Abstract

We present a numerical wave optical model to describe the complex behavior of coaxial and decentered microlens-array-based telescopes illuminated by an incoherent angular spectrum of plane waves. With the use of this model we have been able to observe major performance differences between Galilean and Keplerian setups, which to our knowledge were not described before. The results of the simulations are compared with experimental results; the images of multimode fiber end faces are characterized with respect to transfer efficiency and intensity distribution. The results are also explained by use of modified existing analytical models.

© 2003 Optical Society of America

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References

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  1. K. M. Flood, W. J. Cassarly, “Wide angle beam steering using translation of plural lens arrays,” U.S. patent5,059,008 (22October1991).
  2. E. A. Watson, “Analysis of beam steering with decentered microlens arrays,” Opt. Eng. 32, 2665–2670 (1993).
    [CrossRef]
  3. W. Goltsos, M. Holz, “Agile beam steering using binary optics microlens arrays,” Opt. Eng. 29, 1392–1397 (1990).
    [CrossRef]
  4. M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
    [CrossRef]
  5. T. D. Milster, “Modelling and measurement of a micro-optic beam deflector,” in Design, Modeling, and Control of Laser Beam Optics, Y. Kohanzadeh, G. N. Lawrence, J. G. McCoy, H. Weichel, eds., Proc. SPIE1625, 78–83 (1992).
    [CrossRef]
  6. G. F. Mcdearmon, K. M. Flood, J. M. Finlan, “Comparison of conventional and microlens-array agile beam steerers,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. SPIE2383, 167–178 (1995).
    [CrossRef]
  7. G. Gal, H. E. Morrow, “Internally cooled large aperture microlens array with monolithic integrated micro scanner,” U.S. patent5,415,727 (16May1995).
  8. G. Gal, W. W. Anderson, B. J. Herman, D. M. Shough, “Wavefront correctors for scanning microlens arrays,” U.S. patent5,444,572 (22August1995).
  9. S. Glöckner, R. Göring, “Analysis of a micro-optical light modulator,” Appl. Opt. 36, 1467–1471 (1997).
    [CrossRef] [PubMed]
  10. S. Glöckner, R. Göring, T. Possner, M. Frank, “Micro optical modulators and switches for multimode fiber applications,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 211–219 (1997).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. A. von Pfeil, F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).

2000 (1)

A. von Pfeil, F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).

1997 (1)

1994 (1)

M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
[CrossRef]

1993 (1)

E. A. Watson, “Analysis of beam steering with decentered microlens arrays,” Opt. Eng. 32, 2665–2670 (1993).
[CrossRef]

1990 (1)

W. Goltsos, M. Holz, “Agile beam steering using binary optics microlens arrays,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

Anderson, W. W.

G. Gal, W. W. Anderson, B. J. Herman, D. M. Shough, “Wavefront correctors for scanning microlens arrays,” U.S. patent5,444,572 (22August1995).

Andrews, A. P.

M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
[CrossRef]

Cassarly, W. J.

K. M. Flood, W. J. Cassarly, “Wide angle beam steering using translation of plural lens arrays,” U.S. patent5,059,008 (22October1991).

Finlan, J. M.

G. F. Mcdearmon, K. M. Flood, J. M. Finlan, “Comparison of conventional and microlens-array agile beam steerers,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. SPIE2383, 167–178 (1995).
[CrossRef]

Flood, K. M.

G. F. Mcdearmon, K. M. Flood, J. M. Finlan, “Comparison of conventional and microlens-array agile beam steerers,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. SPIE2383, 167–178 (1995).
[CrossRef]

K. M. Flood, W. J. Cassarly, “Wide angle beam steering using translation of plural lens arrays,” U.S. patent5,059,008 (22October1991).

Frank, M.

S. Glöckner, R. Göring, T. Possner, M. Frank, “Micro optical modulators and switches for multimode fiber applications,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 211–219 (1997).
[CrossRef]

Gal, G.

G. Gal, H. E. Morrow, “Internally cooled large aperture microlens array with monolithic integrated micro scanner,” U.S. patent5,415,727 (16May1995).

G. Gal, W. W. Anderson, B. J. Herman, D. M. Shough, “Wavefront correctors for scanning microlens arrays,” U.S. patent5,444,572 (22August1995).

Glöckner, S.

