in the 1st, 2nd, or 3rd rows are named for later reference. The assumed refractive indices are 3.5 (corresponding to silicon) for the grey area, and 1.0 (corresponding to Air) for the white areas.

Fig. 2.
Fig. 2.

Group velocity as a function of normalized frequency and electric field amplitude distribution at the point of vanishing dispersion for the waveguides (a) W0.8 and (b) W1. Strong field concentration at the boundary of the first row of holes is observed in W0.8 waveguide. On the other hand electric field is evenly distributed among the first and second row of holes in W1 waveguide. Both false color plots refer to the same amplitude scale. Field distribution was calculated with finite integration technique of CST, Darmstadt.

Fig. 3.
Fig. 3.

The normalized reflectivity α as a function of the group index in the (a) W0.8 and (b) W1 waveguides. The boundaries parallel to the direction of propagation are shown in red color and boundaries orthogonal to direction of propagation with blue color. The labels of the curves refer to the boundary labels in Fig. 1.

Fig. 4.
Fig. 4.

Mean free path of the slow light waveguides as a function of group index for the normalized reflectivity αa = 0.3 and different levels of disorder. The lattice constant is set to a typical value of a = 0.4 μm. The dashed lines represent the lengths where constant time delay 10 ps and 1 ns will be obtained.

Equations (4)

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

α=r(Δd/a)·ngr ,
υg=Powerflow(WE+WM)/Λ,
RCC=Nm <(rLD)2>=mRLD,
L=aRa=a(aΔd)2(υg/c)2αa2,

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