Abstract

We discuss a number of design issues that affect the performance tolerances of substrate-mode holograms used for optical interconnect systems. We examine the effects of emulsion uniformity, thickness variation, and index variation on the ability to determine the Bragg angle and the diffraction angle within the substrate accurately. The environmental stability with respect to temperature, laser irradiance, and humidity are considered. Experimental results are presented for substrate-mode holograms fabricated in spin-coated dichromated-gelatin emulsions. The coupling properties for a 1 × 2 multiplexed substrate-mode hologram with two superimposed gratings are also described.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J.-H. Yeh, R. K. Kostuk, “Design issues for substrate mode holograms used in optical interconnects,” in Practical Holography VIII, Stephen A. Benton, ed., Proc. Soc. Photo-Opt. In-strum. Eng.2176, 207–217 (1994).
  2. F. Sauer, “Fabrication of diffractive–reflective optical interconnects for infrared operation based on total internal reflection,” Appl. Opt. 28, 386–388 (1989).
    [Crossref] [PubMed]
  3. R. K. Kostuk, M. Kato, Y.-T. Huang, “Polarization properties of substrate-mode holographic interconnects,” Appl. Opt. 29, 3848–3854 (1990).
    [Crossref] [PubMed]
  4. M. Kato, Y.-T. Huang, R. K. Kostuk, “Multiplexed substrate mode holograms,” J. Opt. Soc. Am. A 7, 1441–1447 (1990).
    [Crossref]
  5. 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]
  6. R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
    [Crossref] [PubMed]
  7. R. C. Kim, E. Chen, F. Lin, “An optical holographic backplane interconnect system,” J. Lightwave Technol. 9, 1650–1656 (1990).
    [Crossref]
  8. J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “High-speed optical bus for multiprocessor systems with substrate mode holograms,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2153, 69–77 (1994).
  9. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep.854 (MIT Lincoln Laboratory, Cambridge, Mass., 1989).
  10. K. Rastani, A. Marrakchi, S. F. Habiby, W. M. Hubbard, H. Gilchrist, R. E. Nahory, “Binary phase Fresnel lenses for generation of two-dimensional beam arrays,” Appl. Opt. 30, 1347–1354 (1991).
    [Crossref] [PubMed]
  11. J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses fabricated by the film deposition,” Appl. Opt. 29, 931–936 (1990).
    [Crossref] [PubMed]
  12. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [Crossref]
  13. H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  14. 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]
  15. K.-Y. Tu, T. Tamir, H. Lee, “Multiple-scattering theory of wave diffraction by superposed volume gratings,” J. Opt. Soc. Am. A 7, 1421–1435 (1990).
    [Crossref]
  16. V. Minier, J. M. Xu, “Coupled-mode analysis of superimposed phase grating guided-wave structures and integrating coupling effects,” Opt. Eng. 32, 2054–2063 (1993).
    [Crossref]
  17. A. Belendez, I. Pascual, A. Fimia, “Model for analyzing the effects of processing on recording material in thick holograms,” J. Opt. Soc. Am. A 9, 1214–1223 (1992).
    [Crossref]
  18. L. T. Blair, L. Solymar, “Double-exposure planar transmission holograms recorded in nonlinear dichromated gelatin,” Appl. Opt. 30, 775–779 (1991).
    [Crossref] [PubMed]
  19. L. T. Blair, L. Solymar, J. Takacs, “Nonlinear recording in dichromated gelatin,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 12–19 (1989).
  20. V. N. Rzhevskii, N. G. Rupchev, “Influence of photochemical processes on the refractive index and layer thickness of dichromated gelatins,” Opt. Specktrosk. 68, 809–810 (1990).
  21. B. J. Chang, C. D. Leonard, “Dichromated gelatin for the fabrication of holographic optical elements,” Appl. Opt. 18, 2407–2417 (1979).
    [Crossref] [PubMed]
  22. T. G. Georgekutty, H.-K. Liu, “Simplified dichromated gelatin hologram recording process,” Appl. Opt. 26, 372–376 (1987).
    [Crossref] [PubMed]
  23. B. J. Chang, “Postprocessing of developed dichromated gelatin holograms,” Opt. Commun. 17, 270–272 (1976).
    [Crossref]
  24. G. M. Naik, A. Mathur, S. V. Pappu, “Dichromated gelatin holograms: an investigation of their environmental stability,” Appl. Opt. 29, 5292–5297 (1990).
    [Crossref] [PubMed]
  25. R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).
  26. R. Kowarschik, “Diffraction efficiency of sequentially stored gratings in transmission volume holograms,” Opt. Acta 25, 67–81 (1978).
    [Crossref]
  27. S. K. Case, “Coupled-wave theory for multiply exposed thick holographic gratings,” J. Opt. Soc. Am. 65, 724–729 (1975).
    [Crossref]
  28. L. Solymar, “Two-dimensional N-coupled wave theory for volume holograms,” Opt. Commun. 23, 199–202 (1977).
    [Crossref]
  29. R. Alferness, S. K. Case, “Coupling in doubly exposed, thick holographic gratings,” J. Opt. Soc. Am. 65, 730–739 (1975).
    [Crossref]
  30. 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).
  31. D. H. R. Vilkomerson, D. Bostwick, “Some effects of emulsion shrinkage on a hologram’s image space,” Appl. Opt. 6, 1270–1272 (1967).
    [Crossref] [PubMed]
  32. R. Pawluczyk, “Modified Brewster angle technique for the measurement of the refractive index of a dichromated gelatin layer,” Appl. Opt. 29, 589–592 (1990).
    [Crossref] [PubMed]
  33. R. J. Archer, “Determination of the properties of films on silicon by the method of ellipsometry,” J. Opt. Soc. Am. 52, 970–977 (1961).
    [Crossref]
  34. T. Kubota, “The bending of interference fringes inside a hologram,” Opt. Acta 26, 731–743 (1979).
    [Crossref]
  35. S. K. Case, “Multiple exposure holography in volume materials,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1976).
  36. J.-H. Yeh, “Board level optical interconnections with substrate mode holograms,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994).