S. Glöckner, R. Göring, “Analysis of a micro-optical light modulator,” Appl. Opt. 36, 1467–1471 (1997).
[CrossRef] [PubMed]

S. Glöckner, R. Göring, T. Possner, M. Frank, “Micro optical modulators and switches for multimode fiber applications,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 211–219 (1997).
[CrossRef]

Goltsos, W.

W. Goltsos, M. Holz, “Agile beam steering using binary optics microlens arrays,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Göring, R.

S. Glöckner, R. Göring, “Analysis of a micro-optical light modulator,” Appl. Opt. 36, 1467–1471 (1997).
[CrossRef] [PubMed]

S. Glöckner, R. Göring, T. Possner, M. Frank, “Micro optical modulators and switches for multimode fiber applications,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 211–219 (1997).
[CrossRef]

Gunning, W. J.

M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
[CrossRef]

Herman, B. J.

G. Gal, W. W. Anderson, B. J. Herman, D. M. Shough, “Wavefront correctors for scanning microlens arrays,” U.S. patent5,444,572 (22August1995).

Holz, M.

W. Goltsos, M. Holz, “Agile beam steering using binary optics microlens arrays,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

Khoshnevisan, M.

M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
[CrossRef]

Mcdearmon, G. F.

G. F. Mcdearmon, K. M. Flood, J. M. Finlan, “Comparison of conventional and microlens-array agile beam steerers,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. SPIE2383, 167–178 (1995).
[CrossRef]

Milster, T. D.

T. D. Milster, “Modelling and measurement of a micro-optic beam deflector,” in Design, Modeling, and Control of Laser Beam Optics, Y. Kohanzadeh, G. N. Lawrence, J. G. McCoy, H. Weichel, eds., Proc. SPIE1625, 78–83 (1992).
[CrossRef]

Morrow, H. E.

G. Gal, H. E. Morrow, “Internally cooled large aperture microlens array with monolithic integrated micro scanner,” U.S. patent5,415,727 (16May1995).

Motamedi, M. E.

M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
[CrossRef]

Possner, T.

S. Glöckner, R. Göring, T. Possner, M. Frank, “Micro optical modulators and switches for multimode fiber applications,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 211–219 (1997).
[CrossRef]

Shough, D. M.

G. Gal, W. W. Anderson, B. J. Herman, D. M. Shough, “Wavefront correctors for scanning microlens arrays,” U.S. patent5,444,572 (22August1995).

von Pfeil, A.

A. von Pfeil, F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).

Watson, E. A.

E. A. Watson, “Analysis of beam steering with decentered microlens arrays,” Opt. Eng. 32, 2665–2670 (1993).
[CrossRef]

Wyrowski, F.

A. von Pfeil, F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).

Appl. Opt. (1)

J. Mod. Opt. (1)

A. von Pfeil, F. Wyrowski, “Wave-optical structure design with the local plane-interface approximation,” J. Mod. Opt. 47, 2335–2350 (2000).

Opt. Eng. (3)

E. A. Watson, “Analysis of beam steering with decentered microlens arrays,” Opt. Eng. 32, 2665–2670 (1993).
[CrossRef]

W. Goltsos, M. Holz, “Agile beam steering using binary optics microlens arrays,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

M. E. Motamedi, A. P. Andrews, W. J. Gunning, M. Khoshnevisan, “Miniaturized micro-optical scanners,” Opt. Eng. 33, 3616–3623 (1994).
[CrossRef]

Other (7)

T. D. Milster, “Modelling and measurement of a micro-optic beam deflector,” in Design, Modeling, and Control of Laser Beam Optics, Y. Kohanzadeh, G. N. Lawrence, J. G. McCoy, H. Weichel, eds., Proc. SPIE1625, 78–83 (1992).
[CrossRef]

G. F. Mcdearmon, K. M. Flood, J. M. Finlan, “Comparison of conventional and microlens-array agile beam steerers,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. SPIE2383, 167–178 (1995).
[CrossRef]

G. Gal, H. E. Morrow, “Internally cooled large aperture microlens array with monolithic integrated micro scanner,” U.S. patent5,415,727 (16May1995).

G. Gal, W. W. Anderson, B. J. Herman, D. M. Shough, “Wavefront correctors for scanning microlens arrays,” U.S. patent5,444,572 (22August1995).

S. Glöckner, R. Göring, T. Possner, M. Frank, “Micro optical modulators and switches for multimode fiber applications,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 211–219 (1997).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

K. M. Flood, W. J. Cassarly, “Wide angle beam steering using translation of plural lens arrays,” U.S. patent5,059,008 (22October1991).

