Abstract

Theoretical results from rigorous coupled-wave analysis are compared with experimental diffraction characteristics for holographically formed dielectric photoresist surface-relief gratings with deep grooves (greater than a grating period) and high diffraction efficiency (>85%). The angular selectivity (at a fixed wavelength) and the wavelength selectivity (at a fixed angle of incidence) are presented for both TE and TM incident polarizations. Modeling the gratings as a surface-relief modulated half-space and using rigorous coupled-wave analysis are shown to produce good general agreement with the experimentally measured diffraction characteristics.

© 1984 Optical Society of America

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References

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  1. R. A. Bartolini, “Characteristics of Relief Phase Holograms Recorded in Photoresist,” Appl. Opt. 13, 129 (1974).
    [CrossRef] [PubMed]
  2. F. Iwata, J. Tsujiuchi, “Characteristics of a Photoresist Hologram and Its Replica,” Appl. Opt. 13, 1327 (1974).
    [CrossRef] [PubMed]
  3. R. Kurtz, R. Owen, “Holographic Recording Materials—A Review,” Opt. Eng. 14, 393 (1975).
  4. M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-Relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
    [CrossRef]
  5. R. C. Enger, S. K. Case, “High-Frequency Holographic Transmission Gratings in Photoresist,” J. Opt. Soc. Am. 73, 1113 (1983).
    [CrossRef]
  6. H. Werlich, G. Sincerbox, B. Yung, “Fabrication of High Efficiency Surface Relief Holograms,” IBM Research Report RJ3912 (1983).
  7. C. J. Kramer, “Hologon Laser Scanners for Nonimpact Printing,” Proc. Soc. Photo-Opt. Instrum Eng. 390, 165 (1982).
  8. M. G. Moharam, T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
    [CrossRef]
  9. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
  10. For example, M. C. Hutley, Diffraction Gratings (Academic, London, 1982).
  11. T. K. Gaylord, M. G. Moharam, “Thin and Thick Gratings: Terminology Clarification,” Appl. Opt. 19, 3271 (1981).
    [CrossRef]
  12. C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Indian Acad. Sci. Sect. A 2, 406 (1935).
  13. C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part II,” Proc. Indian Acad. Sci. Sect. A 2, 413 (1935).
  14. C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part III,” Proc. Indian Acad. Sci. Sect. A 3, 75 (1936).
  15. C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part IV,” Proc. Indian Acad. Sci. Sect A 3, 119 (1936).
  16. R. C. Enger, S. K. Case, “Optical Elements with Ultrahigh Spatial-Frequency Surface Corrugations,” Appl. Opt. 22, 3220 (1983).
    [CrossRef] [PubMed]
  17. M. Gale, K. Knop, Surface Relief Images for Color Reproduction (Focal Press, Woburn, Mass., 1980).

1983 (2)

1982 (2)

C. J. Kramer, “Hologon Laser Scanners for Nonimpact Printing,” Proc. Soc. Photo-Opt. Instrum Eng. 390, 165 (1982).

M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-Relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
[CrossRef]

1981 (2)

M. G. Moharam, T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
[CrossRef]

T. K. Gaylord, M. G. Moharam, “Thin and Thick Gratings: Terminology Clarification,” Appl. Opt. 19, 3271 (1981).
[CrossRef]

1975 (1)

R. Kurtz, R. Owen, “Holographic Recording Materials—A Review,” Opt. Eng. 14, 393 (1975).

1974 (2)

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

1936 (2)

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part III,” Proc. Indian Acad. Sci. Sect. A 3, 75 (1936).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part IV,” Proc. Indian Acad. Sci. Sect A 3, 119 (1936).

1935 (2)

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Indian Acad. Sci. Sect. A 2, 406 (1935).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part II,” Proc. Indian Acad. Sci. Sect. A 2, 413 (1935).

Bartolini, R. A.

Case, S. K.

Enger, R. C.

Gale, M.

M. Gale, K. Knop, Surface Relief Images for Color Reproduction (Focal Press, Woburn, Mass., 1980).

Gaylord, T. K.

Hutley, M. C.

For example, M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

Iwata, F.

Knop, K.

M. Gale, K. Knop, Surface Relief Images for Color Reproduction (Focal Press, Woburn, Mass., 1980).

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

Kramer, C. J.

C. J. Kramer, “Hologon Laser Scanners for Nonimpact Printing,” Proc. Soc. Photo-Opt. Instrum Eng. 390, 165 (1982).

Kurtz, R.

R. Kurtz, R. Owen, “Holographic Recording Materials—A Review,” Opt. Eng. 14, 393 (1975).

Moharam, M. G.

