Abstract

An effective description is developed for a metalodielectric photonic bandgap (PBG) material far beyond the quasi-static limit of traditional effective-medium theories. An analytic approach, recently presented by the authors, is further advanced to provide the complete effective permittivity and permeability functions. Reflection and transmission coefficients are presented for both TM and TE oblique plane-wave incidence, based on the determination of the equivalent impedance for each lattice plane in the crystal and the transfer-matrix method for reconstructing the effect of successive lattice planes. An analysis of the semi-infinite and slab observables yields the anisotropic effective refractive index, effective permittivity, and effective permeability, thus completing the macroscopic description of the interaction of electromagnetic waves with the medium. Among the novel aspects of the analysis is the equivalence of our PBG system with a physically dispersive system at ultraviolet frequencies and the derivation and explanation of the development of high dispersive magnetization (permeability) for these media, independently of the microscopic magnetic properties of the metallic implants.

© 1999 Optical Society of America

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  1. N. G. Alexopoulos, D. R. Jackson, “Fundamental superstrate effects on printed circuit antennas,” IEEE Trans. Antennas Propag. AP-32, 807–816 (1984).
    [CrossRef]
  2. N. G. Alexopoulos, D. R. Jackson, P. B. Katehi, “Criteria for nearly omnidirectional radiation patterns for printed antennas,” IEEE Trans. Antennas Propag. AP-33, 195–205 (1985).
    [CrossRef]
  3. H. Y. Yang, N. G. Alexopoulos, “Gain enhancement methods for printed circuit antennas through multiple superstrates,” IEEE Trans. Antennas Propag. AP-35, 860–863 (1987).
    [CrossRef]
  4. H. Y. Yang, N. G. Alexopoulos, E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. 45, 185–187 (1997).
    [CrossRef]
  5. H. Y. Yang, R. E. Diaz, N. G. Alexopoulos, “Reflection and transmission of waves from multilayer structures with planar-implanted periodic material blocks,” J. Opt. Soc. Am. B 14, 2513–2519 (1997).
    [CrossRef]
  6. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Large omnidirectional band gaps in metalodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
    [CrossRef]
  7. R. Coccioli, T. Itoh, G. Pelosi, “A finite element-generalized network analysis of finite thickness photonic crystals,” in 1997 IEEE MTT-S Digest, pp. 195–198.
  8. E. W. Lucas, T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag. 43, 145–153 (1995).
    [CrossRef]
  9. S. D. Gedney, J. F. Lee, R. Mittra, “A combined FEM/MoM approach to analyze the plane wave diffraction by arbitrary gratings,” IEEE Trans. Antennas Propag. 40, 363–370 (1992).
  10. H. Contopanagos, L. Zhang, N. G. Alexopoulos, “Thin frequency selective lattices integrated in novel compact MIC, MMIC and PCA architectures,” IEEE Trans. Microwave Theory Tech. 46, 1936–1948 (1998).
    [CrossRef]
  11. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York1983), pp. 227–251 and references therein.
  12. C. A. Kyriazidou, H. Contopanagos, W. M. Merrill, N. G. Alexopoulos, “Artificial versus natural crystals: effective wave impedance for printed photonic band gap materials,” IEEE Trans. Antennas Propag. (to be published).
  13. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 764–772 and references therein.
  14. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, UK, 1970), pp. 66–70 and references therein.
  15. W. M. Merrill, C. A. Kyriazidou, H. Contopanagos, N. G. Alexopoulos, “Electromagnetic scattering from a PBG material excited by an electric line source,” IEEE Trans. Microwave Theory Tech. (to be published).
  16. H. Contopanagos, N. G. Alexopoulos, E. Yablonovitch, “High-Q radio frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Tech. 46, 1310–1312 (1998).
    [CrossRef]
  17. H. Contopanagos, E. Yablonovitch, N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultra-thin metallic films from DC to ultraviolet frequencies,” J. Opt. Soc. Am. A (to be published).

