Abstract

We present a theoretical model based on the coupled-mode theory and use this model to analyze the diffraction properties of volume holographic diffusers, such as diffraction efficiency and wavelength sensitivity. For small diffraction angles our results predict that the diffraction efficiency exhibits a blue shift for its maximum value and a dip at the recording wavelength. For color displays we propose and analyze the wavelength-multiplexed volume holograms recorded with three primary colors, red, green, and blue. Furthermore, our results demonstrate the enhancement of wavelength tolerance for a thin holographic medium, which can serve as a wideband diffuser over the entire visible range.

© 1996 Optical Society of America

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  1. M. Wenyon, P. Ralli, “Mass production of volume holographic diffusers,” SID 94 Digest (Society for Information Display, Santa Ana, Calif., 1994), pp. 285–288 (1994).
  2. S. Wadle, D. Wuest, J. Cantalupo, “Holographic diffusers,” Opt. Eng. 33, 213–218 (1994).
    [CrossRef]
  3. S. Wadle, R. S. Lakes, “Holographic diffusers—polarization effects,” Opt. Eng. 33, 1084–1088 (1994).
    [CrossRef]
  4. W. E. Knowles Middleton, “Diffusion of ultraviolet and visible light by ground surfaces of fused quartz,”J. Opt. Soc. Am. 50, 747–749 (1960).
    [CrossRef]
  5. B. S. Hockley, R. Pawluczyk, “Chromatically corrected directional diffusing screen,” U.S. Patent5,046,793 (September10, 1991).
  6. See, for example, P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  7. R. T. Ingwall, M. Troll, “Mechanism of hologram formation in DMP-128 photopolymer,” Opt. Eng. 28, 586–591 (1989).
    [CrossRef]
  8. W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keys, “Photopolymers for holography,” in Practical Holography IV, S. A. Benton, ed., Proc. SPIE1212, 20–29 (1990).
    [CrossRef]
  9. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  10. R. D. Rallison, S. R. Schicker, “Using thick DCG, 30 to 100 microns,” in Practical Holography VII: Imaging and Materials, S. A. Brenton, ed., Proc. SPIE1914, 82–90 (1993).
    [CrossRef]
  11. C. Gu, P. Yeh, “Applications of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
    [CrossRef]
  12. D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
    [CrossRef] [PubMed]
  13. P. Yeh, C. Gu, eds., Photorefractive Materials, Effects, and Applications, Vol. CR48 of Critical Reviews Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994).
  14. C. Gu, J. Hong, I. McMichael, R. Saxena, F. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  15. K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
    [CrossRef] [PubMed]
  16. See, for example, H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).
  17. D. G. Hall, ed., Selected Papers on Coupled-Mode Theory in Guided-Wave Optics, Vol. MS84 of Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).
  18. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

1994 (3)

C. Gu, P. Yeh, “Applications of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
[CrossRef]

S. Wadle, D. Wuest, J. Cantalupo, “Holographic diffusers,” Opt. Eng. 33, 213–218 (1994).
[CrossRef]

S. Wadle, R. S. Lakes, “Holographic diffusers—polarization effects,” Opt. Eng. 33, 1084–1088 (1994).
[CrossRef]

1993 (1)

1992 (1)

1990 (1)

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
[CrossRef] [PubMed]

1989 (1)

R. T. Ingwall, M. Troll, “Mechanism of hologram formation in DMP-128 photopolymer,” Opt. Eng. 28, 586–591 (1989).
[CrossRef]

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1969 (1)

See, for example, H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).

1960 (1)

Brady, D.

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
[CrossRef] [PubMed]

Cantalupo, J.

S. Wadle, D. Wuest, J. Cantalupo, “Holographic diffusers,” Opt. Eng. 33, 213–218 (1994).
[CrossRef]

Curtis, K.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Gu, C.

Gu, X.-G.

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
[CrossRef] [PubMed]

Hockley, B. S.

B. S. Hockley, R. Pawluczyk, “Chromatically corrected directional diffusing screen,” U.S. Patent5,046,793 (September10, 1991).

Hong, J.

Ingwall, R. T.

R. T. Ingwall, M. Troll, “Mechanism of hologram formation in DMP-128 photopolymer,” Opt. Eng. 28, 586–591 (1989).
[CrossRef]

Keys, D. E.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keys, “Photopolymers for holography,” in Practical Holography IV, S. A. Benton, ed., Proc. SPIE1212, 20–29 (1990).
[CrossRef]

Knowles Middleton, W. E.

Kogelnik, H.

See, for example, H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).