1993 (2)

V. Minier, J. M. Xu, “Coupled-mode analysis of superimposed phase grating guided-wave structures and integrating coupling effects,” Opt. Eng. 32, 2054–2063 (1993).
[Crossref]

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[Crossref] [PubMed]

1992 (1)

1991 (2)

1990 (8)

1989 (2)

1987 (1)

1985 (1)

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

1983 (1)

1979 (2)

1978 (1)

R. Kowarschik, “Diffraction efficiency of sequentially stored gratings in transmission volume holograms,” Opt. Acta 25, 67–81 (1978).
[Crossref]

1977 (1)

L. Solymar, “Two-dimensional N-coupled wave theory for volume holograms,” Opt. Commun. 23, 199–202 (1977).
[Crossref]

1976 (1)

B. J. Chang, “Postprocessing of developed dichromated gelatin holograms,” Opt. Commun. 17, 270–272 (1976).
[Crossref]

1975 (2)

1969 (1)

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

1967 (1)

1961 (1)

Alferness, R.

Archer, R. J.

Belendez, A.

Blair, L. T.

L. T. Blair, L. Solymar, “Double-exposure planar transmission holograms recorded in nonlinear dichromated gelatin,” Appl. Opt. 30, 775–779 (1991).
[Crossref] [PubMed]

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear recording in dichromated gelatin,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 12–19 (1989).

Bostwick, D.

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).

Case, S. K.

Chang, B. J.

B. J. Chang, C. D. Leonard, “Dichromated gelatin for the fabrication of holographic optical elements,” Appl. Opt. 18, 2407–2417 (1979).
[Crossref] [PubMed]

B. J. Chang, “Postprocessing of developed dichromated gelatin holograms,” Opt. Commun. 17, 270–272 (1976).
[Crossref]

Chen, E.

R. C. Kim, E. Chen, F. Lin, “An optical holographic backplane interconnect system,” J. Lightwave Technol. 9, 1650–1656 (1990).
[Crossref]

Fimia, A.

