Abstract

We characterize the dispersion relation for electromagnetic-wave propagation in two-dimensional dielectric arrays, using the coherent microwave transient spectroscopy technique. Results of measurements along various symmetry directions of square and triangular lattices are presented. The experimental results are in excellent agreement with theoretical calculations made by using the plane-wave expansion technique. The theoretical calculations predict that transmission via certain modes is forbidden by symmetry, and our experimental results confirm this prediction.

© 1993 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2063 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  3. R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
    [CrossRef] [PubMed]
  4. G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
    [CrossRef] [PubMed]
  5. S. John and R. Rangarajan, “Optimal structures for classical wave localization: an alternative to the Ioffe–Regel criterion,” Phys. Rev. B 38, 10101–10103 (1988).
    [CrossRef]
  6. K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
    [CrossRef] [PubMed]
  7. Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
    [CrossRef] [PubMed]
  8. 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]
  9. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
    [CrossRef]
  10. M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
    [CrossRef]
  11. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
    [CrossRef]
  12. E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
    [CrossRef] [PubMed]
  13. S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
    [CrossRef] [PubMed]
  14. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
    [CrossRef] [PubMed]
  15. W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
    [CrossRef] [PubMed]
  16. Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
    [CrossRef]
  17. G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
    [CrossRef]
  18. Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
    [CrossRef]
  19. W. M. Robertson, G. Arjavalingam, and S. L. Shinde, “Microwave dielectric measurements of zirconia–alumina ceramic composites: a test of the Clausius–Mossotti mixture equations,” J. Appl. Phys. 70, 7648–7650 (1991).
    [CrossRef]
  20. D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
    [CrossRef]

1992 (2)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

1991 (6)

W. M. Robertson, G. Arjavalingam, and S. L. Shinde, “Microwave dielectric measurements of zirconia–alumina ceramic composites: a test of the Clausius–Mossotti mixture equations,” J. Appl. Phys. 70, 7648–7650 (1991).
[CrossRef]

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[CrossRef]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

1990 (4)

G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
[CrossRef]

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[CrossRef] [PubMed]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

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]

1989 (2)

Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
[CrossRef]

Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
[CrossRef]

1988 (2)

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

S. John and R. Rangarajan, “Optimal structures for classical wave localization: an alternative to the Ioffe–Regel criterion,” Phys. Rev. B 38, 10101–10103 (1988).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2063 (1987).
[CrossRef] [PubMed]

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

1985 (1)

R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

1982 (1)

D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Arjavalingam, G.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, and S. L. Shinde, “Microwave dielectric measurements of zirconia–alumina ceramic composites: a test of the Clausius–Mossotti mixture equations,” J. Appl. Phys. 70, 7648–7650 (1991).
[CrossRef]

G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
[CrossRef]

Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Brommer, K. D.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

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]

Dalichaouch, R.

S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

Genack, A. Z.

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

Halbout, J.-M.

G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
[CrossRef]

Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
[CrossRef]

Hilfer, E. S.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[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]

Hulet, R. G.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

Joannopoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

John, S.

S. John and R. Rangarajan, “Optimal structures for classical wave localization: an alternative to the Ioffe–Regel criterion,” Phys. Rev. B 38, 10101–10103 (1988).
[CrossRef]

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

Kleppner, D.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

Kopcsay, G. V.

G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
[CrossRef]

Kurizki, G.

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

Leung, K. M.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[CrossRef] [PubMed]

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[CrossRef] [PubMed]

Maradudin, A. A.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[CrossRef]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

McCall, S. L.

S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Pastol, Y.

G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
[CrossRef]

Platzmann, P. M.

S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

Plihal, M.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[CrossRef]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

Rangarajan, R.

S. John and R. Rangarajan, “Optimal structures for classical wave localization: an alternative to the Ioffe–Regel criterion,” Phys. Rev. B 38, 10101–10103 (1988).
[CrossRef]

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Robertson, W.

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

Robertson, W. M.

W. M. Robertson, G. Arjavalingam, and S. L. Shinde, “Microwave dielectric measurements of zirconia–alumina ceramic composites: a test of the Clausius–Mossotti mixture equations,” J. Appl. Phys. 70, 7648–7650 (1991).
[CrossRef]

Satpathy, S.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

Schultz, S.

S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

Shambrook, A.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[CrossRef]

Sheng, P.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[CrossRef]

Shinde, S. L.

W. M. Robertson, G. Arjavalingam, and S. L. Shinde, “Microwave dielectric measurements of zirconia–alumina ceramic composites: a test of the Clausius–Mossotti mixture equations,” J. Appl. Phys. 70, 7648–7650 (1991).
[CrossRef]

Smith, D.

