Abstract

We show that efficient coupling between fast and slow photonic crystal waveguide modes is possible, provided that there exist strong evanescent modes to match the waveguide fields across the interface. Evanescent modes are required when the propagating modes have substantially different modal fields, which occurs, for example, when coupling an index-guided mode and a gap-guided mode.

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References

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  1. J. B. Khurgin, and R. S. Tucker, Slow light: science and applications (CRC Press, Boca Raton, Fla 2008).
  2. T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2(8), 448–450 (2008).
    [CrossRef]
  3. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
    [CrossRef]
  4. J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007).
    [CrossRef] [PubMed]
  5. T. P. White, L. C. Botten, C. Martijn de Sterke, K. B. Dossou, and R. C. McPhedran, “Efficient slow-light coupling in a photonic crystal waveguide without transition region,” Opt. Lett. 33(22), 2644–2646 (2008).
    [CrossRef] [PubMed]
  6. M. L. Povinelli, S. Johnson, and J. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13(18), 7145–7159 (2005).
    [CrossRef] [PubMed]
  7. P. Velha, J. P. Hugonin, and P. Lalanne, “Compact and efficient injection of light into band-edge slow-modes,” Opt. Express 15(10), 6102–6112 (2007).
    [CrossRef] [PubMed]
  8. C. Li, H. Tian, C. Zheng, and Y. Ji, “Improved line defect structures for slow light transmission in photonic crystal waveguide,” Opt. Commun. 279(1), 214–218 (2007).
    [CrossRef]
  9. 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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
    [CrossRef] [PubMed]
  10. 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. 87(25), 253902 (2001).
    [CrossRef] [PubMed]
  11. J. D. Joannopolous, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals 2nd Ed (Princeton University Press, Princeton, 2008), Ch. 8.

2008 (3)

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2(8), 448–450 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

T. P. White, L. C. Botten, C. Martijn de Sterke, K. B. Dossou, and R. C. McPhedran, “Efficient slow-light coupling in a photonic crystal waveguide without transition region,” Opt. Lett. 33(22), 2644–2646 (2008).
[CrossRef] [PubMed]

2007 (3)

2005 (1)

2004 (1)

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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

2001 (1)

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Botten, L. C.

T. P. White, L. C. Botten, C. Martijn de Sterke, K. B. Dossou, and R. C. McPhedran, “Efficient slow-light coupling in a photonic crystal waveguide without transition region,” Opt. Lett. 33(22), 2644–2646 (2008).
[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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

Dossou, K. B.

Hugonin, J. P.

Ji, Y.

C. Li, H. Tian, C. Zheng, and Y. Ji, “Improved line defect structures for slow light transmission in photonic crystal waveguide,” Opt. Commun. 279(1), 214–218 (2007).
[CrossRef]

Joannopoulos, J.

Johnson, S.

Krauss, T. F.

Lalanne, P.

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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

Li, C.

C. Li, H. Tian, C. Zheng, and Y. Ji, “Improved line defect structures for slow light transmission in photonic crystal waveguide,” Opt. Commun. 279(1), 214–218 (2007).
[CrossRef]

Martijn de Sterke, C.

McPhedran, R. C.

T. P. White, L. C. Botten, C. Martijn de Sterke, K. B. Dossou, and R. C. McPhedran, “Efficient slow-light coupling in a photonic crystal waveguide without transition region,” Opt. Lett. 33(22), 2644–2646 (2008).
[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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

Notomi, M.

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Povinelli, M. L.

Shinya, A.

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Tian, H.

C. Li, H. Tian, C. Zheng, and Y. Ji, “Improved line defect structures for slow light transmission in photonic crystal waveguide,” Opt. Commun. 279(1), 214–218 (2007).
[CrossRef]

Velha, P.

White, T. P.

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Zheng, C.

C. Li, H. Tian, C. Zheng, and Y. Ji, “Improved line defect structures for slow light transmission in photonic crystal waveguide,” Opt. Commun. 279(1), 214–218 (2007).
[CrossRef]

Nat. Photonics (2)

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2(8), 448–450 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Opt. Commun. (1)

C. Li, H. Tian, C. Zheng, and Y. Ji, “Improved line defect structures for slow light transmission in photonic crystal waveguide,” Opt. Commun. 279(1), 214–218 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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 Stat. Nonlin. Soft Matter Phys. 70(5), 056606 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

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. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Other (2)

J. D. Joannopolous, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals 2nd Ed (Princeton University Press, Princeton, 2008), Ch. 8.

J. B. Khurgin, and R. S. Tucker, Slow light: science and applications (CRC Press, Boca Raton, Fla 2008).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the geometries: light is incident from PC1 into PC2, which supports a slow mode. (a) PC2 has a square lattice; PC1 is similar but the lattice is compressed by 10% in the direction parallel to the waveguide (Sect. 2). (b) PC2 has a hexagonal lattice; PC1 is similar, but its lattice is stretched by 7.1% parallel to the waveguide (Sect. 3). Stretching and compression are exaggerated for clarity.

Fig. 2
Fig. 2

Modulus of the electric field vs. position. Shown is: (a) total field in PC1; (b) evanescent field in PC1; (c) forward propagating field in PC1; (d) backward propagating field in PC1; (e) total field in PC2; (f) evanescent field in PC2; (g) forward propagating field in PC2.

Fig. 3
Fig. 3

Projected band structures of (a): PC1, and (b) PC2. The horizontal dotted line gives the frequency of operation. Curves show the waveguide modes. The circle in (a) indicates the position of the anti-crossing between the gap-guided modes and index-guided modes.

Fig. 4
Fig. 4

As in Fig. 2, but for the hexagonal lattice and the modulus of the magnetic field.

Fig. 5
Fig. 5

(a) Longitudinal profile of |Hz| through the hexagonal lattice waveguide centre. The transmittance from PC1 (ng = 4.3) into PC2 (ng = 100) is T = 77%. (b) Similar, but for the field |Ez| in the square lattice waveguide studied in Sect. 2. Here the transmittance from PC1 (ng = 4.629) into PC2 (ng = 100) is T = 16%. The dashed line indicates the interface.

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