Abstract

High-efficiency diffractive elements with a continuous phase-modulation capability can be realized either by means of a surface profile or a refractive-index distribution. We consider the latter approach, expanding on our recent proposal [Appl. Phys. Lett. 66, 917 (1995)] to fabricate graded-index diffractive structures by thermal ion exchange in glass. A rapid approximate method is developed to obtain a predesign of the ion-exchange mask, which is then refined by parametric optimization based on solutions of the full diffusion problem. The use of two consecutive ion-exchange steps and postbaking to enhance the designs is investigated, and some experimental results are provided.

© 1997 Optical Society of America

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  1. F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Progr. Phys. 54, 1481–1571 (1991).
    [CrossRef]
  2. J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics, A. Consortini, ed. (Academic, New York, 1996), pp. 111–123.
    [CrossRef]
  3. T. Suhara, H. Nishihara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–37.
  4. N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
    [CrossRef]
  5. R. L. van Renesse, ed., Optical Document Security (Artech, Boston, 1994).
  6. P. St. Hilaire, S. A. Benton, M. Lucente, “Synthetic aperture holography: a novel approach to three-dimensional displays,” J. Opt. Soc. Am. A 9, 1969–1977 (1992).
    [CrossRef]
  7. J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, Boston, 1994).
  8. M. R. Taghizadeh, J. Turunen, “Synthetic diffractive elements for optical interconnection,” Opt. Comp. Proc. 2, 221–242 (1992).
  9. J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
    [CrossRef]
  10. F. Wyrowski, R. Zuidema, “Diffractive interconnection between a high-power Nd:YAG-laser and a fiber bundle,” Appl. Opt. 33, 6732–6740 (1994).
    [CrossRef] [PubMed]
  11. M. Ekberg, M. Larsson, A. Bolle, S. Hård, “Nd:YAG laser machining with multilevel resist kinoforms,” Appl. Opt. 30, 3604–3606 (1991).
    [CrossRef] [PubMed]
  12. J. J. Clair, C. I. Abitbol, “Recent advances in phase profiles generation,” in Progress in Optics XVI, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 71–117.
    [CrossRef]
  13. M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, D. Prongué, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
    [CrossRef] [PubMed]
  14. M. Ekberg, F. Nikolajeff, M. Larsson, S. Hård, “Proximity-compensated blazed transmission grating manufacture with direct-writing, electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
    [CrossRef] [PubMed]
  15. R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).
  16. H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larsson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist:manufacture and evaluation,” Appl. Opt. 29, 4259–4267 (1990).
    [CrossRef] [PubMed]
  17. W. Däschner, P. Long, M. Larsson, S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
    [CrossRef]
  18. H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer-generated elements,” in Perspectives for Parallel Optical Interconnects, Ph. Lalanne, P. Chavel, eds. (Springer, Berlin, 1993), pp. 71–107.
    [CrossRef]
  19. E. Pawlowski, H. Engel, M. Ferstl, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
    [CrossRef]
  20. K. Iga, “Microoptics,” in International Trends in Optics, J. W. Goodman, ed. (Academic, Boston, 1991), pp. 37–55.
    [CrossRef]
  21. H. M. Smith, ed. Holographic Recording Materials (Springer-Verlag, Berlin, 1977).
    [CrossRef]
  22. B. Messerschmidt, T. Possner, R. Göring, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
    [CrossRef] [PubMed]
  23. J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Index-distributed planar microlenses for three-dimensional micro-optics fabricated by silver-sodium ion exchange in BGG35 substrates,” Appl. Opt. 33, 5919–5924 (1994).
    [CrossRef] [PubMed]
  24. A. Tervonen, “Theoretical analysis of ion-exchanged glass waveguides,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech, Boston, 1992), pp. 73–105.
  25. T. Yatagai, R. Sugawara, H. Hashizume, M. Seki, “Phase-only computer-generated hologram produced by an ion-exchange technique,” Opt. Lett. 13, 952–954 (1988).
    [CrossRef] [PubMed]