Fink, M.

Gaylord, T. K.

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

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]

Georgekutty, T. G.

Gilchrist, H.

Habiby, S. F.

Hetherington, D.

Huang, Y.-T.

Hubbard, W. M.

Jahns, J.

Kato, M.

Kim, R. C.

R. C. Kim, E. Chen, F. Lin, “An optical holographic backplane interconnect system,” J. Lightwave Technol. 9, 1650–1656 (1990).
[Crossref]

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 grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kostuk, R. K.

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[Crossref] [PubMed]

R. K. Kostuk, M. Kato, Y.-T. Huang, “Polarization properties of substrate-mode holographic interconnects,” Appl. Opt. 29, 3848–3854 (1990).
[Crossref] [PubMed]

M. Kato, Y.-T. Huang, R. K. Kostuk, “Multiplexed substrate mode holograms,” J. Opt. Soc. Am. A 7, 1441–1447 (1990).
[Crossref]

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]

J.-H. Yeh, R. K. Kostuk, “Design issues for substrate mode holograms used in optical interconnects,” in Practical Holography VIII, Stephen A. Benton, ed., Proc. Soc. Photo-Opt. In-strum. Eng.2176, 207–217 (1994).

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “High-speed optical bus for multiprocessor systems with substrate mode holograms,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2153, 69–77 (1994).

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).

Kowarschik, R.

R. Kowarschik, “Diffraction efficiency of sequentially stored gratings in transmission volume holograms,” Opt. Acta 25, 67–81 (1978).
[Crossref]

Kubota, T.

T. Kubota, “The bending of interference fringes inside a hologram,” Opt. Acta 26, 731–743 (1979).
[Crossref]

Lee, H.

Leonard, C. D.

Lin, F.

R. C. Kim, E. Chen, F. Lin, “An optical holographic backplane interconnect system,” J. Lightwave Technol. 9, 1650–1656 (1990).
[Crossref]

Liu, H.-K.

Marrakchi, A.

Mathur, A.

Minier, V.

V. Minier, J. M. Xu, “Coupled-mode analysis of superimposed phase grating guided-wave structures and integrating coupling effects,” Opt. Eng. 32, 2054–2063 (1993).
[Crossref]

Moharam, M. G.

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

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]

Nahory, R. E.

Naik, G. M.

Pappu, S. V.

Pascual, I.

Pawluczyk, R.

Rastani, K.

Redmond, I. R.

R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).

Robertson, B.

R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).

Rupchev, N. G.

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

Rzhevskii, V. N.

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

Sauer, F.

Smith, S. D.

R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).

Solymar, L.

L. T. Blair, L. Solymar, “Double-exposure planar transmission holograms recorded in nonlinear dichromated gelatin,” Appl. Opt. 30, 775–779 (1991).
[Crossref] [PubMed]

L. Solymar, “Two-dimensional N-coupled wave theory for volume holograms,” Opt. Commun. 23, 199–202 (1977).
[Crossref]

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear recording in dichromated gelatin,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 12–19 (1989).

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep.854 (MIT Lincoln Laboratory, Cambridge, Mass., 1989).

Taghizadeh, R.

R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).

Takacs, J.

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear recording in dichromated gelatin,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 12–19 (1989).

Tamir, T.

Tu, K.-Y.

K.-Y. Tu, T. Tamir, H. Lee, “Multiple-scattering theory of wave diffraction by superposed volume gratings,” J. Opt. Soc. Am. A 7, 1421–1435 (1990).
[Crossref]

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “High-speed optical bus for multiprocessor systems with substrate mode holograms,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2153, 69–77 (1994).

Vilkomerson, D. H. R.

Walker, A. C.

R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).

Walker, S. J.

Xu, J. M.

V. Minier, J. M. Xu, “Coupled-mode analysis of superimposed phase grating guided-wave structures and integrating coupling effects,” Opt. Eng. 32, 2054–2063 (1993).
[Crossref]

Yeh, J.-H.