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Figures (16)

Fig. 1
Fig. 1

Schematic diagram of a micro-optical scanner that could be used as a multimode fiber switch.

Fig. 2
Fig. 2

Schematic diagram of the numerical wave optical simulation.

Fig. 3
Fig. 3

Experimental setup for determination of the transfer efficiencies of the MLA telescope as a function of lateral decentering (here coupling into a pinhole in front of a photodetector).

Fig. 4
Fig. 4

Experimentally recorded 2D spots: (a) Galilean arrangement, centered; (b) Galilean arrangement, laterally decentered for deflection of the amount of half a grating order; (c) Keplerian arrangement, centered; (d) Keplerian arrangement, laterally decentered for deflection of the amount of half a grating order.

Fig. 5
Fig. 5

Numerical wave optically simulated 2D spots: (a) Galilean arrangement, centered; (b) Galilean arrangement, laterally decentered for deflection of the amount of half a grating order; (c) Keplerian arrangement, centered; (d) Keplerian arrangement, laterally decentered for deflection of the amount of half a grating order.

Fig. 6
Fig. 6

Simulated 1D intensity distribution for a Galilean arrangement: (a) centered (93.4% efficiency), (b) laterally decentered for deflection of the amount of half a grating order (80.4% efficiency).

Fig. 7
Fig. 7

Cross section of the experimentally recorded image of the end face of a multimode fiber with 200-μm core diameter imaged with the use of a MLA telescope in the Galilean arrangement: (a) centered (87.2% efficiency), (b) laterally decentered for deflection of the amount of half a grating order (73.2% efficiency).

Fig. 8
Fig. 8

Simulated 1D intensity distribution of the Keplerian arrangement: (a) centered (81.4% efficiency), (b) laterally decentered for deflection of the amount of half a grating order (85.1% efficiency).

Fig. 9
Fig. 9

Cross section of the experimentally recorded image of the end face of a multimode fiber with 200-μm core diameter imaged with the use of a MLA telescope in the Keplerian arrangement: (a) centered (72.5% efficiency), (b) laterally decentered for deflection of the amount of half a grating order (73.5% efficiency).

Fig. 10
Fig. 10

Cross section of the experimentally recorded image of the end face of a multimode fiber with 200-μm core diameter imaged without the use of a MLA telescope (imaged only with collimating and focusing optics).

Fig. 11
Fig. 11

Schematic diagram of the distribution of intensities of several source points onto the diffraction orders when they are imaged by the Keplerian telescope setup. Left, five source points ○a–○e of the laterally extended object. Their normalized intensity is divided roughly into three equal parts. Right, intensity distribution of several source points between various diffraction orders as a function of the distance of the source point from the optical axis. The oblique thinner lines that connect object and image space represent the directions of propagation of the zeroth diffraction order for each source point. The oblique thicker lines represent the direction of propagation of the center of intensity of the illuminated diffraction order for each source point for 1:1 imaging by the Keplerian setup. In accordance with Eq. (3) one can find the diffraction order with maximum intensity for a given source point by determining the direction of the zeroth order for this point and counting the diffraction order numbers until the order that is closest to the direction of the 1:1 image by the Keplerian setup is found.

Fig. 12
Fig. 12

Simulated 1D intensity distribution for the centered Keplerian arrangement for four values of the pitch of the MLAs: (a) 50-μm pitch, (b) 100-μm pitch, (c) 200-μm pitch, (d) 400-μm pitch (the numerical aperture is fixed to 0.1).

Fig. 13
Fig. 13

Transfer efficiencies of the Keplerian arrangement (for system parameters see Table 1 and Section 3).

Fig. 14
Fig. 14

Transfer efficiencies of the reversed Keplerian arrangement (for system parameters see Table 1 and Section 3).

Fig. 15
Fig. 15

Transfer efficiencies of the Galilean arrangement (for system parameters see Table 1 and Section 3).

Fig. 16
Fig. 16

Influence of lens pitch on transfer efficiency for a given fiber core diameter of 200 μm: (a) reversed Keplerian arrangement, (b) Galilean arrangement (the numerical aperture is fixed at 0.1).

Tables (2)

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Table 1 Parameters of Cylindrical MLAs Used in Experiment and Simulation

Tables Icon

Table 2 Summary of Determined Transfer Efficiencies

Equations (3)

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pr0|f2|+1-Msin θ=mλ mZ.
p r0|f2|=mλ mZ.
pr0|f2|+2 sin θ=mλ mZ.

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