Abstract

A detailed numerical investigation of anomalies in lossy metallic lamellar gratings is presented in a large interval of a wavelength-to-period λ/d ratio. A substantial increase in absorption (a decrease in the total diffracted energy) is observed. If λ/d is small enough (within the homogenized limit), the absorption can reach almost 100%. When the groove width is large enough, the anomalies are connected with mode resonances inside the grooves.

© 1994 Optical Society of America

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References

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  1. R. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
    [CrossRef]
  2. D. Maystre, R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
    [CrossRef]
  3. L. Mashev, E. Popov, E. Loewen, “Brewster effects for deep metallic gratings,” Appl. Opt. 28, 2538–2541 (1989).
    [CrossRef] [PubMed]
  4. N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on grating surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
    [CrossRef]
  5. R. Reinisch, M. Neviere, “Increase in Raman excitation of surface polaritons with surface roughness explained in terms of wood anomalies of gratings,” Opt. Eng. 20, 629–633 (1981).
  6. K. Metcalfe, R. Hester, “Raman scattering from thin polystyrene films on gold diffraction gratings,” Chem. Phys. Lett. 94, 411–414 (1983).
    [CrossRef]
  7. E. Popov, L. Tsonev, “Electromagnetic field enhancement in deep metallic gratings,” Opt. Commun. 69, 193–198 (1989).
    [CrossRef]
  8. M. Neviere, R. Reinisch, “Electromagnetic theory of enhanced nonlinear optical process,” J. Phys. (Paris) 44, C10-349–C10-352 (1983).
    [CrossRef]
  9. R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
    [CrossRef]
  10. J. L. Coutaz, “Experimental study of second-harmonic generation from silver gratings of various groove depths,” J. Opt. Soc. Am. B 4, 105–106 (1987).
    [CrossRef]
  11. D. Maystre, M. Neviere, R. Reinisch, J. L. Coutaz, “Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation,” J. Opt. Soc. Am. B 5, 338–346 (1988).
    [CrossRef]
  12. L. Mashev, E. Popov, E. Loewen, “Total absorption of light by a sinusoidal grating near grazing incidence,” Appl. Opt. 27, 152–154 (1988).
    [CrossRef] [PubMed]
  13. E. Popov, L. Tsonev, “Anomalous light absorption by lamellar grating,” Surf. Sci. 271, L378–L382 (1992).
    [CrossRef]
  14. J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
    [CrossRef]
  15. J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
    [CrossRef]
  16. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
    [CrossRef]
  17. G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
    [CrossRef]
  18. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  19. P. Sheng, R. S. Stepleman, P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
    [CrossRef]
  20. A. A. Maradudin, A. Wirgin, “Resonant electric field enhancement in the vicinity of a bare metallic grating exposed to s-polarized light,” Surf. Sci. 162, 980–984 (1985).
    [CrossRef]
  21. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [CrossRef] [PubMed]
  22. G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
    [CrossRef]
  23. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1984), Vol. 21, Chap. 1.
    [CrossRef]

1992 (2)

1989 (2)

L. Mashev, E. Popov, E. Loewen, “Brewster effects for deep metallic gratings,” Appl. Opt. 28, 2538–2541 (1989).
[CrossRef] [PubMed]

E. Popov, L. Tsonev, “Electromagnetic field enhancement in deep metallic gratings,” Opt. Commun. 69, 193–198 (1989).
[CrossRef]

1988 (2)

1987 (1)

1985 (2)

A. A. Maradudin, A. Wirgin, “Resonant electric field enhancement in the vicinity of a bare metallic grating exposed to s-polarized light,” Surf. Sci. 162, 980–984 (1985).
[CrossRef]

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

1984 (1)

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

1983 (4)

K. Metcalfe, R. Hester, “Raman scattering from thin polystyrene films on gold diffraction gratings,” Chem. Phys. Lett. 94, 411–414 (1983).
[CrossRef]

M. Neviere, R. Reinisch, “Electromagnetic theory of enhanced nonlinear optical process,” J. Phys. (Paris) 44, C10-349–C10-352 (1983).
[CrossRef]

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on grating surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
[CrossRef]

1982 (2)

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

P. Sheng, R. S. Stepleman, P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

1981 (2)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

R. Reinisch, M. Neviere, “Increase in Raman excitation of surface polaritons with surface roughness explained in terms of wood anomalies of gratings,” Opt. Eng. 20, 629–633 (1981).

