Abstract

The characteristics of the plane-wave incidence on a multilayer structure with planar periodic material blocks are presented. The layered media and the implanted blocks are either dielectric or magnetodielectric. Coupled volume integral equations in conjunction with the method of moments are used to determine the displacement electric and magnetic volume current densities within the implanted periodic blocks that are due to an incident plane wave. The displacement currents are treated as secondary sources to determine the transmitted and the reflected waves. The analysis is validated through the comparison with reflectometer measurements and a low-frequency effective medium approach. It is demonstrated that the structures are suitable for both narrow-band and wideband frequency-selective-layer (space filter) applications in millimeter waves, infrareds, and optics where metallic gratings are inappropriate. The presented analytic and numerical approach establishes the basis for the analysis of wave interactions with photonic bandgap material layers.

© 1997 Optical Society of America

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References

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  1. C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., Special issue on development and applications of materialsexhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 279–413 (1993).
  2. P. L. Knight, ed., Special issue on photonic band structures, J. Mod. Opt. 41, 171–395 (1994).
    [CrossRef]
  3. H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. AP-45, 181–183 (1997).
  4. H. Y. D. Yang, “Characteristics of guided and leaky waves on a thin-film structurewith planar material gratings,” IEEE Trans. Microwave Theory Tech. 45, 428–435 (1997).
    [CrossRef]
  5. S. T. Peng, T. Tamir, and H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
    [CrossRef]
  6. K. Sakuda and A. Yariv, “Analysis of optical propagation in a corrugated dielectric waveguide,” Opt. Commun. 8, 1–4 (1973).
    [CrossRef]
  7. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  8. M. C. Hutley, Diffraction Gratings (Academic, San Diego, Calif., 1982).
  9. E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
    [CrossRef]
  10. E. R. Brown, C. D. Parker, and O. B. McMahon, “Effect of surface composition on the radiation pattern from a photonicplanar-dipole antenna,” Appl. Phys. Lett. 64, 3345–3347 (1994).
    [CrossRef]
  11. E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
    [CrossRef]
  12. M. P. Kesler, J. G. Maloney, and B. L. Shirley, “Antennadesign with the use of photonic band-gap materials as all-dielectric planarreflectors,” Microwave Opt. Technol. Lett. 11, (1996).
  13. O. M. Bucci and G. Franceschetti, “Scattering from wedge-tapered absorbers,” IEEE Trans. Antennas Propag. AP-19, 96–104 (1971).
    [CrossRef]
  14. E. F. Kuester and C. L. Holloway, “Comparison of approximations for effective parameters of artificialdielectric,” IEEE Trans. Microwave Theory Techn. 38, 1752–1755 (1990).
    [CrossRef]
  15. E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. I: Theory,” IEEE Trans. Electromagn. Compat. 36, 300–306 (1994).
    [CrossRef]
  16. E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. II: Computedand measured results,” IEEE Trans. Electromagn. Compat. 36, 307–312 (1994).
    [CrossRef]
  17. C. F. Yang, W. D. Burnside, and R. C. Rudduck, “A doubly periodic moment method solution for the analysis and designof an absorber covered wall,” IEEE Trans. Antennas Propag. AP-41, 600–609 (1993).
    [CrossRef]
  18. W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domainfinite difference method,” IEEE Trans. Antennas Propag. AP-44, 798–805 (1996).
  19. R. J. Mittra, C. H. Chan, and T. A. Cwik, “Techniques for analyzing frequency selective surfaces–a review,” Proc. IEEE 76, 1593–1614 (1988).
    [CrossRef]
  20. E. W. Lucas and T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unifiedradiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag. 43, 145–153 (1995).
    [CrossRef]
  21. R. E. Collin, Field Theory of Guided Waves (IEEE, New York, 1991), p. 605.
  22. W. C. Chew, Waves and Fields in InhomogeneousMedia (IEEE, New York, 1994), Chap. 2.
  23. H. Y. D. Yang, “A spectral recursive transformation method for electromagnetic fieldsin generalized anisotropic layered media,” IEEE Trans. Antennas Propag. AP-45, 520–527 (1997).
    [CrossRef]
  24. Phraxos R&D, Inc., “A hollow-metal-dielectric-waveguidereflectometer,” Technical Brief (Phraxos R&D Inc., Santa Monica, Calif., 1995).
  25. J. L. Tsalamengas and N. K. Uzunoglu, “Radiation from a dipole in the proximity of a general anisotropic groundedlayer,” IEEE Trans. Antennas Propag. AP-33, 165–172 (1985).
    [CrossRef]
  26. H-Y. Yang, J. A. Castaneda, and N. G. Alexopoulos, “Surface wave modes of printed circuit on ferrite substrates,” IEEE Trans. Microwave Theory Tech. MTT-40, 613–621 (1992).
    [CrossRef]

1997 (3)

H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. AP-45, 181–183 (1997).