  26. H. C. Bolstad, T. Yatagai, M. Seki, “Optimization of phase-only computer-generated holograms using an ion-exchange process,” Opt. Eng. 31, 1259–1263 (1992).
    [CrossRef]
  27. E. J. Patej, B. Oroń, “Realisation and investigation of phase diffraction gratings in glass,” in Optical Fibres and Their Applications V, R. S. Romaniuk, M. Szustakowski, eds., Proc. SPIE1085, 436–437 (1989).
    [CrossRef]
  28. J. Saarinen, A. Tervonen, J. Turunen, S. Honkanen, “Electric-field assisted silver-film ion-exchange in glass for the fabrication of index-modulated diffractive elements,” in Meeting Digest—Frontiers in Information Optics,Topical Meeting of ICO (International Commission for Optics, Kyoto, Japan, 1994), p. 76.
  29. R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
    [CrossRef]
  30. H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  31. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
    [CrossRef]
  32. P. Ehbets, H. P. Herzig, D. Prongué, M. T. Gale, “High-efficiency continuous surface-relief gratings for two-dimensional array generation,” Opt. Lett. 17, 908–910 (1992).
    [CrossRef] [PubMed]
  33. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
    [CrossRef] [PubMed]
  34. S. Honkanen, A. Tervonen, “Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication,” J. Appl. Phys. 63, 634–639 (1988).
    [CrossRef]
  35. The empirical values for a and b were misprinted in Ref. 34. This is the correct form.
  36. J. Saarinen, J. Turunen, J. Huttunen, “Volume diffraction effects in computer-generated guided-wave holography,” Appl. Opt. 33, 1035–1043 (1994).
    [CrossRef] [PubMed]
  37. J. H. Ferziger, Numerical Methods for Engineering Application (Wiley, New York, 1981).
  38. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  39. N. Yoshikawa, M. Itoh, T. Yatagai, “Quantized phase optimization of two-dimensional Fourier kinoforms by a genetic algorithm,” Opt. Lett. 20, 752–754 (1995).
    [CrossRef] [PubMed]
  40. R. G. Walker, C. D. W. Wilkinson, J. A. H. Wilkinson, “Integrated optical waveguiding structures made by silver ion-exchange in glass. 1: The propagation characteristics of stripe ion-exchanged waveguides; a theoretical and experimental investigation,” Appl. Opt. 22, 1923–1928 (1983).
    [CrossRef]
  41. J. Albert, G. L. Yip, “Insertion loss reduction between single-mode fibers and diffused channel waveguides,” Appl. Opt. 27, 4837–4843 (1988).
    [CrossRef] [PubMed]
  42. J. Saarinen, S. Honkanen, S. I. Najafi, J. Huttunen, “Double ion-exchanged process in glass for the fabrication of computer-generated waveguide holograms,” Appl. Opt. 33, 3353–3359 (1994).
    [CrossRef] [PubMed]
  43. A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
    [CrossRef]
  44. S. D. Fantone, “Refractive index and spectral models for gradient-index materials,” Appl. Opt. 22, 432–440 (1983).
    [CrossRef] [PubMed]
  45. J. M. Inman, J. L. Bentley, S. N. Houde-Walter, “Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient,” J. Non-Cryst. Solids 191, 209–215 (1995).
    [CrossRef]
  46. M. N. Weiss, R. Srivastava, “Determination of ion-exchanged channel waveguide profile parameters by mode-index measurements,” Appl. Opt. 34, 455–458 (1995).
    [CrossRef] [PubMed]
  47. T. Possner, R. Göring, “Transmission phase gratings by ion exchange in optical glasses,” presented at the 10th Topical Meeting of GRIN’92, Santiago de Compostela, Spain, 4–6 October 1992, paper T.2.9.
  48. T. Possner, E. Döpel, R. Göring, “Cylindrical microlenses and transmission phase gratings by silver ion exchange in optical glasses for microoptic applications,” presented at the the Fourth Micro-optics Conference and the 11th Topical Meeting on Gradient-Index Optical Systems, Kawasaki, Japan, 20–22 October 1993, paper K2.
  49. J. L. Coutaz, P. C. Jaussaud, “High index gradient in glass by ion exchange,” Appl. Opt. 21, 1063–1065 (1982).
    [CrossRef] [PubMed]

1995 (6)

W. Däschner, P. Long, M. Larsson, S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[CrossRef]

B. Messerschmidt, T. Possner, R. Göring, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
[CrossRef] [PubMed]

R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
[CrossRef]

N. Yoshikawa, M. Itoh, T. Yatagai, “Quantized phase optimization of two-dimensional Fourier kinoforms by a genetic algorithm,” Opt. Lett. 20, 752–754 (1995).
[CrossRef] [PubMed]