1998 (2)

H. Contopanagos, L. Zhang, N. G. Alexopoulos, “Thin frequency selective lattices integrated in novel compact MIC, MMIC and PCA architectures,” IEEE Trans. Microwave Theory Tech. 46, 1936–1948 (1998).
[CrossRef]

H. Contopanagos, N. G. Alexopoulos, E. Yablonovitch, “High-Q radio frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Tech. 46, 1310–1312 (1998).
[CrossRef]

1997 (2)

H. Y. Yang, R. E. Diaz, N. G. Alexopoulos, “Reflection and transmission of waves from multilayer structures with planar-implanted periodic material blocks,” J. Opt. Soc. Am. B 14, 2513–2519 (1997).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. 45, 185–187 (1997).
[CrossRef]

1996 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Large omnidirectional band gaps in metalodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

1995 (1)

E. W. Lucas, T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag. 43, 145–153 (1995).
[CrossRef]

1992 (1)

S. D. Gedney, J. F. Lee, R. Mittra, “A combined FEM/MoM approach to analyze the plane wave diffraction by arbitrary gratings,” IEEE Trans. Antennas Propag. 40, 363–370 (1992).

1987 (1)

H. Y. Yang, N. G. Alexopoulos, “Gain enhancement methods for printed circuit antennas through multiple superstrates,” IEEE Trans. Antennas Propag. AP-35, 860–863 (1987).
[CrossRef]

1985 (1)

N. G. Alexopoulos, D. R. Jackson, P. B. Katehi, “Criteria for nearly omnidirectional radiation patterns for printed antennas,” IEEE Trans. Antennas Propag. AP-33, 195–205 (1985).
[CrossRef]

1984 (1)

N. G. Alexopoulos, D. R. Jackson, “Fundamental superstrate effects on printed circuit antennas,” IEEE Trans. Antennas Propag. AP-32, 807–816 (1984).
[CrossRef]

Alexopoulos, N. G.

H. Contopanagos, L. Zhang, N. G. Alexopoulos, “Thin frequency selective lattices integrated in novel compact MIC, MMIC and PCA architectures,” IEEE Trans. Microwave Theory Tech. 46, 1936–1948 (1998).
[CrossRef]

H. Contopanagos, N. G. Alexopoulos, E. Yablonovitch, “High-Q radio frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Tech. 46, 1310–1312 (1998).
[CrossRef]

H. Y. Yang, R. E. Diaz, N. G. Alexopoulos, “Reflection and transmission of waves from multilayer structures with planar-implanted periodic material blocks,” J. Opt. Soc. Am. B 14, 2513–2519 (1997).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. 45, 185–187 (1997).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, “Gain enhancement methods for printed circuit antennas through multiple superstrates,” IEEE Trans. Antennas Propag. AP-35, 860–863 (1987).
[CrossRef]

N. G. Alexopoulos, D. R. Jackson, P. B. Katehi, “Criteria for nearly omnidirectional radiation patterns for printed antennas,” IEEE Trans. Antennas Propag. AP-33, 195–205 (1985).
[CrossRef]

N. G. Alexopoulos, D. R. Jackson, “Fundamental superstrate effects on printed circuit antennas,” IEEE Trans. Antennas Propag. AP-32, 807–816 (1984).
[CrossRef]

C. A. Kyriazidou, H. Contopanagos, W. M. Merrill, N. G. Alexopoulos, “Artificial versus natural crystals: effective wave impedance for printed photonic band gap materials,” IEEE Trans. Antennas Propag. (to be published).

W. M. Merrill, C. A. Kyriazidou, H. Contopanagos, N. G. Alexopoulos, “Electromagnetic scattering from a PBG material excited by an electric line source,” IEEE Trans. Microwave Theory Tech. (to be published).

H. Contopanagos, E. Yablonovitch, N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultra-thin metallic films from DC to ultraviolet frequencies,” J. Opt. Soc. Am. A (to be published).

Bohren, C.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York1983), pp. 227–251 and references therein.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, UK, 1970), pp. 66–70 and references therein.

Coccioli, R.

R. Coccioli, T. Itoh, G. Pelosi, “A finite element-generalized network analysis of finite thickness photonic crystals,” in 1997 IEEE MTT-S Digest, pp. 195–198.

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 764–772 and references therein.

Contopanagos, H.

