Abstract

We have developed a plane-wave transfer-matrix method (PWTMM) with the aid of the interpolation technique to analyze the dispersion relation of surface modes in photonic crystal or photonic crystal surface waveguide. The proposed approach has been applied to several surface structures in two-dimensional photonic crystals. The calculated dispersion relation of the surface modes is in good agreement with the result obtained by the conventional plane-wave expansion method in combination with the supercell technique. The developed PWTMM needs to handle only a single unit-cell layer domain and is therefore numerically friendly. The proposed approach can become an efficient and accurate numerical tool to understand and design surface modes in different two-dimensional and three-dimensional photonic crystals with complex geometries.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  3. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
    [CrossRef]
  4. F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311-314 (1996).
    [CrossRef]
  5. F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112-15120 (1999).
    [CrossRef]
  6. J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711-1715 (1996).
    [CrossRef]
  7. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528-530 (1993).
    [CrossRef] [PubMed]
  8. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402(R) (2004).
    [CrossRef]
  9. W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
    [CrossRef]
  10. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
    [CrossRef] [PubMed]
  11. I. Bulu, H. Caglayan, and E. Ozbay, “Beaming of light and enhanced transmission via surface modes of photonic crystals,” Opt. Lett. 30, 3078-3080 (2005).
    [CrossRef] [PubMed]
  12. W. T. Lau and S. H. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915-3917 (2002).
    [CrossRef]
  13. Y. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95, 4538-4544 (2004).
    [CrossRef]
  14. Y. A. Vlasov, N. Moll, and S. J. McNab, “Observation of surface states in a truncated photonic crystal slab,” Opt. Lett. 29, 2175-2177 (2004).
    [CrossRef] [PubMed]
  15. E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
    [CrossRef]
  16. A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
    [CrossRef]
  17. H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
    [CrossRef]
  18. H. Chen, K. K. Tsia, and A. W. Poon, “Surface modes in two-dimensional photonic crystal slabs with a flat dielectric margin,” Opt. Express 14, 7368-7377 (2006).
    [CrossRef] [PubMed]
  19. X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
    [CrossRef]
  20. A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23, 1679-1683 (2006).
    [CrossRef]
  21. A. I. Rahachou and I. V. Zozoulenko, “Light propagation in finite and infinite photonic crystals: The recursive Green's function technique,” Phys. Rev. B 72, 155117 (2005).
    [CrossRef]
  22. J. M. Elson and K. Halterman, “Local density of states analysis of surface wave modes on truncated photonic crystal surfaces with nonlinear material,” Opt. Express 12, 4855-4863 (2004).
    [CrossRef] [PubMed]
  23. N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
    [CrossRef]
  24. Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
    [CrossRef]
  25. L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811-821 (2003).
    [CrossRef]
  26. Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).
    [CrossRef]
  27. Z. Y. Li and K. M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
    [CrossRef]
  28. Z. Y. Li, L. L. Lin, and K. M. Ho, “Light coupling with multimode photonic crystal waveguides,” Appl. Phys. Lett. 84, 4699-4701 (2004).
    [CrossRef]
  29. M. Che, Z. Y. Li, and R. J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystal,” Phys. Rev. A 76, 023809 (2007).
    [CrossRef]
  30. E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interface,” Rev. Mod. Phys. 78, 455-481 (2006).
    [CrossRef]
  31. M. Che and Z. Y. Li, “Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method,” Phys. Rev. B 77, 125138 (2008).
    [CrossRef]
  32. http://ab-initio.mit.edu/wiki/index. php/MIT_Photonic_Bands.
  33. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [CrossRef]
  34. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  35. A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
    [CrossRef]
  36. H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962-13972 (1992).
    [CrossRef]

2008 (2)

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

M. Che and Z. Y. Li, “Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method,” Phys. Rev. B 77, 125138 (2008).
[CrossRef]

2007 (3)

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

M. Che, Z. Y. Li, and R. J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystal,” Phys. Rev. A 76, 023809 (2007).
[CrossRef]

W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
[CrossRef]

2006 (5)

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interface,” Rev. Mod. Phys. 78, 455-481 (2006).
[CrossRef]

A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23, 1679-1683 (2006).
[CrossRef]

H. Chen, K. K. Tsia, and A. W. Poon, “Surface modes in two-dimensional photonic crystal slabs with a flat dielectric margin,” Opt. Express 14, 7368-7377 (2006).
[CrossRef] [PubMed]

2005 (2)

I. Bulu, H. Caglayan, and E. Ozbay, “Beaming of light and enhanced transmission via surface modes of photonic crystals,” Opt. Lett. 30, 3078-3080 (2005).
[CrossRef] [PubMed]

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in finite and infinite photonic crystals: The recursive Green's function technique,” Phys. Rev. B 72, 155117 (2005).
[CrossRef]