H. Y. D. Yang, “Characteristics of guided and leaky waves on a thin-film structurewith planar material gratings,” IEEE Trans. Microwave Theory Tech. 45, 428–435 (1997).
[CrossRef]

H. Y. D. Yang, “A spectral recursive transformation method for electromagnetic fieldsin generalized anisotropic layered media,” IEEE Trans. Antennas Propag. AP-45, 520–527 (1997).
[CrossRef]

1996 (1)

W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domainfinite difference method,” IEEE Trans. Antennas Propag. AP-44, 798–805 (1996).

1995 (1)

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

1994 (5)

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. I: Theory,” IEEE Trans. Electromagn. Compat. 36, 300–306 (1994).
[CrossRef]

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. II: Computedand measured results,” IEEE Trans. Electromagn. Compat. 36, 307–312 (1994).
[CrossRef]

P. L. Knight, ed., Special issue on photonic band structures, J. Mod. Opt. 41, 171–395 (1994).
[CrossRef]

E. R. Brown, C. D. Parker, and O. B. McMahon, “Effect of surface composition on the radiation pattern from a photonicplanar-dipole antenna,” Appl. Phys. Lett. 64, 3345–3347 (1994).
[CrossRef]

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

1993 (3)

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., Special issue on development and applications of materialsexhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 279–413 (1993).

C. F. Yang, W. D. Burnside, and R. C. Rudduck, “A doubly periodic moment method solution for the analysis and designof an absorber covered wall,” IEEE Trans. Antennas Propag. AP-41, 600–609 (1993).
[CrossRef]

E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
[CrossRef]

1992 (1)

H-Y. Yang, J. A. Castaneda, and N. G. Alexopoulos, “Surface wave modes of printed circuit on ferrite substrates,” IEEE Trans. Microwave Theory Tech. MTT-40, 613–621 (1992).
[CrossRef]

1990 (1)

E. F. Kuester and C. L. Holloway, “Comparison of approximations for effective parameters of artificialdielectric,” IEEE Trans. Microwave Theory Techn. 38, 1752–1755 (1990).
[CrossRef]

1988 (1)

R. J. Mittra, C. H. Chan, and T. A. Cwik, “Techniques for analyzing frequency selective surfaces–a review,” Proc. IEEE 76, 1593–1614 (1988).
[CrossRef]

1985 (1)

J. L. Tsalamengas and N. K. Uzunoglu, “Radiation from a dipole in the proximity of a general anisotropic groundedlayer,” IEEE Trans. Antennas Propag. AP-33, 165–172 (1985).
[CrossRef]

1975 (1)

S. T. Peng, T. Tamir, and H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

1973 (1)

K. Sakuda and A. Yariv, “Analysis of optical propagation in a corrugated dielectric waveguide,” Opt. Commun. 8, 1–4 (1973).
[CrossRef]

1971 (1)

O. M. Bucci and G. Franceschetti, “Scattering from wedge-tapered absorbers,” IEEE Trans. Antennas Propag. AP-19, 96–104 (1971).
[CrossRef]

Alexopoulos, N. G.

H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. AP-45, 181–183 (1997).

H-Y. Yang, J. A. Castaneda, and N. G. Alexopoulos, “Surface wave modes of printed circuit on ferrite substrates,” IEEE Trans. Microwave Theory Tech. MTT-40, 613–621 (1992).
[CrossRef]

Balanis, C. A.

W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domainfinite difference method,” IEEE Trans. Antennas Propag. AP-44, 798–805 (1996).

Bertoni, H.

S. T. Peng, T. Tamir, and H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Biswas, R.

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

Bowden, C. M.

