Abstract

High index of refraction crown glasses containing silver oxide have been cast from a melt and used for ion exchange experiments. High quality axial and radial gradient-index profiles were fabricated and the interdiffusion coefficient calculated. Index changes up to 0.08 were achieved in a base glass with nd = 1.61 and Vd = 57.

© 1990 Optical Society of America

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References

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  1. J. B. Caldwell, D. T. Moore, “Design of Gradient-Index Lens Systems for Disk Format Cameras,” Appl. Opt. 25, 3351–3355 (1986).
    [CrossRef] [PubMed]
  2. D. P. Ryan-Howard, “Chromatic Properties of Gradient Index Glass,” Ph.D. Thesis, U. Rochester, New York (1983).
  3. H. Nishi, H. Ichikawa, M. Toyama, I. Kitano, “Gradient-Index Objective Lens for the Compact Disk System,” Appl. Opt. 25, 3340–3344 (1986).
    [CrossRef] [PubMed]
  4. S. N. Houde-Walter, “Gradient Index Profile Control by Ion Exchange in Glass,” Ph.D. Thesis, U. Rochester, New York (1987).
  5. G. Stewart et al., “Planar Optical Waveguides Formed by Ion migration in Glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
    [CrossRef]
  6. M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-Index Formation Processing of a Planar Microlens,” Appl. Opt. 23, 1787–1789 (1984).
    [CrossRef] [PubMed]
  7. D. S. Kindred, D. T. Moore, “Design, Fabrication, and Testing of a Gradient-Index Binocular Objective,” Appl. Opt. 27, 492–495 (1988).
    [CrossRef] [PubMed]
  8. J. B. Caldwell, D. S. Kindred, D. T. Moore, “Large Diameter Radial Gradient Index Glass,” in Technical Digest, Seventh Topical Meeting on Gradient Index Imaging Systems, (Optical Society of America, Washington, DC, 1987), Paper ThD3-1.
  9. S. Ohmi, H. Sakai, Y. Asahara, S. Nakayama, Y. Yoneda, “Gradient-Index Rod Lens Made by a Double Ion-Exchange Process,” Appl. Opt. 27, 496–499 (1988).
    [CrossRef] [PubMed]
  10. J. L. Jackel, “Glass Waveguides Made Using Low Melting Point Nitrate mixtures,” Appl. Opt. 27, 472–475 (1988).
    [CrossRef] [PubMed]
  11. J. Crank, The Mathematics of Diffusion (Oxford U. P., New York, 1975).
  12. Reference 11, p. 14.
  13. Reference 2, p. 39.
  14. Reference 11, p. 73.
  15. Y. Asahara et al., “One-Directional Gradient-Index Slab Lens,” Appl. Opt. 24, 4312–4315 (1985).
    [CrossRef] [PubMed]
  16. J. B. Caldwell, “Sol-Gel Method for Fabricating Gradient Index Glass,” Ph.D. Thesis, U. Rochester, Rochester, NY (1989).
  17. R. F. Bartholomew, “Structure and Properties of the Silver Phosphate System—Infrared and Visible Spectra,” J. Non.-Cryst. Solids 7, 221 (1972).
    [CrossRef]
  18. R. M. Klien et al., “Glass Formation and Properties in the Aluminum Borophosphate System,” Bull. Am. Ceram. Soc. 57, 199 (1978).
  19. Levin et al., Eds. Phase Diagrams for Ceramists (American Ceramic Society, Columbus, OH, 1964).
  20. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Ph.D. Thesis, U. Rochester, Rochester, NY (1982).
  21. Levin et al., Phase Diagrams for Ceramists, 1969 Supplement (American Ceramic Society, Columbus, OH, 1969).
  22. Reference 4, p. 85.
  23. Reference 2, p. 73.
  24. R. W. Wood, Physical Optics (Macmillan, New York, 1905), p. 71.

1988

1986

1985

1984

1978

R. M. Klien et al., “Glass Formation and Properties in the Aluminum Borophosphate System,” Bull. Am. Ceram. Soc. 57, 199 (1978).

