Abstract

We present a generalized picture of out-of-plane diffraction in a two-dimensional photonic crystal using the concept of photonic bands and employing a three-dimensional, equal-frequency-surface analysis. We show that the discrete spots of diffraction pattern in a weakly modulated photonic crystal, including those of conventional diffraction gratings, become continuous when the dielectric modulation becomes finite. Furthermore, in a finite-modulated photonic crystal, the diffraction can take place even in the region prohibited by Bragg’s law: there are available states for the incident light, which are evanescent in the case of a diffraction grating (weakly modulated photonic crystal).

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  3. A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
    [CrossRef]
  4. F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
    [CrossRef]
  5. G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
    [CrossRef]
  6. D. Maystre, “Photonic crystal diffraction gratings,” Opt. Express 8, 209-216 (2000).
    [CrossRef]
  7. Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
    [CrossRef]
  8. V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
    [CrossRef]
  9. V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
    [CrossRef]
  10. M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
    [CrossRef] [PubMed]
  11. 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, 10696-10705 (2000).
    [CrossRef]
  12. G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
    [CrossRef]
  13. J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge U. Press, 1972).
  14. K.-M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  15. K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896-3908 (1998).
    [CrossRef]
  16. T. Prasad, V. Colvin, and D. Mittleman, “Superprism phenomenon in three-dimensional macroporous polymer photonic crystals,” Phys. Rev. B 67, 165103 (2003).
    [CrossRef]
  17. G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
    [CrossRef]
  18. K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982-7986 (1995).
    [CrossRef]
  19. A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
    [CrossRef]
  20. M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
    [CrossRef]

2007 (1)

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
[CrossRef]

2006 (3)

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[CrossRef]

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
[CrossRef]

2005 (1)

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

2003 (2)

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

T. Prasad, V. Colvin, and D. Mittleman, “Superprism phenomenon in three-dimensional macroporous polymer photonic crystals,” Phys. Rev. B 67, 165103 (2003).
[CrossRef]

2002 (2)

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

2001 (1)

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

2000 (3)

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, 10696-10705 (2000).
[CrossRef]

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

D. Maystre, “Photonic crystal diffraction gratings,” Opt. Express 8, 209-216 (2000).
[CrossRef]

1999 (1)

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

1998 (1)

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

1995 (1)

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982-7986 (1995).
[CrossRef]

1990 (1)

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

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

Agio, M.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Alagappan, G.

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
[CrossRef]

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
[CrossRef]

Andreani, L. C.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Arriaga, J.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Astratov, V. N.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

Baryshev, A. V.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Baumberg, J. J.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

Braun, P. V.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Busch, K.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

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, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Charlton, M. B. D.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

Chen, Y.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Colvin, V.

T. Prasad, V. Colvin, and D. Mittleman, “Superprism phenomenon in three-dimensional macroporous polymer photonic crystals,” Phys. Rev. B 67, 165103 (2003).
[CrossRef]

Culshaw, I. S.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

De La Rue, R. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

Diem, M.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Galisteo-López, J. F.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Galli, M.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Garcia-Martin, A.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

García-Santamaría, F.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Halevi, P.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Harris, A.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

Ho, K.-M.

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[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]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Koch, W.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Kosobukin, V. A.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Krauss, T. F.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

Krokhin, A. A.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Limonov, M. F.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Liu, Y. J.

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[CrossRef]

López, C.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Marabelli, F.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Maystre, D.

Meisel, D. C.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Mittleman, D.

T. Prasad, V. Colvin, and D. Mittleman, “Superprism phenomenon in three-dimensional macroporous polymer photonic crystals,” Phys. Rev. B 67, 165103 (2003).
[CrossRef]

Netti, M. C.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

Notomi, M.

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, 10696-10705 (2000).
[CrossRef]

Parker, G. J.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

Patrini, M.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Pereira, S.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Peyrade, D.

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Prasad, T.

T. Prasad, V. Colvin, and D. Mittleman, “Superprism phenomenon in three-dimensional macroporous polymer photonic crystals,” Phys. Rev. B 67, 165103 (2003).
[CrossRef]

Sakoda, K.

