Abstract

We discuss a method for analyzing frequency-selective surfaces (FSS’s) consisting of an array of multiple apertures or patches per unit periodic cell. Based on the modal method, our method is unique in that the multiple apertures or patches within a unit cell need not be identical in size or shape. Applying our technique to thin perfectly conducting sheets perforated with patterns of varying-length narrow rectangular apertures, we demonstrate a pattern of slot apertures that produces a double-resonance spectral transmission profile.

© 1998 Optical Society of America

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  1. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
    [CrossRef]
  2. C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microwave Theory Tech. MTT-21, 1–6 (1973).
    [CrossRef]
  3. R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
    [CrossRef]
  4. J. P. Montgomery, K. R. Davey, “The solution of planar periodic structures using iterative methods,” Electromagnetics 5, 209–235 (1985).
    [CrossRef]
  5. T. K. Wu, ed., Frequency Selective Surface and Grid Array (Wiley, New York, 1995).
  6. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  7. B. A. Munk, R. J. Luebbers, “Reflection properties of two-layered dipole arrays,” IEEE Trans. Antennas Propag. AP-22, 766–773 (1974).
    [CrossRef]
  8. C. C. Chen, “Transmission through a conducting screen perforated periodically with apertures,” IEEE Trans. Microwave Theory Tech. MTT-18, 627–632 (1970).
    [CrossRef]
  9. N. Amitay, V. Galindo, C. P. Wu, Theory and Analysis of Phased Array Antennas (Wiley-Interscience, New York, 1972), pp. 307–309.
  10. R. Mittra, “Relative convergence of the solution of a doubly infinite set of equations,” J. Res. Nat. Bur. Stand. Sect. D 67D, 245–254 (1963).
  11. C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microwave Theory Tech. MTT-19, 475–481 (1971).
    [CrossRef]
  12. C. C. Chen, “Scattering by a two-dimensional periodic array of conducting plates,” IEEE Trans. Antennas Propag. AP-18, 660–665 (1970).
    [CrossRef]
  13. J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
    [CrossRef]
  14. D. H. Dawes, R. C. McPhedran, L. B. Whitbourn, “Thin capacitive meshes on a dielectric boundary: theory and experiment,” Appl. Opt. 28, 3498–3510 (1989).
    [CrossRef] [PubMed]
  15. S. T. Chase, R. D. Joseph, “Resonant array bandpass filters for the far infrared,” Appl. Opt. 22, 1775–1779 (1983).
    [CrossRef] [PubMed]
  16. R. W. Wood, “On a remarkable case of uneven light in a diffraction grating,” Philos. Mag. 4, 396–402 (1902).
    [CrossRef]
  17. Lord Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
    [CrossRef]
  18. R. W. Wood, “Diffraction gratings with controlled groove form and abnormal distribution of intensity,” Philos. Mag. 23, 310–317 (1912).
    [CrossRef]
  19. R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
    [CrossRef]
  20. A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1296 (1965).
    [CrossRef]
  21. R. J. Leubers, B. A. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. AP-26, 536–542 (1978).
    [CrossRef]
  22. C. H. Palmer, F. W. Phelps, “Grating anomalies as a local phenomenon,” J. Opt. Soc. Am. 58, 1184–1188 (1968).
    [CrossRef]
  23. C. H. Palmer, “Diffraction grating anomalies. II. Coarse gratings,” J. Opt. Soc. Am. 46, 50–53 (1956).
    [CrossRef]
  24. R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
    [CrossRef]

1989

1988

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

1985

J. P. Montgomery, K. R. Davey, “The solution of planar periodic structures using iterative methods,” Electromagnetics 5, 209–235 (1985).
[CrossRef]

1983

S. T. Chase, R. D. Joseph, “Resonant array bandpass filters for the far infrared,” Appl. Opt. 22, 1775–1779 (1983).
[CrossRef] [PubMed]

R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

1978

R. J. Leubers, B. A. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. AP-26, 536–542 (1978).
[CrossRef]

1975

J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
[CrossRef]

1974

B. A. Munk, R. J. Luebbers, “Reflection properties of two-layered dipole arrays,” IEEE Trans. Antennas Propag. AP-22, 766–773 (1974).
[CrossRef]

1973

C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microwave Theory Tech. MTT-21, 1–6 (1973).
[CrossRef]

1971

C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microwave Theory Tech. MTT-19, 475–481 (1971).
[CrossRef]

1970

C. C. Chen, “Scattering by a two-dimensional periodic array of conducting plates,” IEEE Trans. Antennas Propag. AP-18, 660–665 (1970).
[CrossRef]

C. C. Chen, “Transmission through a conducting screen perforated periodically with apertures,” IEEE Trans. Microwave Theory Tech. MTT-18, 627–632 (1970).
[CrossRef]

1968

1967

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

1965

1963

R. Mittra, “Relative convergence of the solution of a doubly infinite set of equations,” J. Res. Nat. Bur. Stand. Sect. D 67D, 245–254 (1963).

