Abstract

We present a methodology for analyzing the characteristics of a photosensitive material for holography. When two Gaussian beams of equal intensities are exactly superimposed on the recording material, the modulation of the interference pattern is equal to unity. When they are no longer exactly superimposed, this modulation varies from one to zero depending on the analyzed point. On the other hand, the modulation is constant in a direction that is perpendicular to the incident plane. Therefore it is possible to consider a complete analysis (point by point) of only one holographic grating to measure the diffraction efficiency η at a given modulation versus exposure or for varying modulation (or beam ratio K) for a given exposure. We present the results that are obtained with an experimental setup that was devised for that purpose. From these measurements it was possible to extract various parameters such as refractive-index modulation of the photosensitive support. The tested recording materials consist of films of dichromated gelatin and films of dichromate polyvinyl alcohol.

© 1992 Optical Society of America

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References

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  1. C. Braüchle, D. M. Burland, “Holographic methods for the investigation of photochemical and photophysical properties of molecules,” Angew. Chem. Int. Eds. 22, 582–598 (1983).
    [Crossref]
  2. C. Braüchle, “Holography as a new tool for investigating photochemical reaction in the solid-state,” Mol. Cryst. Liq. Cryst. 96, 83–98 (1983).
    [Crossref]
  3. D. M. Burland, D. Braüchle, “The use of holography to investigate complex photochemical reactions,” J. Chem. Phys. 76, 4502–4512 (1982).
    [Crossref]
  4. C. Braüchle, D. M. Burland, G. C. Bjorklund, “Hydrogen abstraction by benzophenone studied by holographic photochemistry,” J. Phys. Chem. 85, 123–127 (1981).
    [Crossref]
  5. D. M. Burland, “Holographic methods for investigating solid-stade photochemistry,” IEEE J. Quantum Electron. QE-22, 1469–1475 (1986).
    [Crossref]
  6. G. C. Bjorklund, D. M. Burland, D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
    [Crossref]
  7. F. W. Deeg, J. Pinsl, C. Braüchle, “New grating experiments in the study of irreversible photochemical reactions,” IEEE J. Quantum Electron. QE-22, 1476–1486 (1986).
    [Crossref]
  8. F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
    [Crossref]
  9. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

1986 (2)

D. M. Burland, “Holographic methods for investigating solid-stade photochemistry,” IEEE J. Quantum Electron. QE-22, 1469–1475 (1986).
[Crossref]

F. W. Deeg, J. Pinsl, C. Braüchle, “New grating experiments in the study of irreversible photochemical reactions,” IEEE J. Quantum Electron. QE-22, 1476–1486 (1986).
[Crossref]

1983 (3)

F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
[Crossref]

C. Braüchle, D. M. Burland, “Holographic methods for the investigation of photochemical and photophysical properties of molecules,” Angew. Chem. Int. Eds. 22, 582–598 (1983).
[Crossref]

C. Braüchle, “Holography as a new tool for investigating photochemical reaction in the solid-state,” Mol. Cryst. Liq. Cryst. 96, 83–98 (1983).
[Crossref]

1982 (1)

D. M. Burland, D. Braüchle, “The use of holography to investigate complex photochemical reactions,” J. Chem. Phys. 76, 4502–4512 (1982).
[Crossref]

1981 (1)

C. Braüchle, D. M. Burland, G. C. Bjorklund, “Hydrogen abstraction by benzophenone studied by holographic photochemistry,” J. Phys. Chem. 85, 123–127 (1981).
[Crossref]

1980 (1)

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

Alvarez, D. C.

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[Crossref]

Bjorklund, G. C.

C. Braüchle, D. M. Burland, G. C. Bjorklund, “Hydrogen abstraction by benzophenone studied by holographic photochemistry,” J. Phys. Chem. 85, 123–127 (1981).
[Crossref]

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[Crossref]

Braüchle, C.