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[Crossref] [PubMed]

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “High-speed optical bus for multiprocessor systems with substrate mode holograms,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2153, 69–77 (1994).

J.-H. Yeh, R. K. Kostuk, “Design issues for substrate mode holograms used in optical interconnects,” in Practical Holography VIII, Stephen A. Benton, ed., Proc. Soc. Photo-Opt. In-strum. Eng.2176, 207–217 (1994).

J.-H. Yeh, “Board level optical interconnections with substrate mode holograms,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994).

Appl. Opt. (12)

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]

R. K. Kostuk, J.-H. Yeh, M. Fink, “Distributed optical data bus for board level interconnects with a substrate-mode holographic window,” Appl. Opt. 32, 5010–5021 (1993).
[Crossref] [PubMed]

F. Sauer, “Fabrication of diffractive–reflective optical interconnects for infrared operation based on total internal reflection,” Appl. Opt. 28, 386–388 (1989).
[Crossref] [PubMed]

R. K. Kostuk, M. Kato, Y.-T. Huang, “Polarization properties of substrate-mode holographic interconnects,” Appl. Opt. 29, 3848–3854 (1990).
[Crossref] [PubMed]

K. Rastani, A. Marrakchi, S. F. Habiby, W. M. Hubbard, H. Gilchrist, R. E. Nahory, “Binary phase Fresnel lenses for generation of two-dimensional beam arrays,” Appl. Opt. 30, 1347–1354 (1991).
[Crossref] [PubMed]

J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses fabricated by the film deposition,” Appl. Opt. 29, 931–936 (1990).
[Crossref] [PubMed]

L. T. Blair, L. Solymar, “Double-exposure planar transmission holograms recorded in nonlinear dichromated gelatin,” Appl. Opt. 30, 775–779 (1991).
[Crossref] [PubMed]

B. J. Chang, C. D. Leonard, “Dichromated gelatin for the fabrication of holographic optical elements,” Appl. Opt. 18, 2407–2417 (1979).
[Crossref] [PubMed]

T. G. Georgekutty, H.-K. Liu, “Simplified dichromated gelatin hologram recording process,” Appl. Opt. 26, 372–376 (1987).
[Crossref] [PubMed]

G. M. Naik, A. Mathur, S. V. Pappu, “Dichromated gelatin holograms: an investigation of their environmental stability,” Appl. Opt. 29, 5292–5297 (1990).
[Crossref] [PubMed]

D. H. R. Vilkomerson, D. Bostwick, “Some effects of emulsion shrinkage on a hologram’s image space,” Appl. Opt. 6, 1270–1272 (1967).
[Crossref] [PubMed]

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

Bell Syst. Tech. J. (1)

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

J. Lightwave Technol. (1)

R. C. Kim, E. Chen, F. Lin, “An optical holographic backplane interconnect system,” J. Lightwave Technol. 9, 1650–1656 (1990).
[Crossref]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

Opt. Acta (2)

R. Kowarschik, “Diffraction efficiency of sequentially stored gratings in transmission volume holograms,” Opt. Acta 25, 67–81 (1978).
[Crossref]

T. Kubota, “The bending of interference fringes inside a hologram,” Opt. Acta 26, 731–743 (1979).
[Crossref]

Opt. Commun. (2)

L. Solymar, “Two-dimensional N-coupled wave theory for volume holograms,” Opt. Commun. 23, 199–202 (1977).
[Crossref]

B. J. Chang, “Postprocessing of developed dichromated gelatin holograms,” Opt. Commun. 17, 270–272 (1976).
[Crossref]

Opt. Eng. (1)

V. Minier, J. M. Xu, “Coupled-mode analysis of superimposed phase grating guided-wave structures and integrating coupling effects,” Opt. Eng. 32, 2054–2063 (1993).
[Crossref]

Opt. Specktrosk. (1)

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

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)

J.-H. Yeh, R. K. Kostuk, K.-Y. Tu, “High-speed optical bus for multiprocessor systems with substrate mode holograms,” in Optoelectronic Interconnects II, R. T. Chen, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2153, 69–77 (1994).