1956

1935

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

1912

R. W. Wood, “Diffraction gratings with controlled groove form and abnormal distribution of intensity,” Philos. Mag. 23, 310–317 (1912).
[CrossRef]

1907

Lord Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[CrossRef]

1902

R. W. Wood, “On a remarkable case of uneven light in a diffraction grating,” Philos. Mag. 4, 396–402 (1902).
[CrossRef]

Amitay, N.

N. Amitay, V. Galindo, C. P. Wu, Theory and Analysis of Phased Array Antennas (Wiley-Interscience, New York, 1972), pp. 307–309.

Botten, L. C.

R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Chan, C. H.

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Chase, S. T.

Chen, C. C.

C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microwave Theory Tech. MTT-21, 1–6 (1973).
[CrossRef]

C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microwave Theory Tech. MTT-19, 475–481 (1971).
[CrossRef]

C. C. Chen, “Scattering by a two-dimensional periodic array of conducting plates,” IEEE Trans. Antennas Propag. AP-18, 660–665 (1970).
[CrossRef]

C. C. Chen, “Transmission through a conducting screen perforated periodically with apertures,” IEEE Trans. Microwave Theory Tech. MTT-18, 627–632 (1970).
[CrossRef]

Compton, R. C.

R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Cwik, T.

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Davey, K. R.

J. P. Montgomery, K. R. Davey, “The solution of planar periodic structures using iterative methods,” Electromagnetics 5, 209–235 (1985).
[CrossRef]

Dawes, D. H.

Derrick, G. H.

R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Galindo, V.

N. Amitay, V. Galindo, C. P. Wu, Theory and Analysis of Phased Array Antennas (Wiley-Interscience, New York, 1972), pp. 307–309.

Hessel, A.

Joseph, R. D.

Leubers, R. J.

R. J. Leubers, B. A. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. AP-26, 536–542 (1978).
[CrossRef]

Luebbers, R. J.

B. A. Munk, R. J. Luebbers, “Reflection properties of two-layered dipole arrays,” IEEE Trans. Antennas Propag. AP-22, 766–773 (1974).
[CrossRef]

McPhedran, R. C.

D. H. Dawes, R. C. McPhedran, L. B. Whitbourn, “Thin capacitive meshes on a dielectric boundary: theory and experiment,” Appl. Opt. 28, 3498–3510 (1989).
[CrossRef] [PubMed]

R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Mittra, R.

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

R. Mittra, “Relative convergence of the solution of a doubly infinite set of equations,” J. Res. Nat. Bur. Stand. Sect. D 67D, 245–254 (1963).

Montgomery, J. P.

J. P. Montgomery, K. R. Davey, “The solution of planar periodic structures using iterative methods,” Electromagnetics 5, 209–235 (1985).
[CrossRef]

J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
[CrossRef]

Munk, B. A.

R. J. Leubers, B. A. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. AP-26, 536–542 (1978).
[CrossRef]

B. A. Munk, R. J. Luebbers, “Reflection properties of two-layered dipole arrays,” IEEE Trans. Antennas Propag. AP-22, 766–773 (1974).
[CrossRef]

Oliner, A. A.

Palmer, C. H.

Phelps, F. W.

Rayleigh, Lord

Lord Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[CrossRef]

Ulrich, R.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

Whitbourn, L. B.

Wood, R. W.

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

R. W. Wood, “Diffraction gratings with controlled groove form and abnormal distribution of intensity,” Philos. Mag. 23, 310–317 (1912).
[CrossRef]

R. W. Wood, “On a remarkable case of uneven light in a diffraction grating,” Philos. Mag. 4, 396–402 (1902).
[CrossRef]

Wu, C. P.

N. Amitay, V. Galindo, C. P. Wu, Theory and Analysis of Phased Array Antennas (Wiley-Interscience, New York, 1972), pp. 307–309.

Appl. Opt.

Electromagnetics

J. P. Montgomery, K. R. Davey, “The solution of planar periodic structures using iterative methods,” Electromagnetics 5, 209–235 (1985).
[CrossRef]

IEEE Trans. Antennas Propag.

B. A. Munk, R. J. Luebbers, “Reflection properties of two-layered dipole arrays,” IEEE Trans. Antennas Propag. AP-22, 766–773 (1974).
[CrossRef]

R. J. Leubers, B. A. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. AP-26, 536–542 (1978).
[CrossRef]

C. C. Chen, “Scattering by a two-dimensional periodic array of conducting plates,” IEEE Trans. Antennas Propag. AP-18, 660–665 (1970).
[CrossRef]

J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microwave Theory Tech. MTT-19, 475–481 (1971).
[CrossRef]

C. C. Chen, “Transmission through a conducting screen perforated periodically with apertures,” IEEE Trans. Microwave Theory Tech. MTT-18, 627–632 (1970).
[CrossRef]

C. C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microwave Theory Tech. MTT-21, 1–6 (1973).
[CrossRef]

Infrared Phys.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

R. C. Compton, R. C. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

J. Opt. Soc. Am.

J. Res. Nat. Bur. Stand. Sect. D

R. Mittra, “Relative convergence of the solution of a doubly infinite set of equations,” J. Res. Nat. Bur. Stand. Sect. D 67D, 245–254 (1963).

