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

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, 13962�??13972 (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]
  4. H. S. Sözüer and J. P. Dowling, �??Photonic band calculations for woodpile structures,�?? J. Mod. Opt. 41, 231�??239 (1994).
  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]
  8. R. Zengerle, �??Light propagation in singly and doubly periodic planar waveguides,�?? J. Mod. Opt. 34, 1589�??1617 (1987).
  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). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203</a>
  11. D. N. Chigrin, �??Radiation pattern of a classical dipole in a photonic crystal: Photon focusing,�?? Phys. Rev. E 70, 056 611 (2004).
  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]
  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: Refraction like behavior in the vicinity of the photonic band gap,�?? Phys. Rev. B 62, 10 696 (2000).
  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).
  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).
  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). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
  22. 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). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5221">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5221</a>
    [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).

R. Zengerle, �??Light propagation in singly and doubly periodic planar waveguides,�?? J. Mod. Opt. 34, 1589�??1617 (1987).

J. Phys. Condens. Matter (1)

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]

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: Refraction like behavior in the vicinity of the photonic band gap,�?? Phys. Rev. B 62, 10 696 (2000).

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

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).

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]

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).

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]

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.


Metrics