Abstract

We simulate the s-polarized electromagnetic field diffracted by a truncated two-dimensional lattice. We observe strong decay of the transmittivity for frequencies lying in the gaps displayed by the dispersion relation of the infinite crystal and find regular oscillations outside these gaps. The structure of the field in the lattice is explained in terms of modes of its infinite counterpart. In particular, the oscillations are related to the resonance in the layer of propagating Bloch waves, just as in a Fabry–Perot interferometer. This interpretation enables us to retrieve the dispersion relation. Finally, we study the symmetry properties of the modes and show that for certain frequencies the transmissivity of the system is null under symmetric illumination but nonzero under antisymmetric lighting or vice versa.

© 1997 Optical Society of America

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  1. E. Yablonovitch, J. Opt. Soc. Am. B 10, 283–295 (1993), and references therein.
    [CrossRef]
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  3. Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650–2653 (1990).
    [CrossRef] [PubMed]
  4. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152–3155 (1990).
    [CrossRef] [PubMed]
  5. D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, and P. M. Platzman, J. Opt. Soc. Am. B 10, 314–321 (1993).
    [CrossRef]
  6. S. L. McCall and P. M. Platzmann, Phys. Rev. Lett. 67, 2017–2020 (1991).
    [CrossRef] [PubMed]
  7. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322–327 (1993).
    [CrossRef]
  8. T. Suzuki and P. K. L. Yu, J. Opt. Soc. Am. B 12, 570–582 (1995).
    [CrossRef]
  9. J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612–622 (1992).
    [CrossRef] [PubMed]
  10. J. P. Dowling and C. M. Bowden, J. Mod. Opt. 41, 345–351 (1994).
    [CrossRef]
  11. J. B. Pendry and A. MacKinnon, Phys. Rev. Lett. 69, 2772–2775 (1992).
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  12. D. Maystre, Pure Appl. Opt. 3, 975–993 (1994).
    [CrossRef]
  13. S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
    [CrossRef]
  14. E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
    [CrossRef]
  15. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Opt. Lett. 18, 528–530 (1993).
    [CrossRef] [PubMed]
  16. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10,961–10,964 (1991).
    [CrossRef]
  17. W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
    [CrossRef] [PubMed]
  18. K. Sakoda, Phys. Rev. B 12, 4672–4675 (1995).
    [CrossRef]
  19. M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565–8571 (1991).
    [CrossRef]
  20. V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16,835–16,844 (1994).
    [CrossRef]
  21. F. Pincemin, “Etude de la propagation du rayonnement électromagnétique dans les milieux hétérogènes,” Ph.D. dissertation (Ecole Centrale, Paris, 1994), pp. 12–22.
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    [CrossRef]
  23. S. Y. Lin and G. Arjavlingam, J. Opt. Soc. Am. B 11, 2124–2127 (1994).
    [CrossRef]
  24. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  25. F. Pincemin and J. J. Greffet, “Propagation and localization of a surface plasmon polariton on a finite grating,” J. Opt. Soc. Am. B 13, 1499–1509 (1996).
    [CrossRef]
  26. S. E. Sandstrom, G. Tayeb, and R. Petit, J. Electromag. Waves Appl. 7, 631–649 (1993).
  27. C. Desjonquères and M. Spanjaard, Concepts in Surface Physics (Springer-Verlag, Berlin, 1993), pp. 267–293.
  28. V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
    [CrossRef]
  29. S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 48, 14,936–14,943 (1993).
    [CrossRef]
  30. P. Vincent and M. Nevière, Appl. Phys. 20, 345–351 (1979).
    [CrossRef]
  31. J. Y. Suratteau, M. Cadilhac, and R. Petit, J. Opt. (Paris) 20, 273–288 (1983).
    [CrossRef]
  32. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
  33. J. L. Roumiguieres and M. J. Neviere, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” U.S. patent4,389,094 (June21, 1983).

