Abstract

Colorless gradient-index cylindrical lenses with high numerical apertures in slabs 200–1000 μm thick have been fabricated by silver–sodium ion exchange in a specially developed glass. The lenses with numerical apertures of 0.6 are characterized by index profiles and by spherical and chromatic aberration. On-axis focusing properties and the application to the collimation of high-power laser diode bars are discussed.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. R. Leger, W. C. Goltsos, “Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers,” IEEE J. Quantum Electron. 28, 1088–1100 (1992).
    [Crossref]
  2. H. Sakai, S. Shingaki, S. Ohmi, S. Nakayama, K. Nakagawa, T. Izumitani, “One-directional gradient-index slab lens,” Appl. Opt. 24, 4312–4315 (1985).
    [Crossref] [PubMed]
  3. Y. Asahara, H. Sakai, S. Ohmi, S. Nakayama, Y. Yoneda, T. Izumitamni, “Gradient-index slab lens with high numerical aperture,” Appl. Opt. 25, 3384–3387 (1986).
    [Crossref] [PubMed]
  4. T. Findakly, “Glass waveguides by ion-exchange: a review,” Opt. Eng. 24, 244–252 (1985).
  5. R. Araujo, “Colorless glasses containing ion-exchanged silver,” Appl. Opt. 31, 5221–5224 (1992).
    [Crossref] [PubMed]
  6. T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).
  7. S. Ohmi, H. Sakai, Y. Asahara, S. Nakayama, Y. Yoneda, T. Izumitani, “Gradient-index rod lens made by double ion-exchange process,” Appl. Opt. 27, 496–499 (1988).
    [Crossref] [PubMed]
  8. A. Tervonen, “A general model for the fabrication processes of channel waveguides by ion exchange,” J. Appl. Phys. 67, 2746–2752 (1990).
    [Crossref]
  9. T. Possner, B. Messerschmidt, M. Palme, R. Goering, “GRIN-optics with high numerical aperture by silver-exchange,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 69–72.
  10. R. Goering, M. Rothhardt, “Application of the refracted-near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
    [Crossref]
  11. Y. Suematsu, K. Iga, S. Ito, “A light beam waveguide using hyperbolic type gas lenses,” IEEE Trans. Microwave Theory Tech. MTT-14, 657–665 (1966).
    [Crossref]
  12. K. Iga, “Theory for gradient-index imaging,” Appl. Opt. 19, 1039–1043 (1980).
    [Crossref] [PubMed]

1992 (2)

J. R. Leger, W. C. Goltsos, “Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers,” IEEE J. Quantum Electron. 28, 1088–1100 (1992).
[Crossref]

R. Araujo, “Colorless glasses containing ion-exchanged silver,” Appl. Opt. 31, 5221–5224 (1992).
[Crossref] [PubMed]

1991 (1)

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

1990 (1)

A. Tervonen, “A general model for the fabrication processes of channel waveguides by ion exchange,” J. Appl. Phys. 67, 2746–2752 (1990).
[Crossref]

1988 (1)

1986 (2)

R. Goering, M. Rothhardt, “Application of the refracted-near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[Crossref]

Y. Asahara, H. Sakai, S. Ohmi, S. Nakayama, Y. Yoneda, T. Izumitamni, “Gradient-index slab lens with high numerical aperture,” Appl. Opt. 25, 3384–3387 (1986).
[Crossref] [PubMed]

1985 (2)

1980 (1)

1966 (1)

Y. Suematsu, K. Iga, S. Ito, “A light beam waveguide using hyperbolic type gas lenses,” IEEE Trans. Microwave Theory Tech. MTT-14, 657–665 (1966).
[Crossref]

Araujo, R.

Asahara, Y.

Findakly, T.

T. Findakly, “Glass waveguides by ion-exchange: a review,” Opt. Eng. 24, 244–252 (1985).

Goering, R.

R. Goering, M. Rothhardt, “Application of the refracted-near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[Crossref]

T. Possner, B. Messerschmidt, M. Palme, R. Goering, “GRIN-optics with high numerical aperture by silver-exchange,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 69–72.

Goltsos, W. C.

J. R. Leger, W. C. Goltsos, “Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers,” IEEE J. Quantum Electron. 28, 1088–1100 (1992).
[Crossref]

Iga, K.

K. Iga, “Theory for gradient-index imaging,” Appl. Opt. 19, 1039–1043 (1980).
[Crossref] [PubMed]

Y. Suematsu, K. Iga, S. Ito, “A light beam waveguide using hyperbolic type gas lenses,” IEEE Trans. Microwave Theory Tech. MTT-14, 657–665 (1966).
[Crossref]

Ito, S.

Y. Suematsu, K. Iga, S. Ito, “A light beam waveguide using hyperbolic type gas lenses,” IEEE Trans. Microwave Theory Tech. MTT-14, 657–665 (1966).
[Crossref]

Izumitamni, T.

Izumitani, T.

Kahnt, H.

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

Kaps, C.

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

Leger, J. R.

J. R. Leger, W. C. Goltsos, “Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers,” IEEE J. Quantum Electron. 28, 1088–1100 (1992).
[Crossref]

Messerschmidt, B.

T. Possner, B. Messerschmidt, M. Palme, R. Goering, “GRIN-optics with high numerical aperture by silver-exchange,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 69–72.

Mueller, R.

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

Nakagawa, K.

Nakayama, S.

Ohmi, S.

Palme, M.

T. Possner, B. Messerschmidt, M. Palme, R. Goering, “GRIN-optics with high numerical aperture by silver-exchange,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 69–72.

Possner, T.

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

T. Possner, B. Messerschmidt, M. Palme, R. Goering, “GRIN-optics with high numerical aperture by silver-exchange,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 69–72.

