Abstract

We calculate three-dimensional (3D) dispersion relations of woodpile and inverse opal photonic crystals. Inspecting the iso-frequency surfaces of the four lowest-order bands at appropriate frequencies we identify regions where self-collimation of light may be expected. These predictions are verified by means of finite-difference time-domain calculations both for high- and low-index photonic crystals.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13 962–13 972 (1992).
    [Crossref]
  2. K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
    [Crossref]
  3. Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
    [Crossref] [PubMed]
  4. H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
    [Crossref]
  5. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
    [Crossref]
  6. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
    [Crossref]
  7. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
    [Crossref] [PubMed]
  8. R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
    [Crossref]
  9. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
    [Crossref]
  10. D. N. Chigrin, S. Enoch, C. M. S. Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203
    [Crossref] [PubMed]
  11. D. N. Chigrin, “Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,” Phys. Rev. E 70, 056 611 (2004).
    [Crossref]
  12. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004).
    [Crossref] [PubMed]
  13. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
    [Crossref]
  14. T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
    [Crossref]
  15. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).
  16. P. S. J. Russell, “Novel thick-grating beam-squeezing device in Ta2O5 corrugated planar waveguide,” Electron. Lett. 20, 72–73 (1984).
    [Crossref]
  17. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10 696 (2000).
    [Crossref]
  18. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235 107 (2003).
    [Crossref]
  19. J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
    [Crossref]
  20. C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
    [Crossref]
  21. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
    [Crossref] [PubMed]
  22. A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys. Condens. Matter 7, 2217–2224 (1995).
    [Crossref]
  23. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000)
  24. J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12, 5221–5228 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5221
    [Crossref] [PubMed]

2004 (4)

D. N. Chigrin, “Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,” Phys. Rev. E 70, 056 611 (2004).
[Crossref]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004).
[Crossref] [PubMed]

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12, 5221–5228 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5221
[Crossref] [PubMed]

2003 (3)

D. N. Chigrin, S. Enoch, C. M. S. Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express 11, 1203–1211 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203
[Crossref] [PubMed]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235 107 (2003).
[Crossref]

J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
[Crossref]

2002 (2)

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

2001 (2)

2000 (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[Crossref] [PubMed]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10 696 (2000).
[Crossref]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

1998 (3)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

1995 (1)

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys. Condens. Matter 7, 2217–2224 (1995).
[Crossref]

1994 (2)

H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

1992 (1)

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13 962–13 972 (1992).
[Crossref]

1987 (1)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[Crossref]

1984 (1)

P. S. J. Russell, “Novel thick-grating beam-squeezing device in Ta2O5 corrugated planar waveguide,” Electron. Lett. 20, 72–73 (1984).
[Crossref]

Augustin, M.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Baba, T.

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

Bo, X.-Z.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Busch, K.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

Chen, C.

Chichkov, B.

Chigrin, D. N.

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[Crossref] [PubMed]

Dowling, J. P.

H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[Crossref]

Enoch, S.

Etrich, C.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235 107 (2003).
[Crossref]

Fuchs, H.-J.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000)

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, 13 962–13 972 (1992).
[Crossref]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

Iliew, R.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[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, 13 962–13 972 (1992).
[Crossref]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[Crossref] [PubMed]

John, S.

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

Johnson, S. G.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[Crossref] [PubMed]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Kley, E.-B.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Lederer, F.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Luo, C.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

Matsumoto, T.

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

Mizuguchi, J.

J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
[Crossref]

Murakowski, J.

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[Crossref] [PubMed]

Nolte, S.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Norris, D. J.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Notomi, M.

J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
[Crossref]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10 696 (2000).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Ovsianikov, A.

Pendry, J. B.

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys. Condens. Matter 7, 2217–2224 (1995).
[Crossref]

Peschel, U.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Prather, D. W.

Pustai, D. M.

Russell, P. S. J.

P. S. J. Russell, “Novel thick-grating beam-squeezing device in Ta2O5 corrugated planar waveguide,” Electron. Lett. 20, 72–73 (1984).
[Crossref]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Schelle, D.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Schneider, G. J.

Serbin, J.

Sharkawy, A.

Shi, S.

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235 107 (2003).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

Sözüer, H. S.

H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[Crossref]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13 962–13 972 (1992).
[Crossref]

Stewart, W. J.

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys. Condens. Matter 7, 2217–2224 (1995).
[Crossref]

Sturm, J. C.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000)

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Tamura, S.

J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
[Crossref]

Tanaka, Y.

J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
[Crossref]

Tayeb, G.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[Crossref] [PubMed]

Torres, C. M. S.

