Abstract

Comparisons of experiment and theory are presented for transmission spectra over the range 2–15 µm of a set of frequency-selective surfaces consisting of arrays of simple dipole patches of aluminum on or in silicon. The arrays are fabricated by direct-write electron-beam lithography. Important parameters controlling the spectral shape are identified, such as dipole length, spacing, resistance, and dielectric surroundings. The separate influence of these variables is exhibited. Encouraging agreement between simple model calculations and the measurements is found.

© 2001 Optical Society of America

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  1. R. Mittra, C. H. Chan, T. Cwik, “Techniques for analyzing frequency selective surfaces—a review,” IEEE Proc. 76, 1593–1615 (1988).
    [CrossRef]
  2. J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies Press Ltd., Taunton, UK, 1997).
  3. T. K. Wu, Frequency Selective Surface and Grid Array (Wiley, New York, 1995).
  4. F. O’Nians, J. Matson, “Antenna feed system utilizing polarization independent frequency selective intermediate reflector,” U.S. patent3,231,892 (25January1966).
  5. B. A. Munk, R. J. Luebbers, R. D. Fulton, “Transmission through a two-layer array of loaded slots,” IEEE Trans. Antennas Propag. AP-22, 804–807 (1974).
  6. R. Pous, D. M. Pozar, “FSS using aperture coupled microstrip patches,” Electron. Lett. 25, 1136–1138 (1989).
    [CrossRef]
  7. P. Vogel, L. Genzel, “Transmission and reflection of metallic mesh in the far infrared,” Infrared Phys. 4, 257–262 (1964).
    [CrossRef]
  8. P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
    [CrossRef]
  9. A. Mitsuishi, Y. Otsuka, S. Fujita, H. Yoshinaga, “Metal mesh filters in the far infrared region,” Jpn. J. Appl. Phys. 9, 574–577 (1963).
    [CrossRef]
  10. G. D. Holah, S. D. Smith, “Far-infrared interference filters,” J. Phys. E 10, 101–111 (1977).
    [CrossRef]
  11. A. E. Costley, K. H. Hursey, G. F. Neill, J. W. M. Ward, “Free-standing fine-wire grids: their manufacture, performance, and use at millimeter and submillimeter wavelengths,” J. Opt. Soc. Am. 67, 979–982 (1977).
    [CrossRef]
  12. C. L. Mok, W. G. Champers, T. J. Parker, A. E. Costley, “Far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979).
    [CrossRef]
  13. R. Ulrich, T. J. Bridges, M. A. Pollack, “Variable metal mesh coupler for far infrared lasers,” Appl. Opt. 9, 2511–2516 (1970).
    [CrossRef] [PubMed]
  14. R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363–367 (1963).
    [CrossRef]
  15. V. Ya. Balakhanov, “Multiray radiointerferometer for plasma diagnostics,” Sov. Phys. Tech. Phys. 10, 96–99 (1965).
  16. T. Schimert, M. E. Koch, C. H. Chan, “Analysis of scattering from frequency-selective surfaces in the infrared,” J. Opt. Soc. Am. A 7, 1545–1553 (1990).
    [CrossRef]
  17. T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surfaces,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
    [CrossRef]
  18. S. T. Chase, R. D. Joseph, “Resonant array bandpass filters for the far infrared,” Appl. Opt. 22, 1775–1779 (1983).
    [CrossRef] [PubMed]
  19. J. A. Reed, D. M. Byrne, “Using periodicity to control spectral characteristics of an array of narrow slots,” IEEE Antennas Propag. Soc. AP-S Int. Symp. 4, 2376–2379 (1997).
  20. I. Puscasu, D. Spencer, G. D. Boreman, “Refractive-index and element-spacing effects on the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 39, 1570–1574 (2000).
    [CrossRef]
  21. T. Hirata, “Evolution of the infra-red vibrational modes upon thermal oxidation of Si single crystals,” J. Phys. Chem. Solids 58, 1497–1501 (1997).
    [CrossRef]
  22. W. Kaiser, P. H. Keck, C. F. Lange, “Infrared absorption and oxygen content in silicon and germanium,” Phys. Rev. 101, 1264–1268 (1956).
    [CrossRef]
  23. M. K. Gunde, B. Aleksandrov, “Infrared optical constants and roughness factor functions determination: the HTHRTR method,” Appl. Opt. 30, 3186–3196 (1991).
    [CrossRef] [PubMed]
  24. J. I. Pankove, Optical Processes in Semiconductors (Dover, New York, 1975).
  25. W. L. Wolfe, G. J. Zissis, The Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1978), pp. 5–92.
  26. W. L. Schaich is preparing a manuscript to be called “On the theory of frequency selective surfaces.”
  27. J. Van Bladel, Singular Electromagnetic Fields and Sources (Oxford University, Oxford, UK, 1991).
  28. R. F. Harrington, Field Computation by Moment Methods, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, New York, 1992).
  29. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
  30. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22, 1099–1119 (1983).
    [CrossRef] [PubMed]
  31. R. W. Wood, “Anomalous diffractive gratings,” Phys. Rev. 48, 928–936 (1935).
    [CrossRef]
  32. R. H. Ott, R. G. Kouyoujian, L. Peters, “Scattering by a two-dimensional periodic array of narrow plates,” Radio Sci. 2, 1347–1359 (1967).
  33. C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
    [CrossRef]
  34. We have not observed a structure attributable to a “λ” resonance. Such a resonance is not favorably excited by light at normal incidence.
  35. R. J. Luebbers, B. A. Munk, “Some effects of dielectric loading on periodic slot arrays,” IEEE Trans. Antennas Propag. AP-26, 536–542 (1978).
    [CrossRef]
  36. P. Callaghan, E. A. Parker, R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. Part H 138, 448–454 (1991).