Nath, N. S. N.

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part III,” Proc. Indian Acad. Sci. Sect. A 3, 75 (1936).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part IV,” Proc. Indian Acad. Sci. Sect A 3, 119 (1936).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part II,” Proc. Indian Acad. Sci. Sect. A 2, 413 (1935).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Indian Acad. Sci. Sect. A 2, 406 (1935).

Owen, R.

R. Kurtz, R. Owen, “Holographic Recording Materials—A Review,” Opt. Eng. 14, 393 (1975).

Raman, C. V.

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part III,” Proc. Indian Acad. Sci. Sect. A 3, 75 (1936).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part IV,” Proc. Indian Acad. Sci. Sect A 3, 119 (1936).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part II,” Proc. Indian Acad. Sci. Sect. A 2, 413 (1935).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Indian Acad. Sci. Sect. A 2, 406 (1935).

Sincerbox, G.

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of High Efficiency Surface Relief Holograms,” IBM Research Report RJ3912 (1983).

Tsujiuchi, J.

Werlich, H.

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of High Efficiency Surface Relief Holograms,” IBM Research Report RJ3912 (1983).

Yung, B.

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of High Efficiency Surface Relief Holograms,” IBM Research Report RJ3912 (1983).

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

J. Opt. Soc. Am. (3)

Opt. Eng. (1)

R. Kurtz, R. Owen, “Holographic Recording Materials—A Review,” Opt. Eng. 14, 393 (1975).

Proc. Indian Acad. Sci. Sect A (1)

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part IV,” Proc. Indian Acad. Sci. Sect A 3, 119 (1936).

Proc. Indian Acad. Sci. Sect. A (3)

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Indian Acad. Sci. Sect. A 2, 406 (1935).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part II,” Proc. Indian Acad. Sci. Sect. A 2, 413 (1935).

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part III,” Proc. Indian Acad. Sci. Sect. A 3, 75 (1936).

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

C. J. Kramer, “Hologon Laser Scanners for Nonimpact Printing,” Proc. Soc. Photo-Opt. Instrum Eng. 390, 165 (1982).

Other (3)

For example, M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

H. Werlich, G. Sincerbox, B. Yung, “Fabrication of High Efficiency Surface Relief Holograms,” IBM Research Report RJ3912 (1983).

M. Gale, K. Knop, Surface Relief Images for Color Reproduction (Focal Press, Woburn, Mass., 1980).

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Figures (9)

Fig. 1
Fig. 1

Geometry of photoresist surface-relief grating.

Fig. 2
Fig. 2

Scanning electron micrograph of typical photoresist surface-relief grating.

Fig. 3
Fig. 3

Calculated angular dependence of the first-order (i = +1) transmitted diffraction efficiency with wavelength as a parameter for a sinusoidal surface-relief grating for (a) TE (or s) polarization, and (b) TM (or p) polarization. Rapid variations are observed when the electric field is parallel to the grooves (TE polarization).

Fig. 4
Fig. 4

Calculated angular dependence of the first-order (i = +1) transmitted diffraction efficiency with wavelength as a parameter for a square-wave surface-relief grating for (a) TE polarization and (b) TM polarization.

Fig. 5
Fig. 5

Scanning electron micrographs of photoresist surface-relief gratings (a) 7 and (b) 8 analyzed in this work. All gratings were fabricated by IBM.

Fig. 6
Fig. 6

Surface-relief profiles selected for the calculations. The groove depths are 0.65 and 0.59 μm for gratings 7 and 8, respectively.

Fig. 7
Fig. 7

Experimental and theoretical wavelength dependence of the diffraction efficiency for a fixed angle of incidence (θ′ = 36.86°).

Fig. 8
Fig. 8

Experimental and theoretical wavelength dependence of the diffraction efficiency with the angle of incidence continually adjusted to the first Bragg angle (m = 1) for (a) grating 7 and (b) grating 8.

Fig. 9
Fig. 9

Experimental and theoretical angle of incidence dependence of the diffraction efficiency for a fixed wavelength (λ = 458 nm) for TE and TM polarizations.

Equations (6)

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i λ = Λ ( sin θ + n sin θ i ) ,
m λ = 2 Λ sin θ ,
Δ θ = θ + - θ - ,
Δ λ = λ + - λ - ,
θ ± = sin - 1 { n sin θ B ± ( ξ Λ / π d ) [ cos 2 θ B - ( ξ Λ / π d ) 2 ] 1 / 2 1 + ( ξ Λ / π d ) 2 } ,
λ ± = λ B ± 2 n Λ 2 ξ cos θ B / π d .

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