J. M. Inman, J. L. Bentley, S. N. Houde-Walter, “Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient,” J. Non-Cryst. Solids 191, 209–215 (1995).
[CrossRef]

M. N. Weiss, R. Srivastava, “Determination of ion-exchanged channel waveguide profile parameters by mode-index measurements,” Appl. Opt. 34, 455–458 (1995).
[CrossRef] [PubMed]

1994 (7)

1993 (1)

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

1992 (6)

1991 (2)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Progr. Phys. 54, 1481–1571 (1991).
[CrossRef]

M. Ekberg, M. Larsson, A. Bolle, S. Hård, “Nd:YAG laser machining with multilevel resist kinoforms,” Appl. Opt. 30, 3604–3606 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (2)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

1988 (3)

1987 (1)

1986 (1)

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

1983 (2)

1982 (1)

1971 (1)

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Abitbol, C. I.

J. J. Clair, C. I. Abitbol, “Recent advances in phase profiles generation,” in Progress in Optics XVI, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 71–117.
[CrossRef]

Albert, J.

Allebach, J. P.

Andersson, H.

Bähr, J.

Bentley, J. L.

J. M. Inman, J. L. Bentley, S. N. Houde-Walter, “Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient,” J. Non-Cryst. Solids 191, 209–215 (1995).
[CrossRef]

Benton, S. A.

Bolle, A.

Bolstad, H. C.

H. C. Bolstad, T. Yatagai, M. Seki, “Optimization of phase-only computer-generated holograms using an ion-exchange process,” Opt. Eng. 31, 1259–1263 (1992).
[CrossRef]

Brandenburg, A.

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

Bräuer, A.

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

Brenner, K.-H.

Bryngdahl, O.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Progr. Phys. 54, 1481–1571 (1991).
[CrossRef]

Clair, J. J.

J. J. Clair, C. I. Abitbol, “Recent advances in phase profiles generation,” in Progress in Optics XVI, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 71–117.
[CrossRef]

Coutaz, J. L.

Dammann, H.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dannberg, P.

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

Däschner, W.

W. Däschner, P. Long, M. Larsson, S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[CrossRef]

Döpel, E.

T. Possner, E. Döpel, R. Göring, “Cylindrical microlenses and transmission phase gratings by silver ion exchange in optical glasses for microoptic applications,” presented at the the Fourth Micro-optics Conference and the 11th Topical Meeting on Gradient-Index Optical Systems, Kawasaki, Japan, 20–22 October 1993, paper K2.

Ehbets, P.

Ekberg, M.

Engel, H.

E. Pawlowski, H. Engel, M. Ferstl, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Fantone, S. D.

Ferstl, M.

E. Pawlowski, H. Engel, M. Ferstl, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Ferziger, J. H.

J. H. Ferziger, Numerical Methods for Engineering Application (Wiley, New York, 1981).

Gale, M. T.

Göring, R.

B. Messerschmidt, T. Possner, R. Göring, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
[CrossRef] [PubMed]

T. Possner, E. Döpel, R. Göring, “Cylindrical microlenses and transmission phase gratings by silver ion exchange in optical glasses for microoptic applications,” presented at the the Fourth Micro-optics Conference and the 11th Topical Meeting on Gradient-Index Optical Systems, Kawasaki, Japan, 20–22 October 1993, paper K2.

T. Possner, R. Göring, “Transmission phase gratings by ion exchange in optical glasses,” presented at the 10th Topical Meeting of GRIN’92, Santiago de Compostela, Spain, 4–6 October 1992, paper T.2.9.

Görtler, K.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Hård, S.

Hashizume, H.

Herzig, H. P.

P. Ehbets, H. P. Herzig, D. Prongué, M. T. Gale, “High-efficiency continuous surface-relief gratings for two-dimensional array generation,” Opt. Lett. 17, 908–910 (1992).
[CrossRef] [PubMed]

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer-generated elements,” in Perspectives for Parallel Optical Interconnects, Ph. Lalanne, P. Chavel, eds. (Springer, Berlin, 1993), pp. 71–107.
[CrossRef]

Hilaire, P. St.

Honkanen, S.