1996 (1)

1995 (2)

1994 (7)

D. Maystre, Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

J. P. Dowling and C. M. Bowden, J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16,835–16,844 (1994).
[CrossRef]

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

S. Y. Lin and G. Arjavlingam, J. Opt. Soc. Am. B 11, 2124–2127 (1994).
[CrossRef]

1993 (6)

1992 (4)

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612–622 (1992).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

J. B. Pendry and A. MacKinnon, Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

A. Sentenac and J.-J. Greffet, J. Opt. Soc. Am. A 9, 996–1006 (1992).
[CrossRef]

1991 (3)

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10,961–10,964 (1991).
[CrossRef]

S. L. McCall and P. M. Platzmann, Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

1990 (3)

K. M. Leung and Y. F. Liu, Phys. Rev. B 41, 10,188–10,190 (1990).
[CrossRef]

Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

1983 (1)

J. Y. Suratteau, M. Cadilhac, and R. Petit, J. Opt. (Paris) 20, 273–288 (1983).
[CrossRef]

1979 (1)

P. Vincent and M. Nevière, Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Abeyta, A.

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Agafonov, Y.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Arjavalingam, G.

Arjavalingram, G.

W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

Arjavlingam, G.

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).

Biswas, R.

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
[CrossRef]

Bowden, C. M.

J. P. Dowling and C. M. Bowden, J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612–622 (1992).
[CrossRef] [PubMed]

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322–327 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10,961–10,964 (1991).
[CrossRef]

Brunel, M.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Cadilhac, M.

J. Y. Suratteau, M. Cadilhac, and R. Petit, J. Opt. (Paris) 20, 273–288 (1983).
[CrossRef]

Chan, C. T.

S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 48, 14,936–14,943 (1993).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Dalichaouch, R.

Datta, S.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 48, 14,936–14,943 (1993).
[CrossRef]

Desjonquères, C.

C. Desjonquères and M. Spanjaard, Concepts in Surface Physics (Springer-Verlag, Berlin, 1993), pp. 267–293.

Dowling, J. P.

J. P. Dowling and C. M. Bowden, J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612–622 (1992).
[CrossRef] [PubMed]

Erko, A.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Greffet, J. J.

Greffet, J.-J.

Ho, K. M.

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 48, 14,936–14,943 (1993).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Ho, S. Y. K. M.

S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Joannopoulos, J. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322–327 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10,961–10,964 (1991).
[CrossRef]

Kroll, N.

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16,835–16,844 (1994).
[CrossRef]

Leung, K. M.

K. M. Leung and Y. F. Liu, Phys. Rev. B 41, 10,188–10,190 (1990).
[CrossRef]

Lin, S. Y.

Liu, Y. F.

K. M. Leung and Y. F. Liu, Phys. Rev. B 41, 10,188–10,190 (1990).
[CrossRef]

MacKinnon, A.

J. B. Pendry and A. MacKinnon, Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16,835–16,844 (1994).
[CrossRef]

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

Martynov, V.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Maystre, D.

D. Maystre, Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

McCall, S. L.

Meade, R. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322–327 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10,961–10,964 (1991).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).

Neviere, M. J.

J. L. Roumiguieres and M. J. Neviere, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” U.S. patent4,389,094 (June21, 1983).

Nevière, M.

P. Vincent and M. Nevière, Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Ozbay, E.

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Pendry, J. B.

J. B. Pendry and A. MacKinnon, Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

Petit, R.

S. E. Sandstrom, G. Tayeb, and R. Petit, J. Electromag. Waves Appl. 7, 631–649 (1993).

J. Y. Suratteau, M. Cadilhac, and R. Petit, J. Opt. (Paris) 20, 273–288 (1983).
[CrossRef]

Pincemin, F.

F. Pincemin and J. J. Greffet, “Propagation and localization of a surface plasmon polariton on a finite grating,” J. Opt. Soc. Am. B 13, 1499–1509 (1996).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Phys. Rev. B 50, 16,835–16,844 (1994).
[CrossRef]

F. Pincemin, “Etude de la propagation du rayonnement électromagnétique dans les milieux hétérogènes,” Ph.D. dissertation (Ecole Centrale, Paris, 1994), pp. 12–22.

Platzman, P. M.

Platzmann, P. M.

S. L. McCall and P. M. Platzmann, Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

Plihal, M.

