Abstract

Coupling external light signals into a photonic crystal (PhC) waveguide becomes increasingly inefficient as the group velocity of the waveguiding mode slows down. We have systematically studied the efficiency of coupling in the slow light regime for samples with different truncations of the photonic lattice at the coupling interface between a strip waveguide and a PhC waveguide. An inverse power law dependence is found to best fit the experimental scaling of the coupling loss on the group index. Coupling efficiency is significantly improved up to group indices of 100 for a truncation of the lattice that favors the appearance of photonic surface states at the coupling interface in resonance with the slow light mode.

© 2006 Optical Society of America

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  1. Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
    [CrossRef]
  2. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  3. M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
    [CrossRef] [PubMed]
  4. E. Miyai and S. Noda, J. Opt. Soc. Am. B 21, 67 (2004).
    [CrossRef]
  5. J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
    [CrossRef]
  6. P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
    [CrossRef]
  7. Yu. A. Vlasov, N. Moll, and S. J. McNab, Opt. Lett. 29, 2175 (2004).
    [CrossRef] [PubMed]
  8. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 69, 121402(R) (2004).
    [CrossRef]
  9. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]

2005 (1)

E. Dulkeith, S. J. McNab, and Yu. A. Vlasov, Phys. Rev. B 72, 115102 (2005).
[CrossRef]

2004 (7)

M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

E. Miyai and S. Noda, J. Opt. Soc. Am. B 21, 67 (2004).
[CrossRef]

Y. A. Vlasov and S. J. McNab, Opt. Express 12, 1622 (2004).
[CrossRef] [PubMed]

Yu. A. Vlasov, N. Moll, and S. J. McNab, Opt. Lett. 29, 2175 (2004).
[CrossRef] [PubMed]

2003 (2)

S. J. McNab, N. Moll, and Yu. A. Vlasov, Opt. Express 11, 2927 (2003).
[CrossRef] [PubMed]

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

2001 (2)

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

1999 (1)

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Baets, R.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

Bienstman, P.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Dulkeith, E.

E. Dulkeith, S. J. McNab, and Yu. A. Vlasov, Phys. Rev. B 72, 115102 (2005).
[CrossRef]

Fan, S.

M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

Gomyo, A.

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

Gosele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Hirlimann, Ch.

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Hönerlage, B.

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Klein, G.

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Luyssaert, B.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

Marti, J.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

Martin-Moreno, L.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

McNab, S. J.

Miyai, E.

Moll, N.

Moreno, E.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

Muller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Noda, S.

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Petit, S.

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Sanchis, P.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Shirane, M.

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

Soukoulis, C. M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Suh, W.

M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Tokushima, M.

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

Ushida, J.

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

Vlasov, Y. A.

Vlasov, Yu. A.

E. Dulkeith, S. J. McNab, and Yu. A. Vlasov, Phys. Rev. B 72, 115102 (2005).
[CrossRef]

Yu. A. Vlasov, N. Moll, and S. J. McNab, Opt. Lett. 29, 2175 (2004).
[CrossRef] [PubMed]

S. J. McNab, N. Moll, and Yu. A. Vlasov, Opt. Express 11, 2927 (2003).
[CrossRef] [PubMed]

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Wang, Z.

M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Yamada, H.

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yanik, M.

M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, IEEE J. Quantum Electron. 40, 541 (2004).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (3)

J. Ushida, M. Tokushima, M. Shirane, A. Gomyo, and H. Yamada, Phys. Rev. B 68, 155115 (2003).
[CrossRef]

E. Dulkeith, S. J. McNab, and Yu. A. Vlasov, Phys. Rev. B 72, 115102 (2005).
[CrossRef]

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

Phys. Rev. E (1)

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, Phys. Rev. E 60, 1030 (1999).
[CrossRef]

Phys. Rev. Lett. (3)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

M. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Inset, set of low spectral resolution ( 5 nm ) transmission spectra of samples with different terminations of the strip–PhC interface. Black, blue, and red correspond to terminations τ of 0, 0.5, and 0.75, respectively. The magnified portion of the spectra measured with 60 pm resolution is shown in the main graph. The open blue circles show the positions of maxima and minima of oscillations. Right, scanning electron microscope images of the structures investigated.

Fig. 2
Fig. 2

Inset, transmission spectra of a sample with τ = 0.5 measured with an LED ( 60 pm resolution, blue curve) and laser ( 20 pm steps, black curve) as a source. A, Coupling losses of the pair of strip–PhC interfaces measured for different terminations. B, Reflectivity at the strip–PhC interface for different terminations. Black, blue, and red symbols correspond to terminations τ of 0, 0.5, and 0.75. The lines show the results of fitting with an inverse power law with the exponents 0.99 , 1.84 , and 0.72 for τ = 0 , τ = 0.5 , and τ = 0.75 , respectively.

Fig. 3
Fig. 3

A, Projected photonic band diagram of the W1 PhC waveguide calculated with a 3D plane-wave method along the Γ K direction for R a = 0.25 and slab thickness 0.52 a . The solid curve corresponds to the z-even TE-like mode of interest. The dashed curve is the z-odd TE-like mode. The dotted line in B depicts the light line. B, Photonic band diagrams along the Γ M direction of the PhC slab truncated at various terminations τ. C, Frequency position of the surface mode at k = 0.5 for different terminations τ.

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