Abstract

The chances of optical computing are probably best if a large number of processing elements act in parallel. The efficiency of parallel processors depends, among other things, on the time it takes to communicate signals from one processor to any other processor. In an optical parallel processor one hopes to be able to transmit a signal from one processor to any other processor within only one cycle period, no matter how far apart the processors are. Such a global communications network is desirable especially for algorithms with global interactions. The fast Fourier algorithm is an example. We define a degree of globality and we show how speed and globality are related. Our result applies to a specific architecture based on spatial filtering.

© 1989 Optical Society of America

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References

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  1. J. Shamir, “Fundamental Speed Limitations on Parallel Processing,” Appl. Opt. 26, 1567–1567 (1987).
    [CrossRef] [PubMed]
  2. C. Froehly, B. Colombeau, M. Vampouille, “Shaping and Analysis of Picosecond Light Pulses,” Prog. Opt. 20, 63–153 (1982).
    [CrossRef]
  3. H. Bartelt, S. K. Case, A. W. Lohmann, “Visualisation of Light Propagation,” Opt. Commun. 30, 13–19 (1979).
    [CrossRef]
  4. H. Meyer et al., “Design and Performance of a 20-Stage Digital Light Beam Deflector,” Appl. Opt. 11, 1732–1736 (1972).
    [CrossRef] [PubMed]

1987 (1)

1982 (1)

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and Analysis of Picosecond Light Pulses,” Prog. Opt. 20, 63–153 (1982).
[CrossRef]

1979 (1)

H. Bartelt, S. K. Case, A. W. Lohmann, “Visualisation of Light Propagation,” Opt. Commun. 30, 13–19 (1979).
[CrossRef]

1972 (1)

Bartelt, H.

H. Bartelt, S. K. Case, A. W. Lohmann, “Visualisation of Light Propagation,” Opt. Commun. 30, 13–19 (1979).
[CrossRef]

Case, S. K.

H. Bartelt, S. K. Case, A. W. Lohmann, “Visualisation of Light Propagation,” Opt. Commun. 30, 13–19 (1979).
[CrossRef]

Colombeau, B.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and Analysis of Picosecond Light Pulses,” Prog. Opt. 20, 63–153 (1982).
[CrossRef]

Froehly, C.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and Analysis of Picosecond Light Pulses,” Prog. Opt. 20, 63–153 (1982).
[CrossRef]

Lohmann, A. W.

H. Bartelt, S. K. Case, A. W. Lohmann, “Visualisation of Light Propagation,” Opt. Commun. 30, 13–19 (1979).
[CrossRef]

Meyer, H.

Shamir, J.

Vampouille, M.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and Analysis of Picosecond Light Pulses,” Prog. Opt. 20, 63–153 (1982).
[CrossRef]

Appl. Opt. (2)

Opt. Commun. (1)

H. Bartelt, S. K. Case, A. W. Lohmann, “Visualisation of Light Propagation,” Opt. Commun. 30, 13–19 (1979).
[CrossRef]

Prog. Opt. (1)

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and Analysis of Picosecond Light Pulses,” Prog. Opt. 20, 63–153 (1982).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Fermat's principle: (a) minimum path via C and (b) degeneracy: many paths have equal lengths.

Fig. 2
Fig. 2

Image formation as Fermat degeneracy. Group of concentric circles: shapshots of the wave packet.

Fig. 3
Fig. 3

Image formation with double degeneracy. Path length from A and B is the same as from A′ to B′: (a) 4f setup; (b) two tubes in cascade; (c) and (d) equal path lengths from A and from A′ till midway point.

Fig. 4
Fig. 4

Double degenerate image formation: two shapshots of two wave packets that started simultaneously at different input locations.

Fig. 5
Fig. 5

Wave packet traveling through a prism.

Fig. 6
Fig. 6

Shearing of a wave packet by grating diffraction.

Fig. 7
Fig. 7

Wave packet split by a Wollaston prism into two beams with orthogonal polarization. Dots and dashes indicate orientation of the crystal axis within the Wollaston.

Fig. 8
Fig. 8

Grating with two orders used as a spatial filter for (a) fan out, at locations J + J0 and JJ0 respectively (not labelled); emitter located at J, and (b) fan-in.

Fig. 9
Fig. 9

Output plane of the setup in Fig. 8(a): S = shift; δx = resolution length.

Fig. 10
Fig. 10

Spatial filter setup with holographic filter of width B and carrier period d.

Equations (10)

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

L = A B nds extremum .
L / c = Δ t = ( n / c ) d s = d t ; V = c / n = d s / d t .
sin α = λ / d .
Δ t 2 = B sin α / c = m d ( λ / d ) / c = m τ 0 .
I ( t ) rect [ ( t t ) / Δ t 2 ] d t = I out ( t ) .
S = λ f / d .
δ x = λ f / B = S / m .
Δ t 2 = m τ 0 .
m = Δ t 2 / τ 0 = S / δ x .
Δ t 2 / τ 0 = SW .

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