J. Saarinen, S. Honkanen, S. I. Najafi, J. Huttunen, “Double ion-exchanged process in glass for the fabrication of computer-generated waveguide holograms,” Appl. Opt. 33, 3353–3359 (1994).
[CrossRef] [PubMed]

S. Honkanen, A. Tervonen, “Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication,” J. Appl. Phys. 63, 634–639 (1988).
[CrossRef]

J. Saarinen, A. Tervonen, J. Turunen, S. Honkanen, “Electric-field assisted silver-film ion-exchange in glass for the fabrication of index-modulated diffractive elements,” in Meeting Digest—Frontiers in Information Optics,Topical Meeting of ICO (International Commission for Optics, Kyoto, Japan, 1994), p. 76.

Houde-Walter, S. N.

J. M. Inman, J. L. Bentley, S. N. Houde-Walter, “Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient,” J. Non-Cryst. Solids 191, 209–215 (1995).
[CrossRef]

Huttunen, J.

Ichikawa, H.

Iga, K.

K. Iga, “Microoptics,” in International Trends in Optics, J. W. Goodman, ed. (Academic, Boston, 1991), pp. 37–55.
[CrossRef]

Inman, J. M.

J. M. Inman, J. L. Bentley, S. N. Houde-Walter, “Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient,” J. Non-Cryst. Solids 191, 209–215 (1995).
[CrossRef]

Itoh, M.

Jaakkola, T.

Jacobsson, S.

Jahns, J.

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, Boston, 1994).

Jaussaud, P. C.

Karthe, W.

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

Kley, E.-B.

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

Kuisma, S.

Lang, G. K.

Larsson, M.

Lee, S. H.

W. Däschner, P. Long, M. Larsson, S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[CrossRef]

J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, Boston, 1994).

Lehmann, H. W.

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer-generated elements,” in Perspectives for Parallel Optical Interconnects, Ph. Lalanne, P. Chavel, eds. (Springer, Berlin, 1993), pp. 71–107.
[CrossRef]

Long, P.

W. Däschner, P. Long, M. Larsson, S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[CrossRef]

Lucente, M.

Messerschmidt, B.

Miller, J. M.

Morf, R.

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer-generated elements,” in Perspectives for Parallel Optical Interconnects, Ph. Lalanne, P. Chavel, eds. (Springer, Berlin, 1993), pp. 71–107.
[CrossRef]

Najafi, S. I.

Nikolajeff, F.

Nilsson, T.

Nishihara, H.

T. Suhara, H. Nishihara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–37.

Noponen, E.

Oron, B.

E. J. Patej, B. Oroń, “Realisation and investigation of phase diffraction gratings in glass,” in Optical Fibres and Their Applications V, R. S. Romaniuk, M. Szustakowski, eds., Proc. SPIE1085, 436–437 (1989).
[CrossRef]

Patej, E. J.

E. J. Patej, B. Oroń, “Realisation and investigation of phase diffraction gratings in glass,” in Optical Fibres and Their Applications V, R. S. Romaniuk, M. Szustakowski, eds., Proc. SPIE1085, 436–437 (1989).
[CrossRef]

Pawlowski, E.

E. Pawlowski, H. Engel, M. Ferstl, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Possner, T.

B. Messerschmidt, T. Possner, R. Göring, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
[CrossRef] [PubMed]

T. Possner, E. Döpel, R. Göring, “Cylindrical microlenses and transmission phase gratings by silver ion exchange in optical glasses for microoptic applications,” presented at the the Fourth Micro-optics Conference and the 11th Topical Meeting on Gradient-Index Optical Systems, Kawasaki, Japan, 20–22 October 1993, paper K2.

T. Possner, R. Göring, “Transmission phase gratings by ion exchange in optical glasses,” presented at the 10th Topical Meeting of GRIN’92, Santiago de Compostela, Spain, 4–6 October 1992, paper T.2.9.

Prongué, D.

Raynor, J. M.

Saarinen, J.

R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
[CrossRef]

J. Saarinen, J. Turunen, J. Huttunen, “Volume diffraction effects in computer-generated guided-wave holography,” Appl. Opt. 33, 1035–1043 (1994).
[CrossRef] [PubMed]

J. Saarinen, S. Honkanen, S. I. Najafi, J. Huttunen, “Double ion-exchanged process in glass for the fabrication of computer-generated waveguide holograms,” Appl. Opt. 33, 3353–3359 (1994).
[CrossRef] [PubMed]

J. Saarinen, A. Tervonen, J. Turunen, S. Honkanen, “Electric-field assisted silver-film ion-exchange in glass for the fabrication of index-modulated diffractive elements,” in Meeting Digest—Frontiers in Information Optics,Topical Meeting of ICO (International Commission for Optics, Kyoto, Japan, 1994), p. 76.

