Abstract

Determination of the bias refractive index of a holographic emulsion before exposure and after development is an important factor in the design of holographic optical elements. Several experimental methods are discussed for determining the bias index of a volume hologram in dichromated gelatin, and the results for each technique are presented. It is shown experimentally that these measurement methods yield different results for the same hologram, and the cause of the differences is proposed to be a variation of the bias index with depth in the hologram. An index measurement technique is also presented that accounts for variation in the bias index and is shown to yield an accurate value for the bias index.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Belendez, I. Pascual, A. Fimia, “Efficiency of thick phase holograms in the presence of shear-type effects due to processing,” J. Mod. Opt. 39, 889–899 (1992).
    [CrossRef]
  2. R. Pawluczyk, “Modified Brewster angle technique for the measurement of the refractive index of a DCG layer,” Appl. Opt. 29, 589–592 (1990).
    [CrossRef] [PubMed]
  3. X. Chang, Y. Guo, L. Guo, “Measurement of relief depth and refractive index variation of phase hologram,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1732, 612–617 (1992).
  4. V. Rzhevskii, N. Rupchev, “Influence of photochemical processes on the refractive index and layer thickness of dichromated gelatin,” Opt. Spectrosc. 68, 809–810 (1990).
  5. T. A. Shankoff, “Phase holograms in dichromated gelatin,” Appl. Opt. 7, 2101–2105 (1968).
    [CrossRef] [PubMed]
  6. T. C. Billiard, R. Pawluczyk, B. S. Hockley, “The sensitization process of dichromated gelatin,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 104–109 (1989).
  7. J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 268–278 (1991).
  8. T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1914, 91–100 (1993).
  9. W. C. Sweatt, “Designing and constructing thick holographic optical elements,” Appl. Opt. 17, 1220–1227 (1978).
    [CrossRef] [PubMed]
  10. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  11. R. D. Rallison, S. R. Schicker, “Polarization properties of gelatin holograms,” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667, 266–275 (1992).
  12. S. Sjolinder, “Dichromated gelatin and the mechanism of hologram formation,” Photogr. Sci. Eng. 25, 112–118 (1981).
  13. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1986), p. 43.
  14. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), p. 282.
  15. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1988), pp. 104–105.
  16. D. J. Cooke, A. A. Ward, “Reflection-hologram processing for high efficiency in silver-halide emulsions,” Appl. Opt. 23, 934–941 (1984).
    [CrossRef] [PubMed]
  17. R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1990), p. 125.
  18. D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chap. 2.
  19. P. Yen, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 86–88.
  20. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986), pp. 705–708.
  21. N. Chateau, J. C. Saget, P. Chavel, “Diffraction analysis and experimental investigation of reflection-free holographic phase gratings,” J. Eur. Opt. Soc. A 2, 299–314 (1993).
    [CrossRef]
  22. E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. A 4, 2061–2080 (1987).
    [CrossRef]
  23. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 9, 2909–2947 (1969).

1993

N. Chateau, J. C. Saget, P. Chavel, “Diffraction analysis and experimental investigation of reflection-free holographic phase gratings,” J. Eur. Opt. Soc. A 2, 299–314 (1993).
[CrossRef]

1992

A. Belendez, I. Pascual, A. Fimia, “Efficiency of thick phase holograms in the presence of shear-type effects due to processing,” J. Mod. Opt. 39, 889–899 (1992).
[CrossRef]

1990

V. Rzhevskii, N. Rupchev, “Influence of photochemical processes on the refractive index and layer thickness of dichromated gelatin,” Opt. Spectrosc. 68, 809–810 (1990).

R. Pawluczyk, “Modified Brewster angle technique for the measurement of the refractive index of a DCG layer,” Appl. Opt. 29, 589–592 (1990).
[CrossRef] [PubMed]

1987

1984

1983

1981

S. Sjolinder, “Dichromated gelatin and the mechanism of hologram formation,” Photogr. Sci. Eng. 25, 112–118 (1981).

1978

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 9, 2909–2947 (1969).

1968

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), p. 282.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), p. 282.

Belendez, A.

A. Belendez, I. Pascual, A. Fimia, “Efficiency of thick phase holograms in the presence of shear-type effects due to processing,” J. Mod. Opt. 39, 889–899 (1992).
[CrossRef]

Billiard, T. C.

T. C. Billiard, R. Pawluczyk, B. S. Hockley, “The sensitization process of dichromated gelatin,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 104–109 (1989).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1986), p. 43.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986), pp. 705–708.