2000 (2)

I. Puscasu, D. Spencer, G. D. Boreman, “Refractive-index and element-spacing effects on the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 39, 1570–1574 (2000).
[CrossRef]

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

1997 (2)

J. A. Reed, D. M. Byrne, “Using periodicity to control spectral characteristics of an array of narrow slots,” IEEE Antennas Propag. Soc. AP-S Int. Symp. 4, 2376–2379 (1997).

T. Hirata, “Evolution of the infra-red vibrational modes upon thermal oxidation of Si single crystals,” J. Phys. Chem. Solids 58, 1497–1501 (1997).
[CrossRef]

1991 (3)

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surfaces,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

M. K. Gunde, B. Aleksandrov, “Infrared optical constants and roughness factor functions determination: the HTHRTR method,” Appl. Opt. 30, 3186–3196 (1991).
[CrossRef] [PubMed]

P. Callaghan, E. A. Parker, R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. Part H 138, 448–454 (1991).

1990 (1)

1989 (1)

R. Pous, D. M. Pozar, “FSS using aperture coupled microstrip patches,” Electron. Lett. 25, 1136–1138 (1989).
[CrossRef]

1988 (1)

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

1983 (2)

1979 (2)

C. L. Mok, W. G. Champers, T. J. Parker, A. E. Costley, “Far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979).
[CrossRef]

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

1978 (1)

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

1977 (2)

1974 (1)

B. A. Munk, R. J. Luebbers, R. D. Fulton, “Transmission through a two-layer array of loaded slots,” IEEE Trans. Antennas Propag. AP-22, 804–807 (1974).

1970 (1)

1967 (1)

R. H. Ott, R. G. Kouyoujian, L. Peters, “Scattering by a two-dimensional periodic array of narrow plates,” Radio Sci. 2, 1347–1359 (1967).

1965 (1)

V. Ya. Balakhanov, “Multiray radiointerferometer for plasma diagnostics,” Sov. Phys. Tech. Phys. 10, 96–99 (1965).

1964 (1)

P. Vogel, L. Genzel, “Transmission and reflection of metallic mesh in the far infrared,” Infrared Phys. 4, 257–262 (1964).
[CrossRef]

1963 (2)

A. Mitsuishi, Y. Otsuka, S. Fujita, H. Yoshinaga, “Metal mesh filters in the far infrared region,” Jpn. J. Appl. Phys. 9, 574–577 (1963).
[CrossRef]

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363–367 (1963).
[CrossRef]

1956 (1)

W. Kaiser, P. H. Keck, C. F. Lange, “Infrared absorption and oxygen content in silicon and germanium,” Phys. Rev. 101, 1264–1268 (1956).
[CrossRef]

1935 (1)

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

Ade, P. A. R.

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

Aleksandrov, B.

Alexander, R. W.

Balakhanov, V. Ya.

V. Ya. Balakhanov, “Multiray radiointerferometer for plasma diagnostics,” Sov. Phys. Tech. Phys. 10, 96–99 (1965).

Bell, R. J.