Lakes, R. S.

S. Wadle, R. S. Lakes, “Holographic diffusers—polarization effects,” Opt. Eng. 33, 1084–1088 (1994).
[CrossRef]

Lin, S.

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
[CrossRef] [PubMed]

McMichael, I.

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Mok, F.

Monroe, B. M.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keys, “Photopolymers for holography,” in Practical Holography IV, S. A. Benton, ed., Proc. SPIE1212, 20–29 (1990).
[CrossRef]

Pawluczyk, R.

B. S. Hockley, R. Pawluczyk, “Chromatically corrected directional diffusing screen,” U.S. Patent5,046,793 (September10, 1991).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Psaltis, D.

K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
[CrossRef] [PubMed]

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
[CrossRef] [PubMed]

Ralli, P.

M. Wenyon, P. Ralli, “Mass production of volume holographic diffusers,” SID 94 Digest (Society for Information Display, Santa Ana, Calif., 1994), pp. 285–288 (1994).

Rallison, R. D.

R. D. Rallison, S. R. Schicker, “Using thick DCG, 30 to 100 microns,” in Practical Holography VII: Imaging and Materials, S. A. Brenton, ed., Proc. SPIE1914, 82–90 (1993).
[CrossRef]

Saxena, R.

Schicker, S. R.

R. D. Rallison, S. R. Schicker, “Using thick DCG, 30 to 100 microns,” in Practical Holography VII: Imaging and Materials, S. A. Brenton, ed., Proc. SPIE1914, 82–90 (1993).
[CrossRef]

Smothers, W. K.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keys, “Photopolymers for holography,” in Practical Holography IV, S. A. Benton, ed., Proc. SPIE1212, 20–29 (1990).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Troll, M.

R. T. Ingwall, M. Troll, “Mechanism of hologram formation in DMP-128 photopolymer,” Opt. Eng. 28, 586–591 (1989).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Wadle, S.

S. Wadle, D. Wuest, J. Cantalupo, “Holographic diffusers,” Opt. Eng. 33, 213–218 (1994).
[CrossRef]

S. Wadle, R. S. Lakes, “Holographic diffusers—polarization effects,” Opt. Eng. 33, 1084–1088 (1994).
[CrossRef]

Weber, A. M.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keys, “Photopolymers for holography,” in Practical Holography IV, S. A. Benton, ed., Proc. SPIE1212, 20–29 (1990).
[CrossRef]

Wenyon, M.

M. Wenyon, P. Ralli, “Mass production of volume holographic diffusers,” SID 94 Digest (Society for Information Display, Santa Ana, Calif., 1994), pp. 285–288 (1994).

Wuest, D.

S. Wadle, D. Wuest, J. Cantalupo, “Holographic diffusers,” Opt. Eng. 33, 213–218 (1994).
[CrossRef]

Yeh, P.

C. Gu, P. Yeh, “Applications of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
[CrossRef]

See, for example, P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Bell Syst. Tech. J. (1)

See, for example, H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).

Int. J. Nonlinear Opt. Phys. (1)

C. Gu, P. Yeh, “Applications of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (1)

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artifical neural networks,” Nature 343, 325–330 (1990).
[CrossRef] [PubMed]

Opt. Eng. (3)

R. T. Ingwall, M. Troll, “Mechanism of hologram formation in DMP-128 photopolymer,” Opt. Eng. 28, 586–591 (1989).
[CrossRef]

S. Wadle, D. Wuest, J. Cantalupo, “Holographic diffusers,” Opt. Eng. 33, 213–218 (1994).
[CrossRef]

S. Wadle, R. S. Lakes, “Holographic diffusers—polarization effects,” Opt. Eng. 33, 1084–1088 (1994).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Other (8)

R. D. Rallison, S. R. Schicker, “Using thick DCG, 30 to 100 microns,” in Practical Holography VII: Imaging and Materials, S. A. Brenton, ed., Proc. SPIE1914, 82–90 (1993).
[CrossRef]

D. G. Hall, ed., Selected Papers on Coupled-Mode Theory in Guided-Wave Optics, Vol. MS84 of Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keys, “Photopolymers for holography,” in Practical Holography IV, S. A. Benton, ed., Proc. SPIE1212, 20–29 (1990).
[CrossRef]

B. S. Hockley, R. Pawluczyk, “Chromatically corrected directional diffusing screen,” U.S. Patent5,046,793 (September10, 1991).

See, for example, P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

P. Yeh, C. Gu, eds., Photorefractive Materials, Effects, and Applications, Vol. CR48 of Critical Reviews Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994).