1977

G. Stewart et al., “Planar Optical Waveguides Formed by Ion migration in Glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

1972

R. F. Bartholomew, “Structure and Properties of the Silver Phosphate System—Infrared and Visible Spectra,” J. Non.-Cryst. Solids 7, 221 (1972).
[CrossRef]

Asahara, Y.

Bartholomew, R. F.

R. F. Bartholomew, “Structure and Properties of the Silver Phosphate System—Infrared and Visible Spectra,” J. Non.-Cryst. Solids 7, 221 (1972).
[CrossRef]

Caldwell, J. B.

J. B. Caldwell, D. T. Moore, “Design of Gradient-Index Lens Systems for Disk Format Cameras,” Appl. Opt. 25, 3351–3355 (1986).
[CrossRef] [PubMed]

J. B. Caldwell, D. S. Kindred, D. T. Moore, “Large Diameter Radial Gradient Index Glass,” in Technical Digest, Seventh Topical Meeting on Gradient Index Imaging Systems, (Optical Society of America, Washington, DC, 1987), Paper ThD3-1.

J. B. Caldwell, “Sol-Gel Method for Fabricating Gradient Index Glass,” Ph.D. Thesis, U. Rochester, Rochester, NY (1989).

Chiba, T.

Crank, J.

J. Crank, The Mathematics of Diffusion (Oxford U. P., New York, 1975).

Houde-Walter, S. N.

S. N. Houde-Walter, “Gradient Index Profile Control by Ion Exchange in Glass,” Ph.D. Thesis, U. Rochester, New York (1987).

Ichikawa, H.

Iga, K.

Jackel, J. L.

Kindred, D. S.

D. S. Kindred, D. T. Moore, “Design, Fabrication, and Testing of a Gradient-Index Binocular Objective,” Appl. Opt. 27, 492–495 (1988).
[CrossRef] [PubMed]

J. B. Caldwell, D. S. Kindred, D. T. Moore, “Large Diameter Radial Gradient Index Glass,” in Technical Digest, Seventh Topical Meeting on Gradient Index Imaging Systems, (Optical Society of America, Washington, DC, 1987), Paper ThD3-1.

Kitano, I.

Klien, R. M.

R. M. Klien et al., “Glass Formation and Properties in the Aluminum Borophosphate System,” Bull. Am. Ceram. Soc. 57, 199 (1978).

Levin,

Levin et al., Phase Diagrams for Ceramists, 1969 Supplement (American Ceramic Society, Columbus, OH, 1969).

Miceli, J.

J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Ph.D. Thesis, U. Rochester, Rochester, NY (1982).

Moore, D. T.

D. S. Kindred, D. T. Moore, “Design, Fabrication, and Testing of a Gradient-Index Binocular Objective,” Appl. Opt. 27, 492–495 (1988).
[CrossRef] [PubMed]

J. B. Caldwell, D. T. Moore, “Design of Gradient-Index Lens Systems for Disk Format Cameras,” Appl. Opt. 25, 3351–3355 (1986).
[CrossRef] [PubMed]

J. B. Caldwell, D. S. Kindred, D. T. Moore, “Large Diameter Radial Gradient Index Glass,” in Technical Digest, Seventh Topical Meeting on Gradient Index Imaging Systems, (Optical Society of America, Washington, DC, 1987), Paper ThD3-1.

Morinaga, M.

Nakayama, S.

Nishi, H.

Ohmi, S.

Oikawa, M.

Ryan-Howard, D. P.

D. P. Ryan-Howard, “Chromatic Properties of Gradient Index Glass,” Ph.D. Thesis, U. Rochester, New York (1983).

Sakai, H.

Stewart, G.

G. Stewart et al., “Planar Optical Waveguides Formed by Ion migration in Glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Toyama, M.

Usui, T.

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, 1905), p. 71.

Yoneda, Y.

Appl. Opt.

Bull. Am. Ceram. Soc.

R. M. Klien et al., “Glass Formation and Properties in the Aluminum Borophosphate System,” Bull. Am. Ceram. Soc. 57, 199 (1978).

IEEE J. Quantum Electron.