S. L. McCall, P. M. Platzmann, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[CrossRef] [PubMed]

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]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2063 (1987).
[CrossRef] [PubMed]

Zhang, Z.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

Am. J. Phys. (1)

D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Appl. Phys. Lett. (3)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic bandgap in two dimensions,” Appl. Phys. Lett. 61, 495–497 (1992).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, and G. V. Kopcsay, “Coherent broadband microwave spectroscopy using picosecond optoelectronic antennas,” Appl. Phys. Lett. 54, 307–309 (1989).
[CrossRef]

Y. Pastol, G. Arjavalingam, G. V. Kopcsay, and J.-M. Halbout, “Dielectric properties of uniaxial crystals measured with optoelectronically generated transient radiation,” Appl. Phys. Lett. 55, 2277–2279 (1989).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theor. Tech. 38, 615–621 (1990).
[CrossRef]

J. Appl. Phys. (1)

W. M. Robertson, G. Arjavalingam, and S. L. Shinde, “Microwave dielectric measurements of zirconia–alumina ceramic composites: a test of the Clausius–Mossotti mixture equations,” J. Appl. Phys. 70, 7648–7650 (1991).
[CrossRef]

Opt. Commun. (1)

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[CrossRef]

Phys. Rev. B (2)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

S. John and R. Rangarajan, “Optimal structures for classical wave localization: an alternative to the Ioffe–Regel criterion,” Phys. Rev. B 38, 10101–10103 (1988).
[CrossRef]

Phys. Rev. Lett. (11)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[CrossRef] [PubMed]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for coherent microwave transient spectroscopy experiments. The two-dimensional photonic crystal is made of 0.74-mm-diameter, 100-mm-long alumina ceramic rods. Both square and triangular lattices were characterized.

Fig. 2
Fig. 2

Schematic diagram of the (a) square and (b) triangular lattice configurations, showing the lattice constants, cylinder diameters, and principal symmetry directions. d = 0.74 mm, a = 1.87 mm, b = 2.13 mm.

Fig. 3
Fig. 3

Time-domain data for propagation through six rows of rods in the 〈11〉 direction of the square lattice [Fig. 2(a)]: (a) pulse with no sample; (b) electric field polarized parallel to the rods; (c) electric field polarized perpendicular to the rods.

Fig. 4
Fig. 4

Amplitude spectra obtained by Fourier transforming the time-domain data shown in Fig. 3. The dashed curves are the amplitude spectrum obtained with no sample in the beam path. The filled circles joined by the solid curves correspond to the cases of (a) the electric field parallel to the rod axes and (b) the electric field perpendicular to the rod axes.

Fig. 5
Fig. 5

Band structure for propagation along the 〈11〉 direction of the square lattice. The filled circles are the measured values, and the curves are the values calculated theoretically by using the plane wave expansion technique: (a) electric field parallel to rods, TE modes; (b) electric field perpendicular to rods, TM modes.

Fig. 6
Fig. 6

Amplitude spectra obtained by a numerical Fourier transform of the measured time-domain data for propagation through five rows of rods along the 〈y〉 direction of the triangular lattice [Fig. 2(b)]. The dashed curves represent the reference amplitude spectra obtained with no sample in the beam. The filled circles represent the amplitude spectra for (a) the electric field parallel to rods and (b) the electric field perpendicular to rods.

Fig. 7
Fig. 7

Band structure for propagation along the 〈y〉 direction of the triangular lattice. The solid points are the measured values, the lines are the values calculated theoretically by using the plane-wave expansion technique: (a) electric field parallel to rods, TE modes; (b) electric field perpendicular to rods, TM modes.

Fig. 8
Fig. 8

Symmetries of the electric fields associated with the lowest four photonic bands of the square lattice for propagation along the 〈11〉 direction rods. The shaded circles (not to scale) represent the lattice of rods. The states depicted lie at the k = (1/2, 1/2) point of the Brillouin zone. For these modes the electric field is polarized parallel to the rods, and so + (−) indicates regions in which the electric field is oriented into (out of) the page. The modes are even (bands 1, 2, and 4) and odd (band 3) with respect to the mirror plane;-shown as the dashed lines.

Equations (6)

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× ( 1 ( r ) × H ) - ω 2 c 2 H = 0.
H ( r ) = G λ = 1 , 2 h G , λ e λ exp [ i ( k + G ) · r ] ,
n ( f ) = c ϕ 2 π f L + 1 ,
k ( f ) = [ 2 π f n ( f ) ] / c .
= f 1 1 + f 2 2 ,
1 = f 1 1 + f 2 2 ,

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