Abstract

For the conversion of light from edge-emitting laser diodes into symmetric laser beams two main tasks have to be performed: collimation and beam shaping. Generally these two jobs are performed separately. Because of the inherently different divergence angles of the emitted light, collimation with astigmatic lenses generally results in a beam with an elliptically shaped amplitude distribution. This asymmetry has to be compensated for by an anamorphic imaging step to obtain the desired spherical beam profile. It can be advantageous to combine both jobs in one element. We demonstrate the design, the fabrication, and the application of refractive gradient-index elements, which allow one to perform both jobs with a single element. Our astigmatic lenses were fabricated by silver–sodium ion exchange in glass.

© 1995 Optical Society of America

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References

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  1. F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
    [CrossRef]
  2. J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771 (1988).
    [CrossRef]
  3. J. J. Snyder, P. Reichert, T. M. Baer, “Fast diffraction limited cylindrical microlenses,” Appl. Opt. 30, 2743–2747 (1991).
    [CrossRef] [PubMed]
  4. M. Oikawa, K. Iga, “Distributed-index planar microlens,” Appl. Opt. 21, 1052–1056 (1982).
    [CrossRef] [PubMed]
  5. K. Iga, Y. Kokubun, M. Oikawa, Fundamentals of Micro-Optics (Academic, Orlando, Fla., 1984).
  6. Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).
  7. D. D’Amato, R. Centamore, “Two applications for microlens arrays: detector fill factor improvement and laser diode collimation,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1544, 166–175 (1991).
  8. A. E. SiegmanLasers (University Science, Mill Valley, Calif., 1986), Chap. 17.2., pp. 675–680.
  9. Ref. 8, p. 663.
  10. J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Study of 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]
  11. J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.
  12. J. Jahns, B. Acklin, “Integrated planar optical imaging system with high interconnection density,” Opt. Lett. 18, 1594–1596 (1993).
    [CrossRef] [PubMed]
  13. M. Oikawa, H. Nemoto, K. Hamanaka, E. Okuda, “High numerical aperture planar microlens with swelled structures,” Appl. Opt. 29, 4077–4080 (1990).
    [CrossRef] [PubMed]
  14. M. Oikawa, H. Imanishi, T. Kishimoto, “High NA planar microlens for LD array,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, 1751, 246–254 (1992).

1994 (1)

1993 (1)

1992 (1)

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

1982 (1)

Acklin, B.

Asahara, Y.

Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).

Baer, T. M.

Bähr, J.

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Study of 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]

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Brenner, K.-H.

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Study of 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]

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Brubaker, J. L.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Centamore, R.

D. D’Amato, R. Centamore, “Two applications for microlens arrays: detector fill factor improvement and laser diode collimation,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1544, 166–175 (1991).

Cloonan, T. J.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

D’Amato, D.

D. D’Amato, R. Centamore, “Two applications for microlens arrays: detector fill factor improvement and laser diode collimation,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1544, 166–175 (1991).

Hamanaka, K.

Herron, M. J.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Hinterlong, S. J.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Iga, K.

M. Oikawa, K. Iga, “Distributed-index planar microlens,” Appl. Opt. 21, 1052–1056 (1982).
[CrossRef] [PubMed]

K. Iga, Y. Kokubun, M. Oikawa, Fundamentals of Micro-Optics (Academic, Orlando, Fla., 1984).

Imanishi, H.

M. Oikawa, H. Imanishi, T. Kishimoto, “High NA planar microlens for LD array,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, 1751, 246–254 (1992).

Jahns, J.

Kishimoto, T.

M. Oikawa, H. Imanishi, T. Kishimoto, “High NA planar microlens for LD array,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, 1751, 246–254 (1992).

Kokubun, Y.

K. Iga, Y. Kokubun, M. Oikawa, Fundamentals of Micro-Optics (Academic, Orlando, Fla., 1984).

Leger, J. R.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Lentine, A. L.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

McCormick, F. B.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Moisel, J.

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Morrison, R. L.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Nakayama, S.

Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).

Nemoto, H.

Oikawa, M.

M. Oikawa, H. Nemoto, K. Hamanaka, E. Okuda, “High numerical aperture planar microlens with swelled structures,” Appl. Opt. 29, 4077–4080 (1990).
[CrossRef] [PubMed]

M. Oikawa, K. Iga, “Distributed-index planar microlens,” Appl. Opt. 21, 1052–1056 (1982).
[CrossRef] [PubMed]

K. Iga, Y. Kokubun, M. Oikawa, Fundamentals of Micro-Optics (Academic, Orlando, Fla., 1984).

M. Oikawa, H. Imanishi, T. Kishimoto, “High NA planar microlens for LD array,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, 1751, 246–254 (1992).

Okuda, E.

Omi, S.

Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).

Reichert, P.

Sakai, H.

Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).

