Abstract

We present novel, to our knowledge, methods for the analytical design and recording of planar holographic optical elements in thick materials. The recording of each planar holographic element is done by interference of two aspherical waves that are derived from appropriately designed computer-generated holograms such that the element has the desired grating function for minimizing aberrations and closely fulfills the Bragg condition over its entire area. The design and recording methods are described, along with calculated results of representative elements.

© 1998 Optical Society of America

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References

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  1. R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
    [CrossRef]
  2. H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
    [CrossRef]
  3. A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
    [CrossRef]
  4. I. Glaser, “Compact lenslet array based holographic correlator/convolver,” Opt. Lett. 20, 1565–1567 (1995).
    [CrossRef] [PubMed]
  5. J. Jahns, S. Walker, “Imaging with planar optical systems,” Opt. Commun. 76, 313–317 (1989).
    [CrossRef]
  6. R. K. Kostuk, Y. T. Huang, D. Hetherington, M. Kato, “Reducing alignment and chromatic sensitivity of holographic optical interconnects with substrate-mode holograms,” Appl. Opt. 28, 4939–4944 (1989).
    [CrossRef] [PubMed]
  7. Y. Amitai, “Design of wavelength-division multiplexing/demultiplexing using substrate mode holographic elements,” Opt. Commun. 98, 24–28 (1993).
    [CrossRef]
  8. S. Reinhorn, S. Gorodeisky, A. A. Friesem, Y. Amitai, “Fourier transformation with planar holographic doublet,” Opt. Lett. 20, 495–497 (1995).
    [CrossRef] [PubMed]
  9. H. Kogelnik, “Coupled wave theory for thick holograms and their applications,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).
  10. K. Winick, “Designing efficient aberration-free holographic lenses in the presence of a construction-reconstruction wavelength shift,” J. Opt. Soc. Am. 72, 143–148 (1982).
    [CrossRef]
  11. Y. Amitai, J. Goodman, “Design of substrate-mode holographic interconnects with different recording and readout wavelengths,” Appl. Opt. 30, 2376–2381 (1991).
    [CrossRef] [PubMed]
  12. Y. Amitai, A. A. Friesem, “Design of holographic optical elements by using recursive techniques,” J. Opt. Soc. Am. 5, 702–712 (1988).
    [CrossRef]
  13. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
    [CrossRef] [PubMed]
  14. Y. Amitai, A. A. Friesem, “Combining low aberration and high diffraction efficiency in holographic optical elements,” Opt. Lett. 13, 883–885 (1988).
    [CrossRef] [PubMed]
  15. R. C. Fairchild, J. R. Fienup, “Computer originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).
  16. J. N. Latta, “Computer-based analysis of holography using ray tracing,” Appl. Opt. 10, 2698–2710 (1971).
    [CrossRef] [PubMed]
  17. R. W. Meier, “Magnification and third-order aberrations in holography,” J. Opt. Soc. Am. 55, 987–992 (1965).
  18. E. B. Champagne, “Nonparaxial imaging magnification and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
    [CrossRef]
  19. E. Hasman, A. A. Friesem, “Analytic optimization for holographic optical elements,” J. Opt. Soc. Am. A 6, 62–72 (1989).
    [CrossRef]
  20. J. Kedmi, A. A. Friesem, “Optimized holographic optical element,” J. Opt. Soc. Am. A 3, 2011–2018 (1986).
    [CrossRef]
  21. E. Socol, Y. Amitai, A. A. Friesem, “Design of planar optical interconnects,” in Ninth Meeting on Optical Engineering in Israel, I. Shladov, ed., Proc. SPIE2426, 433–442 (1995).
    [CrossRef]

1995

1993

Y. Amitai, “Design of wavelength-division multiplexing/demultiplexing using substrate mode holographic elements,” Opt. Commun. 98, 24–28 (1993).
[CrossRef]

1992

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

1991

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
[CrossRef]

Y. Amitai, J. Goodman, “Design of substrate-mode holographic interconnects with different recording and readout wavelengths,” Appl. Opt. 30, 2376–2381 (1991).
[CrossRef] [PubMed]