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep.854 (MIT Lincoln Laboratory, Cambridge, Mass., 1989).

J.-H. Yeh, R. K. Kostuk, “Design issues for substrate mode holograms used in optical interconnects,” in Practical Holography VIII, Stephen A. Benton, ed., Proc. Soc. Photo-Opt. In-strum. Eng.2176, 207–217 (1994).

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear recording in dichromated gelatin,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 12–19 (1989).

R. Taghizadeh, I. R. Redmond, B. Robertson, A. C. Walker, S. D. Smith, “High efficiency holographic optical elements for all-optical digital computing,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 265–274 (1989).

S. K. Case, “Multiple exposure holography in volume materials,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1976).

J.-H. Yeh, “Board level optical interconnections with substrate mode holograms,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994).

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).

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 (24)

Fig. 1
Fig. 1

(a) Geometry of a transmission SMH and (b) the corresponding Bragg diagrams.

Fig. 2
Fig. 2

Rotation of the K vector due to a change in the emulsion thickness before exposure and after processing.

Fig. 3
Fig. 3

Bragg-angle shift Δθ in air as a function of ΔT.

Fig. 4
Fig. 4

Diffraction angle in the substrate θs and the efficiency loss as a function of ΔT for SMH’s reconstructed with a normally incident beam.

Fig. 5
Fig. 5

Constant Δθ lines as functions of nr and DT.

Fig. 6
Fig. 6

Bragg-angle shift Δθ in air as a function of nr.

Fig. 7
Fig. 7

Diffraction angle in the substrate θs and the efficiency loss as a function of nr for SMH’s reconstructed with a normally incident beam.

Fig. 8
Fig. 8

Measurements of Bragg-angle shift versus exposure energy. The accuracy of the Δθ measurements is ±0.02°.

Fig. 9
Fig. 9

Experimental setup for measuring Bragg-angle shift Δθ and diffraction angle within the substrate θs. The detector is used for the Δθ measurement (maximum efficiency), and a mirror on rotation stage B and two apertures (a, b) are used for the θs measurement.

Fig. 10
Fig. 10

Measurements of emulsion thickness Tr for SMH’s recorded with various exposure levels. The measurement accuracy is ±0.01 μm.

Fig. 11
Fig. 11

Measurements of diffraction angle θs versus exposure energy. The accuracy of the θs measurements is ±0.05°.

Fig. 12
Fig. 12

Sensitivity of diffraction angle θs to the variation in incident angle θi. The accuracy of the θs measurements is ±0.05°.

Fig. 13
Fig. 13

Measurements and theoretical calculation of the FWHM angular bandwidth. The accuracy of the efficiency measurements is better than 0.5%.

Fig. 14
Fig. 14

Measurements of the normalized average (a) diffraction efficiency and (b) Bragg-angle shift as a function of temperature for different sets of SMH’s.

Fig. 15
Fig. 15

Schematic of a multiplexed SMH designed with a common Bragg angle in the direction of normal incidence for superimposed gratings.

Fig. 16
Fig. 16

(a) Schematic of a 1 × 2 multiplexed SMH with two superimposed gratings and (b) its Bragg diagram.

Fig. 17
Fig. 17

Effect of emulsion-thickness change on the grating structure of a 1 × 2 multiplexed SMH. Δω is defined as positive in (a) and as negative in (b).

Fig. 18
Fig. 18

Diffraction efficiencies of a 1 × 2 multiplexed SMH (η1 = η2) as a function of n1 = n2 for Δω = 0° and Δω = ±1.0°, respectively.

Fig. 19
Fig. 19

(a) Schematic for a 1 × 2 multiplexed SMH used in the cross-coupling mode and (b) the detailed coupling process that occurs in the multiplexed grating region.

Fig. 20
Fig. 20

Diffraction efficiencies η, η+, ηL, and ηR as a function of n1 = n2 for a 1 × 2 multiplexed SMH used in the cross-coupling mode.