F. W. Deeg, J. Pinsl, C. Braüchle, “New grating experiments in the study of irreversible photochemical reactions,” IEEE J. Quantum Electron. QE-22, 1476–1486 (1986).
[Crossref]

F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
[Crossref]

C. Braüchle, D. M. Burland, “Holographic methods for the investigation of photochemical and photophysical properties of molecules,” Angew. Chem. Int. Eds. 22, 582–598 (1983).
[Crossref]

C. Braüchle, “Holography as a new tool for investigating photochemical reaction in the solid-state,” Mol. Cryst. Liq. Cryst. 96, 83–98 (1983).
[Crossref]

C. Braüchle, D. M. Burland, G. C. Bjorklund, “Hydrogen abstraction by benzophenone studied by holographic photochemistry,” J. Phys. Chem. 85, 123–127 (1981).
[Crossref]

Braüchle, D.

D. M. Burland, D. Braüchle, “The use of holography to investigate complex photochemical reactions,” J. Chem. Phys. 76, 4502–4512 (1982).
[Crossref]

Burland, D. M.

D. M. Burland, “Holographic methods for investigating solid-stade photochemistry,” IEEE J. Quantum Electron. QE-22, 1469–1475 (1986).
[Crossref]

C. Braüchle, D. M. Burland, “Holographic methods for the investigation of photochemical and photophysical properties of molecules,” Angew. Chem. Int. Eds. 22, 582–598 (1983).
[Crossref]

D. M. Burland, D. Braüchle, “The use of holography to investigate complex photochemical reactions,” J. Chem. Phys. 76, 4502–4512 (1982).
[Crossref]

C. Braüchle, D. M. Burland, G. C. Bjorklund, “Hydrogen abstraction by benzophenone studied by holographic photochemistry,” J. Phys. Chem. 85, 123–127 (1981).
[Crossref]

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[Crossref]

Deeg, F. W.

F. W. Deeg, J. Pinsl, C. Braüchle, “New grating experiments in the study of irreversible photochemical reactions,” IEEE J. Quantum Electron. QE-22, 1476–1486 (1986).
[Crossref]

F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

Pinsl, J.

F. W. Deeg, J. Pinsl, C. Braüchle, “New grating experiments in the study of irreversible photochemical reactions,” IEEE J. Quantum Electron. QE-22, 1476–1486 (1986).
[Crossref]

F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
[Crossref]

Voitlander, J.

F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
[Crossref]

Angew. Chem. Int. Eds. (1)

C. Braüchle, D. M. Burland, “Holographic methods for the investigation of photochemical and photophysical properties of molecules,” Angew. Chem. Int. Eds. 22, 582–598 (1983).
[Crossref]

Bell. Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

IEEE J. Quantum Electron. (2)

D. M. Burland, “Holographic methods for investigating solid-stade photochemistry,” IEEE J. Quantum Electron. QE-22, 1469–1475 (1986).
[Crossref]

F. W. Deeg, J. Pinsl, C. Braüchle, “New grating experiments in the study of irreversible photochemical reactions,” IEEE J. Quantum Electron. QE-22, 1476–1486 (1986).
[Crossref]

J. Chem. Phys. (3)

F. W. Deeg, J. Pinsl, C. Braüchle, J. Voitlander, “The evaluation of photochemical quantum yields by holography,” J. Chem. Phys. 79, 1229–1234 (1983).
[Crossref]

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, “A holographic technique for investigating photochemical reactions,” J. Chem. Phys. 73, 4321–4328 (1980).
[Crossref]

D. M. Burland, D. Braüchle, “The use of holography to investigate complex photochemical reactions,” J. Chem. Phys. 76, 4502–4512 (1982).
[Crossref]

J. Phys. Chem. (1)

C. Braüchle, D. M. Burland, G. C. Bjorklund, “Hydrogen abstraction by benzophenone studied by holographic photochemistry,” J. Phys. Chem. 85, 123–127 (1981).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

C. Braüchle, “Holography as a new tool for investigating photochemical reaction in the solid-state,” Mol. Cryst. Liq. Cryst. 96, 83–98 (1983).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1

Gaussian distribution of the intensity profile of a laser beam (TEM00): Imax is the maximum intensity, Xc is the position of the central maximum, R is the distance from the center where I/Imax = 1/e2 = 0.1353.

Fig. 2
Fig. 2

Extension of the Gaussian profile as a function of incidence angle θ of the writing beams.

Fig. 3
Fig. 3

Isointensity curves of a Gaussian profile for two values of incidence angle θ: (a) θ = 15°, (b) θ = 40°; Imax = 100 mW/cm2, R = 17 mm. The intensity differential between two consecutive curves is 5 mW/cm2.