Salmio, R.-P.

R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
[CrossRef]

Schütz, H.

Seki, M.

H. C. Bolstad, T. Yatagai, M. Seki, “Optimization of phase-only computer-generated holograms using an ion-exchange process,” Opt. Eng. 31, 1259–1263 (1992).
[CrossRef]

T. Yatagai, R. Sugawara, H. Hashizume, M. Seki, “Phase-only computer-generated hologram produced by an ion-exchange technique,” Opt. Lett. 13, 952–954 (1988).
[CrossRef] [PubMed]

Seldowitz, M. A.

Sinzinger, S.

Spick, T.

Srivastava, R.

Streibl, N.

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

Sugawara, R.

Suhara, T.

T. Suhara, H. Nishihara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–37.

Sweeney, D. W.

Taghizadeh, M. R.

Tervonen, A.

R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
[CrossRef]

S. Honkanen, A. Tervonen, “Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication,” J. Appl. Phys. 63, 634–639 (1988).
[CrossRef]

J. Saarinen, A. Tervonen, J. Turunen, S. Honkanen, “Electric-field assisted silver-film ion-exchange in glass for the fabrication of index-modulated diffractive elements,” in Meeting Digest—Frontiers in Information Optics,Topical Meeting of ICO (International Commission for Optics, Kyoto, Japan, 1994), p. 76.

A. Tervonen, “Theoretical analysis of ion-exchanged glass waveguides,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech, Boston, 1992), pp. 73–105.

Testorf, M.

Turunen, J.

R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
[CrossRef]

J. Saarinen, J. Turunen, J. Huttunen, “Volume diffraction effects in computer-generated guided-wave holography,” Appl. Opt. 33, 1035–1043 (1994).
[CrossRef] [PubMed]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

M. R. Taghizadeh, J. Turunen, “Synthetic diffractive elements for optical interconnection,” Opt. Comp. Proc. 2, 221–242 (1992).

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

J. Saarinen, A. Tervonen, J. Turunen, S. Honkanen, “Electric-field assisted silver-film ion-exchange in glass for the fabrication of index-modulated diffractive elements,” in Meeting Digest—Frontiers in Information Optics,Topical Meeting of ICO (International Commission for Optics, Kyoto, Japan, 1994), p. 76.

J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics, A. Consortini, ed. (Academic, New York, 1996), pp. 111–123.
[CrossRef]

Vasara, A.

Waldhäusl, R.

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

Walker, R. G.

Weiss, M. N.

Westerholm, J.

Wilkinson, C. D. W.

Wilkinson, J. A. H.

Wyrowski, F.

F. Wyrowski, R. Zuidema, “Diffractive interconnection between a high-power Nd:YAG-laser and a fiber bundle,” Appl. Opt. 33, 6732–6740 (1994).
[CrossRef] [PubMed]

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Progr. Phys. 54, 1481–1571 (1991).
[CrossRef]

J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics, A. Consortini, ed. (Academic, New York, 1996), pp. 111–123.
[CrossRef]

Yatagai, T.

Yip, G. L.

Yoshikawa, N.

Zuidema, R.

Appl. Opt. (16)

F. Wyrowski, R. Zuidema, “Diffractive interconnection between a high-power Nd:YAG-laser and a fiber bundle,” Appl. Opt. 33, 6732–6740 (1994).
[CrossRef] [PubMed]

M. Ekberg, M. Larsson, A. Bolle, S. Hård, “Nd:YAG laser machining with multilevel resist kinoforms,” Appl. Opt. 30, 3604–3606 (1991).
[CrossRef] [PubMed]

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, D. Prongué, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
[CrossRef] [PubMed]

M. Ekberg, F. Nikolajeff, M. Larsson, S. Hård, “Proximity-compensated blazed transmission grating manufacture with direct-writing, electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
[CrossRef] [PubMed]

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larsson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist:manufacture and evaluation,” Appl. Opt. 29, 4259–4267 (1990).
[CrossRef] [PubMed]

B. Messerschmidt, T. Possner, R. Göring, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
[CrossRef] [PubMed]

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Index-distributed planar microlenses for three-dimensional micro-optics fabricated by silver-sodium ion exchange in BGG35 substrates,” Appl. Opt. 33, 5919–5924 (1994).
[CrossRef] [PubMed]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

