Abstract

We suggest a novel and general approach to the design of photonic-crystal directional couplers operating in the slow-light regime. We predict, based on a general symmetry analysis, that robust tunneling of slow-light pulses is possible between antisymmetrically coupled photonic crystal waveguides. We demonstrate, through Bloch mode frequency-domain and finite-difference time-domain (FDTD) simulations that, for all pulses with strongly reduced group velocities at the photonic band-gap edge, complete switching occurs at a fixed coupling length of just a few unit cells of the photonic crystal.

© 2008 Optical Society of America

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  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]
  2. H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
    [CrossRef] [PubMed]
  3. R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage Pedersen, and P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Express 13,7861-7871 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7861.
    [CrossRef] [PubMed]
  4. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-1-219.
    [CrossRef] [PubMed]
  5. S. C. Huang, M. Kato, E. Kuramochi, C. P. Lee, and M. Notomi, "Time-domain and spectral-domain investigation of inflection-point slow-light modes in photonic crystal coupled waveguides," Opt. Express 15,3543-3549 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3543.
    [CrossRef] [PubMed]
  6. A. V. Lavrinenko, A. Tetu, L. H. Frandsen, J. Fage Pedersen, and P. I. Borel, "Optimization of photonic crystal 60 degrees waveguide bends for broadband and slow-light transmission," Appl. Phys. B 87,53-56 (2007).
    [CrossRef]
  7. Y. Sugimoto et al., "Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides," Appl. Phys. Lett. 83,3236-3238 (2003).
    [CrossRef]
  8. D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85,1101-1103 (2004).
    [CrossRef]
  9. D. Mori and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Express 13,9398-9408 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-23-9398.
    [CrossRef] [PubMed]
  10. N. Yamamoto, T. Ogawa, and K. Komori, "Photonic crystal directional coupler switch with small switching length and wide bandwidth," Opt. Express 14,1223-1229 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-3-1223.
    [CrossRef] [PubMed]
  11. Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
    [CrossRef]
  12. M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3,211-219 (2004).
    [CrossRef] [PubMed]
  13. R. S. Jacobsen et al., "Strained silicon as a new electro-optic material," Nature 441,199-202 (2006).
    [CrossRef] [PubMed]
  14. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
  15. P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, "Photonic Bloch waves and photonic band gaps," in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., (Plenum, New York, 1995), pp. 585-633.
  16. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8,173-190 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173.
    [CrossRef] [PubMed]
  17. L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
    [CrossRef]
  18. K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219,120-143 (2006).
    [CrossRef]
  19. R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. Hulst, van, K. Asakawa, and L. Kuipers, "The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides," Opt. Express 14,1658-1672 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1658.
    [CrossRef] [PubMed]
  20. 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. 94,033903-4 (2005).
    [CrossRef] [PubMed]
  21. 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 72,161318-4 (2005).
    [CrossRef]
  22. 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]

2007

2006

2005

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. 94,033903-4 (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 72,161318-4 (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]

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
[CrossRef] [PubMed]

R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage Pedersen, and P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Express 13,7861-7871 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7861.
[CrossRef] [PubMed]

D. Mori and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Express 13,9398-9408 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-23-9398.
[CrossRef] [PubMed]

2004

D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85,1101-1103 (2004).
[CrossRef]

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3,211-219 (2004).
[CrossRef] [PubMed]

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

2003

Y. Sugimoto et al., "Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides," Appl. Phys. Lett. 83,3236-3238 (2003).
[CrossRef]

2001

Asatryan, A. A.

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Baba, T.

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
[CrossRef] [PubMed]

Borel, P. I.

Botten, L. C.

K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219,120-143 (2006).
[CrossRef]

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Byrne, M. A.

K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219,120-143 (2006).
[CrossRef]

de Sterke, C. M.

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Dossou, K.

K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219,120-143 (2006).
[CrossRef]

Engelen, R. J. P.

Fage Pedersen, J.

Frandsen, L. H.

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
[CrossRef] [PubMed]

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]

Han, P. D.

Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
[CrossRef]

Huang, S. C.

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. 94,033903-4 (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 72,161318-4 (2005).
[CrossRef]

Hulst, N. F.

R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. Hulst, van, K. Asakawa, and L. Kuipers, "The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides," Opt. Express 14,1658-1672 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1658.
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
[CrossRef] [PubMed]

Ikeda, N.

Jacobsen, R. S.