Campbell, E. W.

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1914, 91–100 (1993).

Chang, X.

X. Chang, Y. Guo, L. Guo, “Measurement of relief depth and refractive index variation of phase hologram,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1732, 612–617 (1992).

Chateau, N.

N. Chateau, J. C. Saget, P. Chavel, “Diffraction analysis and experimental investigation of reflection-free holographic phase gratings,” J. Eur. Opt. Soc. A 2, 299–314 (1993).
[CrossRef]

Chavel, P.

N. Chateau, J. C. Saget, P. Chavel, “Diffraction analysis and experimental investigation of reflection-free holographic phase gratings,” J. Eur. Opt. Soc. A 2, 299–314 (1993).
[CrossRef]

Cooke, D. J.

Fimia, A.

A. Belendez, I. Pascual, A. Fimia, “Efficiency of thick phase holograms in the presence of shear-type effects due to processing,” J. Mod. Opt. 39, 889–899 (1992).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Guo, L.

X. Chang, Y. Guo, L. Guo, “Measurement of relief depth and refractive index variation of phase hologram,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1732, 612–617 (1992).

Guo, Y.

X. Chang, Y. Guo, L. Guo, “Measurement of relief depth and refractive index variation of phase hologram,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1732, 612–617 (1992).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1988), pp. 104–105.

Hockley, B. S.

T. C. Billiard, R. Pawluczyk, B. S. Hockley, “The sensitization process of dichromated gelatin,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 104–109 (1989).

Kim, T. J.

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1914, 91–100 (1993).

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 9, 2909–2947 (1969).

Kostuk, R. K.

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1914, 91–100 (1993).

Loeffler, M. F.

J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 268–278 (1991).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chap. 2.

Moharam, M. G.

Pascual, I.

A. Belendez, I. Pascual, A. Fimia, “Efficiency of thick phase holograms in the presence of shear-type effects due to processing,” J. Mod. Opt. 39, 889–899 (1992).
[CrossRef]

Pawluczyk, R.

R. Pawluczyk, “Modified Brewster angle technique for the measurement of the refractive index of a DCG layer,” Appl. Opt. 29, 589–592 (1990).
[CrossRef] [PubMed]

T. C. Billiard, R. Pawluczyk, B. S. Hockley, “The sensitization process of dichromated gelatin,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 104–109 (1989).

Rallison, R. D.

R. D. Rallison, S. R. Schicker, “Polarization properties of gelatin holograms,” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667, 266–275 (1992).

Rupchev, N.

V. Rzhevskii, N. Rupchev, “Influence of photochemical processes on the refractive index and layer thickness of dichromated gelatin,” Opt. Spectrosc. 68, 809–810 (1990).

Rzhevskii, V.

V. Rzhevskii, N. Rupchev, “Influence of photochemical processes on the refractive index and layer thickness of dichromated gelatin,” Opt. Spectrosc. 68, 809–810 (1990).

Saget, J. C.

N. Chateau, J. C. Saget, P. Chavel, “Diffraction analysis and experimental investigation of reflection-free holographic phase gratings,” J. Eur. Opt. Soc. A 2, 299–314 (1993).
[CrossRef]

Salter, J. L.

J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 268–278 (1991).

Schicker, S. R.

R. D. Rallison, S. R. Schicker, “Polarization properties of gelatin holograms,” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667, 266–275 (1992).

Shankoff, T. A.

Sjolinder, S.

S. Sjolinder, “Dichromated gelatin and the mechanism of hologram formation,” Photogr. Sci. Eng. 25, 112–118 (1981).

Sweatt, W. C.

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1990), p. 125.

Ward, A. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1986), p. 43.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986), pp. 705–708.

Yen, P.

P. Yen, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 86–88.

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 9, 2909–2947 (1969).

J. Eur. Opt. Soc. A

N. Chateau, J. C. Saget, P. Chavel, “Diffraction analysis and experimental investigation of reflection-free holographic phase gratings,” J. Eur. Opt. Soc. A 2, 299–314 (1993).
[CrossRef]

J. Mod. Opt.

A. Belendez, I. Pascual, A. Fimia, “Efficiency of thick phase holograms in the presence of shear-type effects due to processing,” J. Mod. Opt. 39, 889–899 (1992).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Spectrosc.

V. Rzhevskii, N. Rupchev, “Influence of photochemical processes on the refractive index and layer thickness of dichromated gelatin,” Opt. Spectrosc. 68, 809–810 (1990).