2004 (6)

Z. Y. Li, L. L. Lin, and K. M. Ho, “Light coupling with multimode photonic crystal waveguides,” Appl. Phys. Lett. 84, 4699-4701 (2004).
[CrossRef]

Y. A. Vlasov, N. Moll, and S. J. McNab, “Observation of surface states in a truncated photonic crystal slab,” Opt. Lett. 29, 2175-2177 (2004).
[CrossRef] [PubMed]

J. M. Elson and K. Halterman, “Local density of states analysis of surface wave modes on truncated photonic crystal surfaces with nonlinear material,” Opt. Express 12, 4855-4863 (2004).
[CrossRef] [PubMed]

Y. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95, 4538-4544 (2004).
[CrossRef]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

2003 (4)

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811-821 (2003).
[CrossRef]

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).
[CrossRef]

Z. Y. Li and K. M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

2002 (2)

W. T. Lau and S. H. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915-3917 (2002).
[CrossRef]

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

2001 (1)

X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
[CrossRef]

1999 (1)

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112-15120 (1999).
[CrossRef]

1997 (1)

1996 (3)

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
[CrossRef]

J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711-1715 (1996).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311-314 (1996).
[CrossRef]

1993 (1)

1992 (1)

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Arjavalingam, G.

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528-530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Bulu, I.

Caglayan, H.

Chan, C. T.

X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
[CrossRef]

Che, M.

M. Che and Z. Y. Li, “Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method,” Phys. Rev. B 77, 125138 (2008).
[CrossRef]

M. Che, Z. Y. Li, and R. J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystal,” Phys. Rev. A 76, 023809 (2007).
[CrossRef]

Chen, H.

Cheng, T. H.

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

Choi, H. G.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Elson, J. M.

J. M. Elson and K. Halterman, “Local density of states analysis of surface wave modes on truncated photonic crystal surfaces with nonlinear material,” Opt. Express 12, 4855-4863 (2004).
[CrossRef] [PubMed]

J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711-1715 (1996).
[CrossRef]

Fan, S. H.

W. T. Lau and S. H. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915-3917 (2002).
[CrossRef]

Garcia-Vidal, F. J.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

Gosele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112-15120 (1999).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311-314 (1996).
[CrossRef]

Halterman, K.

Haus, J. W.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Ho, K. M.

Z. Y. Li, L. L. Lin, and K. M. Ho, “Light coupling with multimode photonic crystal waveguides,” Appl. Phys. Lett. 84, 4699-4701 (2004).
[CrossRef]

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811-821 (2003).
[CrossRef]

Z. Y. Li and K. M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

Inguva, R.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Istrate, E.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interface,” Rev. Mod. Phys. 78, 455-481 (2006).
[CrossRef]

Joannopoulos, J. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528-530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

Kee, C. S.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Khoo, E. H.

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

Kim, J. E.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Kim, M. W.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Lau, W. T.

W. T. Lau and S. H. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915-3917 (2002).
[CrossRef]

Lee, S. G.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Li, E. P.

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

Li, J.

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

Li, L.

Li, L. M.

X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
[CrossRef]

Li, Z. Y.

M. Che and Z. Y. Li, “Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method,” Phys. Rev. B 77, 125138 (2008).
[CrossRef]

M. Che, Z. Y. Li, and R. J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystal,” Phys. Rev. A 76, 023809 (2007).
[CrossRef]

Z. Y. Li, L. L. Lin, and K. M. Ho, “Light coupling with multimode photonic crystal waveguides,” Appl. Phys. Lett. 84, 4699-4701 (2004).
[CrossRef]

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).
[CrossRef]

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[CrossRef]

Z. Y. Li and K. M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811-821 (2003).
[CrossRef]

Lin, L. L.

Z. Y. Li, L. L. Lin, and K. M. Ho, “Light coupling with multimode photonic crystal waveguides,” Appl. Phys. Lett. 84, 4699-4701 (2004).
[CrossRef]

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811-821 (2003).
[CrossRef]

Liu, A. Q.

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

Liu, R. J.

M. Che, Z. Y. Li, and R. J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystal,” Phys. Rev. A 76, 023809 (2007).
[CrossRef]

Malkova, N.

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Martin-Moreno, L.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, N. Moll, and S. J. McNab, “Observation of surface states in a truncated photonic crystal slab,” Opt. Lett. 29, 2175-2177 (2004).
[CrossRef] [PubMed]

Y. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95, 4538-4544 (2004).
[CrossRef]

Meade, R. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528-530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

Moll, N.

Y. A. Vlasov, N. Moll, and S. J. McNab, “Observation of surface states in a truncated photonic crystal slab,” Opt. Lett. 29, 2175-2177 (2004).
[CrossRef] [PubMed]

Y. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95, 4538-4544 (2004).
[CrossRef]

Moreno, E.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

Moroz, A.

