Abstract

The need for DC balancing phase pixels in ferroelectric liquid-crystal-on-silicon spatial light modulators leads to control schemes that limit their use in beam steering applications where a continuous display of a routing hologram is required. By analyzing the phase redundancy in binary phase holograms, a new DC balancing algorithm has been developed that allows more general beam splitting and multiple beam steering functions. The theoretical derivation of the algorithm and experimentally measured properties of the optical beams are presented and discussed.

© 2007 Optical Society of America

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References

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  1. C. A. T. H. Tee, W. A. Crossland, T. D. Wilkinson, and A. B. Davey, Opt. Eng. 39, 2527 (2000).
    [CrossRef]
  2. C. J. Henderson, D. G. Leyva, and T. D. Wilkinson, J. Lightwave Technol. 24, 1989 (2006).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  4. R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).
  5. O. Ripoll, V. Kettunen, and H. P. Herzig, Opt. Eng. 43, 2549 (2004).
    [CrossRef]
  6. M. A. A. Neil, M. J. Booth, and T. Wilson, Opt. Lett. 23, 1849 (1998).
    [CrossRef]

2006 (1)

2004 (1)

O. Ripoll, V. Kettunen, and H. P. Herzig, Opt. Eng. 43, 2549 (2004).
[CrossRef]

2000 (1)

C. A. T. H. Tee, W. A. Crossland, T. D. Wilkinson, and A. B. Davey, Opt. Eng. 39, 2527 (2000).
[CrossRef]

1998 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

J. Lightwave Technol. (1)

Opt. Eng. (2)

C. A. T. H. Tee, W. A. Crossland, T. D. Wilkinson, and A. B. Davey, Opt. Eng. 39, 2527 (2000).
[CrossRef]

O. Ripoll, V. Kettunen, and H. P. Herzig, Opt. Eng. 43, 2549 (2004).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (5)

Fig. 1
Fig. 1

Argand diagram of a phase pixel in the continuous hologram undergoing phase shifting of ϕ, n = 12 . Point A represents the original phase θ. Point B represents shifted phase θ + ϕ .

Fig. 2
Fig. 2

Schematic of the optical system.

Fig. 3
Fig. 3

Generated binary phase holograms at (a) 0 24 × 2 π phase shift, (b) 6 24 × 2 π phase shift, (c) 12 24 × 2 π phase shift, (d) 18 24 × 2 π phase shift, and (e) 24 24 × 2 π phase shift. Other multiples of phase shifted holograms are not shown.

Fig. 4
Fig. 4

Output from receiver A for (a) an inverse frame balancing and (b) a new balancing scheme with number of shifts n = 24 .

Fig. 5
Fig. 5

Eye diagram from the two receivers with PRBS of 100 Mbit s after the laser beam was split with the new DC balancing method. Time axis scale: 5 ns div . (a) Output from receiver A ( 20 mV div ) and (b) Output from receiver B ( 5 mV div ) .

Equations (5)

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h ( x , y ) = exp [ j θ ( x , y ) ] exp ( j ϕ ) .
ϕ = 2 π n ,
h binary ( x , y ) = { 1 , if cos ( θ + ϕ ) > 0 1 , otherwise .
h binary ( x , y ) = 2 π [ exp ( j θ ) exp ( j ϕ ) + exp ( j θ ) exp ( j ϕ ) 1 3 exp ( 3 j θ ) exp ( 3 j ϕ ) 1 3 exp ( 3 j θ ) exp ( 3 j ϕ ) + ] .
12 frames 24 × 60 Hz = 8.33 ms ,

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