1979 (2)

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[CrossRef]

1976 (1)

D. Maystre, R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[CrossRef]

1902 (1)

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

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Bouchitte, G.

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

Chartier, G.

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

Clauss, G.

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

Coutaz, J. L.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Eloy, J. F.

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

Fox, J. R.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

Galaup, J. P.

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

Garcia, N.

N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on grating surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Hester, R.

K. Metcalfe, R. Hester, “Raman scattering from thin polystyrene films on gold diffraction gratings,” Chem. Phys. Lett. 94, 411–414 (1983).
[CrossRef]

Hutley, M. C.

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

Loewen, E.

Maradudin, A. A.

A. A. Maradudin, A. Wirgin, “Resonant electric field enhancement in the vicinity of a bare metallic grating exposed to s-polarized light,” Surf. Sci. 162, 980–984 (1985).
[CrossRef]

Mashev, L.

Maystre, D.

D. Maystre, M. Neviere, R. Reinisch, J. L. Coutaz, “Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation,” J. Opt. Soc. Am. B 5, 338–346 (1988).
[CrossRef]

D. Maystre, R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[CrossRef]

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1984), Vol. 21, Chap. 1.
[CrossRef]

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Metcalfe, K.

K. Metcalfe, R. Hester, “Raman scattering from thin polystyrene films on gold diffraction gratings,” Chem. Phys. Lett. 94, 411–414 (1983).
[CrossRef]

Moharam, M. G.

Neviere, M.

D. Maystre, M. Neviere, R. Reinisch, J. L. Coutaz, “Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation,” J. Opt. Soc. Am. B 5, 338–346 (1988).
[CrossRef]

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

M. Neviere, R. Reinisch, “Electromagnetic theory of enhanced nonlinear optical process,” J. Phys. (Paris) 44, C10-349–C10-352 (1983).
[CrossRef]

R. Reinisch, M. Neviere, “Increase in Raman excitation of surface polaritons with surface roughness explained in terms of wood anomalies of gratings,” Opt. Eng. 20, 629–633 (1981).

Petit, R.

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

D. Maystre, R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[CrossRef]

Popov, E.

E. Popov, L. Tsonev, “Anomalous light absorption by lamellar grating,” Surf. Sci. 271, L378–L382 (1992).
[CrossRef]

L. Mashev, E. Popov, E. Loewen, “Brewster effects for deep metallic gratings,” Appl. Opt. 28, 2538–2541 (1989).
[CrossRef] [PubMed]

E. Popov, L. Tsonev, “Electromagnetic field enhancement in deep metallic gratings,” Opt. Commun. 69, 193–198 (1989).
[CrossRef]

L. Mashev, E. Popov, E. Loewen, “Total absorption of light by a sinusoidal grating near grazing incidence,” Appl. Opt. 27, 152–154 (1988).
[CrossRef] [PubMed]

Reinisch, R.

D. Maystre, M. Neviere, R. Reinisch, J. L. Coutaz, “Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation,” J. Opt. Soc. Am. B 5, 338–346 (1988).
[CrossRef]

M. Neviere, R. Reinisch, “Electromagnetic theory of enhanced nonlinear optical process,” J. Phys. (Paris) 44, C10-349–C10-352 (1983).
[CrossRef]

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

R. Reinisch, M. Neviere, “Increase in Raman excitation of surface polaritons with surface roughness explained in terms of wood anomalies of gratings,” Opt. Eng. 20, 629–633 (1981).

Sanda, P. N.

P. Sheng, R. S. Stepleman, P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Sheng, P.

P. Sheng, R. S. Stepleman, P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Stepleman, R. S.

P. Sheng, R. S. Stepleman, P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Tayeb, G.

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

Tsonev, L.

E. Popov, L. Tsonev, “Anomalous light absorption by lamellar grating,” Surf. Sci. 271, L378–L382 (1992).
[CrossRef]

E. Popov, L. Tsonev, “Electromagnetic field enhancement in deep metallic gratings,” Opt. Commun. 69, 193–198 (1989).
[CrossRef]

Wilson, I. J.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[CrossRef]

Wirgin, A.

A. A. Maradudin, A. Wirgin, “Resonant electric field enhancement in the vicinity of a bare metallic grating exposed to s-polarized light,” Surf. Sci. 162, 980–984 (1985).
[CrossRef]

Wood, R.

