Abstract

Li’s Fourier factorization rules [J. Opt. Soc. Am. A 13, 1870 (1996)] should be applied to achieve a fast convergence rate in the analysis of diffraction gratings with the Fourier modal method. I show, however, that Li’s inverse rule cannot be applied for periodic patterns of graphene when the conventional boundary condition is used. I derive an approximate boundary condition in which a nonzero but sufficiently small height is assumed for the boundary. The proposed boundary condition enables us to apply the inverse rule, leading to a significantly improved convergence rate. A periodic array of graphene ribbons is in fact a special type of finite-conductivity strip grating, and thus the proposed approach is also applicable to these kinds of structures.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
    [CrossRef]
  2. A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
    [CrossRef]
  3. A. Vakil and N. Engheta, Science 332, 1291 (2011).
    [CrossRef]
  4. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
    [CrossRef]
  5. S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
    [CrossRef]
  6. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
    [CrossRef]
  7. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
    [CrossRef]
  8. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, Opt. Express 20, 28017 (2012).
    [CrossRef]
  9. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
    [CrossRef]
  10. M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).
  11. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981).
    [CrossRef]
  12. L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, Appl. Opt. 38, 304 (1999).
    [CrossRef]
  13. A. Khavasi, K. Mehrany, and B. Rashidian, J. Opt. Soc. Am. B 24, 2676 (2007).
    [CrossRef]
  14. A. Khavasi, A. Kazemi Jahromi, and K. Mehrany, J. Opt. Soc. Am. A 25, 1564 (2008).
    [CrossRef]
  15. R. Hall and R. Mittra, IEEE Trans. Antennas Propag. 33, 1009 (1985).
    [CrossRef]
  16. R. Hall, R. Mittra, and K. Mitzner, IEEE Trans. Antennas Propag. 36, 504 (1988).
    [CrossRef]
  17. K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 35, 46 (1987).
    [CrossRef]
  18. K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 36, 415 (1988).
    [CrossRef]
  19. F. Montiel and M. Nevière, Opt. Commun. 101, 151 (1993).
    [CrossRef]
  20. S. Peng and C. Shiao, in Microwave Symposium Digest (IEEE, 1994), p. 879.
  21. L. Li, J. Opt. Soc. Am. A 13, 1870 (1996).
    [CrossRef]
  22. D. J. Griffiths and R. College, Introduction to Electrodynamics (Prentice Hall, 1999).
  23. F. H. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
    [CrossRef]
  24. S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, Phys. Rev. Lett. 108, 047401 (2012).
    [CrossRef]
  25. L. Li, J. Opt. Soc. Am. A 13, 1024 (1996).
    [CrossRef]
  26. A. Khavasi and K. Mehrany, IEEE Trans. Antennas Propag. 57, 1115 (2009).
    [CrossRef]
  27. A. Khavasi and K. Mehrany, Opt. Commun. 284, 3211 (2011).
    [CrossRef]
  28. L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
    [CrossRef]
  29. ee.sharif.ir/~khavasi/index_files/Page1077.htm .

2012 (5)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
[CrossRef]

S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, Opt. Express 20, 28017 (2012).
[CrossRef]

2011 (4)

A. Khavasi and K. Mehrany, Opt. Commun. 284, 3211 (2011).
[CrossRef]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

2010 (2)

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

2009 (1)

A. Khavasi and K. Mehrany, IEEE Trans. Antennas Propag. 57, 1115 (2009).
[CrossRef]

2008 (1)

2007 (1)

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

1999 (1)

1997 (1)

1996 (2)

1993 (1)

F. Montiel and M. Nevière, Opt. Commun. 101, 151 (1993).
[CrossRef]

1988 (2)

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 36, 415 (1988).
[CrossRef]

R. Hall, R. Mittra, and K. Mitzner, IEEE Trans. Antennas Propag. 36, 504 (1988).
[CrossRef]

1987 (1)

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 35, 46 (1987).
[CrossRef]

1985 (1)

R. Hall and R. Mittra, IEEE Trans. Antennas Propag. 33, 1009 (1985).
[CrossRef]

1981 (1)

Alaee, R.

Bae, S.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Balakrishnan, J.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Chandezon, J.

Chang, D. E.

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

College, R.

D. J. Griffiths and R. College, Introduction to Electrodynamics (Prentice Hall, 1999).

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Engheta, N.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Farhat, M.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

García de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

Garcia-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
[CrossRef]

Gaylord, T. K.

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Granet, G.

Griffiths, D. J.

D. J. Griffiths and R. College, Introduction to Electrodynamics (Prentice Hall, 1999).

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Guinea, F.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
[CrossRef]

Hall, R.

R. Hall, R. Mittra, and K. Mitzner, IEEE Trans. Antennas Propag. 36, 504 (1988).
[CrossRef]

R. Hall and R. Mittra, IEEE Trans. Antennas Propag. 33, 1009 (1985).
[CrossRef]

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Kazemi Jahromi, A.

Khavasi, A.

Kim, H.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Kim, H. R.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Koppens, F. H.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

Lederer, F.

Lee, Y.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Lei, T.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Li, L.

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

Martin-Moreno, L.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
[CrossRef]

Matsunaga, T.

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 36, 415 (1988).
[CrossRef]

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 35, 46 (1987).
[CrossRef]

Mehrany, K.

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Mittra, R.

R. Hall, R. Mittra, and K. Mitzner, IEEE Trans. Antennas Propag. 36, 504 (1988).
[CrossRef]

R. Hall and R. Mittra, IEEE Trans. Antennas Propag. 33, 1009 (1985).
[CrossRef]

Mitzner, K.