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., Special issue on development and applications of materialsexhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 279–413 (1993).

Brown, E. R.

E. R. Brown, C. D. Parker, and O. B. McMahon, “Effect of surface composition on the radiation pattern from a photonicplanar-dipole antenna,” Appl. Phys. Lett. 64, 3345–3347 (1994).
[CrossRef]

E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
[CrossRef]

Bucci, O. M.

O. M. Bucci and G. Franceschetti, “Scattering from wedge-tapered absorbers,” IEEE Trans. Antennas Propag. AP-19, 96–104 (1971).
[CrossRef]

Burnside, W. D.

C. F. Yang, W. D. Burnside, and R. C. Rudduck, “A doubly periodic moment method solution for the analysis and designof an absorber covered wall,” IEEE Trans. Antennas Propag. AP-41, 600–609 (1993).
[CrossRef]

Castaneda, J. A.

H-Y. Yang, J. A. Castaneda, and N. G. Alexopoulos, “Surface wave modes of printed circuit on ferrite substrates,” IEEE Trans. Microwave Theory Tech. MTT-40, 613–621 (1992).
[CrossRef]

Chan, C. H.

R. J. Mittra, C. H. Chan, and T. A. Cwik, “Techniques for analyzing frequency selective surfaces–a review,” Proc. IEEE 76, 1593–1614 (1988).
[CrossRef]

Cwik, T. A.

R. J. Mittra, C. H. Chan, and T. A. Cwik, “Techniques for analyzing frequency selective surfaces–a review,” Proc. IEEE 76, 1593–1614 (1988).
[CrossRef]

Dowling, J. P.

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., Special issue on development and applications of materialsexhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 279–413 (1993).

Everitt, H. O.

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., Special issue on development and applications of materialsexhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 279–413 (1993).

Fontana, T. P.

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

Franceschetti, G.

O. M. Bucci and G. Franceschetti, “Scattering from wedge-tapered absorbers,” IEEE Trans. Antennas Propag. AP-19, 96–104 (1971).
[CrossRef]

Ho, K. M.

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

Holloway, C. L.

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. II: Computedand measured results,” IEEE Trans. Electromagn. Compat. 36, 307–312 (1994).
[CrossRef]

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. I: Theory,” IEEE Trans. Electromagn. Compat. 36, 300–306 (1994).
[CrossRef]

E. F. Kuester and C. L. Holloway, “Comparison of approximations for effective parameters of artificialdielectric,” IEEE Trans. Microwave Theory Techn. 38, 1752–1755 (1990).
[CrossRef]

Knight, P. L.

P. L. Knight, ed., Special issue on photonic band structures, J. Mod. Opt. 41, 171–395 (1994).
[CrossRef]

Kuester, E. F.

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. I: Theory,” IEEE Trans. Electromagn. Compat. 36, 300–306 (1994).
[CrossRef]

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. II: Computedand measured results,” IEEE Trans. Electromagn. Compat. 36, 307–312 (1994).
[CrossRef]

E. F. Kuester and C. L. Holloway, “Comparison of approximations for effective parameters of artificialdielectric,” IEEE Trans. Microwave Theory Techn. 38, 1752–1755 (1990).
[CrossRef]

Liu, K.

W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domainfinite difference method,” IEEE Trans. Antennas Propag. AP-44, 798–805 (1996).

Lucas, E. W.

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

McMahon, O. B.

E. R. Brown, C. D. Parker, and O. B. McMahon, “Effect of surface composition on the radiation pattern from a photonicplanar-dipole antenna,” Appl. Phys. Lett. 64, 3345–3347 (1994).
[CrossRef]

Mittra, R. J.

R. J. Mittra, C. H. Chan, and T. A. Cwik, “Techniques for analyzing frequency selective surfaces–a review,” Proc. IEEE 76, 1593–1614 (1988).
[CrossRef]

Ozbay, E.

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

Parker, C. D.

E. R. Brown, C. D. Parker, and O. B. McMahon, “Effect of surface composition on the radiation pattern from a photonicplanar-dipole antenna,” Appl. Phys. Lett. 64, 3345–3347 (1994).
[CrossRef]

E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
[CrossRef]

Peng, S. T.