Sasian, J. M.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Scott, M. L.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Siegman, A. E.

A. E. SiegmanLasers (University Science, Mill Valley, Calif., 1986), Chap. 17.2., pp. 675–680.

Singer, W.

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Sinzinger, S.

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Study of 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]

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Snyder, J. J.

Spick, T.

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Study of 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]

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Testorf, M.

J. Bähr, K.-H. Brenner, S. Sinzinger, T. Spick, M. Testorf, “Study of 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]

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

Tooley, F. A. P.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Walker, S. L.

F. B. McCormick, F. A. P. Tooley, T. J. Cloonan, J. L. Brubaker, A. L. Lentine, R. L. Morrison, S. J. Hinterlong, M. J. Herron, S. L. Walker, J. M. Sasian, “Experimental investigation of a free-space optical switching network by using symmetric self-electro-optic-effect devices,” Appl. Opt. 26, 5431–5445 (1992).
[CrossRef]

Yoneda, Y.

Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).

Appl. Opt. (5)

Appl. Phys. Lett. (1)

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Opt. Lett. (1)

Other (7)

M. Oikawa, H. Imanishi, T. Kishimoto, “High NA planar microlens for LD array,” in Miniature and Micro-Optics: Fabrication, C. Roychoudhuri, W. B. Veldkamp, 1751, 246–254 (1992).

J. Bähr, K.-H. Brenner, J. Moisel, W. Singer, S. Sinzinger, T. Spick, M. Testorf, “Modifications of the imaging properties of ion-exchange microlenses by mask shaping,” presented at the Gradient-Index Topical Meeting of the Optical Society of America, Santiago de Compostela, Spain, 4–6 October 1992.

K. Iga, Y. Kokubun, M. Oikawa, Fundamentals of Micro-Optics (Academic, Orlando, Fla., 1984).

Y. Asahara, S. Omi, H. Sakai, S. Nakayama, Y. Yoneda, “Gradient refractive index type anamorphic planar microlens and method of producing the same,” U.S. patent4,805,997 (30May1986); see also Appl. Opt. 25, 2625 (1989).

D. D’Amato, R. Centamore, “Two applications for microlens arrays: detector fill factor improvement and laser diode collimation,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1544, 166–175 (1991).

A. E. SiegmanLasers (University Science, Mill Valley, Calif., 1986), Chap. 17.2., pp. 675–680.

Ref. 8, p. 663.

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Figures (12)

Fig. 1
Fig. 1

Cross sections of an edge-emitting laser diode in the x and they directions.

Fig. 2
Fig. 2

Elliptic mask used for the fabrication of astigmatic GRIN elements by the ion-exchange process (diameters are 300 μm and 100 μm).

Fig. 3
Fig. 3

Interferogram of an array of astigmatic GRIN microlenses.

Fig. 4
Fig. 4

Contour plot of the measured phase distribution (in units of π) of an astigmatic GRIN element (mask diameters for fabrication are 250 μm and 50 μm).

Fig. 5
Fig. 5

Line scans in the two perpendicular directions of the measured phase distribution of the astigmatic GRIN element: (a) the whole phase element and (b) the center section of the phase element.

Fig. 6
Fig. 6

Crossed bars used in an imaging experiment to demonstrate the astigmatic behavior of the GRIN microlenses.

Fig. 7
Fig. 7

Images of the object shown in Fig. 6: (a) the image formed by the astigmatic GRIN lens along the axis with the smaller diameter and thus also the smaller focal length; (b) the image formed in the perpendicular direction (long focal length).

Fig. 8
Fig. 8

Experimental setup for the collimation experiment.

Fig. 9
Fig. 9

Image of the emitting surface of the laser.

Fig. 10
Fig. 10

Symmetric amplitude profile at the distance z 0 behind the laser diode.

Fig. 11
Fig. 11

Series of pictures of the laser beam at various distances from the diode: (a) without and (b) with the astigmatic microlens.

Fig. 12
Fig. 12

Array of astigmatic GRIN elements integrated with an array of laser diodes.

Tables (1)

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Table 1 Parameters of a Selection of Fabricated Astigmatic Gradient-Index Microlenses

Equations (4)

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u ( x , y ) = A 0 exp [ ( x 2 2 σ x , 0 2 + y 2 2 σ y , 0 2 ) ] .
σ x 2 ( z ) = 4 π 2 σ x , 0 4 + λ 2 z 2 4 π 2 σ x , 0 2 , σ y 2 ( z ) = 4 π 2 σ y , 0 4 + λ 2 z 2 4 π 2 σ y , 0 2 .
σ x ( z 0 ) = σ y ( z 0 ) z 0 = 2 π λ σ x , 0 σ y , 0 .
f x = z 0 + 4 π 2 σ x , 0 4 λ 2 z 0 , f y = z 0 + 4 π 2 σ y , 0 4 λ 2 z 0 .

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