Philos. Mag.

R. W. Wood, “On a remarkable case of uneven light in a diffraction grating,” Philos. Mag. 4, 396–402 (1902).
[CrossRef]

Lord Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[CrossRef]

R. W. Wood, “Diffraction gratings with controlled groove form and abnormal distribution of intensity,” Philos. Mag. 23, 310–317 (1912).
[CrossRef]

Phys. Rev.

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Proc. IEEE

R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” Proc. IEEE 76, 1593–1615 (1988).
[CrossRef]

Other

T. K. Wu, ed., Frequency Selective Surface and Grid Array (Wiley, New York, 1995).

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

N. Amitay, V. Galindo, C. P. Wu, Theory and Analysis of Phased Array Antennas (Wiley-Interscience, New York, 1972), pp. 307–309.

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Figures (7)

Fig. 1
Fig. 1

Typical geometric configuration for a FSS with multiple apertures within a periodic cell.

Fig. 2
Fig. 2

(a) FSS geometry used as the baseline configuration. (b) Zeroth-order transmission spectral profile for the baseline configuration of (a). In this example dx=dy=6.0 µm, a =5.0 µm, and b=0.5 µm.

Fig. 3
Fig. 3

(a) Geometry used for a FSS consisting of a rectangular array of two different apertures per periodic cell (columns of long slots alternate with columns of short slots). (b) Zeroth-order transmission spectral profiles for (a) with the short slot apertures ranging in length from a2=4.0 µm to a2=5.0 µm (b2 =0.5 µm). The long slot apertures were constant at a1 =5.0 µm and b1=0.5 µm; the periodicity was dx=6.0 µm and dy=12.0 µm.

Fig. 4
Fig. 4

(a) Geometry used for a FSS consisting of a rectangular array of two different apertures per periodic cell (rows of long slots alternate with rows of short slots). (b) Zeroth-order transmission spectral profiles for (a) with the short slot apertures ranging in length from a2=4.0 µm to a2=5.0 µm (b2 =0.5 µm). The long slot apertures were constant at a1 =5.0 µm and b1=0.5 µm; the periodicity was dx=12.0 µm and dy=6.0 µm.

Fig. 5
Fig. 5

(a) Geometry used for a FSS consisting of a triangular array of two different apertures per periodic cell (long slots alternate with short slots). (b) Zeroth-order transmission spectral profiles for (a) with the short slot apertures ranging in length from a2=0.5 µm to a2=3.5 µm (b2=0.5 µm). The long slot apertures were constant at a1=5.0 µm and b1=0.5 µm; the periodicity was dx=12.0 µm, dy=6.0 µm, and α=45°. (c) Zeroth-order transmission spectral profiles for (a) with the short slot apertures ranging in length from a2=3.75 µm to a2 =5.0 µm. All other dimensions are the same as in (b). The dual-resonance nature of the FSS is clearly evident in this figure.

Fig. 6
Fig. 6

(a) FSS with rectangular array of slot apertures. Slot dimensions were 5.0 µm × 0.5 µm with period c=62 µm. (b) FSS with triangular array of slot apertures. Slot dimensions are the same as Fig. 6(a) with period dx=12.0 µm and dy=6.0 µm (α =45°). The nearest-neighbor distance is c=62 µm. (c) FSS with triangular array of two different apertures per periodic cell (alternating slots rotated 90°). Slot dimensions and periodicity are the same as in (b). (d) Zeroth-order transmission spectral profiles for (a)–(c).

Fig. 7
Fig. 7

(a) Typical geometry of a FSS consisting of a triangular array of a single aperture per periodic cell used for baseline comparisons. (b) Zeroth-order transmission spectral profiles for (a). In this example, b=0.5 µm was held constant, and dx =12.0 µm, dy=6.0 µm, and α=45° (resulting in a nearest-neighbor distance of c=62 µm).

Equations (12)

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E¯t=i=1NE¯t(i)=i=1Nl=12mnFmnl(i)Ψ¯mnl(i),
2r=12A00rξ00rΦ¯00r=pqr=12(ξpqr+Ypqr)×Φ¯pqrapertureE¯t·Φ¯pqr*da,
2r=12A00rξ00rC00r(i)mnl*
=pqr=12GpqrCpqr(i)mnl*×j=1Nmnl=12Fmnl(j)Cpqr(j)mnl,
Gpqr=ξpqr+Ypqr,
Cpqr(j)mnl=jth-apertureΨ¯mnlj·Φ¯pqr*da.
2(Iminili(i))=j=1N(Yminili(i, j)mjnjlj)(Fmjnjlj(j)),
2[I]=[Y][F].
Yminili(i, j)mjnjlj=pqr=12Gpqr(Cpqr(i)minili)*Cpqr(j)mjnjlj
Iminili(i)=r=12A00rξ00r(C00r(i)minili)*.
δ0pδ0qApqr+Rpqr=Bpqr=j=1NmjnjljFmjnjlj(j)Cpqr(j)mjnjlj,
λr=2.11+b2LL.

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