Fig. 21
Fig. 21

Effect of emulsion-thickness change (ΔT) on the diffraction angles of the output beams for a 1 × 2 multiplexed SMH used in the cross-coupling mode.

Fig. 22
Fig. 22

Sensitivity of θ2 and θ1 to the Δω variation.

Fig. 23
Fig. 23

Diffraction efficiencies η, η+, ηL, and ηR as a function of n1 = n2 with Δω = 1.0° for a 1 × 2 multiplexed SMH reconstructed with beam σ1.

Fig. 24
Fig. 24

Trade-off between FWHM angular bandwidth ΔθB and fan-out N as a function of emulsion thickness T.

Tables (2)

Tables Icon

Table 1 Design Parameters for Substrate-Mode Holograms

Tables Icon

Table 2 Processing Procedures for Dichromated-Gelatin Film Plates

Equations (25)

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

Λ c Λ r = sin ϕ c sin ϕ r ,
tan ϕ r tan ϕ c = T r T c = 1 + Δ T ,
T r δ r T c + δ c 1 Δ T T r + δ r T c δ c 1 ,
η = 1 2 sin 2 [ ( 2 ) 1 / 2 ν ] ,
η + = 1 8 sin 2 [ 2 ( 2 ) 1 / 2 ν ] ,
η L = 1 4 { 1 + cos 2 [ ( 2 ) 1 / 2 ν ] } 2 ,
η R = 4 sin 8 [ ν / ( 2 ) 1 / 2 ] ,
ν = π n 1 T λ ( cos θ r 2 ) 1 / 2 .
η 0 = cos 2 ( m ν m 2 ) 1 / 2 ,
η i = ν i 2 sin 2 ( m ν m 2 ) 1 / 2 m ν m 2 , i = 1 , , N ,
ν i = π n i T λ ( cos θ r 2 ) 1 / 2 ,
n i = λ ( cos θ r 2 ) 1 / 2 π T ( η i η tot ) 1 / 2 sin 1 ( η tot ) 1 / 2 ,
η tot = η i = 1 η 0 = 1 cos 2 ( ν m 2 ) 1 / 2 = sin 2 ( ν m 2 ) 1 / 2 .
i = 1 N n i n max .
N 1 / 2 2 T n max λ ( cos θ r 2 ) 1 / 2 .
Δ θ B = 2 sin 1 { n sin [ ϕ + cos 1 × ( 0 . 4 Λ cos θ r 2 T + λ 2 n Λ ) ] } .
ν T = sin 1 ( η tot ) 1 / 2 .
η i η j = ( ν i ν j ) 2 .
ν T 2 = ν m 2 = ν 1 2 + + ν i 2 + + ν N 2 = η 1 η i ν i 2 + + η i η i ν i 2 + + η N η i ν i 2 = ν i 2 η i η i = ν i 2 η i η tot . ν T = ( η tot η i ) 1 / 2 ν i .
ν T = sin 1 ( η tot ) 1 / 2 = ( η tot η i ) 1 / 2 π n i T λ ( cos θ r 2 ) 1 / 2 n i = λ ( cos θ r 2 ) 1 / 2 π T ( η i η tot ) 1 / 2 sin 1 ( η tot ) 1 / 2 .
η = ν 2 sin 2 ( ξ 2 + ν 2 ) 1 / 2 ν 2 + ξ 2 ,
ξ = T 2 cos θ r 2 [ 2 π Λ cos ( θ f ϕ ) πλ n Λ 2 ] ,
η = 1 2 = ( π / 2 ) 2 sin 2 [ ( π / 2 ) 2 + ξ 2 ] 1 / 2 ( π / 2 ) 2 + ξ 2 .
θ f ϕ = cos 1 ( 0 . 4 Λ cos θ r 2 T + L 2 n Λ ) .
Δ θ B = 2 θ f = 2 sin 1 { n sin [ ϕ + cos 1 ( 0 . 4 Λ cos θ r 2 T + λ 2 n Λ ) ] } .

Metrics