J. Saarinen, J. Turunen, J. Huttunen, “Volume diffraction effects in computer-generated guided-wave holography,” Appl. Opt. 33, 1035–1043 (1994).
[CrossRef] [PubMed]

R. G. Walker, C. D. W. Wilkinson, J. A. H. Wilkinson, “Integrated optical waveguiding structures made by silver ion-exchange in glass. 1: The propagation characteristics of stripe ion-exchanged waveguides; a theoretical and experimental investigation,” Appl. Opt. 22, 1923–1928 (1983).
[CrossRef]

J. Albert, G. L. Yip, “Insertion loss reduction between single-mode fibers and diffused channel waveguides,” Appl. Opt. 27, 4837–4843 (1988).
[CrossRef] [PubMed]

J. Saarinen, S. Honkanen, S. I. Najafi, J. Huttunen, “Double ion-exchanged process in glass for the fabrication of computer-generated waveguide holograms,” Appl. Opt. 33, 3353–3359 (1994).
[CrossRef] [PubMed]

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
[CrossRef] [PubMed]

S. D. Fantone, “Refractive index and spectral models for gradient-index materials,” Appl. Opt. 22, 432–440 (1983).
[CrossRef] [PubMed]

M. N. Weiss, R. Srivastava, “Determination of ion-exchanged channel waveguide profile parameters by mode-index measurements,” Appl. Opt. 34, 455–458 (1995).
[CrossRef] [PubMed]

J. L. Coutaz, P. C. Jaussaud, “High index gradient in glass by ion exchange,” Appl. Opt. 21, 1063–1065 (1982).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

R.-P. Salmio, J. Saarinen, J. Turunen, A. Tervonen, “Graded-index diffractive elements by thermal ion exchange in glass,” Appl. Phys. Lett. 66, 917–919 (1995).
[CrossRef]

Int. J. Optoelectron. (1)

R. Waldhäusl, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Highly efficient blazed grating couplers in planar polymer waveguides,” Int. J. Optoelectron. 8, 529–536 (1993).

J. Appl. Phys. (1)

S. Honkanen, A. Tervonen, “Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication,” J. Appl. Phys. 63, 634–639 (1988).
[CrossRef]

J. Lightwave Technol. (1)

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

J. Mod. Opt. (1)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

J. Non-Cryst. Solids (1)

J. M. Inman, J. L. Bentley, S. N. Houde-Walter, “Modeling ion-exchanged glass photonics: the modified quasi-chemical diffusion coefficient,” J. Non-Cryst. Solids 191, 209–215 (1995).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

W. Däschner, P. Long, M. Larsson, S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[CrossRef]

Opt. Commun. (1)

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Comp. Proc. (1)

M. R. Taghizadeh, J. Turunen, “Synthetic diffractive elements for optical interconnection,” Opt. Comp. Proc. 2, 221–242 (1992).

Opt. Eng. (3)

E. Pawlowski, H. Engel, M. Ferstl, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

H. C. Bolstad, T. Yatagai, M. Seki, “Optimization of phase-only computer-generated holograms using an ion-exchange process,” Opt. Eng. 31, 1259–1263 (1992).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

Rep. Progr. Phys. (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Progr. Phys. 54, 1481–1571 (1991).
[CrossRef]

Other (15)

J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics, A. Consortini, ed. (Academic, New York, 1996), pp. 111–123.
[CrossRef]

T. Suhara, H. Nishihara, “Micro Fresnel lenses,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 1–37.

R. L. van Renesse, ed., Optical Document Security (Artech, Boston, 1994).

J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, Boston, 1994).

K. Iga, “Microoptics,” in International Trends in Optics, J. W. Goodman, ed. (Academic, Boston, 1991), pp. 37–55.
[CrossRef]

H. M. Smith, ed. Holographic Recording Materials (Springer-Verlag, Berlin, 1977).
[CrossRef]

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer-generated elements,” in Perspectives for Parallel Optical Interconnects, Ph. Lalanne, P. Chavel, eds. (Springer, Berlin, 1993), pp. 71–107.
[CrossRef]

J. J. Clair, C. I. Abitbol, “Recent advances in phase profiles generation,” in Progress in Optics XVI, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 71–117.
[CrossRef]

E. J. Patej, B. Oroń, “Realisation and investigation of phase diffraction gratings in glass,” in Optical Fibres and Their Applications V, R. S. Romaniuk, M. Szustakowski, eds., Proc. SPIE1085, 436–437 (1989).
[CrossRef]

J. Saarinen, A. Tervonen, J. Turunen, S. Honkanen, “Electric-field assisted silver-film ion-exchange in glass for the fabrication of index-modulated diffractive elements,” in Meeting Digest—Frontiers in Information Optics,Topical Meeting of ICO (International Commission for Optics, Kyoto, Japan, 1994), p. 76.

