Abstract

We theoretically and experimentally investigate the response, in the visible and in the near infrared, of micrometer- and submicrometer-period lamellar metal transmission gratings in vacuum and on silica and GaAs substrates. We use a coupled-wave analysis to characterize the grating response as a function of wavelength, period, grating profile, and dielectric constant of the metal and the substrate. Losses to the metal, which have been neglected in prior studies, are shown to be as large as 80% of the incident optical power. Absorption in the metal and the substrate, associated with complex refractive indices, leads to a broadening and a reduction in amplitude of Rayleigh wavelength resonance features in the transmission efficiency and reduces the extinction between orthogonal polarizations in the wire-grid polarizer limit. The results of transmission and photocurrent studies performed on metal–semiconductor–metal photodiodes fabricated on GaAs or GaAs–AlGaAs heterostructure substrates demonstrate the rigorous nature of the coupled-wave analysis, indicate experimental limitations for the application of an infinite grating approximation to model finite-period structures, and provide evidence for the presence of surface electromagnetic waves in the forward-diffracted optical intensity distribution. Qualitative agreement is also obtained between coupled-wave analysis results and transmission data reported in the literature for gold gratings on silica.

© 1995 Optical Society of America

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  1. H. Hertz, Electric Waves (Macmillan, London, 1893), p. 177.
  2. H. duBois, H. Rubens, “Polarization of long-wave heat rays by means of a wire grating,” Ann. Physik 35, 243–276 (1911).
  3. J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
    [CrossRef]
  4. J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
    [CrossRef]
  5. N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).
  6. E. Chen, S. Y. Chou, “Transmissive polarization effects in sub-wavelength thin metal films,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CTuK35.
  7. G. R. Bird, M. Parrish, “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. 50, 886–891 (1960).
    [CrossRef]
  8. See, e.g., H. Lamb, “On the reflection and transmission of electric waves by a metallic grating,” Proc. London Math. Soc. 29, 523–544 (1898),or G. L. Baldwin, A. E. Heins, “On the diffraction of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118 (1954).
  9. W. V. Ignatowsky, “Theory of the grating,” Ann. Physik 44, 369–436 (1914).
  10. W. K. Pursley, “The transmission of electromagnetic waves through wire diffraction gratings,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1956).
  11. E. A. Lewis, J. P. Casey, “Electromagnetic reflection and transmission by gratings of resistive wires,” J. Appl. Phys. 23, 605–608 (1952).
    [CrossRef]
  12. J. Pavageau, J. Bousquet, “Diffraction by a conducting grating and calculation of resolution,” Opt. Acta 17, 469–478 (1970).
    [CrossRef]
  13. M. Nevière, M. Cadilhac, “A new formation of the problem of diffraction of a plane wave by an infinitely conducting grating—general case,” Opt. Commun. 3, 379–383 (1971).
  14. M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their application to optics,” Nouv. Rev. Opt. 5, 65–77 (1974).
    [CrossRef]
  15. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  16. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
    [CrossRef]
  17. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  18. See, e.g., M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 123–126.
    [CrossRef]
  19. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [CrossRef]
  20. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
    [CrossRef]
  21. M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
    [CrossRef]
  22. For a discussion of eigensystems, see, e.g., H. Anton, Elementary Linear Algebra (Wiley, New York, 1984), Chap. 6, p. 269.
  23. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985), Part II, p. 719.
  24. For a review of the field of MSM-PD’s, see, e.g., J. Kuhl, “Contact-free characterization of electronic and optoelectronic devices with ultrashort laser pulses,” in Ultrashort Processes in Condensed Matter, W. E. Bron, ed., Vol. 314 of NATO Advanced Institutes Science Series B: Physics (Plenum, New York, 1993), pp. 164–185.
    [CrossRef]
  25. S. Y. Chou, Y. Liu, P. B. Fischer, “Tera-hertz metal–semiconductor–metal photodetectors with 25 nm finger spacing and finger width,” Appl. Phys. Lett. 61, 477–479 (1992).
    [CrossRef]
  26. Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
    [CrossRef]
  27. R. Deleuil, “Construction and use of an apparatus intended for the study of irregular dioptres and gratings by millimeter waves,” Opt. Acta 16, 23–25 (1969).
    [CrossRef]
  28. See, e.g., E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 10, p. 427.
  29. R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
    [CrossRef]