Fig. 4
Fig. 4

Three-dimension profile of incident intensity of the photosensitive material when the two beams are not superimposed perfectly.

Fig. 5
Fig. 5

Visibility of the fringes of the interference figure obtained with Fig. 4 profiles. For a given value of x, visibility is constant in the y direction.

Fig. 6
Fig. 6

Experimental setup for the grating recording. M1–M3 are mirrors, IT and ID are the transmitted and diffracted intensities.

Fig. 7
Fig. 7

Experimental setup for the grating analysis: VBS is the variable beam splitter, DF is the density filter, PDi (i = 1, 2, 3) are the photodetectors, R is the rotating table and the x-y scanning device.

Fig. 8
Fig. 8

Theoretical and experimental profiles of writing beams (y = 0): (a) ∊ = 0 mm, (b) ∊ = 10 mm, (c) ∊ = 30 mm, (d) ∊ = 40 mm.

Fig. 9
Fig. 9

Actual profiles [Itot (x, y)] of the total incident intensity in the recording material: (a) ∊ = 0 mm, (b) ∊ = 10 mm, (c) ∊ = 30 mm, (d) ∊ = 40 mm.

Fig. 10
Fig. 10

Diffraction efficiency η of DCG as a function of x for a given y (y = 10 mm).

Fig. 11
Fig. 11

Diffraction efficiency η of DCG as a function of exposure E(x, y). This figure was obtained from 6000 points.

Fig. 12
Fig. 12

Modulation of the refractive index n1 of the recording material used (DCG in this case) as a function of exposure E(x, y).

Fig. 13
Fig. 13

Diffraction efficiency η of DC PVA films as a function of y for a given x: (a) x = 60mm, (b) x = 57.5 mm, (c) x = 54.2 mm, (d) x = 51.7 mm.

Fig. 14
Fig. 14

Diffraction efficiency of DC PVA films as a function of exposure E(x, y). This figure was obtained from the corresponding data of Fig. 13. (a) K = 1, (b) K = 0.5, (c) K = 0.2, (d) K = 0.1.

Tables (1)

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Table I Development of DCG

Equations (15)

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I ( x , y ) = I max exp [ - 2 ( x 2 + y 2 ) R 2 ] ,
I R ( x , y ) = I R , max exp { - 2 R 2 [ ( x - x C R ) 2 cos 2 θ + ( y - y C R ) 2 ] } ,
I O ( x , y ) = I O , max exp { - 2 R 2 [ ( x - x C O ) 2 cos 2 ( - θ ) + ( y - y C O ) 2 ] } ,
I R ( x , y ) = I R , max exp × { - 2 R 2 [ [ x - ( x C R - x d ) ] 2 cos 2 θ + ( y - y C R ) 2 ] } , I O ( x , y ) = I O , max exp × { - 2 R 2 [ [ x - ( x C O + x d ) ] 2 cos 2 ( - θ ) + ( y - y C O ) 2 ] } ,
= λ 2 sin θ ,
η = I D I i ,
I ( x , y ) = [ I R ( x , y ) + I O ( x , y ) ] [ 1 + V cos ( 2 π x Λ ) ] ,
V ( x , y ) = 2 [ I R ( x , y ) I O ( x , y ) ] 1 / 2 I R ( x , y ) + I O ( x , y )
η = I D I i = exp ( - 2 α 0 d cos θ 1 ) ( sin 2 π n 1 d λ cos θ 1 + sinh 2 α 1 d 2 cos θ 1 ) ,
n ( x ) = n 0 + n 1 cos ( 2 π x ) + n 2 cos ( 4 π x ) + .
η = sin 2 ( π n 1 d λ 1 cos θ 1 ) ,
η = ( π n 1 d λ 1 cos θ 1 ) 2 .
I max = 100 mW / cm 2 , R = 17 mm , x C R = x C O = 60 mm , y C R = y C O = 30 mm .
η = sin 2 [ π n 1 ( x , y ) d λ 1 cos ( θ 1 ) ] .
n 1 ( x , y ) = arcsin η λ 1 cos ( θ 1 ) π d

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