S. T. Peng, T. Tamir, and H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Rudduck, R. C.

C. F. Yang, W. D. Burnside, and R. C. Rudduck, “A doubly periodic moment method solution for the analysis and designof an absorber covered wall,” IEEE Trans. Antennas Propag. AP-41, 600–609 (1993).
[CrossRef]

Sakuda, K.

K. Sakuda and A. Yariv, “Analysis of optical propagation in a corrugated dielectric waveguide,” Opt. Commun. 8, 1–4 (1973).
[CrossRef]

Sigalas, M.

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

Sun, W.

W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domainfinite difference method,” IEEE Trans. Antennas Propag. AP-44, 798–805 (1996).

Tamir, T.

S. T. Peng, T. Tamir, and H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Tsalamengas, J. L.

J. L. Tsalamengas and N. K. Uzunoglu, “Radiation from a dipole in the proximity of a general anisotropic groundedlayer,” IEEE Trans. Antennas Propag. AP-33, 165–172 (1985).
[CrossRef]

Tuttle, G.

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

Uzunoglu, N. K.

J. L. Tsalamengas and N. K. Uzunoglu, “Radiation from a dipole in the proximity of a general anisotropic groundedlayer,” IEEE Trans. Antennas Propag. AP-33, 165–172 (1985).
[CrossRef]

Yablonovitch, E.

H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. AP-45, 181–183 (1997).

E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
[CrossRef]

Yang, C. F.

C. F. Yang, W. D. Burnside, and R. C. Rudduck, “A doubly periodic moment method solution for the analysis and designof an absorber covered wall,” IEEE Trans. Antennas Propag. AP-41, 600–609 (1993).
[CrossRef]

Yang, H. Y. D.

H. Y. D. Yang, “Characteristics of guided and leaky waves on a thin-film structurewith planar material gratings,” IEEE Trans. Microwave Theory Tech. 45, 428–435 (1997).
[CrossRef]

H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. AP-45, 181–183 (1997).

H. Y. D. Yang, “A spectral recursive transformation method for electromagnetic fieldsin generalized anisotropic layered media,” IEEE Trans. Antennas Propag. AP-45, 520–527 (1997).
[CrossRef]

Yang, H-Y.

H-Y. Yang, J. A. Castaneda, and N. G. Alexopoulos, “Surface wave modes of printed circuit on ferrite substrates,” IEEE Trans. Microwave Theory Tech. MTT-40, 613–621 (1992).
[CrossRef]

Yariv, A.

K. Sakuda and A. Yariv, “Analysis of optical propagation in a corrugated dielectric waveguide,” Opt. Commun. 8, 1–4 (1973).
[CrossRef]

Appl. Phys. Lett. (2)

E. R. Brown, C. D. Parker, and O. B. McMahon, “Effect of surface composition on the radiation pattern from a photonicplanar-dipole antenna,” Appl. Phys. Lett. 64, 3345–3347 (1994).
[CrossRef]

E. Ozbay, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2062 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (7)

H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, “Photonic band-gap materials for high-gain printed circuit antennas,” IEEE Trans. Antennas Propag. AP-45, 181–183 (1997).

O. M. Bucci and G. Franceschetti, “Scattering from wedge-tapered absorbers,” IEEE Trans. Antennas Propag. AP-19, 96–104 (1971).
[CrossRef]

C. F. Yang, W. D. Burnside, and R. C. Rudduck, “A doubly periodic moment method solution for the analysis and designof an absorber covered wall,” IEEE Trans. Antennas Propag. AP-41, 600–609 (1993).
[CrossRef]

W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domainfinite difference method,” IEEE Trans. Antennas Propag. AP-44, 798–805 (1996).

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

H. Y. D. Yang, “A spectral recursive transformation method for electromagnetic fieldsin generalized anisotropic layered media,” IEEE Trans. Antennas Propag. AP-45, 520–527 (1997).
[CrossRef]

J. L. Tsalamengas and N. K. Uzunoglu, “Radiation from a dipole in the proximity of a general anisotropic groundedlayer,” IEEE Trans. Antennas Propag. AP-33, 165–172 (1985).
[CrossRef]

IEEE Trans. Electromagn. Compat. (2)

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. I: Theory,” IEEE Trans. Electromagn. Compat. 36, 300–306 (1994).
[CrossRef]

