Abstract

The properties of relief phase holograms in unhardened dichromated gelatin have been investigated. Relief holograms are particularly attractive when it is desired to duplicate the stored information. Unhardened layers of gelatin were exposed with two collimated laser beams and developed by washing away the unexposed material. This resulted in high quality gratings with very low scattering. By varying the spatial frequency, it was found that the depth of modulation starts to decrease approximately linearly at a few microns grating spacing. This limited spatial resolution was shown not to be a property of the basic photochemical process of polymerization but due to a development step. Larger modulation and diffraction efficiencies can be produced at the higher frequencies by other development procedures, but they also result in increased scattering which is incompatible with high quality holograms.

© 1971 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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1970 (1)

1968 (2)

T. A. Shankoff, Appl. Opt. 7, 2102 (1968).
[Crossref]

T. A. Shankoff, R. K. Curran, Appl. Phys. Lett. 13, 239 (1968).
[Crossref]

1966 (3)

1965 (1)

W. T. Cathey, J. Opt. Soc. Amer. 55, 457 (1965).
[Crossref]

Bartolini, R. A.

R. A. Bartolini, W. J. Hannan, C. S. Ih, RCA Labs; private communication.

Billings, B. C.

Brumm, D. B.

Cathey, W. T.

W. T. Cathey, J. Opt. Soc. Amer. 55, 457 (1965).
[Crossref]

Curran, R. K.

R. K. Curran, T. A. Shankoff, Appl. Opt. 9, 1651 (1970).
[Crossref] [PubMed]

T. A. Shankoff, R. K. Curran, Appl. Phys. Lett. 13, 239 (1968).
[Crossref]

Hannan, W. J.

R. A. Bartolini, W. J. Hannan, C. S. Ih, RCA Labs; private communication.

Harris, F. S.

Ih, C. S.

R. A. Bartolini, W. J. Hannan, C. S. Ih, RCA Labs; private communication.

Kosar, J.

J. Kosar, Light-Sensitive Systems (Wiley, New York, 1965), Chap. 2.

Meier, R. W.

Shankoff, T. A.

R. K. Curran, T. A. Shankoff, Appl. Opt. 9, 1651 (1970).
[Crossref] [PubMed]

T. A. Shankoff, Appl. Opt. 7, 2102 (1968).
[Crossref]

T. A. Shankoff, R. K. Curran, Appl. Phys. Lett. 13, 239 (1968).
[Crossref]

Sherman, G. C.

Urbach, J. C.

Watson, G. N.

E. T. Whittaker, G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge U.P., Cambridge, 1965), Sec. 17.23.

Whittaker, E. T.

E. T. Whittaker, G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge U.P., Cambridge, 1965), Sec. 17.23.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

T. A. Shankoff, R. K. Curran, Appl. Phys. Lett. 13, 239 (1968).
[Crossref]

J. Opt. Soc. Amer. (1)

W. T. Cathey, J. Opt. Soc. Amer. 55, 457 (1965).
[Crossref]

Other (3)

J. Kosar, Light-Sensitive Systems (Wiley, New York, 1965), Chap. 2.

E. T. Whittaker, G. N. Watson, A Course in Modern Analysis, 4th ed. (Cambridge U.P., Cambridge, 1965), Sec. 17.23.

R. A. Bartolini, W. J. Hannan, C. S. Ih, RCA Labs; private communication.

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Figures (6)

Fig. 1
Fig. 1

Diffraction efficiency of a DCG layer, 0.7 μm thick, during exposure with 441-nm light. The points are experimental, the curves are calculated for a sinusoidal phase variation: Curve A represents 100% modulation, curve B, 82%. The two parameters in Eq. (15) are adjusted to fit the experimental points up to the peak of the curve.

Fig. 2
Fig. 2

Photomicrograph of a well developed grating of 6.3-μm spacing (630×).

Fig. 3
Fig. 3

Experimental diffraction efficiencies for three water-developed gratings. The curves are the calculated values from Eq. (8) with the values of a chosen to produce the best fit to the data. Note that Eq. (8) applies only for integer values of n. The complete curves are only shown to provide continuity.

Fig. 4
Fig. 4

Measured diffraction efficiencies for the 6.3-μm water-developed grating (×). The smooth curves are the best fits of the theoretical equation for two diffracent phase profiles: (A) sinusoidal variation with a = 4.2; (B) square wave variation.

Fig. 5
Fig. 5

Maximum depth of modulation, Δd vs grating period, D.

Fig. 6
Fig. 6

Scanning electron micrographs of two gratings of 0.85-μm spacings both of which were developed in water and isopropyl alcohol (5020×): (a) 3-sec exposure, high efficiency and high scattering, (b) 5-sec exposure, low efficiency and low scattering.

Tables (1)

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Table I Reflection Diffraction Efficiencies of Gratings Developed in Water Only

Equations (19)

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φ [ x + ( 2 π / β ) ] = φ ( x ) .
E = E 0 e i φ ( x ) ,
E = 1 2 a 0 e 0 e i k x sin θ 0 + n = 1 [ a n 2 e 0 e i ( k sin θ 0 + n β ) x + a n 2 e 0 e i ( k sin θ 0 - n β ) x ] ,
a n = β π 0 2 π / β e i φ ( τ ) cos n β τ d τ .
η ± n = I ± n I 0 = | a n 2 | 2
sin θ 0 ± n ( β / k ) < 1.
φ ( x ) = a cos β x + b ,
η ± n = J n 2 ( a ) .
I = I 0 ( 1 + cos β x ) .
D = 2 π / β = λ / ( 2 sin α )
Δ n ( r ) = N ( r ) δ n ,
Δ n max = N 0 δ n .
Δ φ ( r ) = 2 π d λ Δ n ( r ) = N ( r ) N 0 Δ φ max .
d N ( r ) / d t = [ N 0 - N ( r ) ] σ F ( r )
N ( r ) = N 0 ( 1 - e - α 0 F ( r ) t / N 0 ) = N 0 ( 1 - e - α 0 I ( r ) t / h ν N 0 ) ,
η 1 ( t ) = | β 2 π 0 2 π / β exp [ i Δ φ max ( 1 - e - α 0 I 0 ( 1 + cos β τ ) t / h ν N 0 ) ] × cos β τ d τ | 2 .
Δ φ max = 0.04
α 0 I 0 / h ν N 0 = 0.074 sec - 1 .
Δ d = a λ / 2 π .

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