1994 (2)

J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
[CrossRef]

J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
[CrossRef]

1993 (1)

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

1992 (2)

S. Y. Chou, Y. Liu, P. B. Fischer, “Tera-hertz metal–semiconductor–metal photodetectors with 25 nm finger spacing and finger width,” Appl. Phys. Lett. 61, 477–479 (1992).
[CrossRef]

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

1987 (1)

1986 (1)

1983 (2)

1981 (1)

1974 (1)

M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their application to optics,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

1971 (1)

M. Nevière, M. Cadilhac, “A new formation of the problem of diffraction of a plane wave by an infinitely conducting grating—general case,” Opt. Commun. 3, 379–383 (1971).

1970 (1)

J. Pavageau, J. Bousquet, “Diffraction by a conducting grating and calculation of resolution,” Opt. Acta 17, 469–478 (1970).
[CrossRef]

1969 (1)

R. Deleuil, “Construction and use of an apparatus intended for the study of irregular dioptres and gratings by millimeter waves,” Opt. Acta 16, 23–25 (1969).
[CrossRef]

1960 (1)

1952 (1)

E. A. Lewis, J. P. Casey, “Electromagnetic reflection and transmission by gratings of resistive wires,” J. Appl. Phys. 23, 605–608 (1952).
[CrossRef]

1935 (1)

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

1914 (1)

W. V. Ignatowsky, “Theory of the grating,” Ann. Physik 44, 369–436 (1914).

1911 (1)

H. duBois, H. Rubens, “Polarization of long-wave heat rays by means of a wire grating,” Ann. Physik 35, 243–276 (1911).

1898 (1)

See, e.g., H. Lamb, “On the reflection and transmission of electric waves by a metallic grating,” Proc. London Math. Soc. 29, 523–544 (1898),or G. L. Baldwin, A. E. Heins, “On the diffraction of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118 (1954).

Adams, J. A.

J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
[CrossRef]

Allam, J.

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

Anton, H.

For a discussion of eigensystems, see, e.g., H. Anton, Elementary Linear Algebra (Wiley, New York, 1984), Chap. 6, p. 269.

Baynes, N.

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

Bird, G. R.

Boker, J.

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

Bousquet, J.

J. Pavageau, J. Bousquet, “Diffraction by a conducting grating and calculation of resolution,” Opt. Acta 17, 469–478 (1970).
[CrossRef]

Cadilhac, M.

M. Nevière, M. Cadilhac, “A new formation of the problem of diffraction of a plane wave by an infinitely conducting grating—general case,” Opt. Commun. 3, 379–383 (1971).

Casey, J. P.

E. A. Lewis, J. P. Casey, “Electromagnetic reflection and transmission by gratings of resistive wires,” J. Appl. Phys. 23, 605–608 (1952).
[CrossRef]

Chen, E.

E. Chen, S. Y. Chou, “Transmissive polarization effects in sub-wavelength thin metal films,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CTuK35.

Chou, S. Y.

S. Y. Chou, Y. Liu, P. B. Fischer, “Tera-hertz metal–semiconductor–metal photodetectors with 25 nm finger spacing and finger width,” Appl. Phys. Lett. 61, 477–479 (1992).
[CrossRef]

E. Chen, S. Y. Chou, “Transmissive polarization effects in sub-wavelength thin metal films,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CTuK35.

Cleaver, J.

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

Conn, D. R.

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

Deleuil, R.

R. Deleuil, “Construction and use of an apparatus intended for the study of irregular dioptres and gratings by millimeter waves,” Opt. Acta 16, 23–25 (1969).
[CrossRef]

duBois, H.

H. duBois, H. Rubens, “Polarization of long-wave heat rays by means of a wire grating,” Ann. Physik 35, 243–276 (1911).

Falcone, R. W.

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

Feng, Y.

J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
[CrossRef]

Fischer, P. B.

