Abstract

Experimental results of thermal emittance from deep gratings are presented along with a theoretical discussion. We have found that for a certain grating geometry thermal emission peaks coincide with the cutoff frequencies of slab waveguides. The coincidence was found with s- but not p-polarized emission. This suggests that coupling between grating fins for s-polarized emission is small. It was also found that emission peaks do not correlate directly with the well-known grating equation for these deep gratings.

© 1992 Optical Society of America

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References

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  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  3. M. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal Press, New York, 1980).
  4. R. C. Enger, S. K. Case, “Optical elements with ultra high spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [Crossref] [PubMed]
  5. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [Crossref]
  6. P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
    [Crossref]
  7. P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
    [Crossref]
  8. P. J. Hesketh, “The emittance of heavily doped microconfigured silicon surfaces,” Ph.D. dissertation. (University of Pennsylvania, Philadelphia, Pa., 1986).
  9. P. J. Hesketh, “The emittance of heavily doped microconfigured silicon surfaces,” Ph.D. dissertation. (University of Pennsylvania, Philadelphia, Pa., 1986).
  10. T. K. Wang, “Thermal Radiation from dieletric grating surfaces” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1989).
  11. T. K. Wang, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces: III. Undoped silicon: the normal direction in shallow lamellar gratings,” Infrared Phys. 32, 477–488 (1991).
    [Crossref]
  12. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
    [Crossref]
  13. C. H. Palmer, F. C. Evering, F. M. Nelson, “Diffraction anomalies for gratings of rectangular profile,” Appl. Opt. 4, 1271–1274 (1965).
    [Crossref]
  14. M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
    [Crossref]
  15. Rayleigh, “The remarkable case of diffraction spectra,” Philos. Mag. 14, 60–65 (1907).
    [Crossref]
  16. A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965).
    [Crossref]
  17. U. Fano, “Theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Somerfeld’s waves),” J. Opt. Soc. Am. 31, 213–222 (1941).
    [Crossref]
  18. C. H. Palmer, H. W. LeBrun, “Anomalous behavior of blazed gratings,” Appl. Opt. 11, 907–913 (1972).
    [Crossref] [PubMed]
  19. A. Wirgin, A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
    [Crossref]
  20. A thorough discussion of the basic theory is presented in R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [Crossref]
  21. T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
    [Crossref]
  22. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  23. C. H. Palmer, F. C. Evering, J. “Diffraction anomalies with a dielectric grating,” Opt. Soc. Am. 54, 844–845 (1964).
    [Crossref]

1991 (1)

T. K. Wang, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces: III. Undoped silicon: the normal direction in shallow lamellar gratings,” Infrared Phys. 32, 477–488 (1991).
[Crossref]

1988 (2)

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[Crossref]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

1985 (1)

A. Wirgin, A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[Crossref]

1983 (2)

R. C. Enger, S. K. Case, “Optical elements with ultra high spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[Crossref] [PubMed]

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[Crossref]

1982 (1)

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[Crossref]

1973 (1)

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[Crossref]

1972 (1)

1965 (2)

1964 (1)

C. H. Palmer, F. C. Evering, J. “Diffraction anomalies with a dielectric grating,” Opt. Soc. Am. 54, 844–845 (1964).
[Crossref]

1941 (1)

1907 (1)

Rayleigh, “The remarkable case of diffraction spectra,” Philos. Mag. 14, 60–65 (1907).
[Crossref]

1902 (1)

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

Bird, V. M.

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[Crossref]

Case, S. K.

Enger, R. C.

Evering, F. C.

C. H. Palmer, F. C. Evering, F. M. Nelson, “Diffraction anomalies for gratings of rectangular profile,” Appl. Opt. 4, 1271–1274 (1965).
[Crossref]

C. H. Palmer, F. C. Evering, J. “Diffraction anomalies with a dielectric grating,” Opt. Soc. Am. 54, 844–845 (1964).
[Crossref]

Fano, U.

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[Crossref]

Gale, M.

M. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal Press, New York, 1980).

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[Crossref]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[Crossref]

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[Crossref]

P. J. Hesketh, “The emittance of heavily doped microconfigured silicon surfaces,” Ph.D. dissertation. (University of Pennsylvania, Philadelphia, Pa., 1986).

P. J. Hesketh, “The emittance of heavily doped microconfigured silicon surfaces,” Ph.D. dissertation. (University of Pennsylvania, Philadelphia, Pa., 1986).

Hessel, A.

