Abstract

Studies of the refraction and dispersion properties of two-dimensional (2D) photonic-crystal (PC) slab waveguides are reported. The photonic band structure is strongly modified in a slab PC, and only a small number of bands satisfy the guiding conditions imposed by the lack of translation symmetry in the direction perpendicular to the slab; however, it was found that a significant number of the guided modes retain the giant refraction and strong dispersion properties discovered previously in pure 2D PCs. A small change in incident angle resulted in a dramatic change in refraction angle. Furthermore, the dispersion surface exhibited a strong dependence on the frequency, resulting in a superprism effect similar to what has been predicted for pure 2D PCs. In the silicon-based slab PC studied, refraction angles as high as nearly 70° were predicted for incident angles of less than 7°, and frequency components differing by 3% were separated by 15°. The demonstration of giant refraction and superprism phenomena in slab waveguide PCs open the possibility of developing new classes of optical devices that can, for example, be used to develop 2D optical integrated circuits for communications and computing.

© 2002 Optical Society of America

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References

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2002 (1)

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

2001 (1)

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125108 (2001).
[CrossRef]

2000 (2)

P. Paddon and J. F. Young, Phys. Rev. B 61, 2090 (2000).
[CrossRef]

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

1999 (2)

1998 (2)

A. J. Ward and J. B. Pendry, Comput. Phys. Commun. 112, 23 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

1996 (2)

L. Zhao and A. C. Cangellaris, IEEE Trans. Microwave Theory Tech. 44, 2555 (1996).
[CrossRef]

S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, Opt. Lett. 21, 1771 (1996).
[CrossRef] [PubMed]

1995 (1)

C. T. Chan, Q. L. Lu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

1994 (1)

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 63, 1950 (1987).
[CrossRef]

Benisty, H.

Berenger, J. P.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Cangellaris, A. C.

L. Zhao and A. C. Cangellaris, IEEE Trans. Microwave Theory Tech. 44, 2555 (1996).
[CrossRef]

Cassagne, D.

Chan, C. T.

C. T. Chan, Q. L. Lu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

Dapkus, P. D.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

De La Rue, R. M.

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Hietala, V. M.

Ho, K. M.

C. T. Chan, Q. L. Lu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

Houdre, R.

Joannopoulos, J. D.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

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

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Jones, E. D.

Jouanin, C.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

King, J. S.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Krauss, T. F.

Labilloy, D.

Liddell, C.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

Lin, S.-Y.

Lu, Q. L.

C. T. Chan, Q. L. Lu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

Meade, R. D.

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

Neff, C. W.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

O’Brien, J. D.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

Ochiai, T.

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125108 (2001).
[CrossRef]

Oesterle, U.

Paddon, P.

P. Paddon and J. F. Young, Phys. Rev. B 61, 2090 (2000).
[CrossRef]

Painter, O.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

Park, W.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

Pendry, J. B.

A. J. Ward and J. B. Pendry, Comput. Phys. Commun. 112, 23 (1998).
[CrossRef]

Rattier, M.

Sakoda, K.

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125108 (2001).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Scherer, A.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

Smith, C. J. M.

Srinivasan, K.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

Summers, C. J.

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Tomina, A.

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Wang, L.

Ward, A. J.

A. J. Ward and J. B. Pendry, Comput. Phys. Commun. 112, 23 (1998).
[CrossRef]

Weisbuch, C.

Winn, J. N.

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

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 63, 1950 (1987).
[CrossRef]

Young, J. F.

P. Paddon and J. F. Young, Phys. Rev. B 61, 2090 (2000).
[CrossRef]

Zhao, L.

L. Zhao and A. C. Cangellaris, IEEE Trans. Microwave Theory Tech. 44, 2555 (1996).
[CrossRef]

Comput. Phys. Commun. (1)

A. J. Ward and J. B. Pendry, Comput. Phys. Commun. 112, 23 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

L. Zhao and A. C. Cangellaris, IEEE Trans. Microwave Theory Tech. 44, 2555 (1996).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A (1)

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (5)

H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, 10096 (1998).
[CrossRef]

T. Ochiai and K. Sakoda, Phys. Rev. B 63, 125108 (2001).
[CrossRef]

P. Paddon and J. F. Young, Phys. Rev. B 61, 2090 (2000).
[CrossRef]

C. T. Chan, Q. L. Lu, and K. M. Ho, Phys. Rev. B 51, 16635 (1995).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, Phys. Rev. B 60, 5751 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 63, 1950 (1987).
[CrossRef]

Phys. Status Solidi B (1)

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, Phys. Status Solidi B 229, 949 (2002).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Photonic band structure of a thin slab of Si patterned with a 2D triangular lattice of air holes. Only the even modes with respect to reflection in the mirror plane are displayed.

Fig. 2
Fig. 2

Calculated refraction angles for normalized frequencies between 0.357 and 0.364. The incident angle is measured from the ΓM direction. Inset, dispersion diagram calculated at a normalized frequency of 0.357. The circle represents the cutoff line outside of which is the guiding regime.

Fig. 3
Fig. 3

Calculated refraction angles for normalized frequencies between 0.425 and 0.440. The incident angle is measured from the ΓK direction. Inset, dispersion diagram calculated at a normalized frequency of 0.430. The circle represents the cutoff line outside of which is the guiding regime.

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