1989

1988

Y. Amitai, A. A. Friesem, “Design of holographic optical elements by using recursive techniques,” J. Opt. Soc. Am. 5, 702–712 (1988).
[CrossRef]

Y. Amitai, A. A. Friesem, “Combining low aberration and high diffraction efficiency in holographic optical elements,” Opt. Lett. 13, 883–885 (1988).
[CrossRef] [PubMed]

1986

1982

1974

1971

1969

H. Kogelnik, “Coupled wave theory for thick holograms and their applications,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

1967

1965

Amitai, Y.

S. Reinhorn, S. Gorodeisky, A. A. Friesem, Y. Amitai, “Fourier transformation with planar holographic doublet,” Opt. Lett. 20, 495–497 (1995).
[CrossRef] [PubMed]

Y. Amitai, “Design of wavelength-division multiplexing/demultiplexing using substrate mode holographic elements,” Opt. Commun. 98, 24–28 (1993).
[CrossRef]

Y. Amitai, J. Goodman, “Design of substrate-mode holographic interconnects with different recording and readout wavelengths,” Appl. Opt. 30, 2376–2381 (1991).
[CrossRef] [PubMed]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

Y. Amitai, A. A. Friesem, “Design of holographic optical elements by using recursive techniques,” J. Opt. Soc. Am. 5, 702–712 (1988).
[CrossRef]

Y. Amitai, A. A. Friesem, “Combining low aberration and high diffraction efficiency in holographic optical elements,” Opt. Lett. 13, 883–885 (1988).
[CrossRef] [PubMed]

E. Socol, Y. Amitai, A. A. Friesem, “Design of planar optical interconnects,” in Ninth Meeting on Optical Engineering in Israel, I. Shladov, ed., Proc. SPIE2426, 433–442 (1995).
[CrossRef]

Caufield, J. H.

A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
[CrossRef]

Champagne, E. B.

Chen, R. T.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

Fienup, J. R.

R. C. Fairchild, J. R. Fienup, “Computer originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

Friesem, A. A.

Glaser, I.

Goodman, J.

Goodman, J. W.

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

Gorodeisky, S.

Hasman, E.

Hetherington, D.

Huang, Q.

A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
[CrossRef]

Huang, Y. T.

Jahns, J.

J. Jahns, S. Walker, “Imaging with planar optical systems,” Opt. Commun. 76, 313–317 (1989).
[CrossRef]

Jannson, T.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

Kato, M.

Kedmi, J.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick holograms and their applications,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

Kostuk, R. K.

Latta, J. N.

Lee, W. H.

Lu, H.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

Meier, R. W.

Morozov, V. N.

A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
[CrossRef]

Ozaktas, H. M.

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

Putilin, A. N.

A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
[CrossRef]

Reinhorn, S.

Robinson, D.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

Savant, G.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

Socol, E.

E. Socol, Y. Amitai, A. A. Friesem, “Design of planar optical interconnects,” in Ninth Meeting on Optical Engineering in Israel, I. Shladov, ed., Proc. SPIE2426, 433–442 (1995).
[CrossRef]

Walker, S.

J. Jahns, S. Walker, “Imaging with planar optical systems,” Opt. Commun. 76, 313–317 (1989).
[CrossRef]

Wang, M.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

Winick, K.

Appl. Opt.

Bell. Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick holograms and their applications,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

J. Lightwave Technol.

R. T. Chen, H. Lu, D. Robinson, M. Wang, G. Savant, T. Jannson, “Guided wave planar optical interconnects using highly multiplexed polymer waveguide holograms,” J. Lightwave Technol. 10, 888–897 (1992).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

Y. Amitai, “Design of wavelength-division multiplexing/demultiplexing using substrate mode holographic elements,” Opt. Commun. 98, 24–28 (1993).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

J. Jahns, S. Walker, “Imaging with planar optical systems,” Opt. Commun. 76, 313–317 (1989).
[CrossRef]

Opt. Eng.