Joannopoulos, J. D.

Johnson, S. G.

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
[CrossRef] [PubMed]

Kato, M.

Komori, K.

Korterik, J. P.

R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. Hulst, van, K. Asakawa, and L. Kuipers, "The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides," Opt. Express 14,1658-1672 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1658.
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94,073903-4 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

Kuipers, L.

Kuramochi, E.

Langtry, T. N.

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Lavrinenko, A. V.

Lee, C. P.

Lu, X. D.

Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
[CrossRef]

McNab, S. J.

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]

McPhedran, R. C.

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Michaeli, A.

Mori, D.

Moulin, G.

Notomi, M.

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.

Ogawa, T.

Peucheret, C.

Quan, Y. J.

Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
[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. 94,033903-4 (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 72,161318-4 (2005).
[CrossRef]

Salib, M.

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 72,161318-4 (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. 94,033903-4 (2005).
[CrossRef] [PubMed]

Soljacic, M.

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3,211-219 (2004).
[CrossRef] [PubMed]

Sugimoto, Y.

Tetu, A.

A. V. Lavrinenko, A. Tetu, L. H. Frandsen, J. Fage Pedersen, and P. I. Borel, "Optimization of photonic crystal 60 degrees waveguide bends for broadband and slow-light transmission," Appl. Phys. B 87,53-56 (2007).
[CrossRef]

Vlasov, Y. A.

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]

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 72,161318-4 (2005).
[CrossRef]

Watanabe, Y.

White, T. P.

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]

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Wu, L.

Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
[CrossRef]

Yamamoto, N.

Ye, Z. C.

Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
[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. 94,033903-4 (2005).
[CrossRef] [PubMed]

Yuan, X. D.

Zsigri, B.

Appl. Phys. B

A. V. Lavrinenko, A. Tetu, L. H. Frandsen, J. Fage Pedersen, and P. I. Borel, "Optimization of photonic crystal 60 degrees waveguide bends for broadband and slow-light transmission," Appl. Phys. B 87,53-56 (2007).
[CrossRef]

Appl. Phys. Lett.

Y. Sugimoto et al., "Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides," Appl. Phys. Lett. 83,3236-3238 (2003).
[CrossRef]

D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85,1101-1103 (2004).
[CrossRef]

J. Comput. Phys.

K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219,120-143 (2006).
[CrossRef]

Nat. Mater.

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3,211-219 (2004).
[CrossRef] [PubMed]

Nature

R. S. Jacobsen et al., "Strained silicon as a new electro-optic material," Nature 441,199-202 (2006).
[CrossRef] [PubMed]

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. Commun.

Y. J. Quan, P. D. Han, X. D. Lu, Z. C. Ye, and L. Wu, "Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes," Opt. Commun. 270,203-206 (2007).
[CrossRef]

Opt. Express

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]

R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage Pedersen, and P. I. Borel, "Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides," Opt. Express 13,7861-7871 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-7861.
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-1-219.
[CrossRef] [PubMed]

S. C. Huang, M. Kato, E. Kuramochi, C. P. Lee, and M. Notomi, "Time-domain and spectral-domain investigation of inflection-point slow-light modes in photonic crystal coupled waveguides," Opt. Express 15,3543-3549 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3543.
[CrossRef] [PubMed]

D. Mori and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Express 13,9398-9408 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-23-9398.
[CrossRef] [PubMed]

N. Yamamoto, T. Ogawa, and K. Komori, "Photonic crystal directional coupler switch with small switching length and wide bandwidth," Opt. Express 14,1223-1229 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-3-1223.
[CrossRef] [PubMed]

R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. Hulst, van, K. Asakawa, and L. Kuipers, "The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides," Opt. Express 14,1658-1672 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1658.
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8,173-190 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173.
[CrossRef] [PubMed]

Phys. Rev. B

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 72,161318-4 (2005).
[CrossRef]

Phys. Rev. E

L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory," Phys. Rev. E 70,056606-13 (2004).
[CrossRef]

Phys. Rev. Lett.

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. 94,033903-4 (2005).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, "Photonic Bloch waves and photonic band gaps," in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., (Plenum, New York, 1995), pp. 585-633.