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

Muller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Ning, C. Z.

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Oh, S. S.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Ozbay, E.

Parka, H. Y.

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

Pinjala, D.

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

Poon, A. W.

Rahachou, A. I.

A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23, 1679-1683 (2006).
[CrossRef]

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in finite and infinite photonic crystals: The recursive Green's function technique,” Phys. Rev. B 72, 155117 (2005).
[CrossRef]

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112-15120 (1999).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311-314 (1996).
[CrossRef]

Rappe, A. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18, 528-530 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Robertson, W. M.

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Sargent, E. H.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interface,” Rev. Mod. Phys. 78, 455-481 (2006).
[CrossRef]

Smigaj, W.

W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
[CrossRef]

Soukoulis, C. M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Sözüer, H. S.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Tran, P.

J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711-1715 (1996).
[CrossRef]

Tsia, K. K.

Vlasov, Y. A.

Y. A. Vlasov, N. Moll, and S. J. McNab, “Observation of surface states in a truncated photonic crystal slab,” Opt. Lett. 29, 2175-2177 (2004).
[CrossRef] [PubMed]

Y. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95, 4538-4544 (2004).
[CrossRef]

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Winn, J.

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Zhang, X. D.

X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
[CrossRef]

Zhang, Z. Q.

X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
[CrossRef]

Zozoulenko, I. V.

A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23, 1679-1683 (2006).
[CrossRef]

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in finite and infinite photonic crystals: The recursive Green's function technique,” Phys. Rev. B 72, 155117 (2005).
[CrossRef]

Appl. Phys. Lett. (4)

W. T. Lau and S. H. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915-3917 (2002).
[CrossRef]

E. H. Khoo, T. H. Cheng, A. Q. Liu, J. Li, and D. Pinjala, “Transmitting light efficiently on photonic crystal surface waveguide bend,” Appl. Phys. Lett. 91, 171109 (2007).
[CrossRef]

A. Q. Liu, E. H. Khoo, T. H. Cheng, E. P. Li, and J. Li, “A frequency-selective circulator via mode coupling between surface waveguide and resonators,” Appl. Phys. Lett. 92, 021119 (2008).
[CrossRef]

Z. Y. Li, L. L. Lin, and K. M. Ho, “Light coupling with multimode photonic crystal waveguides,” Appl. Phys. Lett. 84, 4699-4701 (2004).
[CrossRef]

J. Appl. Phys. (3)

H. G. Choi, S. S. Oh, S. G. Lee, M. W. Kim, J. E. Kim, H. Y. Parka, and C. S. Kee, “Coupling characteristics of surface modes in truncated two-dimensional photonic crystals,” J. Appl. Phys. 100, 123105 (2006).
[CrossRef]

L. L. Lin, Z. Y. Li, and K. M. Ho, “Lattice symmetry applied in transfer-matrix methods for photonic crystals,” J. Appl. Phys. 94, 811-821 (2003).
[CrossRef]

Y. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95, 4538-4544 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

M. Che, Z. Y. Li, and R. J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystal,” Phys. Rev. A 76, 023809 (2007).
[CrossRef]

Phys. Rev. B (13)

M. Che and Z. Y. Li, “Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method,” Phys. Rev. B 77, 125138 (2008).
[CrossRef]

A. I. Rahachou and I. V. Zozoulenko, “Light propagation in finite and infinite photonic crystals: The recursive Green's function technique,” Phys. Rev. B 72, 155117 (2005).
[CrossRef]

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

X. D. Zhang, L. M. Li, Z. Q. Zhang, and C. T. Chan, “Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method,” Phys. Rev. B 63, 125114 (2001).
[CrossRef]

N. Malkova and C. Z. Ning, “Shockley and Tamm surface states in photonic crystals,” Phys. Rev. B 73, 113113 (2006).
[CrossRef]

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).
[CrossRef]

Z. Y. Li and K. M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane,” Phys. Rev. B 59, 15112-15120 (1999).
[CrossRef]

J. M. Elson and P. Tran, “Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal,” Phys. Rev. B 54, 1711-1715 (1996).
[CrossRef]

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402(R) (2004).
[CrossRef]

W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
[CrossRef]

Phys. Rev. E (1)

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E 67, 046607 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interface,” Rev. Mod. Phys. 78, 455-481 (2006).
[CrossRef]

Solid State Commun. (1)

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311-314 (1996).
[CrossRef]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, 1995).

http://ab-initio.mit.edu/wiki/index. php/MIT_Photonic_Bands.