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

Rappe, A. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Opt. Lett. 18, 528–530 (1993).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322–327 (1993).
[CrossRef]

W. M. Robertson, G. Arjavalingram, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10,961–10,964 (1991).
[CrossRef]

Robertson, W. M.

Roshupkin, D. V.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Roumiguieres, J. L.

J. L. Roumiguieres and M. J. Neviere, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” U.S. patent4,389,094 (June21, 1983).

Sakoda, K.

K. Sakoda, Phys. Rev. B 12, 4672–4675 (1995).
[CrossRef]

Sandstrom, S. E.

S. E. Sandstrom, G. Tayeb, and R. Petit, J. Electromag. Waves Appl. 7, 631–649 (1993).

Satpathy, S.

Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

Schultz, S.

Sentenac, A.

Sigalas, M.

S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
[CrossRef]

Smith, D. R.

Soukoulis, C. M.

S. Y. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 85, 413–416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 48, 14,936–14,943 (1993).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Spanjaard, M.

C. Desjonquères and M. Spanjaard, Concepts in Surface Physics (Springer-Verlag, Berlin, 1993), pp. 267–293.

Suratteau, J. Y.

J. Y. Suratteau, M. Cadilhac, and R. Petit, J. Opt. (Paris) 20, 273–288 (1983).
[CrossRef]

Suzuki, T.

Tayeb, G.

S. E. Sandstrom, G. Tayeb, and R. Petit, J. Electromag. Waves Appl. 7, 631–649 (1993).

Tringides, M.

E. Ozbay, A. Abeyta, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and S. Y. K. M. Ho, Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Vincent, P.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

P. Vincent and M. Nevière, Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Yablonovitch, E.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Yu, P. K. L.

Yuakshin, A.

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Zhang, Z.

Z. Zhang and S. Satpathy, Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

Appl. Phys. (1)

P. Vincent and M. Nevière, Appl. Phys. 20, 345–351 (1979).
[CrossRef]

J. Electromag. Waves Appl. (1)

S. E. Sandstrom, G. Tayeb, and R. Petit, J. Electromag. Waves Appl. 7, 631–649 (1993).

J. Mod. Opt. (1)

J. P. Dowling and C. M. Bowden, J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

J. Opt. (Paris) (1)

J. Y. Suratteau, M. Cadilhac, and R. Petit, J. Opt. (Paris) 20, 273–288 (1983).
[CrossRef]

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

J. Opt. Soc. Am. B (6)

Nucl. Instrum. Methods Phys. Res. A (1)

V. Martynov, P. Vincent, M. Brunel, D. V. Roshupkin, Y. Agafonov, A. Erko, and A. Yuakshin, Nucl. Instrum. Methods Phys. Res. A 339, 617–625 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612–622 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (7)

K. M. Leung and Y. F. Liu, Phys. Rev. B 41, 10,188–10,190 (1990).
[CrossRef]

K. Sakoda, Phys. Rev. B 12, 4672–4675 (1995).
[CrossRef]

M. Plihal and A. A. Maradudin, Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Geometry of the finite lattice. In most calculations 1=1 and 2=10; however, in Section 5, 1=10 and 2=1. The study of the near field in Figs. 5, 6, and 812 below is done within the rectangular region of width 3a delimited by the solid line.

Fig. 2
Fig. 2

Photonic band structure of the infinite lattice.

Fig. 3
Fig. 3

Band structure of the lattice restricted to the [MΓ] domain. The inset shows the bands of the reference homogeneous medium. The numbering of the bands of the perturbed medium is deduced from that of the homogeneous one. For example, band 4 increases monotonically from 0.32 to 0.38 as the Bloch wave vector increases. The filled squares show the values of the Bloch wave vector calculated with Eqs. (18) and (19) for ωa/2πc corresponding to peaks and nodes of the nine-layer transmissivity plotted in Fig. 4 under normal incidence and in Fig. 7 below under -2 Littrow mounting.

Fig. 4
Fig. 4

Transmitted power versus ωa/2πc of the finite lattice for different thicknesses at normal incidence.