Photogr. Sci. Eng.

S. Sjolinder, “Dichromated gelatin and the mechanism of hologram formation,” Photogr. Sci. Eng. 25, 112–118 (1981).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1986), p. 43.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989), p. 282.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1988), pp. 104–105.

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1990), p. 125.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chap. 2.

P. Yen, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 86–88.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1986), pp. 705–708.

T. C. Billiard, R. Pawluczyk, B. S. Hockley, “The sensitization process of dichromated gelatin,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 104–109 (1989).

J. L. Salter, M. F. Loeffler, “Comparison of dichromated gelatin and DuPont HRF-700 photopolymer as media for holographic notch filters,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 268–278 (1991).

T. J. Kim, E. W. Campbell, R. K. Kostuk, “Determination of average refractive index of spin coated DCG films for HOE fabrication,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1914, 91–100 (1993).

R. D. Rallison, S. R. Schicker, “Polarization properties of gelatin holograms,” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667, 266–275 (1992).

X. Chang, Y. Guo, L. Guo, “Measurement of relief depth and refractive index variation of phase hologram,” in Holographics International ’92, Y. N. Denisyuk, F. Wyrowski, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1732, 612–617 (1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

(a) Volume hologram that shows shrinkage and shear between construction and reconstruction. (b) Fringe rotation that is due to shrinkage, shear, and shrinkage and shear (from left to right).

Fig. 2
Fig. 2

TE and TM diffraction efficiencies versus grating strength for 60° interbeam angle polarization beam-splitting hologram.

Fig. 3
Fig. 3

Variation in reconstruction Bragg angle versus bias index for several values of the fringe rotation factor m.

Fig. 4
Fig. 4

TM reflectivity versus incidence angle for a volume hologram and an isotropic film of the same thickness and bias index.

Fig. 5
Fig. 5

Transmissivity about the critical angle for a volume hologram and an isotropic film of the same thickness and bias index.

Fig. 6
Fig. 6

Twyman–Green interferometer for measuring the bias index of a volume hologram and example of fringe images showing relative fringe shifts when the trench is not index matched. M’s, mirrors; BS, beam splitter.

Fig. 7
Fig. 7

Single-pass propagation phase delay between a volume hologram and an isotropic film.

Fig. 8
Fig. 8

Reflected and transmitted intensities for TE-polarized light versus incidence angle for a volume hologram and an isotropic film of the same thickness and bias index.

Fig. 9
Fig. 9

Variation of bias permittivity ∊0 and permittivity modulation ∊1 with depth into hologram and 10 hologram approximations of the variations.

Fig. 10
Fig. 10

Rigorous coupled-wave calculation of the TE reflectivity of a hologram with the permittivity and the permittivity modulation shown in Fig. 9, and the best least-squares fit of Airy formulas to the RCWA calculations.

Tables (1)

Tables Icon

Table 1 Measured Indices for Polarization Beam-Splitting Hologram

Equations (21)

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

( r ) = 0 ( z ) + i i ( z ) cos ( K i · r ) ,
n 0 ( z ) [ 0 ( z ) ] 1 / 2 .
tan ( ϕ r ) = m sw tan ( ϕ c ) ,
m sw = 1 / T , T = t r / t c .
m sh = [ tan ( ϕ c ) + tan ( δ ) ] / tan ( ϕ c ) ,
tan ( δ ) = s / t c .
m = m sw m sh = [ tan ( ϕ c ) + tan ( δ ) ] / [ T tan ( ϕ c ) ] .
tan ( Ө Brewster ) = n tran / n inc ,
sin ( Ө critical ) = n tran / n inc ,
OPL 1 OPL 2 = m λ / 2 ,
OPL 1 , 2 = 2 n 1 , 2 t r / cos ( θ 1 , 2 ) ,
R s = | r s | 2 ,
R p = | r p | 2 .
( x , z ) = 0 ( z ) + 1 ( z ) cos ( K x ) ,
0 ( z ) = a 1 ( z ) ,
1 ( z ) = b c exp ( α z ) .
η = sin 2 [ π Δ n t r λ cos ( θ B ) r · s ] = sin 2 ( C r · s ) ,
Δ n = 1 / ( 2 n 0 ) ,
TE : r TE · s TE = 1 ,
TE : r TM · s TM = cos ( 2 θ B ) .
2 n 0 Λ sin ( θ B ) = m λ ,

Metrics