S. Y. Chou, Y. Liu, P. B. Fischer, “Tera-hertz metal–semiconductor–metal photodetectors with 25 nm finger spacing and finger width,” Appl. Phys. Lett. 61, 477–479 (1992).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

Gordon, S. P.

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

Hecht, E.

See, e.g., E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 10, p. 427.

Hertz, H.

H. Hertz, Electric Waves (Macmillan, London, 1893), p. 177.

Ignatowsky, W. V.

W. V. Ignatowsky, “Theory of the grating,” Ann. Physik 44, 369–436 (1914).

Kapteyn, H. C.

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

Kuhl, J.

For a review of the field of MSM-PD’s, see, e.g., J. Kuhl, “Contact-free characterization of electronic and optoelectronic devices with ultrashort laser pulses,” in Ultrashort Processes in Condensed Matter, W. E. Bron, ed., Vol. 314 of NATO Advanced Institutes Science Series B: Physics (Plenum, New York, 1993), pp. 164–185.
[CrossRef]

Kuta, J. J.

J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
[CrossRef]

J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
[CrossRef]

Lamb, H.

See, e.g., H. Lamb, “On the reflection and transmission of electric waves by a metallic grating,” Proc. London Math. Soc. 29, 523–544 (1898),or G. L. Baldwin, A. E. Heins, “On the diffraction of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118 (1954).

Landheer, D.

J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
[CrossRef]

J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
[CrossRef]

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

Lewis, E. A.

E. A. Lewis, J. P. Casey, “Electromagnetic reflection and transmission by gratings of resistive wires,” J. Appl. Phys. 23, 605–608 (1952).
[CrossRef]

Li, Z. M.

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

Liu, Y.

S. Y. Chou, Y. Liu, P. B. Fischer, “Tera-hertz metal–semiconductor–metal photodetectors with 25 nm finger spacing and finger width,” Appl. Phys. Lett. 61, 477–479 (1992).
[CrossRef]

McDonald, R. I.

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

Mishima, T.

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

Moharam, M. G.

Murnane, M. M.

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

Nevière, M.

M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their application to optics,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

M. Nevière, M. Cadilhac, “A new formation of the problem of diffraction of a plane wave by an infinitely conducting grating—general case,” Opt. Commun. 3, 379–383 (1971).

See, e.g., M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 123–126.
[CrossRef]

Ogawa, K.

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

Ohbu, I.

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

Parrish, M.

Pavageau, J.

J. Pavageau, J. Bousquet, “Diffraction by a conducting grating and calculation of resolution,” Opt. Acta 17, 469–478 (1970).
[CrossRef]

Petit, R.

M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their application to optics,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

Pursley, W. K.

W. K. Pursley, “The transmission of electromagnetic waves through wire diffraction gratings,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1956).

Rubens, H.

H. duBois, H. Rubens, “Polarization of long-wave heat rays by means of a wire grating,” Ann. Physik 35, 243–276 (1911).

Sipe, J. E.

Surridge, R.

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

van Driel, H. M.

J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
[CrossRef]

J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
[CrossRef]

Veilleux, M.

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

Vincent, P.

M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their application to optics,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

Wood, R. W.

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

Xu, J. M.

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

Ann. Physik (2)

H. duBois, H. Rubens, “Polarization of long-wave heat rays by means of a wire grating,” Ann. Physik 35, 243–276 (1911).

W. V. Ignatowsky, “Theory of the grating,” Ann. Physik 44, 369–436 (1914).

Appl. Phys. Lett. (4)

J. J. Kuta, H. M. van Driel, D. Landheer, J. A. Adams, “Polarization and wavelength dependence of metal–semiconductor–metal photodetector response,” Appl. Phys. Lett. 64, 140–142 (1994).
[CrossRef]

J. J. Kuta, H. M. van Driel, D. Landheer, Y. Feng, “Polarization dependence of the temporal response of metal–semiconductor–metal photodiodes,” Appl. Phys. Lett. 65, 3146–3148 (1994).
[CrossRef]

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Boker, E. N. Glytsis, R. W. Falcone, “Efficient coupling of high-intensity subpicosecond laser pulses into solids,” Appl. Phys. Lett. 62, 1068–1070 (1993).
[CrossRef]