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

Appl. Opt. (3)

Chem. Phys. Lett. (1)

K. Metcalfe, R. Hester, “Raman scattering from thin polystyrene films on gold diffraction gratings,” Chem. Phys. Lett. 94, 411–414 (1983).
[CrossRef]

Electromagnetics (1)

G. Bouchitte, R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. (Paris) (1)

M. Neviere, R. Reinisch, “Electromagnetic theory of enhanced nonlinear optical process,” J. Phys. (Paris) 44, C10-349–C10-352 (1983).
[CrossRef]

J. Phys. (Paris) Lett. (1)

R. Reinisch, G. Chartier, M. Neviere, M. C. Hutley, G. Clauss, J. P. Galaup, J. F. Eloy, “Experiment of diffraction in nonlinear optics: second harmonic generation by a nonlinear grating,” J. Phys. (Paris) Lett. 44, L1007–L1012 (1983).
[CrossRef]

Opt. Acta (4)

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981); L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

G. Tayeb, R. Petit, “On the numerical study of deep conducting lamellar diffraction gratings,” Opt. Acta 31, 1361–1365 (1984).
[CrossRef]

Opt. Commun. (3)

E. Popov, L. Tsonev, “Electromagnetic field enhancement in deep metallic gratings,” Opt. Commun. 69, 193–198 (1989).
[CrossRef]

N. Garcia, “Exact calculations of p-polarized electromagnetic fields incident on grating surfaces: surface polariton resonances,” Opt. Commun. 45, 307–310 (1983).
[CrossRef]

D. Maystre, R. Petit, “Brewster incidence for metallic gratings,” Opt. Commun. 17, 196–200 (1976).
[CrossRef]

Opt. Eng. (1)

R. Reinisch, M. Neviere, “Increase in Raman excitation of surface polaritons with surface roughness explained in terms of wood anomalies of gratings,” Opt. Eng. 20, 629–633 (1981).

Philos. Mag. (1)

R. 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 (1)

P. Sheng, R. S. Stepleman, P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Surf. Sci. (2)

A. A. Maradudin, A. Wirgin, “Resonant electric field enhancement in the vicinity of a bare metallic grating exposed to s-polarized light,” Surf. Sci. 162, 980–984 (1985).
[CrossRef]

E. Popov, L. Tsonev, “Anomalous light absorption by lamellar grating,” Surf. Sci. 271, L378–L382 (1992).
[CrossRef]

Other (1)

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1984), Vol. 21, Chap. 1.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of a lamellar grating.

Fig. 2
Fig. 2

Total energy diffracted by the grating (the sum of diffracted order efficiencies) as a function of period d (given in micrometers) and the filling factor w/d (w is the lamella thickness). Groove depth h = 1 μm, wavelength λ = 1 μm. The TE-polarized light has normal incidence on a metallic grating with a refractive index equal to 0.4 + i4.4.

Fig. 3
Fig. 3

Total reflected energy (solid curve) normalized with respect to the incident wave energy and the zeroth-order efficiency (dotted curve) as a function of filling factor w/d for fixed period d = 2.99 μm. The other parameters are the same as those in Fig. 2.

Fig. 4
Fig. 4

Maps of the electromagnetic energy density inside the groove, which corresponds to Fig. 2: (a) w/d = 0.85; (b) w/d = 0.84, (c) w/d = 0.82. Units of the x and y axes are in micrometers. Period d = 2.99 μm.

Fig. 5
Fig. 5

Same as Fig. 4 except that w/d = 0.49.

Fig. 6
Fig. 6

Same as Fig. 4 except that w/d = 0.15.

Fig. 7
Fig. 7

Map of the TE-field component E z for d = 1 μm and w/d = 0.53. The heavy solid line represents the groove profile.

Fig. 8
Fig. 8

Reflectivity as a function of the filling factor w/d for d = 0.01 μm. Solid curve, modal theory results; asterisks, reflectivity of a layer with a refractive index given by the homogenization formula [Eq. (3)].

Fig. 9
Fig. 9

Angular dependence of reflectivity for the grating discussed in Fig. 8 for two consecutive lamella width values, as indicated in the figure.

Equations (3)

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

w / d = 1 - c i / d ,
d - w = c i ,
n 2 = n 1 2 ( d - w ) / d + n 2 2 w / d ,

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