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982-7986 (1995).
[CrossRef]

Samusev, K. B.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Shum, P.

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
[CrossRef]

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
[CrossRef]

Skolnick, M. S.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

Soukoulis, C. M.

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Stevenson, R. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

Sun, X. W.

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
[CrossRef]

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[CrossRef]

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
[CrossRef]

Usvyat, D. E.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

von Freymann, G.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Wegener, M.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

Whittaker, D. M.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[CrossRef]

Yablonovitch, E.

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

Yu, M. B.

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
[CrossRef]

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
[CrossRef]

Ziman, J. M.

J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge U. Press, 1972).

Zoorob, M. E.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[CrossRef]

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, and K. Busch, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614-616 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Tunable dispersion properties of a liquid crystal infiltrated into a two-dimensional photonic crystal,” IEEE J. Quantum Electron. 42, 404-409 (2006).
[CrossRef]

M. Patrini, M. Galli, F. Marabelli, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Photonic bands in patterned silicon-on-insulator waveguides,” IEEE J. Quantum Electron. 38, 885-890 (2002).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (8)

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: Experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982-7986 (1995).
[CrossRef]

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255-R16258 (1999).
[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, 10696-10705 (2000).
[CrossRef]

G. Alagappan, X. W. Sun, M. B. Yu, and P. Shum, “Out-of-plane dispersion of a two-dimensional photonic crystal,” Phys. Rev. B 75, 113104 (2007).
[CrossRef]

T. Prasad, V. Colvin, and D. Mittleman, “Superprism phenomenon in three-dimensional macroporous polymer photonic crystals,” Phys. Rev. B 67, 165103 (2003).
[CrossRef]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (4)

K.-M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526-1529 (2001).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

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

Other (1)

J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge U. Press, 1972).

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 (5)

Fig. 1
Fig. 1

(a) Reciprocal lattice and BZ of a hexagonal lattice. (b) Cross section of EFS of WPC with n av = 1.75 , for ω = 0.75 along k x axis (within the BZ). Bands 2, 4, and 6 overlap with bands 3, 5, and 7, respectively, along k x axis. (c) 3D plot of EFS [ ω = h ( k x , k y , k z ) ] corresponding to band 2. (d) 3D plot of EFS [ ω = h ( k x , k y , k z ) ] corresponding to band 4.

Fig. 2
Fig. 2

(a) Cross section of EFS of FPC with f = 0.25 and an averaged index of 1.75 for ω = 0.75 along k x axis (within the BZ). (b) 3D plot of EFS [ ω = h ( k x , k y , k z ) ] corresponding to band 3. (c) 3D plot of EFS [ ω = h ( k x , k y , k z ) ] corresponding to band 7.

Fig. 3
Fig. 3

Discrete curves: α o versus α for a WPC with n av = 1.75 ( ω = 0.75 ) for bands 2 (center, blue) and 4 (upper and lower, red) shown in Figs. 1c, 1d, respectively. Continuous curves: α o versus α for a FPC with f = 0.25 and an averaged index of 1.75 ( ω = 0.75 ) for band 3 (straight curve, green) and 7 (sinusoidal curve, pink) shown in Figs. 2b, 2c, respectively.

Fig. 4
Fig. 4

(a) Variations of band 2 [Fig. 1c] with respect to ω with a step of 0.02 in a WPC along k x axis and within the BZ. (b) Variations of band 3 [Fig. 2b] with respect to ω with a step of 0.02 in a FPC along k x axis and within the BZ. (c) k z as a function of ω for WPC and FPC, respectively, at β = 0 , showing the diffraction limit.

Fig. 5
Fig. 5

(a) SEM image of the sample (viewed at 45° to the surface normal). The inset in (a) shows a sketch of the cross section of the sample. The thickness of the SiN and the silica layer are 250 nm and 2 μ m , respectively. The depth of the air holes is 350 nm . (b) Simulated diffraction pattern at ω = 0.63 . (c) Experimental photograph of the diffraction pattern at ω = 0.63 . (d) α o versus α for band 7–8.

Metrics