Hutley, M. C.

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[Crossref]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

Knop, K.

M. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal Press, New York, 1980).

LeBrun, H. W.

Maradudin, A. A.

A. Wirgin, A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[Crossref]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[Crossref]

Nelson, F. M.

Oliner, A. A.

Palmer, C. H.

Rayleigh,

Rayleigh, “The remarkable case of diffraction spectra,” Philos. Mag. 14, 60–65 (1907).
[Crossref]

Wang, T. K.

T. K. Wang, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces: III. Undoped silicon: the normal direction in shallow lamellar gratings,” Infrared Phys. 32, 477–488 (1991).
[Crossref]

T. K. Wang, “Thermal Radiation from dieletric grating surfaces” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1989).

Wirgin, A.

A. Wirgin, A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[Crossref]

Wood, R. W.

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

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Zemel, J. N.

T. K. Wang, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces: III. Undoped silicon: the normal direction in shallow lamellar gratings,” Infrared Phys. 32, 477–488 (1991).
[Crossref]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[Crossref]

Appl. Opt. (4)

Appl. Phys. B (1)

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[Crossref]

Appl. Phys. Lett. (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[Crossref]

Infrared Phys. (1)

T. K. Wang, J. N. Zemel, “Polarized spectral emittance from periodic micromachined surfaces: III. Undoped silicon: the normal direction in shallow lamellar gratings,” Infrared Phys. 32, 477–488 (1991).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[Crossref]

Opt. Soc. Am. (1)

C. H. Palmer, F. C. Evering, J. “Diffraction anomalies with a dielectric grating,” Opt. Soc. Am. 54, 844–845 (1964).
[Crossref]

Philos. Mag. (2)

Rayleigh, “The remarkable case of diffraction spectra,” Philos. Mag. 14, 60–65 (1907).
[Crossref]

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

Phys. Rev. B (3)

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. II Doped silicon: angular variation,” Phys. Rev. B 37, 10803–10813 (1988).
[Crossref]

A. Wirgin, A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985).
[Crossref]

Phys. Rev. Lett. (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Other (6)

M. Gale, K. Knop, Surface-Relief Images for Color Reproduction (Focal Press, New York, 1980).

P. J. Hesketh, “The emittance of heavily doped microconfigured silicon surfaces,” Ph.D. dissertation. (University of Pennsylvania, Philadelphia, Pa., 1986).

P. J. Hesketh, “The emittance of heavily doped microconfigured silicon surfaces,” Ph.D. dissertation. (University of Pennsylvania, Philadelphia, Pa., 1986).

T. K. Wang, “Thermal Radiation from dieletric grating surfaces” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1989).

A thorough discussion of the basic theory is presented in R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[Crossref]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

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Figures (7)

Fig. 1
Fig. 1

Schematic drawing of a sample showing the nomenclature of the dimensions and polarizations. Note that the normal direction n in this case is also the direction of observation. The inset shows the propagation vectors defined in the text.

Fig. 2
Fig. 2

Schematic drawing of the experimental setup. A/D; analog to digital.

Fig. 3
Fig. 3

Normal spectral p- and s-polarized emittance of deep gratings with Λ = 10 μm.

Fig. 4
Fig. 4

Normal spectral p- and s-polarized emittance of deep gratings with Λ = 14 μm.

Fig. 5
Fig. 5

Normal spectral p- and s-polarized emittance of deep gratings with Λ = 18 μm.

Fig. 6
Fig. 6

Normal spectral p- and s-polarized emittance of deep gratings with Λ = 22 μm.

Fig. 7
Fig. 7

Comparison between TE waveguide modes and maxima of normal spectral s-polarized emittance: (a) Λ = 22 μm, H = 30.6 μm, L = 13.04 μm; (b) Λ = 22 μm, H = 24 μm, L = 13.47 μm; (c)Λ = 18 μm, H = 22 μm, L = 12.5 μm.

Tables (1)

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Table I Dimensions of the Intrinsic Silicon Gratings

Equations (5)

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tan [ κ ( Λ L ) ] = 2 κγ ( κ 2 γ 2 ) TE ,
tan [ κ ( Λ L ) ] = 2 n 1 2 κγ ( κ 2 n 1 4 γ 2 ) TM ,
κ = ( n 1 2 k 0 2 β 2 ) 1 / 2 ,
γ = ( k 0 2 β 2 ) 1 / 2 .
k cutoff = m π ( Λ L ) ( n 1 2 1 ) 1 / 2 .

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