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber arrays. II: Computedand measured results,” IEEE Trans. Electromagn. Compat. 36, 307–312 (1994).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

H. Y. D. Yang, “Characteristics of guided and leaky waves on a thin-film structurewith planar material gratings,” IEEE Trans. Microwave Theory Tech. 45, 428–435 (1997).
[CrossRef]

S. T. Peng, T. Tamir, and H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

H-Y. Yang, J. A. Castaneda, and N. G. Alexopoulos, “Surface wave modes of printed circuit on ferrite substrates,” IEEE Trans. Microwave Theory Tech. MTT-40, 613–621 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Techn. (1)

E. F. Kuester and C. L. Holloway, “Comparison of approximations for effective parameters of artificialdielectric,” IEEE Trans. Microwave Theory Techn. 38, 1752–1755 (1990).
[CrossRef]

J. Mod. Opt. (1)

P. L. Knight, ed., Special issue on photonic band structures, J. Mod. Opt. 41, 171–395 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., Special issue on development and applications of materialsexhibiting photonic band gaps, J. Opt. Soc. Am. B 10, 279–413 (1993).

E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
[CrossRef]

Opt. Commun. (1)

K. Sakuda and A. Yariv, “Analysis of optical propagation in a corrugated dielectric waveguide,” Opt. Commun. 8, 1–4 (1973).
[CrossRef]

Proc. IEEE (1)

R. J. Mittra, C. H. Chan, and T. A. Cwik, “Techniques for analyzing frequency selective surfaces–a review,” Proc. IEEE 76, 1593–1614 (1988).
[CrossRef]

Other (6)

R. E. Collin, Field Theory of Guided Waves (IEEE, New York, 1991), p. 605.

W. C. Chew, Waves and Fields in InhomogeneousMedia (IEEE, New York, 1994), Chap. 2.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).

M. C. Hutley, Diffraction Gratings (Academic, San Diego, Calif., 1982).

M. P. Kesler, J. G. Maloney, and B. L. Shirley, “Antennadesign with the use of photonic band-gap materials as all-dielectric planarreflectors,” Microwave Opt. Technol. Lett. 11, (1996).

Phraxos R&D, Inc., “A hollow-metal-dielectric-waveguidereflectometer,” Technical Brief (Phraxos R&D Inc., Santa Monica, Calif., 1995).

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Figures (13)

Fig. 1
Fig. 1

Geometry of infinite planar arrays of material blocks in a multilayer structure.

Fig. 2
Fig. 2

Unit cell of two-dimensional periodic material blocks within layered media.

Fig. 3
Fig. 3

Reflection from a three-layer dielectric structure with planar material gratings. A TM wave with incident angles θ =45° and ϕ=30°.

Fig. 4
Fig. 4

Reflection from a three-layer dielectric structure with planar magnetodielectric gratings. TM incidence with angles θ=30° and ϕ=60°. Implants r=2 and μr=4.

Fig. 5
Fig. 5

Photograph of machined planar periodic blocks on a Teflon layer.

Fig. 6
Fig. 6

Normally incident plane-wave reflection from a Teflon (r=2) layer with planar periodic blocks.

Fig. 7
Fig. 7

Normally incident plane-wave transmission through a Teflon (r=2) layer with planar periodic blocks.

Fig. 8
Fig. 8

Specular reflection of a TM plane wave from a dielectric slab (r=4) with planar material blocks (r=10). a=b =2 cm, L=W=1 cm, h=T=0.2 cm.

Fig. 9
Fig. 9

Specular transmission of a TM plane wave from a dielectric slab (r=4) with planar material blocks (r=10). a =b=2 cm, L=W=1 cm, and h=T=0.2 cm.

Fig. 10
Fig. 10

Transmission of a normally incident plane wave from a three-layer dielectric structure with planar magneto dielectric blocks (r=10 and μr=4).

Fig. 11
Fig. 11

Power coefficients for a dielectric slab (r=3.5) with infinite planar arrays of embedded lossy dielectric blocks (r =20 and conductivity 4 1/Ωm). a=b=2 cm, L=W =1 cm, h=0.2 cm, Δ=0.15 cm, and T=0.05 cm.