Rothhardt, M.

R. Goering, M. Rothhardt, “Application of the refracted-near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[Crossref]

Sakai, H.

Schreiter, G.

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

Shingaki, S.

Suematsu, Y.

Y. Suematsu, K. Iga, S. Ito, “A light beam waveguide using hyperbolic type gas lenses,” IEEE Trans. Microwave Theory Tech. MTT-14, 657–665 (1966).
[Crossref]

Tervonen, A.

A. Tervonen, “A general model for the fabrication processes of channel waveguides by ion exchange,” J. Appl. Phys. 67, 2746–2752 (1990).
[Crossref]

Yoneda, Y.

Appl. Opt. (5)

Glastech. Ber. (1)

T. Possner, G. Schreiter, R. Mueller, C. Kaps, H. Kahnt, “Special glass for integrated and microoptics,” Glastech. Ber. 64, 185–190 (1991).

IEEE J. Quantum Electron. (1)

J. R. Leger, W. C. Goltsos, “Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers,” IEEE J. Quantum Electron. 28, 1088–1100 (1992).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

Y. Suematsu, K. Iga, S. Ito, “A light beam waveguide using hyperbolic type gas lenses,” IEEE Trans. Microwave Theory Tech. MTT-14, 657–665 (1966).
[Crossref]

J. Appl. Phys. (1)

A. Tervonen, “A general model for the fabrication processes of channel waveguides by ion exchange,” J. Appl. Phys. 67, 2746–2752 (1990).
[Crossref]

J. Opt. Commun. (1)

R. Goering, M. Rothhardt, “Application of the refracted-near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7, 82–85 (1986).
[Crossref]

Opt. Eng. (1)

T. Findakly, “Glass waveguides by ion-exchange: a review,” Opt. Eng. 24, 244–252 (1985).

Other (1)

T. Possner, B. Messerschmidt, M. Palme, R. Goering, “GRIN-optics with high numerical aperture by silver-exchange,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 69–72.

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 (15)

Fig. 1
Fig. 1

Principle of the silver–sodium exchange process: (a) sodium-containing substrate glass, (b) silver stuffing process, (c) burying process.

Fig. 2
Fig. 2

Homogeneous index profile n 2(x) at 633 nm in a 750-μm-thick slab.

Fig. 3
Fig. 3

Refractive index n as a function of wavelength λ: A, initial glass; B, stuffed glass.

Fig. 4
Fig. 4

Index profiles n 2(x) measured at 633 nm in 750-μm-thick slabs after various exchange periods of the burying step.

Fig. 5
Fig. 5

Profile parameters h 4′, h 4, and h 6 as a function of exchange period t A ; h 4′ was used as the optimizing parameter.

Fig. 6
Fig. 6

Index profiles n 2(x) produced after annealing is performed at 450 °C for 20 and 60 min compared with the initial profile (t T , annealing time).

Fig. 7
Fig. 7

Optimizing parameter h 4′ and the difference in the square of index Δ(n 2) as a function of annealing time t T :, fitted h 4′ parameters from measured index profiles; ▲, measured values of Δ(n 2).

Fig. 8
Fig. 8

Transmission T of a 500-μm slab as a function of wavelength λ: A, substrate glass; B, stuffed glass.

Fig. 9
Fig. 9

LSA(x 2′) in 750-μm-thick slabs calculated from index profiles measured after several exchange periods t A of the burying step.

Fig. 10
Fig. 10

LSA(x 2′) in 1000-μm-thick slabs calculated from index profiles measured after annealing is performed for various periods t T (A, 40 min; B, 60 min) relative to the unannealed profile, C.

Fig. 11
Fig. 11

Best intensity profile I(x) and MTF(f x ) calculated by FFT of a GRIN cylindrical lens with an optimized two-step profile (h 4 = 5.87, h 6 = −71.2).

Fig. 12
Fig. 12

g(λ) calculated from Eqs. (4)(6) for a lens investigated experimentally with n 0 2 = 2.6834, g* = 0.7482 mm−1, h 4* = −4.32, h 6* = −11.83, d l = 0.724 mm, and n R 2 = 2.411 for λ = 633 nm.

Fig. 13
Fig. 13

Working distance s(λ) of the lens of length z l = 1.842 mm characterized in Fig. 12: crosses, error bars of the points measured.

Fig. 14
Fig. 14

Angular characteristic of the strongly divergent light emitted by the laser diode. □, measured values.

Fig. 15
Fig. 15

Schematic diagram of the measuring system: z = 200 mm, d S = 5 mm.

Equations (6)

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

n 2 ( x ) = n 0 2 [ 1 - ( g x ) 2 + h 4 ( g x ) 4 + h 6 ( g x ) 6 ] .
f ( λ ) = 1 n 0 ( λ ) g ( λ ) sin [ g ( λ ) z l ] , s ( λ ) = 1 n 0 ( λ ) g ( λ ) tan [ g ( λ ) z l ] .
n 2 ( x ) = n S 2 + Δ ( n 2 ) max c Ag ( x ) ,
g ( λ ) = g * [ C ( λ ) ] 1 / 2 ,             h 4 ( λ ) = h 4 * C ( λ ) ,             h 6 ( λ ) = h 6 * C 2 ( λ ) .
C ( λ ) = n R 2 ( λ ) - n 0 2 ( λ ) n 0 2 ( λ ) [ - ( g * d l 2 ) 2 + h 4 * ( g * d l 2 ) 4 + h 6 * ( g * d l 2 ) 6 ] .
n 0 ( λ ) = 1.6191 + 7614 ( nm 2 ) / λ 2 , n R ( λ ) = 1.5402 + 5114 ( nm 2 ) / λ 2 .

Metrics