Abstract

A light modulator with microlens arrays in a confocal arrangement and with various filters in the common focal plane of the arrays, which are translated with the help of piezoelectric actuators, is proposed. The theoretical analysis deals with the influence of the lens arrays on the performance of the modulator. The system is investigated for spatially incoherent beams. It is shown that the configuration is suited for efficient modulation of radiation emitted by multimode fibers. A choice of the proper focal length of the microlens arrays and lens pitch d results in a good transmission efficiency (above 90%) combined with a large number of possible switching states.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Göring, W. Berner, E.-B. Kley, “Miniaturized optical system for beam deflection and modulation,” in Miniature and Micro-optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc SPIE1992, 54—61 (1993).
  2. M. F. Lewis, R. A. Wilson, “The use of lenslet arrays in spatial light modulators,” Pure Appl. Opt. 3, 143–150 (1994).
    [CrossRef]
  3. W. Goltsos, M. Holz, “Agile beam steering using binary optics microlens arrays,” Opt. Eng. 29, 1392–1397 (1990).
    [CrossRef]
  4. E. A. Watson, “Analysis of beam steering with decentered microlens arrays,” Opt. Eng. 32, 2665–2670 (1993).
    [CrossRef]
  5. J. B. DeVelis, G. B. Parrent, G. O. Reynolds, B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE, Bellingham, Wash.1989), Chap. 3, p. 15.
  6. W. G. Driscoll, W. Vaugham, Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 2, p. 32.
  7. 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. Motamedi, L. Beiser, eds., Proc SPIE2383, pp. 167–178 (1995).
    [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 1, pp. 13–14.

1994 (1)

M. F. Lewis, R. A. Wilson, “The use of lenslet arrays in spatial light modulators,” Pure Appl. Opt. 3, 143–150 (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]

Berner, W.

R. Göring, W. Berner, E.-B. Kley, “Miniaturized optical system for beam deflection and modulation,” in Miniature and Micro-optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc SPIE1992, 54—61 (1993).

DeVelis, J. B.

J. B. DeVelis, G. B. Parrent, G. O. Reynolds, B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE, Bellingham, Wash.1989), Chap. 3, p. 15.

Driscoll, W. G.

W. G. Driscoll, W. Vaugham, Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 2, p. 32.

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. Motamedi, L. Beiser, eds., Proc SPIE2383, pp. 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. Motamedi, L. Beiser, eds., Proc SPIE2383, pp. 167–178 (1995).
[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), Chap. 1, pp. 13–14.

Göring, R.

R. Göring, W. Berner, E.-B. Kley, “Miniaturized optical system for beam deflection and modulation,” in Miniature and Micro-optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc SPIE1992, 54—61 (1993).

Holz, M.

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

Kley, E.-B.

R. Göring, W. Berner, E.-B. Kley, “Miniaturized optical system for beam deflection and modulation,” in Miniature and Micro-optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc SPIE1992, 54—61 (1993).

Lewis, M. F.

M. F. Lewis, R. A. Wilson, “The use of lenslet arrays in spatial light modulators,” Pure Appl. Opt. 3, 143–150 (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. Motamedi, L. Beiser, eds., Proc SPIE2383, pp. 167–178 (1995).
[CrossRef]

Parrent, G. B.

J. B. DeVelis, G. B. Parrent, G. O. Reynolds, B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE, Bellingham, Wash.1989), Chap. 3, p. 15.

Reynolds, G. O.

J. B. DeVelis, G. B. Parrent, G. O. Reynolds, B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE, Bellingham, Wash.1989), Chap. 3, p. 15.

Thompson, B. J.

J. B. DeVelis, G. B. Parrent, G. O. Reynolds, B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE, Bellingham, Wash.1989), Chap. 3, p. 15.

Vaugham, W.

W. G. Driscoll, W. Vaugham, Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 2, p. 32.

Watson, E. A.

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

Wilson, R. A.

M. F. Lewis, R. A. Wilson, “The use of lenslet arrays in spatial light modulators,” Pure Appl. Opt. 3, 143–150 (1994).
[CrossRef]

Opt. Eng. (2)

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

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

Pure Appl. Opt. (1)

M. F. Lewis, R. A. Wilson, “The use of lenslet arrays in spatial light modulators,” Pure Appl. Opt. 3, 143–150 (1994).
[CrossRef]

Other (5)

R. Göring, W. Berner, E.-B. Kley, “Miniaturized optical system for beam deflection and modulation,” in Miniature and Micro-optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc SPIE1992, 54—61 (1993).

J. B. DeVelis, G. B. Parrent, G. O. Reynolds, B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics, (SPIE, Bellingham, Wash.1989), Chap. 3, p. 15.

W. G. Driscoll, W. Vaugham, Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 2, p. 32.

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. Motamedi, L. Beiser, eds., Proc SPIE2383, pp. 167–178 (1995).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 1, pp. 13–14.

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 (9)

Fig. 1
Fig. 1

Principle of a micro-optical intensity modulator for multimode fiber radiation.

Fig. 2
Fig. 2

Search for the point-spread function of incoming waves with tilt against the optical axis.

Fig. 3
Fig. 3

Rays and wave fronts before and after the lens arrays.

Fig. 4
Fig. 4

Phase distribution after the arrays: (a) the phase can be described as a sum of ϕ1 and ϕ2, (b) a periodic wave front aberration ϕ ab is introduced. Fill factor F is taken into consideration; c is a constant.

Fig. 5
Fig. 5

Light concentration in the common focal plane of the lenslets of the arrays.

Fig. 6
Fig. 6

κ and fill factor F for different maximum incident angles θmax and f-numbers f 1/#.

Fig. 7
Fig. 7

Definition of the efficiency χ of the system: χ is the ratio of the output energy in directions - M θmax ≤ θ2M θmax and the input energy in directions -θmax ≤ θ1 ≤ θmax.

Fig. 8
Fig. 8

Efficiency χ for f 1/# = 2.5, λ/2 d = 1.67 mrad.

Fig. 9
Fig. 9

Efficiency χ for f 1/# = 5, λ/2 d = 1.67 mrad.

Equations (18)

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

tx=rectxdFexp-i2πλsin θ1+sin θ2xexpiϕab.
ux=1DFexpi 2πλsin θ1xrectxD×1dcombxdtx.
Ufx=1DFδfx-sin θ1λ D sincDfx  combdfxTfx, Ufx=1dDFn=-sincDfx-sin θ1λ-ndTnd,
Tnd=-rectxdFexp-i2πλsin θ1+sin θ2x×expiϕabexp-i2πndxdx, Tnd=-dF/2dF/2expiϕabexp-i2πxnd+sin θ1+sin θ2λxdx.
Ufx=1dDFn=- sincDfx-sin θ1λ-nd×-dF/2dF/2expiϕabexp-i2π×nd+sin θ1+sin θ2λxdx.
limDD sincDfx-sin θλ-nd2=δfx-sin θλ-nd,
ηn=1Fd2-dF/2dF/2expiϕabexp-2π×nd+sin θ1+sin θ2λxdx2.
ηn=F sinc2nd+sin θ1+sin θ2λdF.
ηideal=-dF/2dF/2expiϕabxdx2d2F2f=VF.
ũx˜, θ1=ũx˜+Mθpf, θ1-θp with θp=λ/d1+M.
κ=d2h=12f1/# tan θmax.
f2=f1κ-1κ+1
M=1F=κ+1κ-1
rectx=1 : x1/20 : x>1/2,
sincx=sin πxπx,
combx=n=-δx-n,
rectx=sincfx,
combx=combfx.

Metrics