Fig. 12
Fig. 12

Field transmission coefficient for a dielectric slab (r =3.5) with infinite planar arrays of embedded lossy dielectric blocks 1=3.5, a=b=2 cm, L=W=1 cm, h=0.2 cm, Δ =0.15 cm, and T=0.05 cm. Normal incidence θi=ϕi=0.

Fig. 13
Fig. 13

δ current source in a three-layer structure. The geometry is for Green's function derivation.

Tables (2)

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Table 1 Convergence Check for Case I: TM Wave

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Table 2 Convergence Check for Case I: TE Wave

Equations (38)

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×E=-jωμ0(μe-μ2)ζ(r)H-jωμ2μ0H,
×H=jω0(e-2)ζ(r)E+jω20E.
Jm=jωμ0(μe-μ2)ζ(r)H,
Je=jω0(e-2)ζ(r)E.
E=v[G]·Jedv+v[Z]·Jmdv,
H=v[Y]·Jedv+v[R]·Jmdv,
[G]=GxxGxyGxzGyxGyyGyzGzxGzyGzz.
Uuv(x, x, y, y)
=1abm=-n=-U˜uv(kx, ky)exp[-jkx(x-x)-jky(y-y)],
kx=2mπa+k0 sin θi cos ϕi,
ky=2mπb+k0 sin θi sin ϕi,
E=mx=1Mxmy=1Mymz=1MzAmxmymzf(mx, my, mz),
H=mx=1Mxmy=1Mymz=1MzBmxmymzf(mx, my, mz),
Vi+Ai=jm=-n=-[g]ijmn[Aj(e-2)]+jm=-n=-[z]ijmn·Bj(μe-μ2),
Ii+Bi=jm=-n=-[y]ijmn[Aj(e-2)]+jm=-n=-[r]ijmn·Bj(μe-μ2),
[g]ijmn=jω0abΔz2Qijmnzj-Δz/2zj+Δz/2zi-Δz/2zi+Δz/2×[G˜(kx, ky, z, z)]dzdz,
[y]ijmn=jω0abΔz2Qijmnzj-Δz/2zj+Δz/2zi-Δz/2zi+Δz/2×[Y˜(kx, ky, z, z)]dzdz,
[z]ijmn=jωμ0abΔz2Qijmnzj-Δz/2zj+Δz/2zi-Δz/2zi+Δz/2×[Z˜(kx, ky, z, z)]dzdz,
[r]ijmn=jωμ0abΔz2Qijmnzj-Δz/2zj+Δz/2zi-Δz/2zi+Δz/2×[R˜(kx, ky, z, z)]dzdz,
Qijmn=exp[-jkx(xi-xj)]exp[-jky(yi-yj)]×sin2(kxΔx/2)(kxΔx/2)2sin2(kyΔy/2)(kyΔy/2)2.
Vi=Einf(mx, my, mz)dv,
Ii=Hinf(mx, my, mz)dv.
[Ψ(z)]=kxH˜x+kyH˜ykyH˜x-kxH˜ykxE˜x+kyE˜ykyE˜x-kxE˜y.
[Ψ(z)]=q0A˜-jω0B˜q0B˜jωμ0A˜exp[-q0(z-h3)],zh3,
[Ψ(z)]=-q4C˜-jω0D˜-q4D˜jωμ0C˜exp(q4z),z0,
[Ψ(z=0)]=C˜D˜00
[Ψ(z)]=[Ti(z-z0)][Ψ(z0)],
[Ti(z)]
=cosh qiz00τ1 sinh qiz0cosh qizτ2 sinh qiz001τ2sinh qizcosh qiz01τ1sinh qiz00cosh qiz,
[T2(z-h2)][T1(h2-h3)][Ψ(h3)]
-[T2(z-h1)][T3(h1)][Ψ(0)]=[J˜].
[J˜]=-kykx00,kxky00,00k2ω020,
[T1(h2-h3)][Ψ(h3)]-[T2(h2-h1)][T3(h1)][Ψ(0)]
=[T2(h2-z)][J˜],
[Ψ(z)]=[T2(z-h1)][T3(h1)][Ψ(0)].
[T2(h1-h2)][T1(h2-h3)][Ψ(h3)]-[T3(h1)][Ψ(0)]
=[T2(h1-z)][J˜],
[Ψ(z)]=[T2(z-h2)][T1(h2-h3)][Ψ(h3)].

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