Bell, R. R.

Bell, S. E.

Boreman, G. D.

I. Puscasu, D. Spencer, G. D. Boreman, “Refractive-index and element-spacing effects on the spectral behavior of infrared frequency-selective surfaces,” Appl. Opt. 39, 1570–1574 (2000).
[CrossRef]

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

Bridges, T. J.

Brouns, A. J.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surfaces,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

Byrne, D. M.

J. A. Reed, D. M. Byrne, “Using periodicity to control spectral characteristics of an array of narrow slots,” IEEE Antennas Propag. Soc. AP-S Int. Symp. 4, 2376–2379 (1997).

Callaghan, P.

P. Callaghan, E. A. Parker, R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. Part H 138, 448–454 (1991).

Champers, W. G.

C. L. Mok, W. G. Champers, T. J. Parker, A. E. Costley, “Far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979).
[CrossRef]

Chan, C. H.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surfaces,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

T. Schimert, M. E. Koch, C. H. Chan, “Analysis of scattering from frequency-selective surfaces in the infrared,” J. Opt. Soc. Am. A 7, 1545–1553 (1990).
[CrossRef]

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

Chase, S. T.

Codreanu, I.

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

Costley, A. E.

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

C. L. Mok, W. G. Champers, T. J. Parker, A. E. Costley, “Far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979).
[CrossRef]

A. E. Costley, K. H. Hursey, G. F. Neill, J. W. M. Ward, “Free-standing fine-wire grids: their manufacture, performance, and use at millimeter and submillimeter wavelengths,” J. Opt. Soc. Am. 67, 979–982 (1977).
[CrossRef]

Cunningham, C. T.

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

Cwik, T.

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

Fujita, S.

A. Mitsuishi, Y. Otsuka, S. Fujita, H. Yoshinaga, “Metal mesh filters in the far infrared region,” Jpn. J. Appl. Phys. 9, 574–577 (1963).
[CrossRef]

Fulton, R. D.

B. A. Munk, R. J. Luebbers, R. D. Fulton, “Transmission through a two-layer array of loaded slots,” IEEE Trans. Antennas Propag. AP-22, 804–807 (1974).

Fumeaux, C.

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

Genzel, L.

P. Vogel, L. Genzel, “Transmission and reflection of metallic mesh in the far infrared,” Infrared Phys. 4, 257–262 (1964).
[CrossRef]

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363–367 (1963).
[CrossRef]

Gonzalez, J.

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

Gritz, M.

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

Gunde, M. K.

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, New York, 1992).

Hirata, T.

T. Hirata, “Evolution of the infra-red vibrational modes upon thermal oxidation of Si single crystals,” J. Phys. Chem. Solids 58, 1497–1501 (1997).
[CrossRef]

Holah, G. D.

G. D. Holah, S. D. Smith, “Far-infrared interference filters,” J. Phys. E 10, 101–111 (1977).
[CrossRef]

Hursey, K. H.

Joseph, R. D.

Kaiser, W.

W. Kaiser, P. H. Keck, C. F. Lange, “Infrared absorption and oxygen content in silicon and germanium,” Phys. Rev. 101, 1264–1268 (1956).
[CrossRef]

Keck, P. H.

W. Kaiser, P. H. Keck, C. F. Lange, “Infrared absorption and oxygen content in silicon and germanium,” Phys. Rev. 101, 1264–1268 (1956).
[CrossRef]

Koch, M. E.

Kouyoujian, R. G.

R. H. Ott, R. G. Kouyoujian, L. Peters, “Scattering by a two-dimensional periodic array of narrow plates,” Radio Sci. 2, 1347–1359 (1967).

Lange, C. F.

W. Kaiser, P. H. Keck, C. F. Lange, “Infrared absorption and oxygen content in silicon and germanium,” Phys. Rev. 101, 1264–1268 (1956).
[CrossRef]

Langley, R. J.

P. Callaghan, E. A. Parker, R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. Part H 138, 448–454 (1991).

Long, L. L.

Luebbers, R. J.

R. J. Luebbers, 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, R. D. Fulton, “Transmission through a two-layer array of loaded slots,” IEEE Trans. Antennas Propag. AP-22, 804–807 (1974).

Matson, J.

F. O’Nians, J. Matson, “Antenna feed system utilizing polarization independent frequency selective intermediate reflector,” U.S. patent3,231,892 (25January1966).