S. Y. Chou, Y. Liu, P. B. Fischer, “Tera-hertz metal–semiconductor–metal photodetectors with 25 nm finger spacing and finger width,” Appl. Phys. Lett. 61, 477–479 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. M. Li, D. Landheer, M. Veilleux, D. R. Conn, R. Surridge, J. M. Xu, R. I. McDonald, “Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector,” IEEE Photon. Technol. Lett. 4, 473–476 (1992);for the heterostructure substrate used for this study, the growth parameters expressed in the notation of this reference were tch = 195 nm, tbuf = 150 nm, tDBR1 = 67 nm, tDBR2 = 60 nm, x = 1, y = 0.3.
[CrossRef]

J. Appl. Phys. (1)

E. A. Lewis, J. P. Casey, “Electromagnetic reflection and transmission by gratings of resistive wires,” J. Appl. Phys. 23, 605–608 (1952).
[CrossRef]

J. Opt. Soc. Am. (4)

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

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

Nouv. Rev. Opt. (1)

M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their application to optics,” Nouv. Rev. Opt. 5, 65–77 (1974).
[CrossRef]

Opt. Acta (2)

J. Pavageau, J. Bousquet, “Diffraction by a conducting grating and calculation of resolution,” Opt. Acta 17, 469–478 (1970).
[CrossRef]

R. Deleuil, “Construction and use of an apparatus intended for the study of irregular dioptres and gratings by millimeter waves,” Opt. Acta 16, 23–25 (1969).
[CrossRef]

Opt. Commun. (1)

M. Nevière, M. Cadilhac, “A new formation of the problem of diffraction of a plane wave by an infinitely conducting grating—general case,” Opt. Commun. 3, 379–383 (1971).

Phys. Rev. (1)

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

Proc. London Math. Soc. (1)

See, e.g., H. Lamb, “On the reflection and transmission of electric waves by a metallic grating,” Proc. London Math. Soc. 29, 523–544 (1898),or G. L. Baldwin, A. E. Heins, “On the diffraction of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118 (1954).

Other (9)

W. K. Pursley, “The transmission of electromagnetic waves through wire diffraction gratings,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1956).

N. Baynes, J. Allam, J. Cleaver, K. Ogawa, I. Ohbu, T. Mishima, “Scaling characteristics of picosecond interdigitated photodetectors,” in Proceedings of the International Symposium on GaAs and Related Compounds, H. S. Rupprecht, G. Weimann, eds., Institute of Physics Conference Series 136 (Institute of Physics, Bristol, UK, 1994).

E. Chen, S. Y. Chou, “Transmissive polarization effects in sub-wavelength thin metal films,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CTuK35.

H. Hertz, Electric Waves (Macmillan, London, 1893), p. 177.

See, e.g., M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980), pp. 123–126.
[CrossRef]

See, e.g., E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 10, p. 427.

For a discussion of eigensystems, see, e.g., H. Anton, Elementary Linear Algebra (Wiley, New York, 1984), Chap. 6, p. 269.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985), Part II, p. 719.

For a review of the field of MSM-PD’s, see, e.g., J. Kuhl, “Contact-free characterization of electronic and optoelectronic devices with ultrashort laser pulses,” in Ultrashort Processes in Condensed Matter, W. E. Bron, ed., Vol. 314 of NATO Advanced Institutes Science Series B: Physics (Plenum, New York, 1993), pp. 164–185.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Grating geometry used for CWA.

Fig. 2
Fig. 2

CWA results for a lamellar gold grating in vacuum with a/Λ = 0.5, d = 100 nm for λ = 1350 nm (solid curves), and λ = 400 nm (dashed curves). (a) Total forward-diffraction efficiency, (b) absorption losses to gold for E- and H-mode polarizations as a function of Λ/λ.

Fig. 3
Fig. 3

Total forward-diffraction efficiency of E-mode (solid curves) and of H-mode (dashed curves) polarizations as a function of d for λ = 400 nm, a/Λ = 0.5, and (a) Λ = 200 nm, (b) Λ = 400 nm, (c) Λ = 600 nm.