H. Contopanagos, N. G. Alexopoulos, E. Yablonovitch, “High-Q radio frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Tech. 46, 1310–1312 (1998).
[CrossRef]

H. Contopanagos, L. Zhang, N. G. Alexopoulos, “Thin frequency selective lattices integrated in novel compact MIC, MMIC and PCA architectures,” IEEE Trans. Microwave Theory Tech. 46, 1936–1948 (1998).
[CrossRef]

C. A. Kyriazidou, H. Contopanagos, W. M. Merrill, N. G. Alexopoulos, “Artificial versus natural crystals: effective wave impedance for printed photonic band gap materials,” IEEE Trans. Antennas Propag. (to be published).

W. M. Merrill, C. A. Kyriazidou, H. Contopanagos, N. G. Alexopoulos, “Electromagnetic scattering from a PBG material excited by an electric line source,” IEEE Trans. Microwave Theory Tech. (to be published).

H. Contopanagos, E. Yablonovitch, N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultra-thin metallic films from DC to ultraviolet frequencies,” J. Opt. Soc. Am. A (to be published).

Diaz, R. E.

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Large omnidirectional band gaps in metalodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

Fontana, T. P.

E. W. Lucas, T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag. 43, 145–153 (1995).
[CrossRef]

Gedney, S. D.

S. D. Gedney, J. F. Lee, R. Mittra, “A combined FEM/MoM approach to analyze the plane wave diffraction by arbitrary gratings,” IEEE Trans. Antennas Propag. 40, 363–370 (1992).

Huffman, D.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York1983), pp. 227–251 and references therein.

Itoh, T.

R. Coccioli, T. Itoh, G. Pelosi, “A finite element-generalized network analysis of finite thickness photonic crystals,” in 1997 IEEE MTT-S Digest, pp. 195–198.

Jackson, D. R.

N. G. Alexopoulos, D. R. Jackson, P. B. Katehi, “Criteria for nearly omnidirectional radiation patterns for printed antennas,” IEEE Trans. Antennas Propag. AP-33, 195–205 (1985).
[CrossRef]

N. G. Alexopoulos, D. R. Jackson, “Fundamental superstrate effects on printed circuit antennas,” IEEE Trans. Antennas Propag. AP-32, 807–816 (1984).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Large omnidirectional band gaps in metalodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

Katehi, P. B.

N. G. Alexopoulos, D. R. Jackson, P. B. Katehi, “Criteria for nearly omnidirectional radiation patterns for printed antennas,” IEEE Trans. Antennas Propag. AP-33, 195–205 (1985).
[CrossRef]

Kyriazidou, C. A.

W. M. Merrill, C. A. Kyriazidou, H. Contopanagos, N. G. Alexopoulos, “Electromagnetic scattering from a PBG material excited by an electric line source,” IEEE Trans. Microwave Theory Tech. (to be published).

C. A. Kyriazidou, H. Contopanagos, W. M. Merrill, N. G. Alexopoulos, “Artificial versus natural crystals: effective wave impedance for printed photonic band gap materials,” IEEE Trans. Antennas Propag. (to be published).

Lee, J. F.

S. D. Gedney, J. F. Lee, R. Mittra, “A combined FEM/MoM approach to analyze the plane wave diffraction by arbitrary gratings,” IEEE Trans. Antennas Propag. 40, 363–370 (1992).

Lucas, E. W.

E. W. Lucas, T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag. 43, 145–153 (1995).
[CrossRef]

Merrill, W. M.

C. A. Kyriazidou, H. Contopanagos, W. M. Merrill, N. G. Alexopoulos, “Artificial versus natural crystals: effective wave impedance for printed photonic band gap materials,” IEEE Trans. Antennas Propag. (to be published).

W. M. Merrill, C. A. Kyriazidou, H. Contopanagos, N. G. Alexopoulos, “Electromagnetic scattering from a PBG material excited by an electric line source,” IEEE Trans. Microwave Theory Tech. (to be published).

Mittra, R.

S. D. Gedney, J. F. Lee, R. Mittra, “A combined FEM/MoM approach to analyze the plane wave diffraction by arbitrary gratings,” IEEE Trans. Antennas Propag. 40, 363–370 (1992).

