Abstract

Coupled-wave analysis is used to design binary gratings with high efficiencies (70–80%). The binary designs have grating periods greater than one wavelength but use subwavelength structures within each period in order to achieve high efficiency.

© 1992 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 707.
  2. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  3. R. Petit, G. Bouchitte, “Replacement of a very fine grating by a stratified layer: homogenization techniques, and the multiple-scale method,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moire Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 25–31(1987).
  4. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  5. W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A8, 549–553 (1991).
    [CrossRef]
  6. M. C. Hutley, “Coherent photofabrication,” Opt. Eng. 15, 190–196 (1976).
  7. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  8. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  9. W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.
  10. G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” MIT Lincoln Laboratory Tech. Rep. 914 (MIT Lincoln Laboratory, Lexington, Mass., 1March1991), approved for public release.

1991 (1)

W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A8, 549–553 (1991).
[CrossRef]

1990 (1)

1986 (1)

1985 (1)

1982 (1)

1976 (1)

M. C. Hutley, “Coherent photofabrication,” Opt. Eng. 15, 190–196 (1976).

Baird, W. E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 707.

Bouchitte, G.

R. Petit, G. Bouchitte, “Replacement of a very fine grating by a stratified layer: homogenization techniques, and the multiple-scale method,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moire Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 25–31(1987).

Cescato, L. H.

Chen, C-L.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.

Gaither, S. A.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.

Gaylord, T. K.

Gluch, E.

Hutley, M. C.

M. C. Hutley, “Coherent photofabrication,” Opt. Eng. 15, 190–196 (1976).

Moharam, M. G.

Osborne, T. R.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.

Petit, R.

R. Petit, G. Bouchitte, “Replacement of a very fine grating by a stratified layer: homogenization techniques, and the multiple-scale method,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moire Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 25–31(1987).

Southwell, W. H.

W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A8, 549–553 (1991).
[CrossRef]

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[CrossRef] [PubMed]

Streibl, N.

Swanson, G. J.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” MIT Lincoln Laboratory Tech. Rep. 914 (MIT Lincoln Laboratory, Lexington, Mass., 1March1991), approved for public release.

Veldkamp, W. B.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 707.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

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

W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A8, 549–553 (1991).
[CrossRef]

Opt. Eng. (1)

M. C. Hutley, “Coherent photofabrication,” Opt. Eng. 15, 190–196 (1976).

Other (4)

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT Lincoln Laboratory Project Rep. ODT-20 (MIT Lincoln Laboratory, Lexington, Mass., 23August1989), approved for public release.

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multilevel diffractive optical elements,” MIT Lincoln Laboratory Tech. Rep. 914 (MIT Lincoln Laboratory, Lexington, Mass., 1March1991), approved for public release.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 707.

R. Petit, G. Bouchitte, “Replacement of a very fine grating by a stratified layer: homogenization techniques, and the multiple-scale method,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moire Phenomena III, J. M. Lerner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.815, 25–31(1987).

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Figures (11)

Fig. 1
Fig. 1

Graded-index grating introduces a linear phase shift.

Fig. 2
Fig. 2

Scalar design introduces a binary phase shift.

Fig. 3
Fig. 3

Binary grating behaves as a graded-index grating.

Fig. 4
Fig. 4

Notation for a binary grating.

Fig. 5
Fig. 5

Comparison of Fourier coefficients (a) |an/cn|; (b) arg(an) − arg(cn).

Fig. 6
Fig. 6

Effect of λ/(n0t).

Fig. 7
Fig. 7

Chain of approximations.

Fig. 8
Fig. 8

Changing depth d.

Fig. 9
Fig. 9

Changing period T.

Fig. 10
Fig. 10

Changing incident angle, TE polarization.

Fig. 11
Fig. 11

Changing incident angle, TM polarization.

Equations (15)

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( x ) = n 2 ( x ) = ( 1 + x Δ ) 2 .
( x ) = n = - a n exp ( j 2 π n x ) ,
a n = { 1 + Δ + Δ 2 / 3 , n = 0 Δ / ( 2 π 2 n 2 ) + j ( Δ 2 + 2 Δ ) / ( 2 π n ) , else .
i = 1 I α i - i = 1 I - 1 β i = ( 3 + 2 Δ ) / ( 6 + 3 Δ ) ,
i = 1 I cos ( 2 π n α i ) - i = 1 I - 1 cos ( 2 π n β i ) = 0             for n = 1 to I - 1 ,
i = 1 I sin ( 2 π n α i ) - i = 1 I - 1 sin ( 2 π n β i ) = 1 / [ n π ( 2 + Δ ) ]             for n = 1 to I - 1.
α i = i / ( I + 1 ) , β i = i / I .
t = T / I .
c n = { 1 + Δ + Δ 2 / 2 n = 0 j ( Δ 2 + 2 Δ ) / ( 2 π n ) 0 < n < I of no concern I n .
I T n 0 / λ = λ / ( n 0 t ) .
t = λ / ( 2 n 0 ) ,             I = T / t ,             d = λ / ( n 0 - 1 ) .
δ t t I = λ 4 n 0 2 λ T .
d δ t = 4 n 0 2 n 0 - 1 T λ .
λ = 1.0 μ m ,             T = 4.0 μ m ,             n 0 = 2.0.
t = 0.25 μ m ,             I = 16 subperiods , d = 1.0 μ m ,             δ t = 15.6 nm .

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