Fig. 5
Fig. 5

Real part of the electric field in the nine-layer lattice, restricted to the region depicted in Fig. 1 (1.5 periods along x). The dashed lines are the x and y axes, and the solid lines indicate the position of the crystal along y and delineate the different cells along x. The structure is illuminated with a normally incident plane wave, (1=1, 2=10), and ωa/2πc=0.263 corresponds to a peak of transmissivity in Fig. 4.

Fig. 6
Fig. 6

Same as Fig. 5 but with the structure illuminated under -2 Littrow mounting, sin(θinc)=2πc/(2ωa1). inc=31°, 1=10, 2=1. ωa/2πc=0.307 corresponds to a node of transmissivity in Fig. 7. The only propagative mode that can be excited at this frequency is antisymmetric (it belongs to band 5; see Fig. 3).

Fig. 7
Fig. 7

Transmitted power versus ωa/2πc of the nine-layer lattice under -2 Littrow mounting. 1=1, 2=10, and the angle of incidence is chosen such that sin(θinc)=2πc/(2ωa1).

Fig. 8
Fig. 8

Same as Fig. 6 but with ωa/2πc=0.33 and θinc=28°. Both symmetric and antisymmetric modes (which belong to bands 4–6) can be excited at this frequency.

Fig. 9
Fig. 9

Same as Fig. 8 but with the structure symmetrically illuminated by two plane waves of equal amplitude and vertically opposite angles of incidence θinc1=28°, θinc2=-28°. Two symmetric modes (which belong to bands 4 and 6) can be excited with this illumination.

Fig. 10
Fig. 10

Same as Fig. 9 but with the structure antisymmetrically illuminated by two plane waves of opposite amplitude and opposite angles of incidence θinc1=28°, θinc2=-28°. Only one antisymmetric mode (which belongs to band 5) can be excited with this illumination.

Fig. 11
Fig. 11

Same as Fig. 6, ωa/2πc=0.307, but with the structure symmetrically illuminated by two plane waves of equal amplitude and opposite angles of incidence θinc1=31°, θinc2=-31°. The propagative antisymmetric mode of band 5 cannot be excited with this illumination; therefore only evanescent symmetric modes exist inside the structure, and the transmissivity is almost null.

Fig. 12
Fig. 12

Same as Fig. 11 but with the structure antisymmetrically illuminated by two plane waves of opposite amplitude and opposite angles of incidence. The propagative antisymmetric mode that belongs to band 5 can be excited with this illumination; thus the transmissivity is important.

Fig. 13
Fig. 13

Illustration of the transmission of the truncated lattice when the only propagative modes of the infinite structure are antisymmetric. The opposite results are obtained at frequencies for which the only propagative modes are symmetric.

Equations (23)

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Gi=πa2ai,i=1, 2.
ΔE(r)+ω2c2(r)E(r)=0,
ΔE(r)+ω2c2[(r)-]E(r)=-ω2c2E(r),
=1+22.
E(r)=exp(iq·r)Uq(r),
Einc(x, y)=exp(iκincx-iγincy)uz,
κinc=1 ωcsin(θinc),γinc=1 ω2c2-κinc21/2,
Im(γinc)>0.
ΔE+t(x, y) ω2c2E=0,
E(x, y)=Einc(x, y)+ΩΓ(x-x, y, y)×ω2c2[t(x, y)-1] * E(x, y)dxdy,
ΔΓ(x-x, z, z)+1 ω2c2Γ(x-x, z, z)
=nδ(x-x+2na)δ(z-z)
E(r)=exp(iκincx)F(x, y),
E(r)=qAqUq(r)exp(iq·r),
qx=κinc-nπ/a,
qx<π/a
f(r)=exp(iq·r)Uq(r)
=exp(iq·r)GCG exp(iG·r),
g(r)=exp(iq+·r)GCG exp(iG+·r),
E(r)A exp(iq·r)GCG exp(iG·r)+B×exp(iq+·r)GCG exp(iG+·r).
2qyL+2 arg(R)=2nπ,n=0, 1, 2, 
2qyL+2 arg(R)=(2n+1)π,n=0, 1, 2, ,
κinc=1 ωcsin(θinc)=π/a.

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