Pelosi, G.

R. Coccioli, T. Itoh, G. Pelosi, “A finite element-generalized network analysis of finite thickness photonic crystals,” in 1997 IEEE MTT-S Digest, pp. 195–198.

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Large omnidirectional band gaps in metalodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, UK, 1970), pp. 66–70 and references therein.

Yablonovitch, E.

H. Contopanagos, N. G. Alexopoulos, E. Yablonovitch, “High-Q radio frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Tech. 46, 1310–1312 (1998).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. 45, 185–187 (1997).
[CrossRef]

H. Contopanagos, E. Yablonovitch, N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultra-thin metallic films from DC to ultraviolet frequencies,” J. Opt. Soc. Am. A (to be published).

Yang, H. Y.

H. Y. Yang, R. E. Diaz, N. G. Alexopoulos, “Reflection and transmission of waves from multilayer structures with planar-implanted periodic material blocks,” J. Opt. Soc. Am. B 14, 2513–2519 (1997).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. 45, 185–187 (1997).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, “Gain enhancement methods for printed circuit antennas through multiple superstrates,” IEEE Trans. Antennas Propag. AP-35, 860–863 (1987).
[CrossRef]

Zhang, L.

H. Contopanagos, L. Zhang, N. G. Alexopoulos, “Thin frequency selective lattices integrated in novel compact MIC, MMIC and PCA architectures,” IEEE Trans. Microwave Theory Tech. 46, 1936–1948 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

E. W. Lucas, T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag. 43, 145–153 (1995).
[CrossRef]

S. D. Gedney, J. F. Lee, R. Mittra, “A combined FEM/MoM approach to analyze the plane wave diffraction by arbitrary gratings,” IEEE Trans. Antennas Propag. 40, 363–370 (1992).

N. G. Alexopoulos, D. R. Jackson, “Fundamental superstrate effects on printed circuit antennas,” IEEE Trans. Antennas Propag. AP-32, 807–816 (1984).
[CrossRef]

N. G. Alexopoulos, D. R. Jackson, P. B. Katehi, “Criteria for nearly omnidirectional radiation patterns for printed antennas,” IEEE Trans. Antennas Propag. AP-33, 195–205 (1985).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, “Gain enhancement methods for printed circuit antennas through multiple superstrates,” IEEE Trans. Antennas Propag. AP-35, 860–863 (1987).
[CrossRef]

H. Y. Yang, N. G. Alexopoulos, E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. 45, 185–187 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

H. Contopanagos, N. G. Alexopoulos, E. Yablonovitch, “High-Q radio frequency structures using one-dimensionally periodic metallic films,” IEEE Trans. Microwave Theory Tech. 46, 1310–1312 (1998).
[CrossRef]

H. Contopanagos, L. Zhang, N. G. Alexopoulos, “Thin frequency selective lattices integrated in novel compact MIC, MMIC and PCA architectures,” IEEE Trans. Microwave Theory Tech. 46, 1936–1948 (1998).
[CrossRef]

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

Phys. Rev. B (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Large omnidirectional band gaps in metalodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

Other (7)

R. Coccioli, T. Itoh, G. Pelosi, “A finite element-generalized network analysis of finite thickness photonic crystals,” in 1997 IEEE MTT-S Digest, pp. 195–198.

H. Contopanagos, E. Yablonovitch, N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultra-thin metallic films from DC to ultraviolet frequencies,” J. Opt. Soc. Am. A (to be published).

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York1983), pp. 227–251 and references therein.

C. A. Kyriazidou, H. Contopanagos, W. M. Merrill, N. G. Alexopoulos, “Artificial versus natural crystals: effective wave impedance for printed photonic band gap materials,” IEEE Trans. Antennas Propag. (to be published).

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 764–772 and references therein.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, UK, 1970), pp. 66–70 and references therein.

W. M. Merrill, C. A. Kyriazidou, H. Contopanagos, N. G. Alexopoulos, “Electromagnetic scattering from a PBG material excited by an electric line source,” IEEE Trans. Microwave Theory Tech. (to be published).

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