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 (12)

Fig. 1
Fig. 1

(a) Schematic configurations of a 2D truncated PC structure built in a square lattice of dielectric rod embedded in the air background that will support localized surface modes. The rods in the topmost layer are truncated along their diameter into a semicircular shape. The surface is taken to be parallel to the y axis direction. (b) The configuration of one-half of the supercell used in the CPWM. The complete supercell (symmetric with respect to the z axis) consists of m complete cylinders, two semicircular cylinders, and an air layer of length d 0 .

Fig. 2
Fig. 2

Schematic diagram of the PWTMM used to handle the surface mode propagation behavior through a truncated 2D PC structure. The surface mode problem is modeled by wave scattering at the surface of a bare semi-infinite photonic crystal surrounded by air.

Fig. 3
Fig. 3

Calculated photonic band structures for a square lattice of dielectric cylinders with radius r = 0.20 a and a refractive index of n = 3.4 in air under the TM polarization mode. The fundamental TM bandgap is indicated between the two dashed lines.

Fig. 4
Fig. 4

Calculated dispersion relation of the surface modes for the structures shown in Fig. 1a by means of PWTMM (open circle curve) and CPWM (solid curve, red online), respectively. The shaded regions represent the upper and lower edges of the photonic bandgap. The slanted solid line (blue online) is the light cone.

Fig. 5
Fig. 5

Calculated electric field intensity E x 2 pattern at y = 0 (the line y = 0 passes through the center of the cylinders) corresponding to the surface modes as investigated in Fig. 4. Two different modes are considered. The surface of the structure is located at the coordinate of z = 0 .

Fig. 6
Fig. 6

Schematic diagram of the PWTMM used to handle the surface mode propagation behavior through a 2D PC structure with the radius of the topmost surface rods being reduced to 0.1 a . The 2D PC structure is made from a square lattice of dielectric rods embedded in the air background. The surface mode problem is modeled by wave scattering at the surface of a grating-coated semi-infinite photonic crystal surrounded by air.

Fig. 7
Fig. 7

Calculated dispersion relation of the surface modes for the structures shown in Fig. 6 by means of PWTMM (open circle curve) and CPWM (solid curve, red online), respectively. The shaded regions represent the upper and lower edges of the photonic bandgap. The slanted solid line (blue online) is the light cone.

Fig. 8
Fig. 8

Calculated electric field intensity E x 2 pattern at y = 0 (the line y = 0 passes through the center of cylinders) corresponding to the surface modes as investigated in Fig. 7. Two different surface modes are considered. The center of the topmost cylinder layer is located at the coordinate of z = 0.5 a .

Fig. 9
Fig. 9

(a) Schematic configurations of a 2D PC structure made from a triangular lattice of air holes embedded in a dielectric background of refractive index 3.4. The air hole has a radius of r = 0.35 a . The dielectric margin of width d = 0.80 a spans between the flat sidewall and the edge of the first row of holes. (b) Schematic diagram of the PWTMM used to handle the surface mode propagation behavior through the PC structure in (a). The surface mode problem is modeled by wave scattering at a bare semi-infinite photonic crystal coated with a homogeneous dielectric medium.

Fig. 10
Fig. 10

Calculated photonic band structure for a triangular lattice of air cylinders of radius r = 0.35 a and refractive index of dielectric background n = 3.4 for TE mode. The fundamental TE bandgap is indicated between the two dashed lines.

Fig. 11
Fig. 11

Calculated dispersion relation of the surface modes for the structures shown in Fig. 9a by means of PWTMM (open circle curve) and CPWM (solid curve, red online), respectively. The shaded regions represent the upper and lower edges of the photonic bandgap. The solid line (blue online) is the light cone. Two surface modes are supported in the structure.

Fig. 12
Fig. 12

Calculated magnetic field intensity H x 2 pattern at y = 0 (the line y = 0 passes through the center of the cylinders) corresponding to the first surface mode as investigated in Fig. 11. Two different surface modes are considered. The outer surface of the homogeneous layer is located at the coordinate of z = 0 .

Equations (9)

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

T [ Ω + Ω ] = e i k a 3 [ Ω + Ω ] ,
T S = S Λ ,
S 1 [ Ω 0 + Ω 0 ] = [ Σ 0 + Σ 0 ]
Ω 0 + = S 11 Σ 0 + , Ω 0 = S 21 Σ 0 + .
S 11 Σ 0 + = 0 .
[ Ω 1 + Ω 0 ] = [ S a ( 11 ) S a ( 12 ) S a ( 21 ) S a ( 22 ) ] [ Ω 0 + Ω 1 ] .
[ Ω 1 + Ω 1 ] = [ S 11 S 12 S 21 S 22 ] [ Σ 0 + Σ 0 ] ,
Ω 0 + = ( S a ( 11 ) ) 1 [ S 11 S a ( 12 ) S 21 ] Σ 0 + .
det { ( S a ( 11 ) ) 1 [ S 11 S a ( 12 ) S 21 ] } = 0 .

Metrics