Abstract

We predict the existence of evanescent modes with unlocked phases in two-dimensional (2D) dielectric periodic structures. Contrary to what is known for one-dimensional structures, where evanescent fields lock to the host modulation, we show that in 2D systems a new class of evanescent modes exists with an unlocked real part of the wave vector. Hence, beams constructed from such unlocked evanescent waves can exhibit spatial effects. A significant focalization of a beam propagating within the band gap of a flat photonic crystal slab is also shown. The predicted phenomenon is expected to be generic for spatially modulated materials.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef]
  2. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef]
  3. M. Notomi, Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
    [CrossRef]
  5. D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, Opt. Express 11, 1203 (2003).
    [CrossRef]
  6. R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
    [CrossRef]
  7. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, Opt. Lett. 29, 50 (2004).
    [CrossRef]
  8. K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  9. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  10. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
    [CrossRef]
  11. P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
    [CrossRef]
  12. P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
    [CrossRef]
  13. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  14. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
    [CrossRef]
  15. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
    [CrossRef]
  16. Y. C. Hsue and T. J. Yang, Phys. Rev. E 70, 016706 (2004).
    [CrossRef]
  17. V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
    [CrossRef]
  18. V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
    [CrossRef]
  19. M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
    [CrossRef]
  20. C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
    [CrossRef]
  21. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).
  22. V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
    [CrossRef]

2011 (1)

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

2010 (2)

V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

2009 (1)

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
[CrossRef]

2007 (1)

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

2006 (3)

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

2004 (3)

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, Opt. Lett. 29, 50 (2004).
[CrossRef]

Y. C. Hsue and T. J. Yang, Phys. Rev. E 70, 016706 (2004).
[CrossRef]

2003 (4)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
[CrossRef]

D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, Opt. Express 11, 1203 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

2002 (1)

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

2000 (2)

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

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

1987 (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Achaoui, Y.

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
[CrossRef]

Augustin, M.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Benchabane, S.

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
[CrossRef]

Botey, M.

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

Cai, L. Z.

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Castiñeira-Ibáñez, S.

V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
[CrossRef]

Chen, C.

Chigrin, D.

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Danckaert, J.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

der Sande, G. V.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

Enoch, S.

Etrich, C.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Feng, C. S.

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Fuchs, H. J.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Garcia-Raffi, L. M.

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
[CrossRef]

Gelens, L.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

Herrero, R.

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Hladky-Hennion, A. C.

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

Hsue, Y. C.

Y. C. Hsue and T. J. Yang, Phys. Rev. E 70, 016706 (2004).
[CrossRef]

Iliew, R. R.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
[CrossRef]

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

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
[CrossRef]

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

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Khelif, A.

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
[CrossRef]

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).

Kockaert, P.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Laude, V.

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
[CrossRef]

Lederer, F.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Li, P. J.

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
[CrossRef]

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

Mei., L. M.

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Murakowski, J.

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
[CrossRef]

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]

Peschel, U.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Prather, D. W.

Pustai, D. M.

Romero-García, V.

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
[CrossRef]

Sánchez-Pérez, J. V.

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Schneider, G. J.

Sharkawy, A.

Shi, S.

Sotomayor Torres, C.

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Staliunas, K.

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tassin, P.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Tayeb, G.

Tlidi, M.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tunnermann, A.

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Van der Sande, G.

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Vasseur, J. O.

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

Venkataraman, S.

Veretennicoff, I.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Wei, S. S.

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Yang, T. J.

Y. C. Hsue and T. J. Yang, Phys. Rev. E 70, 016706 (2004).
[CrossRef]

Yang, X. L.

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

V. Romero-García, J. V. Sánchez-Pérez, S. Castiñeira-Ibáñez, and L. M. Garcia-Raffi, Appl. Phys. Lett. 96, 124102 (2010).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

R. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, and A. Tunnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Chaos (1)

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. V. der Sande, P. Kockaert, and M. Tlidi, Chaos 17, 037116 (2007).
[CrossRef]

J. Phys. D (1)

C. S. Feng, L. M. Mei., L. Z. Cai, X. L. Yang, S. S. Wei, and P. J. Li, J. Phys. D 39, 4316 (2006).
[CrossRef]

Nature (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

P. Kockaert, P. Tassin, G. Van der Sande, I. Veretennicoff, and M. Tlidi, Phys. Rev. A 74, 033822 (2006).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

Phys. Rev. B (5)

V. Romero-García, J. O. Vasseur, A. C. Hladky-Hennion, L. M. Garcia-Raffi, and J. V. Sánchez-Pérez, Phys. Rev. B 84, 212302 (2011).
[CrossRef]

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, Phys. Rev. B 80, 092301 (2009).
[CrossRef]

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 45115 (2003).
[CrossRef]

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

Phys. Rev. E (2)

Y. C. Hsue and T. J. Yang, Phys. Rev. E 70, 016706 (2004).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

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

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Other (1)

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

TM complex dispersion relations calculated by the EPWE method for a high contrast PhC, ε1/ε2=11.34, made of a square lattice of cylinders with radius R=0.15a, where a is the lattice constant; for propagation along (a) ΓX and (b) ΓM. The real and imaginary parts of k, kr and ki (horizontal axis) are represented, depending on frequency, ω (vertical axis), in normalized units, where c is the speed of light in a vacuum. The shaded areas show evanescent locked/unlocked modes.

Fig. 2.
Fig. 2.

TM band structure and complex dispersion relations calculated by the EPWE method, for the structure of Fig. 1. Isofrequency contours at two frequencies; (a)/(b) and (d)/(e) depict the real/imaginary parts of k. In (a)/(d) black (dark) lines correspond to the first propagation band, while blue/orange (light) lines correspond to the locked/unlocked evanescent modes. (c) Conventional representation of the band diagram, showing real parts of both evanescent and propagating bands.

Fig. 3.
Fig. 3.

Focalization of an evanescent beam by a low contrast PhC slab, ε1/ε2=1.5, made of a square lattice of cylinders, with R=0.2a. (a) Isofrequency contours at ωa/2πc=0.633 for complex k’s. (b) Instantaneous field distribution inside and behind the system, for an incident Gaussian beam with the same central frequency, width ω0=2a, propagating along ΓM; the dotted line shows propagation in free space at 1/e2 maximum intensity. (c) ΓM band diagram, whit the unlocked mode in the shaded area. (d) Transmitted intensity map along the propagation direction, x, on the beam axis (z=0) for different normalized central wavelengths (vertical axis).

Metrics