Abstract

We derive closed-form expressions for the effective index of subwavelength gratings up to the fourth and the second order for TE and TM polarization, respectively. These expressions are valid for arbitrary grating structures and are a generalization of previous results obtained for lamellar gratings with one groove per period (a structure often called a two-component layered medium). The effective-medium-theory predictions are carefully validated with exact electromagnetic theories for slanted and unslanted sinusoidally modulated volume gratings and for classical mounting. It is shown that, even for large period-to-wavelength ratios near the cutoff value, the form birefringence is accurately predicted at any angle of incidence.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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1997 (1)

1996 (2)

C. Gu, P. Yeh, “Form birefringence dispersion in periodic layered media,” Opt. Lett. 21, 504–506 (1996).
[CrossRef] [PubMed]

Ph. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

1995 (2)

1993 (1)

1992 (1)

1991 (1)

1990 (1)

1987 (1)

1986 (1)

1985 (2)

T. K. Gaylord, M. G. Moharam, “Analysis and application of optical diffraction by grating,” Proc. IEEE 73, 894–936 (1985).
[CrossRef]

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

1983 (2)

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

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

1982 (3)

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasi-static limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

1978 (1)

P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Baird, W. E.

Bell, J. M.

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasi-static limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1984), p. 62.

Botten, L. C.

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Bouchitté, G.

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

Campbell, G.

Case, S. K.

Cescato, L. H.

Chen, F. T.

Craig, M. S.

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Craighead, H. G.

Derrick, G. H.

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasi-static limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

Enger, R. C.

Flanders, D. C.

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

Gaylord, T. K.

Gluch, E.

Gu, C.

Gunning, W. J.

Haidner, H.

Hutley, M. C.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Kimura, Y.

Kipfer, P.

Kostuk, R. K.

Lalanne, Ph.

Ph. Lalanne, D. Lemercier-Lalanne, “Depth dependence of the effective properties of subwavelength gratings,” J. Opt. Soc. Am. A 14, 450–458 (1997).
[CrossRef]

Ph. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Lemercier-Lalanne, D.

Ph. Lalanne, D. Lemercier-Lalanne, “Depth dependence of the effective properties of subwavelength gratings,” J. Opt. Soc. Am. A 14, 450–458 (1997).
[CrossRef]

Ph. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Maystre, D.

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasi-static limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Motamedi, M. E.

Nevière, N.

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Nishida, N.

Ono, Y.

Otha, Y.

Petit, R.

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

Raguin, D. H.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Southwell, W. H.

Stork, W.

Streibl, N.

Wilson, S. J.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1984), p. 62.

Yeh, P.

C. Gu, P. Yeh, “Form birefringence dispersion in periodic layered media,” Opt. Lett. 21, 504–506 (1996).
[CrossRef] [PubMed]

P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
[CrossRef]

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chap. 6.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

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

Electromagnetics (1)

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

J. Mod. Opt. (1)

Ph. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

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

Opt. Acta (3)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

J. M. Bell, G. H. Derrick, R. C. McPhedran, “Diffraction gratings in the quasi-static limit,” Opt. Acta 29, 1475–1489 (1982).
[CrossRef]

R. C. McPhedran, L. C. Botten, M. S. Craig, N. Nevière, D. Maystre, “Lossy lamellar gratings in the quasi-static limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Opt. Commun. (1)

P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and application of optical diffraction by grating,” Proc. IEEE 73, 894–936 (1985).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (2)

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chap. 6.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1984), p. 62.

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