R. C. Fairchild, J. R. Fienup, “Computer originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

A. N. Putilin, V. N. Morozov, Q. Huang, J. H. Caufield, “Waveguide holograms with white light illumination,” Opt. Eng. 30, 1615–1619 (1991).
[CrossRef]

Opt. Lett.

Other

E. Socol, Y. Amitai, A. A. Friesem, “Design of planar optical interconnects,” in Ninth Meeting on Optical Engineering in Israel, I. Shladov, ed., Proc. SPIE2426, 433–442 (1995).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Geometry for recording the final HOE with recording wave fronts derived from CGH’s.

Fig. 2
Fig. 2

Coordinate system for recording and readout of the HOE.

Fig. 3
Fig. 3

Computer-originated holographic optical element in a planar configuration.

Fig. 4
Fig. 4

Calculated diffraction efficiency for a spherical lens that has a grating function ϕ h d spherical.

Fig. 5
Fig. 5

Calculated diffraction efficiency for cylindrical lenses that have grating functions (a) ϕ h d cylindrical,x and (b) ϕ h d cylindrical,y .

Fig. 6
Fig. 6

Calculated diffraction efficiency for an imaging lens with a grating function ϕ h d imaging.

Equations (23)

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

ϕ i x ,   y = ϕ c x ,   y ± ϕ h x ,   y ,
ϕ h x ,   y = ϕ o x ,   y - ϕ r x ,   y ,
k ˆ q = λ p 2 π ϕ q ,
k h = λ o 2 π ϕ h x ,   y = λ o Λ x x ,   y   x ˆ + λ o Λ y x ,   y   y ˆ ,
Λ x x ,   y = λ o sin   β o x ,   y cos   α o x ,   y - sin   β r x ,   y cos   α r x ,   y , Λ y x ,   y = λ o sin   α o x ,   y - sin   α r x ,   y ,
k x i = k x c ± μ k x h , k y i = k y c ± μ k y h , k z i = ± 1 - k x i 2 - k y i 2 1 / 2 ,
sign k z i = sign k z c ,     transmission   hologram , sign k z i = - sign k z c ,     reflection   hologram .
k h x ,   y = k ˆ i x ,   y - k ˆ c x ,   y = 1 μ k ˆ o x ,   y - k ˆ r x ,   y .
k h d x ,   y = λ c 2 π ϕ h d x ,   y .
k x h d x ,   y = k x i x ,   y - k x c x ,   y , k y h d x ,   y = k y i x ,   y - k y c x ,   y , k z h d x ,   y = 1 - k x h d 2 x ,   y - k x h d 2 x ,   y 1 / 2 .
k r x ,   y = k r x ,   y = 0 .
ϕ r d x ,   y = 2 π λ o     k r x ,   y d x .
ϕ o d x ,   y = ϕ h d x ,   y + ϕ r d x ,   y .
ϕ h d spherical x ,   y = - 2 π λ c x 2 + y 2 + z 2 1 / 2 - nx   sin   θ ,
k x c = - x n x 2 + y 2 + z 2 1 / 2 , k y c = - y n x 2 + y 2 + z 2 1 / 2 , k z c = 1 - k x c 2 - k y c 2 1 / 2 .
k x i = sin   θ , k y i = 0 , k z i = 1 - k x i 2 - k y i 2 1 / 2 .
S - μ k x i - k x c , C - μ k z i - k z c .
k x o - k x r = S , k z o - k z r = C .
k x r = - b + b 2 - 4 ac 2 a ,
a = 4 S 2 + 4 C 2 , b = 4 S 3 + 4 C 2 S , c = S 4 + C 4 - 4 C 2 + 2 C 2 S 2 .
ϕ h d cylindrical , x x ,   y = - 2 π λ c x 2 + z 2 - nx   sin   θ .
ϕ h d cylindrical , y x ,   y = - 2 π λ c y 2 + z 2 - nx   sin   θ .
ϕ h d imaging x ,   y = - 2 π λ c x 2 + y 2 + z 2 1 / 2 - n x - x o 2 + y 2 + z o 2 1 / 2 .

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