M. Wenyon, P. Ralli, “Mass production of volume holographic diffusers,” SID 94 Digest (Society for Information Display, Santa Ana, Calif., 1994), pp. 285–288 (1994).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram for recording a holographic diffuser. The beam splitters are denoted by BS.

Fig. 2
Fig. 2

Reading the recorded volume hologram with a planar reading wave. Since the diffracted beams propagate in all directions, the hologram works as a diffuser, i.e., the hologram reconstruction process diffuses the reading plane wave.

Fig. 3
Fig. 3

k-space representation of the Bragg mismatch that is due to wavelength deviation. The inner and outer circles correspond to the normal surfaces at the recording and reading wavelengths, respectively. The grating Kg is recorded with two plane waves, k0 and kg . If the wavelength during readout is different from that during recording, there will be a Bragg mismatch Δβ in the z direction. The diffraction angle θg deviates from the angle between the two recording plane waves, θgr.

Fig. 4
Fig. 4

Diffraction efficiency versus incident wavelength and diffraction angle. The gratings are recorded at 645 nm by a plane wave and a diffused wave, which is decomposed into ten plane waves in the simulation.

Fig. 5
Fig. 5

Diffraction efficiency versus incident wavelength for the diffracted plane wave satisfying Bragg’s condition in the transverse direction with the first grating. The diffraction angle is related to the incident wavelength by Eq. (8). The gratings are recorded at 645 nm with a plane wave and a diffused wave, which is decomposed into ten plane waves in the simulation.

Fig. 6
Fig. 6

Diffraction efficiency versus incident wavelength and diffraction angle. The 30 gratings are wavelength-multiplexed holograms, each of which is recorded with a plane wave and a diffused wave that is decomposed into ten plane waves. The recording wavelengths are chosen to be red (645 nm), green (540 nm), and blue (470 nm). (a) Diffractions due to the gratings recorded by red illumination, (b) diffractions due to the gratings recorded by green illumination, (c) diffractions due to the gratings recorded by blue illumination.

Fig. 7
Fig. 7

Diffraction efficiency versus incident wavelength and diffraction angle of a thin holographic medium with a thickness of 20 μm. The gratings are recorded monochromatically at 645 nm with a plane wave and a diffused wave, which is decomposed into ten plane waves in the simulation.

Tables (4)

Tables Icon

Table 1 Wave Vectors of Incident Waves in Recording

Tables Icon

Table 2 Relative Amplitudes and Wave Vectors of the Multiple Gratings Recorded by Monochromatic Illumination

Tables Icon

Table 3 Relative Amplitudes and Wave Vectors of the Multiple Gratings Recorded by RGB Illuminations

Tables Icon

Table 4 Relative Amplitudes and Wave Vectors of Multiple Gratings Recorded by Red Illumination for a Thin Medium

Equations (12)

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= 0 r [ 1 + Δ ( r ) ] ,
Δ ( x , y , z ) = g g exp ( i K g · r ) + c . c .
Δ n ( x , y , z ) = g n g exp ( i K g · r ) + c . c .
E = m A m ( z ) exp [ i ( ω t k m · r ) ] + c . c .,
2 E + ω 2 μ 0 r [ 1 + Δ g ( r ) ] E = 0 ,
{ m ( d 2 A m d z 2 2 i k m z d A m d z ) exp [ i ( k m · r ) ] + m g ω 2 μ 0 r g A m exp [ i ( k m · r + K g · r ) ] + m g ω 2 μ 0 r g * A m × exp [ i ( k m · r K g · r ) ] } + c . c . = 0 ,
d A a d z = i m a g ω 2 μ 0 r g 2 β a A m × exp [ i ( β a β m K g z ) z ]
d A a d z = i m a g ω 2 μ 0 r g * 2 β a A m × exp [ i ( β a β m K g z ) z ] ,
k a x k m x K g x = 0 , k a y k m y K g y = 0 .
sin θ g = λ λ r sin θ g r ,
d A 0 d z = i g = 1 10 | ω 2 μ 0 r g 2 β 0 | exp ( i ϕ g ) A g exp ( i Δ β g z ) , d A g d z = i | ω 2 μ 0 r g 2 β g | exp ( i ϕ g ) A 0 exp ( i Δ β g z ) ,
d A 0 d z = i g = 1 10 | ω 2 μ 0 r g 2 β 0 | A g exp ( i Δ β g z ) , d A g d z = i | ω 2 μ 0 r g 2 β g | A 0 exp ( i Δ β g z ) .

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