Abstract

Multilevel phase holograms for monochromatic radiation at a wavelength of 10.6 μm are recorded as surface relief gratings with multilevel discrete binary steps. Our experiments show that diffraction efficiencies close to 90% can be achieved both for transmissive and reflective elements. The reduction of efficiency due to errors in the depth and the width of the step levels is considered.

© 1991 Optical Society of America

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References

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  1. W. H. Lee, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–232.
    [CrossRef]
  2. R. Magnusson, T. K. Gaylord, J. Opt. Soc. Am. 68, 806 (1978).
    [CrossRef]
  3. L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
    [CrossRef]
  4. G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).
  5. M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 72, 1383 (1982).
  6. M. W. Farn, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 1211, 125 (1990).
  7. E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
    [CrossRef]

1990 (2)

M. W. Farn, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 1211, 125 (1990).

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

1989 (1)

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

1982 (1)

M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 72, 1383 (1982).

1978 (1)

1972 (1)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
[CrossRef]

Cohen, R.

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

d’Auria, L.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
[CrossRef]

Davidson, N.

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

Farn, M. W.

M. W. Farn, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 1211, 125 (1990).

Friesem, A. A.

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 72, 1383 (1982).

R. Magnusson, T. K. Gaylord, J. Opt. Soc. Am. 68, 806 (1978).
[CrossRef]

Goodman, J. W.

M. W. Farn, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 1211, 125 (1990).

Hasman, E.

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

Huignard, J. P.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
[CrossRef]

Lee, W. H.

W. H. Lee, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–232.
[CrossRef]

Magnusson, R.

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 72, 1383 (1982).

Nagler, M.

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

Roy, A. M.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
[CrossRef]

Spitz, E.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
[CrossRef]

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

J. Opt. Soc. Am. (2)

M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 72, 1383 (1982).

R. Magnusson, T. K. Gaylord, J. Opt. Soc. Am. 68, 806 (1978).
[CrossRef]

Meas. Sci. Technol. (1)

E. Hasman, N. Davidson, A. A. Friesem, M. Nagler, R. Cohen, Meas. Sci. Technol. 1, 59 (1990).
[CrossRef]

Opt. Commun. (1)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, Opt. Commun. 5, 232 (1972).
[CrossRef]

Opt. Eng. (1)

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. W. Farn, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 1211, 125 (1990).

Other (1)

W. H. Lee, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–232.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Actual quantized phase F(ϕ) as a function of the desired hologram phase ϕ.

Fig. 2
Fig. 2

Diffraction efficiency η1 as a function of the relative etch depth error δd for N = 2, 4, 8, 16, and infinity step levels.

Fig. 3
Fig. 3

Diffraction efficiency η1 as a function of the relative step width error δw for N = 2, 4, 8, and 16 step levels.

Fig. 4
Fig. 4

Surface profilometer traces for typical etched sections: (a) 8 levels of the reflective element, (b) 16 levels of the transmissive element.

Fig. 5
Fig. 5

Relative power of the light as a function of the displacement of the knife edge (solid curve) and the corresponding intensity distribution (dashed curve).

Equations (8)

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Q = 2 π λ T n Λ 2 ,
H = exp [ i F ( ϕ ) ] ,
exp [ i F ( ϕ ) ] = l = - C l exp ( i l ϕ ) ,
C l = 1 2 π 0 2 π exp [ i F ( ϕ ) - i l ϕ ] d ϕ .
η l = C l 2 k = - C k 2 ,
η 1 = C 1 2 = [ N π sin ( π N ) ] 2 .
Δ m = λ Δ n 2 m .
η 1 = | 1 2 π [ exp ( - i 2 π N ) - 1 ] [ 1 - exp ( - i 2 π δ d ) 1 - exp ( - i 2 π N δ d ) ] | 2 .

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