G. Stewart et al., “Planar Optical Waveguides Formed by Ion migration in Glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

J. Non.-Cryst. Solids

R. F. Bartholomew, “Structure and Properties of the Silver Phosphate System—Infrared and Visible Spectra,” J. Non.-Cryst. Solids 7, 221 (1972).
[CrossRef]

Other

S. N. Houde-Walter, “Gradient Index Profile Control by Ion Exchange in Glass,” Ph.D. Thesis, U. Rochester, New York (1987).

D. P. Ryan-Howard, “Chromatic Properties of Gradient Index Glass,” Ph.D. Thesis, U. Rochester, New York (1983).

J. B. Caldwell, D. S. Kindred, D. T. Moore, “Large Diameter Radial Gradient Index Glass,” in Technical Digest, Seventh Topical Meeting on Gradient Index Imaging Systems, (Optical Society of America, Washington, DC, 1987), Paper ThD3-1.

J. B. Caldwell, “Sol-Gel Method for Fabricating Gradient Index Glass,” Ph.D. Thesis, U. Rochester, Rochester, NY (1989).

Levin et al., Eds. Phase Diagrams for Ceramists (American Ceramic Society, Columbus, OH, 1964).

J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Ph.D. Thesis, U. Rochester, Rochester, NY (1982).

Levin et al., Phase Diagrams for Ceramists, 1969 Supplement (American Ceramic Society, Columbus, OH, 1969).

Reference 4, p. 85.

Reference 2, p. 73.

R. W. Wood, Physical Optics (Macmillan, New York, 1905), p. 71.

J. Crank, The Mathematics of Diffusion (Oxford U. P., New York, 1975).

Reference 11, p. 14.

Reference 2, p. 39.

Reference 11, p. 73.

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Figures (8)

Fig. 1
Fig. 1

Axial GRIN profile at 632.8 nm produced by Na+ for Ag+ exchange in a glass with 20 Ag2O + 15Al2O3 + 65 P2O5 composition at 500°C for 24 h in 50 ZnCl2 + 50 NaCl.

Fig. 2
Fig. 2

Radial GRIN profile at 632.8 nm produced in SAP-8 glass after 72 h at 480°C in 50 ZnCl2 + 50 NaCl.

Fig. 3
Fig. 3

Measured concentration gradient of Ag2O in the glass after ion exchange for the axial gradient compared to the error function, which is the solution to the diffusion equation for a constant diffusion coefficient.

Fig. 4
Fig. 4

Index of refraction vs silver concentration in the axial gradient glass.

Fig. 5
Fig. 5

Diagram of a Wood lens.

Fig. 6
Fig. 6

Photograph taken with radial Ag2O GRIN (Wood) lens at f/25 in white light. The index profile of this lens is shown in Fig. 2.

Fig. 7
Fig. 7

Photograph of USAF 1951 resolution target taken with an Ag2O gradient Wood lens at f/25 in white light.

Fig. 8
Fig. 8

Calculated MTF of the Wood lens made by Na+ for Ag+ exchange.

Tables (1)

Tables Icon

Table I Batch and Measured Compositions of a Series of Glasses In the xAg2O + y Na2O + z Al2O3 + (1 − xyz) P2O5 System Given In Mole

Equations (16)

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

A salt + B glass A glass + B salt .
C t = [ D C ] ,
C t = x [ D C x ] ,
C = C 0 at x = 0 for t 0 ,
C = 0 at t = 0 for x 0.
C = C 0 erfc { x 4 D t } ,
erfc ( z ) = 1 - erf ( z ) = 1 - 2 π 0 z exp ( - η 2 ) d η .
n = n 0 + Δ n erfc { x 4 D t } .
C t = 1 r [ r ( r D C r ) ]
C = C 0 at r = r 0 for t 0 ,
c = 0 for r r 0 at t = 0.
C = C 0 [ 1 - 2 r 0 n = 1 exp ( - D α n 2 t ) J 0 ( r α n ) α n J 1 ( r 0 α n ) ] .
D t r 0 2 = 0.10 ,
n = 1.57 - 0.00955 r 2 - 0.00014 r 4 ,
f = - 1 2 N 10 t ,
N = N 00 + N 10 r 2 + N 20 r 4 + .

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