Abstract

We report a systematic analysis of anomalous refractive effects at interfaces between two photonic crystal waveguide arrays. Discrete negative refraction can be easily predicted from the sign of the coupling coefficient between adjacent waveguides, regardless of handedness of propagation.

© 2006 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  3. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]
  4. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Y. S. Kivshar, and W. Krolikowski, Opt. Lett. 30, 2293 (2005).
    [CrossRef] [PubMed]
  5. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  6. R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, Opt. Express 13, 8596 (2005).
    [CrossRef] [PubMed]
  7. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, Opt. Lett. 30, 2894 (2005).
    [CrossRef] [PubMed]
  8. T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 863 (2005).
    [CrossRef]
  9. W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
    [CrossRef]
  10. C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, Opt. Lett. 29, 1384 (2004).
    [CrossRef]
  11. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]

2005 (4)

2004 (1)

2002 (3)

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Asatryan, A. A.

Botten, L. C.

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Conforti, M.

De Angelis, C.

de Sterke, C. M.

Fan, S.

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

Gajic, R.

Hingerl, K.

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

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

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

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

Kamalakis, T.

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 863 (2005).
[CrossRef]

Kivshar, Y. S.

Krolikowski, W.

Kuchar, F.

Lau, W. T.

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Locatelli, A.

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

McPhedran, R. C.

Meisels, R.

Modotto, D.

Neshev, D. N.

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Rosberg, C. R.

Sphicopoulos, T.

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 863 (2005).
[CrossRef]

Sukhorukov, A. A.

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

White, T. P.

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

W. T. Lau and S. Fan, Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 863 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Projected band structure of the NIM waveguide.

Fig. 2
Fig. 2

Projected band structure of NIM couplers: even (solid curves) and odd (dashed–dotted curves) supermodes. a, Two-rod coupler; b, three-rod coupler.

Fig. 3
Fig. 3

Isofrequency curves in the ( k x , k z ) plane: first array (solid curves) and second array (dashed–dotted curves), normal to the interface (dashed lines), wave vectors (thinner arrows), and group velocities (thicker arrows). a, RHA–RHA interface, C with the same signs; b, RHA–LHA interface, C with the opposite signs; c, RHA–RHA interface, C with the opposite signs; d, RHA–LHA interface, C with the same signs.

Fig. 4
Fig. 4

Schematic view of interfaces between the following PC arrays: a, four-rod PIM and three-rod PIM arrays; b, two-rod NIM and zero-rod PIM arrays.

Fig. 5
Fig. 5

Time-averaged evolution of the field intensity. Black means high intensity. The units of the axes are micrometers, a, RHA 1 RHA 2 RHA 1 interfaces with opposite signs of C; b, LHA–RHA interface with the same signs of C.

Equations (2)

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i d A n d z + β A n + C ( A n + 1 + A n 1 ) = 0 ,
C = k 0 2 W δ ϵ r u 1 * u 2 d W 2 β W u 1 2 d W 2 j W u 1 * ( u 1 z ) d W ,

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