Supplementary Material (4)

» Media 1: GIF (915 KB)     
» Media 2: GIF (1521 KB)     
» Media 3: GIF (1224 KB)     
» Media 4: GIF (1552 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Characteristic types of band-edge dispersion for slow-light modes in photonic-crystal waveguides. (a) Band-edge is reached at the symmetry points of the Brillouin zone k=0,±π/a. (b) Band-edge is reached inside the Brillouin zone for kk 0≠0,±π/a. Open circles mark the lower band-edge, and closed circles-modes with positive slope of dispersion curves (and, accordingly, positive group velocities) for the frequency tuned close to the band-edge.

Fig. 2.
Fig. 2.

Examples of photonic crystal couplers (top row) and their corresponding dispersion diagram (bottom row) with different number of rows (N) between the W1 waveguides in a hexagonal lattice: (a) N=1, (b) N=2, and (c) N=3. Solid and dashed lines correspond to fundamental and higher-order modes. The hole radius (normalized to the lattice constant) is 0.3, and 0.42 — for the central row in (a) and (c). Open circles indicate the lower band-edges, where slow-light modes are considered. Dotted lines mark the light-lines, and grey shading in (a) marks the 2D photonic band.

Fig. 3.
Fig. 3.

Simulations of pulse propagation through the symmetric coupler shown in Fig. 2(a), top. The central frequency of the pulse (ω=0.21238) is tuned close to the gap-edge, indicated by the open circle in 2(a), bottom. (a,b) Snapshots of the magnetic field intensity at different time steps, as indicated by labels. Animation shows the full temporal dynamics. (c) Field intensities along the centres of two coupled waveguides, at the time frame corresponding to plot (a). The lattice constant is 400nm, the input pulse duration is 500fs, and the corresponding normalized pulse bandwidth Δω=0.002. The estimated pulse velocity is Vg c/115. [Media 1]

Fig. 4.
Fig. 4.

Simulations of pulse propagation through the symmetric coupler shown in Fig. 2(c), top. The central frequency of the pulse (ω=0.2197) is tuned close to the gap-edge, indicated by the open circle in 2(c), bottom. The estimated pulse velocity is Vg c/60. Parameter values and the notation are as given in Fig. 3. [Media 2]

Fig. 5.
Fig. 5.

(a,b) Intensity (top) and phase (bottom) of the transverse magnetic field distributions for the band-edge modes of antisymmetric coupler [shown in Fig. 2(b)] at ω≃0.214 with (a) positive (k=0.44) and (b) negative (k=-0.41) wavenumbers, respectively. (c) Intensity of the simultaneously excited modes.

Fig. 6.
Fig. 6.

(a) Dependence of the group velocities on the frequency detuning from the band-edge (in logarithmic scale) shown for modes with positive (solid line) and negative (dashed line) wavenumbers, and (b) the corresponding dependence of the coupling length on frequency detuning.

Fig. 7.
Fig. 7.

Simulations of pulse propagation through the antisymmetric coupler shown in Fig. 2(b), top. (a–d) Snapshots of the magnetic field intensity at different time-steps as indicated by the labels. Animations show the full temporal dynamics. (e) Field intensities along the centres of two coupled waveguides, corresponding to figure (a). The central wavelength of the pulse spectrum is (a,b,e) tuned close to the band-edge and (c,d) tuned further away from the band-edge as indicated by labels. The lattice constant is 400nm, the input pulse duration is 500fs, and the corresponding normalized pulse bandwidth Δω=0.002. The estimated pulse velocity is (a,b,e) Vg c/96 and (c,d) Vg c/71. [Media 3][Media 4]

Equations (8)

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ω ( k ) = ω ( k + 2 π a ) ,
ψ ( x , z ; ω , k ) = ψ ( x , z ; ω , k + 2 π a ) ,
ω ( k ) ω ( k ) and ψ ( x , z ; ω , k ) = ψ * ( x , z ; ω , k ) .
ω ω 0 + D 2 ( k k 0 ) 2 + D 3 ( k k 0 ) 3 ,
k ω ω 0 s k 0 + σ [ ω ω 0 D 2 ] 1 2 s D 3 2 ( D 2 ) 2 ( ω ω 0 ) ,
V g = d ω dk 2 σ D 2 [ ω ω 0 D 2 ] 1 2 + 2 s D 3 D 2 ( ω ω 0 ) .
L c π a arg exp { i [ k s = + 1 k s = 1 ] a } 1 π a arg exp { i [ 2 k 0 D 3 ( D 2 ) 2 ( ω ω 0 ) ] a } 1 ,
L c ( ω ω 0 ) π a arg exp { i 2 k 0 a } 1 .

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