Mitsuishi, A.

A. Mitsuishi, Y. Otsuka, S. Fujita, H. Yoshinaga, “Metal mesh filters in the far infrared region,” Jpn. J. Appl. Phys. 9, 574–577 (1963).
[CrossRef]

Mittra, R.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surfaces,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

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

Mok, C. L.

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

C. L. Mok, W. G. Champers, T. J. Parker, A. E. Costley, “Far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979).
[CrossRef]

Munk, B. A.

R. J. Luebbers, 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, R. D. Fulton, “Transmission through a two-layer array of loaded slots,” IEEE Trans. Antennas Propag. AP-22, 804–807 (1974).

Neill, G. F.

Neill, G. L.

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

O’Nians, F.

F. O’Nians, J. Matson, “Antenna feed system utilizing polarization independent frequency selective intermediate reflector,” U.S. patent3,231,892 (25January1966).

Ordal, M. A.

Otsuka, Y.

A. Mitsuishi, Y. Otsuka, S. Fujita, H. Yoshinaga, “Metal mesh filters in the far infrared region,” Jpn. J. Appl. Phys. 9, 574–577 (1963).
[CrossRef]

Ott, R. H.

R. H. Ott, R. G. Kouyoujian, L. Peters, “Scattering by a two-dimensional periodic array of narrow plates,” Radio Sci. 2, 1347–1359 (1967).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

Pankove, J. I.

J. I. Pankove, Optical Processes in Semiconductors (Dover, New York, 1975).

Parker, E. A.

P. Callaghan, E. A. Parker, R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. Part H 138, 448–454 (1991).

Parker, T. J.

C. L. Mok, W. G. Champers, T. J. Parker, A. E. Costley, “Far-infrared performance and application of free-standing grids wound from 5µm diameter tungsten wire,” Infrared Phys. 19, 437–442 (1979).
[CrossRef]

P. A. R. Ade, A. E. Costley, C. T. Cunningham, C. L. Mok, G. L. Neill, T. J. Parker, “Free-standing grids wound 5 µm diameter wire for spectroscopy at far-infrared wavelengths,” Infrared Phys. 19, 599–601 (1979).
[CrossRef]

Peters, L.

R. H. Ott, R. G. Kouyoujian, L. Peters, “Scattering by a two-dimensional periodic array of narrow plates,” Radio Sci. 2, 1347–1359 (1967).

Pollack, M. A.

Pous, R.

R. Pous, D. M. Pozar, “FSS using aperture coupled microstrip patches,” Electron. Lett. 25, 1136–1138 (1989).
[CrossRef]

Pozar, D. M.

R. Pous, D. M. Pozar, “FSS using aperture coupled microstrip patches,” Electron. Lett. 25, 1136–1138 (1989).
[CrossRef]

Puscasu, I.

Reed, J. A.

J. A. Reed, D. M. Byrne, “Using periodicity to control spectral characteristics of an array of narrow slots,” IEEE Antennas Propag. Soc. AP-S Int. Symp. 4, 2376–2379 (1997).

Renk, K. F.

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363–367 (1963).
[CrossRef]

Schaich, W. L.

C. Fumeaux, M. Gritz, I. Codreanu, W. L. Schaich, J. Gonzalez, G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Phys. 41, 271–281 (2000).
[CrossRef]

W. L. Schaich is preparing a manuscript to be called “On the theory of frequency selective surfaces.”

Schimert, T.

Schimert, T. R.

T. R. Schimert, A. J. Brouns, C. H. Chan, R. Mittra, “Investigation of millimeter-wave scattering from frequency selective surfaces,” IEEE Trans. Microwave Theory Tech. 39, 315–322 (1991).
[CrossRef]

Smith, S. D.

G. D. Holah, S. D. Smith, “Far-infrared interference filters,” J. Phys. E 10, 101–111 (1977).
[CrossRef]

Spencer, D.

Ulrich, R.

R. Ulrich, T. J. Bridges, M. A. Pollack, “Variable metal mesh coupler for far infrared lasers,” Appl. Opt. 9, 2511–2516 (1970).
[CrossRef] [PubMed]

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry–Perot type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363–367 (1963).
[CrossRef]

Van Bladel, J.

J. Van Bladel, Singular Electromagnetic Fields and Sources (Oxford University, Oxford, UK, 1991).

Vardaxoglou, J. C.

J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies Press Ltd., Taunton, UK, 1997).

