Abstract

A binary fan-out kinoform for focusing and splitting an incident beam into a 4 × 4 spot array, with a largest deflection angle of 28°, was designed, fabricated in GaAs, and evaluated. The kinoform was defined in resist with electron-beam lithography and etched into GaAs with chemically assisted ion-beam etching. Light at wavelength 0.98 μm from a single-mode fiber was used to illuminate the kinoform. The efficiency was measured to be 34%, and the uniformity error for the 4 × 4 spots was 29%. Although the typical feature size of the kinoform is only roughly two wavelengths, we found that the scalar theory of diffraction can be used. A first kinoform was designed with the customary Fresnel-diffraction theory, which was found to be too coarse, resulting in a fan-out exhibiting some distortion. A second kinoform was designed with the more rigorous Fresnel–Kirchhoff expression, and its fan-out shows no distortion.

© 1996 Optical Society of America

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References

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  1. K. Rastani, M. Orenstein, E. Kapon, A. C. Von Lehmen, “Integration of planar Fresnel microlenses with vertical-cavity surface-emitting laser arrays,” Opt. Lett. 16, 919–921 (1991).
    [CrossRef] [PubMed]
  2. L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
    [CrossRef]
  3. M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).
  4. F. Koyama, S. Kinoshita, K. Iga, “Room-temperature continuous wave lasing characteristics of a GaAs vertical cavity surface-emitting laser,” Appl. Phys. Lett. 55, 221–222 (1989).
    [CrossRef]
  5. M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 34–42 (1991).
  6. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 10.
  7. M. Hagberg, B. Jonsson, A. G. Larsson, “Investigation of chemically assisted ion beam etching for the fabrication of vertical ultrahigh quality facets in GaAs,” J. Vac. Sci. Technol. B 12, 555–566 (1994).
    [CrossRef]

1995 (1)

L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
[CrossRef]

1994 (1)

M. Hagberg, B. Jonsson, A. G. Larsson, “Investigation of chemically assisted ion beam etching for the fabrication of vertical ultrahigh quality facets in GaAs,” J. Vac. Sci. Technol. B 12, 555–566 (1994).
[CrossRef]

1991 (1)

1989 (1)

F. Koyama, S. Kinoshita, K. Iga, “Room-temperature continuous wave lasing characteristics of a GaAs vertical cavity surface-emitting laser,” Appl. Phys. Lett. 55, 221–222 (1989).
[CrossRef]

Carson, R. F.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Du, T. C.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Fan, L.

L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
[CrossRef]

Farn, M. W.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 34–42 (1991).

Grodzinski, P.

L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
[CrossRef]

Hagberg, M.

M. Hagberg, B. Jonsson, A. G. Larsson, “Investigation of chemically assisted ion beam etching for the fabrication of vertical ultrahigh quality facets in GaAs,” J. Vac. Sci. Technol. B 12, 555–566 (1994).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 10.

Iga, K.

F. Koyama, S. Kinoshita, K. Iga, “Room-temperature continuous wave lasing characteristics of a GaAs vertical cavity surface-emitting laser,” Appl. Phys. Lett. 55, 221–222 (1989).
[CrossRef]

Jonsson, B.

M. Hagberg, B. Jonsson, A. G. Larsson, “Investigation of chemically assisted ion beam etching for the fabrication of vertical ultrahigh quality facets in GaAs,” J. Vac. Sci. Technol. B 12, 555–566 (1994).
[CrossRef]

Kapon, E.

Kilcoyne, S. P.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Kinoshita, S.

F. Koyama, S. Kinoshita, K. Iga, “Room-temperature continuous wave lasing characteristics of a GaAs vertical cavity surface-emitting laser,” Appl. Phys. Lett. 55, 221–222 (1989).
[CrossRef]

Koyama, F.

F. Koyama, S. Kinoshita, K. Iga, “Room-temperature continuous wave lasing characteristics of a GaAs vertical cavity surface-emitting laser,” Appl. Phys. Lett. 55, 221–222 (1989).
[CrossRef]

Larsson, A. G.

M. Hagberg, B. Jonsson, A. G. Larsson, “Investigation of chemically assisted ion beam etching for the fabrication of vertical ultrahigh quality facets in GaAs,” J. Vac. Sci. Technol. B 12, 555–566 (1994).
[CrossRef]

Lear, K. L.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Lee, H. C.

L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
[CrossRef]

Orenstein, M.

Rastani, K.

Schneider, R. P.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Vawter, G. A.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Von Lehmen, A. C.

Warren, M. E.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Wendt, J. R.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Wu, M. C.

L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
[CrossRef]

Zolper, J. C.

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

Appl. Phys. Lett. (1)

F. Koyama, S. Kinoshita, K. Iga, “Room-temperature continuous wave lasing characteristics of a GaAs vertical cavity surface-emitting laser,” Appl. Phys. Lett. 55, 221–222 (1989).
[CrossRef]

Electron. Lett. (1)

L. Fan, M. C. Wu, H. C. Lee, P. Grodzinski, “Novel vertical-cavity surface-emitting lasers with integrated optical beam router,” Electron. Lett. 31, 729–730 (1995).
[CrossRef]

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

M. Hagberg, B. Jonsson, A. G. Larsson, “Investigation of chemically assisted ion beam etching for the fabrication of vertical ultrahigh quality facets in GaAs,” J. Vac. Sci. Technol. B 12, 555–566 (1994).
[CrossRef]

Opt. Lett. (1)

Other (3)

M. E. Warren, T. C. Du, J. R. Wendt, G. A. Vawter, R. F. Carson, K. L. Lear, S. P. Kilcoyne, R. P. Schneider, J. C. Zolper, “Integration of diffractive lenses with addressable vertical-cavity laser arrays,” in Circular-Grating Light-Emitting Sources, S. I. Najafi, M. Fallahi, N. Peyghambarian, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2398, 12–20 (1995).

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1555, 34–42 (1991).

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987), Chap. 10.

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Figures (10)

Fig. 1
Fig. 1

Experimental setup for the evaluation of the fan-out kinoform etched in GaAs.

Fig. 2
Fig. 2

Method A algorithm for calculating the kinoform relief.

Fig. 3
Fig. 3

Binary kinoform designed with Method A.

Fig. 4
Fig. 4

Method B algorithm for calculating the kinoform relief.

Fig. 5
Fig. 5

Desired diffraction-plane intensity distribution used as an input to the Method A algorithm. The Method A algorithm tries to find a kinoform that produces this distribution when evaluated with Fresnel-diffraction theory.

Fig. 6
Fig. 6

Diffraction-plane intensity distribution evaluated with the Fresnel–Kirchhoff theory.

Fig. 7
Fig. 7

Binary kinoform designed with Method B.

Fig. 8
Fig. 8

Scanning electron micrograph of a central portion of the kinoform designed with Method B and etched in GaAs.

Fig. 9
Fig. 9

Measured intensity distribution from the Method A kinoform.

Fig. 10
Fig. 10

Measured intensity distribution from the Method B kinoform.

Equations (2)

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uniformity error = I max I min I max + I min ,
A diff = kinoform pixels A kin exp ( i k r kd ) r kd ( 1 + cos    α 2 ) ,

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