Fig. 4
Fig. 4

Absorption losses for E-mode (solid curves) and H-mode (dashed curves) polarizations as a function of d for the structures discussed in Fig. 3.

Fig. 5
Fig. 5

Total forward-diffraction efficiency of E-mode (solid curves) and H-mode (dashed curves) polarizations as a function of a/Λ for λ = 400 nm, d = 100 nm, and (a) Λ = 200 nm, (b) Λ = 400 nm, (c) Λ = 600 nm.

Fig. 6
Fig. 6

Absorption losses for E-mode (solid curves) and H-mode (dashed curves) polarizations as a function of a/Λ for the structures discussed in Fig. 5.

Fig. 7
Fig. 7

Total forward-diffraction efficiency obtained from CWA of the gold grating discussed in Fig. 2, for λ = 1350 nm (solid curves), and η from a Green-function (GF) analysis of an infinite grating with a/Λ = 0.5, d ≪ λ, and infinite metal conductivity (dashed curves) for E- and H-mode polarizations as a function of Λ/λ.

Fig. 8
Fig. 8

Total forward-diffraction efficiency for a lamellar gold grating on silica with a/Λ = 0.5, d = 100 nm for λ = 1350 nm (solid curves), and λ = 400 nm (dashed curves), with (a) E-mode and (b) H-mode polarizations.

Fig. 9
Fig. 9

Zeroth-order forward-diffraction efficiencies at λ = 633 nm for E-mode (solid curves) and H-mode (dashed curves) polarizations as a function of Λ and experimental transmission efficiencies at λ = 633 nm of a gold lamellar transmission grating on a silica substrate for E-mode (●) and H-mode (+) polarizations. Grating parameters: a/Λ = 0.5, d = 50 nm.

Fig. 10
Fig. 10

Total forward-diffraction efficiency for a lamellar gold grating on GaAs with a/Λ = 0.5, d = 100 nm for λ = 1350 nm (solid curves) and for λ = 400 nm (dashed curves), with (a) E-mode and (b) H-mode polarizations.

Fig. 11
Fig. 11

(a) Electrode pattern of a MSM-PD and (b) cross section of a MSM-PD indicating an incident photon of energy ℏω, electrode bias +/−, and a photogenerated electron–hole pair.

Fig. 12
Fig. 12

CWA zeroth-mode forward-diffraction efficiencies for E-mode (solid curves) and H-mode (dashed curves) polarizations as a function of λ and experimental transmission efficiencies of GaAs MSM-PD’s for λ = 1060, 1319, 1523 nm for E-mode (▲) and H-mode (●) polarizations. CWA grating parameter values: (a) Λ = 400 nm, a = 190 nm, d = 110 nm; (b) Λ = 400 nm, a = 200 nm, d = 70 nm; (c) Λ = 800 nm, a = 420 nm, d = 115 nm.

Fig. 13
Fig. 13

Ratio of E-mode- to H-mode-polarization total forward-diffraction efficiencies obtained by CWA (solid curves) as a function of λ and corresponding ratio of GaAs and GaAs–AlGaAs MSM-PD photocurrent measurements (●) for λ = 543, 634, 805 nm, with CWA parameters of (a) Λ = 800 nm, a = 460 nm, d = 65 nm; (b) Λ = 800 nm, a = 400 nm, d = 110 nm; (c) Λ = 400 nm, a = 200 nm, d = 110 nm. Each dashed line indicates a ratio of unity.

Fig. 14
Fig. 14

Calculated E-mode forward-diffracted optical field intensity for a lamellar gold grating on GaAs as a function of position for a depth less than 50 nm in the substrate. The field values are from a CWA of a grating with Λ = 400 nm, λ = 760 nm, a = 200 nm, d = 110 nm, and normal incidence. The metallization covers 100 < x < 200 nm and 400 < x < 500 nm.

Equations (5)

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2 E + [ E · ( / ) ] + k 2 ( x , z ) E = 0 ,
2 H + ( / ) × × H + k 2 ( x , z ) H = 0 ,
× E = j ω μ 0 H ,
× H = j ω 0 ( x , z ) E .
2 H + [ ( / ) · ] H + k 2 ( x , z ) H = 0 .

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