Tünnermann, A.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

Venkataraman, S.

Vlasov, Y. A.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

Ward, A. J.

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys. Condens. Matter 7, 2217–2224 (1995).
[Crossref]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[Crossref] [PubMed]

Zengerle, R.

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[Crossref]

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Appl. Phys. Lett. (4)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[Crossref]

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81, 2352–2354 (2002).
[Crossref]

Electron. Lett. (1)

P. S. J. Russell, “Novel thick-grating beam-squeezing device in Ta2O5 corrugated planar waveguide,” Electron. Lett. 20, 72–73 (1984).
[Crossref]

J. Mod. Opt. (2)

H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[Crossref]

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[Crossref]

J. Phys. Condens. Matter (1)

A. J. Ward, J. B. Pendry, and W. J. Stewart, “Photonic dispersion surfaces,” J. Phys. Condens. Matter 7, 2217–2224 (1995).
[Crossref]

Nature (2)

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[Crossref] [PubMed]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (4)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10 696 (2000).
[Crossref]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235 107 (2003).
[Crossref]

J. Mizuguchi, Y. Tanaka, S. Tamura, and M. Notomi, “Focusing of light in a three-dimensional cubic photonic crystal,” Phys. Rev. B 67, 075 109 (2003).
[Crossref]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: Convergence problems with the plane-wave method,” Phys. Rev. B 45, 13 962–13 972 (1992).
[Crossref]

Phys. Rev. E (3)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[Crossref]

D. N. Chigrin, “Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,” Phys. Rev. E 70, 056 611 (2004).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. E 58, R10 096 (1998).

Science (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–606 (2000).
[Crossref] [PubMed]

Sol. State. Comm. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic Band Gaps in Three Dimensions: New Layer-by-Layer Periodic Structures,” Sol. State. Comm. 89, 413–416 (1994).
[Crossref]

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000)

Supplementary Material (1)

» Media 1: AVI (2409 KB)     

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 (8)

Fig. 1.
Fig. 1.

Bandstructure for the fcc woodpile structure with f = 28%, n = 3.4 (left) and f = 40%, n = 1.6 (middle) and for the inverse opal with n = 3.4 (right). X′, U′, K′ and W′ are the high symmetry points with the larger z components of k, obtained by exchanging k y and k z of X, U, K and W.

Fig. 2.
Fig. 2.

IFSs of the high-index woodpile crystal for (a) band 1 at Ω = 0.44, (b) band 2 at Ω = 0.44, (c) band 3 at Ω = 0.69 and (d) band 4 at Ω = 0.73. The curvature is mapped onto the IFSs (see color bars). The values of the black isolines of lowest curvatures are 0.2, 0.3, 0.4 for (a), 0.5, 0.6, 0.7 for (b), 0.2, 0.3, 0.4 for (c) and 0.4, 0.5, 0.6 for (d). The red lines show the outline of a square and a hexagonal face of the BZ.

Fig. 3.
Fig. 3.

Rendered 3D energy density in the woodpile PC with n = 3.4 for Ω = 0.44 (left) and Ω = 0.35 (right). The wire source is located at the origin and oriented along z.

Fig. 4.
Fig. 4.

IFS (left) and rendered 3D energy density of the FDTD calculation (right) for the woodpile PC with n = 1.6 for Ω = 0.73. The curvature is mapped onto the IFS. The values of the black isolines of lowest curvatures are 0.2, 0.5, 0.6. Note that in the FDTD simulation the structure is rotated by 45° in the x-y plane compared to the conventional fcc cell used for the IFS.

Fig. 5.
Fig. 5.

IFSs of the inverse opal structure for (a) band 3 at Ω = 0.54, (b) band 4 at Ω = 0.54, (c) band 3 at Ω = 0.58 and (d) band 4 at Ω = 0.58. The curvature is mapped onto the IFSs (see color bars). The values of the black isolines of lowest curvatures are 0.2, 0.3, 0.4. The red lines show the outline of a square and a hexagonal face of the BZ.

Fig. 6.
Fig. 6.

Rendered 3D energy density in the inverse opal with n = 3.4 for Ω = 0.54 (left) and Ω = 0.58 (right). The wire source is located at the origin and oriented along z.

Fig. 7.
Fig. 7.

Movie (2.4 MByte) of H z in the plane z = 0 for the inverse opal at Ω = 0.54.

Fig. 8.
Fig. 8.

IFSs of the inverse opal structure for (a) band 8 at Ω = 0.78 and (b) band 9 at Ω = 0.84. The curvature is mapped onto the IFSs (see color bars).

Metrics