Vogel, P.

P. Vogel, L. Genzel, “Transmission and reflection of metallic mesh in the far infrared,” Infrared Phys. 4, 257–262 (1964).
[CrossRef]

Ward, C. A.

Ward, J. W. M.

Wolfe, W. L.

W. L. Wolfe, G. J. Zissis, The Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1978), pp. 5–92.

Wood, R. W.

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

Wu, T. K.

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

Yoshinaga, H.

A. Mitsuishi, Y. Otsuka, S. Fujita, H. Yoshinaga, “Metal mesh filters in the far infrared region,” Jpn. J. Appl. Phys. 9, 574–577 (1963).
[CrossRef]

Zissis, G. J.

W. L. Wolfe, G. J. Zissis, The Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1978), pp. 5–92.

Appl. Opt. (5)

Electron. Lett. (1)

R. Pous, D. M. Pozar, “FSS using aperture coupled microstrip patches,” Electron. Lett. 25, 1136–1138 (1989).
[CrossRef]

IEE Proc. Part H (1)

P. Callaghan, E. A. Parker, R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. Part H 138, 448–454 (1991).

IEEE Antennas Propag. Soc. AP-S Int. Symp. (1)

J. A. Reed, D. M. Byrne, “Using periodicity to control spectral characteristics of an array of narrow slots,” IEEE Antennas Propag. Soc. AP-S Int. Symp. 4, 2376–2379 (1997).

IEEE Proc. (1)

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

IEEE Trans. Antennas Propag. (2)

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We have not observed a structure attributable to a “λ” resonance. Such a resonance is not favorably excited by light at normal incidence.

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Figures (8)

Fig. 1
Fig. 1

Scanning electron micrograph of a patch array.

Fig. 2
Fig. 2

Transmission through both a bare Si substrate and a substrate covered with a dipole array with w y = 0.8 µm, w z = 0.1 µm, D z = 0.3 µm, and D y = 0.6 µm. The ratio of these two measurements is the quantity that will be compared with theory.

Fig. 3
Fig. 3

Computed spectra of the relative transmission, T/ T o , versus vacuum wavelength λ. For the solid curves the patch array has w y = 0.8 µm, w z = 0.1 µm, D y = 0.3 µm, and D z = 0.6 µm; whereas for the dashed curves D y is increased to 1.0 µm. The two thick curves (with the lowest values of T/T o at its minimum) in part (a) treat the patches as perfect electrical conductors. For the remaining curves in part (a), R 0 of Eq. (2) is successively 1, 3, 5 Ω/sq with R 1 = 0, which smoothly weakens and broadens the main minimum. For part (b), R 0 is fixed at 4 Ω/sq and R 1 is varied through 1, 3, 5 Ω/sq, which smoothly shifts the dipole resonance to a longer wavelength. The two thick curves in part (b) have (R 0, R 1) = (4, 3) Ω/sq, the values used for all the plots in Figs. 47 below.

Fig. 4
Fig. 4

Comparison of measured and calculated spectra of the relative transmission, T/ T o, versus vacuum wavelength λ. The conducting patches all have w y = 0.8 µm, w z = 0.1 µm, and D z = 0.6 µm. Different values of D y label the different curves. The experimental or theoretical curves are shown in part (a) or (b), respectively.

Fig. 5
Fig. 5

Same as Fig. 4 except here D y = 1 µm and different values of D z label the different curves.

Fig. 6
Fig. 6

Same as Fig. 4 except here d y = w y + D y = 2 µm and different values of w y label the curves.

Fig. 7
Fig. 7

Same as Fig. 4 except here D z = 0.3 µm and D y = 0.6 µm for solid curves or D y = 1 µm for dashed curves. The results are seen to change considerably when an overlayer is added.

Fig. 8
Fig. 8

Comparison of measured and calculated spectra of the relative transmission, T/ T o , versus vacuum wavelength λ. The experimental data are from Ref. 20. See text for input theoretical parameters. The results with w y ≅ 0.8 µm (1.6 µm) have a dipole resonance near λ = 5 µm (9 µm). For the solid (dashed) curves the number of patches in a unit cell is one (two).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Jy(y, z)=jdj cos(2j+1)π2y˜θ(1-|y˜|)θ(1-|z˜|),
R=R0-i(λ1/λ)R1,
λj,k=nj2dy2+k2dz21/2,
λr=2.1wy1+wy/2wz

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