R. Hall, R. Mittra, and K. Mitzner, IEEE Trans. Antennas Propag. 36, 504 (1988).
[CrossRef]

Moharam, M. G.

Montiel, F.

F. Montiel and M. Nevière, Opt. Commun. 101, 151 (1993).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Nevière, M.

F. Montiel and M. Nevière, Opt. Commun. 101, 151 (1993).
[CrossRef]

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

Nikitin, A. Y.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
[CrossRef]

Noda, T.

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 36, 415 (1988).
[CrossRef]

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 35, 46 (1987).
[CrossRef]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Park, J.-S.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Peng, S.

S. Peng and C. Shiao, in Microwave Symposium Digest (IEEE, 1994), p. 879.

Plumey, J.-P.

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Popov, E.

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

Rashidian, B.

Rockstuhl, C.

Shiao, C.

S. Peng and C. Shiao, in Microwave Symposium Digest (IEEE, 1994), p. 879.

Song, Y. I.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Uchida, K.

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 36, 415 (1988).
[CrossRef]

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 35, 46 (1987).
[CrossRef]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Vakil, A.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Xu, X.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Zheng, Y.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

ACS Nano (1)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (5)

R. Hall and R. Mittra, IEEE Trans. Antennas Propag. 33, 1009 (1985).
[CrossRef]

R. Hall, R. Mittra, and K. Mitzner, IEEE Trans. Antennas Propag. 36, 504 (1988).
[CrossRef]

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 35, 46 (1987).
[CrossRef]

K. Uchida, T. Noda, and T. Matsunaga, IEEE Trans. Antennas Propag. 36, 415 (1988).
[CrossRef]

A. Khavasi and K. Mehrany, IEEE Trans. Antennas Propag. 57, 1115 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

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

Nano Lett. (2)

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Nat. Nanotechnol. (1)

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, and Y. I. Song, Nat. Nanotechnol. 5, 574 (2010).
[CrossRef]

Nat. Photonics (1)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Opt. Commun. (2)

A. Khavasi and K. Mehrany, Opt. Commun. 284, 3211 (2011).
[CrossRef]

F. Montiel and M. Nevière, Opt. Commun. 101, 151 (1993).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 85, 081405 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, Phys. Rev. Lett. 108, 047401 (2012).
[CrossRef]

Science (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Other (4)

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

ee.sharif.ir/~khavasi/index_files/Page1077.htm .

S. Peng and C. Shiao, in Microwave Symposium Digest (IEEE, 1994), p. 879.

D. J. Griffiths and R. College, Introduction to Electrodynamics (Prentice Hall, 1999).

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 (4)

Fig. 1.
Fig. 1.

Geometry of the studied structure: a periodic array of graphene ribbons of width w and period L, illuminated with a TM polarized plane wave. The array is placed between two dielectric half-spaces with permittivities ε1 and ε2.

Fig. 2.
Fig. 2.

Rectangular closed loop of length l and height h, used for the deriving boundary condition.

Fig. 3.
Fig. 3.

Absorption versus wavelength for a periodic array of graphene ribbons whose parameters in accordance with Fig. 1 are L=8μm, w=L/2, ε1=3ε0, and ε2=4ε0. Relaxation time and Fermi energy for graphene are τ=0.25ps and EF=0.6eV, respectively. The results are obtained by using Eq. (12) (solid line), Eq. (18) with h=w/20 (dashed line) and h=w/10 (dotted line), and the nonzero-thickness model (dots). The results extracted from Fig. 2 of [7] (circles) are also depicted.

Fig. 4.
Fig. 4.

Relative error, in the calculation of absorption, in terms of truncation order (N) using Eq. (12) (solid line), Eq. (18) with h=w/20 (dashed line) and h=w/20 (dotted line), and the nonzero-thickness model (dashed-dotted line). The structure is the same as Fig. 3 and the wavelength is λ=80μm.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

n×(E1E2)=0,
n×(H1H2)=σs(x)Et,
σs=e2EFπ2ii2πτ1ω+e24[H(ω2EF)iπln|ω2EFω+2EF|],
Hjy=n(ajneikjznz+bjneikjznz)eikxnx,
Ejx=nkjznωεj(ajneikjznzbjneikjznz)eikxnx,
kxn=k0n1sinθ2πLn,
kjzn=k02nj2kxn2,
σs(x)={σs0<x<w0w<x<L=nσnei2πLnx,
k1znωε1(a1nb1n)k2znωε2(a2nb2n)=0,
(a1n+b1n)(a2n+b2n)=mσnmk2zmωε2(a2mb2m).
[η1η1II][a1b1]=[η2η2I+η2[[σ]]Iη2[[σ]]][a2b2],
[η2η1Iη2[[σ]]I][a2b1]=[η1η2IIη2[[σ]]][a1b2].
DE1n=Re(k1znk1z0)|b1n|2,
DE2n=Re(ε1k2znε2k1z0)|a2n|2.
[H1y(x,z=h/2)H2y(x,z=h/2)]l=h/2h/20l(σs(x)δ(z)+iωε)Ex(x,z)dydz,
H1y(x,z=h/2)H2y(x,z=h/2)=σseff(x)Ex(x,z=0),
a1neik1znh/2+b1neik1znh/2a2neik2znh/2b2neik2znh/2=m[[1/σeff]]nm1k2zmωε2(a2mb2m).
[η2η1α21η2[[1/σeff]]1α11][a2b1]=[η1η2α1α2η2[[1/σeff]]1][a1b2],

Metrics