A. Tervonen, “Theoretical analysis of ion-exchanged glass waveguides,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech, Boston, 1992), pp. 73–105.

The empirical values for a and b were misprinted in Ref. 34. This is the correct form.

J. H. Ferziger, Numerical Methods for Engineering Application (Wiley, New York, 1981).

T. Possner, R. Göring, “Transmission phase gratings by ion exchange in optical glasses,” presented at the 10th Topical Meeting of GRIN’92, Santiago de Compostela, Spain, 4–6 October 1992, paper T.2.9.

T. Possner, E. Döpel, R. Göring, “Cylindrical microlenses and transmission phase gratings by silver ion exchange in optical glasses for microoptic applications,” presented at the the Fourth Micro-optics Conference and the 11th Topical Meeting on Gradient-Index Optical Systems, Kawasaki, Japan, 20–22 October 1993, paper K2.

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Figures (10)

Fig. 1
Fig. 1

(a) Fabrication of a graded refractive-index profile in glass by thermal ion exchange with a binary mask: several curves of constant refractive index are shown. (b) Time evolution of the phase-delay profile of the ion-exchanged element.

Fig. 2
Fig. 2

Comparison of the relative concentration of ions A, evaluated by the exact solution of the diffusion equation (solid curve) and the linear superposition principle (dashed curve).

Fig. 3
Fig. 3

(a) Equal-refractive-index curves within one period of a 1 → 5 beam splitter in Table 1. (b) Time evolution of the phase-delay profile.

Fig. 4
Fig. 4

Diffusion depth after an ion exchange of 30,000 s as a function of aperture width c with M = 0.3 and DA = 2.0 × 10-15 in Eq. (6).

Fig. 5
Fig. 5

Two-step process to fabricate the five-beam element, showing the equal-refractive-index curves after the (a) first and (b) second step, and the time evolution of the phase-delay profile during the (c) first and (d) second step.

Fig. 6
Fig. 6

Equal-refractive-index curves for the 1 → 9 beam splitter after the (a) masked ion-exchange process and (c) postbaking. Also shown are time evolutions of phase-delay profiles during the (b) ion-exchange process and (d) postbaking.

Fig. 7
Fig. 7

Fabrication error analysis for the 1 → 5 beam splitter made by single-step ion exchange, showing the effect of (a) random aperture displacement and (b) error in aperture sizes at several temperatures.

Fig. 8
Fig. 8

Fabrication error analysis for the 1 → 5 beam splitter made by two-step ion-exchange, showing the effect of (a) misalignment of the second mask and (b) error in aperture sizes.

Fig. 9
Fig. 9

(a) Photograph of the far-field diffraction pattern of the 1 → 5 beam splitter fabricated by using two-step ion-exchange. (b) Measured efficiencies ηm of the diffraction orders.

Fig. 10
Fig. 10

Measured diffraction patterns of the 1 → 5 beam splitter (a) without and (b) with a liquid-gate setup are dissimilar as a result of surface swelling.

Tables (1)

Tables Icon

Table 1 Theoretical Uniformity Errors U and Diffraction Efficiencies η of some 1 → M Beam-Splitter Elements, and Efficiencies ηb and ηc of Binary and Continuous Surface-Relief Elements

Equations (12)

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

η=mW ηm,
U=ηmax-ηmin/ηmax+ηmin,
ϕx, t=k-0Δnx, z, tdz,
Tm=1d0dexpiϕx, texp-i2πmx/ddx,
ηm=Tm2
tCx, z, t=·DACx, z, t1-αCx, z, t.
DAT=a exp-b/T,
ϕx, t=j=1Jϕjx, t; cj, xj
=mWηm-ηˆ/M2,
Δnexpx, z=-n0-1ΔVx, z/Vx, z.
Δzx=-0ΔVx, z/Vx, zdz.
Δϕx-0 Δnexpx, zdz+kn0-1Δzx=0.

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