Abstract

A previously suggested birefringence-customized modular optical interconnect technique is extended for lens-free relay operation. Various lens-free relay imaging models are developed. We claim that the lens-free relay system is important in simplifying an optical interconnect system whenever the imaging conditions permit. To verify the validity of various proposed concepts, we experimentally implemented some 8 × 8 optical permutation modules. High-power efficiency and low channel cross talk were experimentally observed. In general, the larger the channel spacing, the less the cross talk. A quantitative cross-talk measurement of the lens-free relay system shows that, for a fixed channel width of 0.5 mm and channel spacings of 0.5, 1, and 2 mm, a less than -20-dB cross-talk performance can be guaranteed for lens-free relay distances of 40, 280, and 430 mm, respectively.

© 1998 Optical Society of America

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References

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  1. L. Liu, Y. Li, “Free-space optical shuffle implementations by use of birefringence-customized modular optics,” Appl. Opt. 36, 3854–3865 (1997).
    [CrossRef] [PubMed]
  2. W. Kulcke, K. Kosanke, E. Max, M. A. Habegger, T. J. Harris, H. Fleisher, “Digital light deflectors,” Appl. Opt. 5, 1657–1667 (1966).
    [CrossRef] [PubMed]
  3. K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
    [CrossRef]
  4. T. W. Stone, J. M. Battiato, “Optical array generation and interconnection using birefringent slabs,” Appl. Opt. 33, 182–191 (1994).
    [CrossRef] [PubMed]
  5. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  6. P. Belland, J. P. Crenn, “Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture,” Appl. Opt. 21, 522–527 (1982).
    [CrossRef] [PubMed]
  7. A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 40, 453–488 (1961).
  8. M. J. Quinn, Parallel Computing: Theory and Practice (McGraw-Hill, New York, 1993), Chap. 4.

1997 (1)

1994 (1)

1990 (1)

K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
[CrossRef]

1982 (1)

1966 (1)

1961 (1)

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 40, 453–488 (1961).

Battiato, J. M.

Belland, P.

Crenn, J. P.

Fleisher, H.

Fox, A. G.

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 40, 453–488 (1961).

Habegger, M. A.

Harris, T. J.

Hogari, K.

K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
[CrossRef]

Kosanke, K.

Kulcke, W.

Li, T.

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 40, 453–488 (1961).

Li, Y.

Liu, L.

Matsumoto, T.

K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
[CrossRef]

Max, E.

Noguchi, K.

K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
[CrossRef]

Quinn, M. J.

M. J. Quinn, Parallel Computing: Theory and Practice (McGraw-Hill, New York, 1993), Chap. 4.

Sakano, T.

K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Stone, T. W.

Appl. Opt. (4)

Bell Sys. Tech. J. (1)

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 40, 453–488 (1961).

Electron. Lett. (1)

K. Noguchi, K. Hogari, T. Sakano, T. Matsumoto, “Rearrangeable multichannel free-space optical switch using polarization multiplexing technique,” Electron. Lett. 26, 1325–1326 (1990).
[CrossRef]

Other (2)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

M. J. Quinn, Parallel Computing: Theory and Practice (McGraw-Hill, New York, 1993), Chap. 4.

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Figures (10)

Fig. 1
Fig. 1

Basic birefringence-customized optical interconnect building block.

Fig. 2
Fig. 2

Stacked module for a 2-D 8 × 8 cube C n-1 permutation (n = 6).

Fig. 3
Fig. 3

Stacked modules for 2-D butterfly permutations (n = 4) of B(n/2), B (n/2), and B.

Fig. 4
Fig. 4

Lens-free relay system with periodically spaced apertures.

Fig. 5
Fig. 5

Experimental results for a cube C n-1 module (n = 6): (a) Input spot pattern. (b) Intermediate spot pattern. (c) Output spot pattern.

Fig. 6
Fig. 6

Experimental results of a butterfly B module (n = 6): (a) Input spot pattern. (b) Intermediate spot pattern. (c) Output spot pattern.

Fig. 7
Fig. 7

Experimental results of superbutterfly B(2) module (n = 6): (a) Input spot pattern. (b) Intermediate spot pattern. (c) Output spot pattern.

Fig. 8
Fig. 8

Photograph of an optical cube C n-1 module.

Fig. 9
Fig. 9

Efficiency and cross talk of aperture-limited diffractive transmissions.

Fig. 10
Fig. 10

Power-efficiency data for light transmission through a sequence of six circular apertures.

Equations (33)

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tan   α = n o 2 - n e 2 n o 2 sin 2   θ + n e 2 cos 2   θ sin   2 θ 2 ,
I r = x 2 + y 2 1 / 2 = A 0 W 0 W z exp - x 2 + y 2 W 2 z 2 .
W z = W 0 1 + λ z π n W 0 2 2 1 / 2 ,
δ = exp - 2 a 2 / W 2 .
W 0 / W 0 = 1 - δ .
δ 0.33 N f - 3 / 2 ,     N f 1 ,
δ 1 = exp - 2 a 2 / W 1 2 .
W 2 L = 1 - δ 1 W 1 1 + λ L π n W 1 2 2 1 / 2 .
δ 2 = δ 1 1 / 1 - δ 1 2 1 + λ L / π n W 1 2 2 .
δ 2 = δ 1 1 + 2 δ 1 .
δ s = 0.33 1 a λ n   tan   α kT a 3 / 2 ,
δ s = 9.78 k a μ m 3 / 2 .
1 - δ ¯ M = 1 - δ 1 1 - δ 2 1 - δ M .
δ ¯ = δ 1 + δ 2 + + δ M M .
W 1 2 = λ kT 2 π δ 1 / 4 n   tan   α .
P 1 = π n δ 1 / 4 tan   α 2 λ k   ln 1 / δ 1 / 2 .
P 1 = 24.07   δ 1 / 8 k   ln 1 / δ 1 / 2 spots / mm .
P s = n   tan   α 4 λ k δ 0.33 2 / 3 ,
P s = 136.5   δ 2 / 3 k .
L Cn = 2 n / 2 - 1 T tan   α ,
L Bn = 1 + 2 n - 2 1 / 2 T tan   α .
i ,   j = a n - 1 a n - 2   n / 2 ,   a n / 2 - 1     a 1 a 0 ,
C k A :   a n - 1     a n / 2 ,   a n / 2 - 1     a 1 a 0 = a n - 1     a ¯ k     a n / 2 ,   a n / 2 - 1     a 1 a 0 .
B A :   a n - 1 a n - 2     a n / 2 ,   a n / 2 - 1     a 1 a 0 = a 0 a n - 2     a n / 2 ,   a n / 2 - 1     a 1 a n - 1 .
p ,   q = a n - 1 2 n / 2 - 1 + a n - 2 2 n / 2 - 2 +     a n / 2 + 1 2 + a n / 2 ,   a n / 2 - 1 2 n / 2 - 1 + a n / 2 - 2 2 n / 2 - 2 +   a 1 2 + a 0 .
p ,   q p ,   q , a 0 = a n - 1 , p ,   q p 2 n / 2 - 1 ,   q ± 1 , a 0 a n - 1 .
Z = 1 + 2 n - 2 1 / 2 , tan   γ = 2 n / 2 - 1 .
B k A = a n - 1 a n - 21     a n / 2 ,   a n / 2 - 1   a k + 1 a 0 a k - 1     a 1 a k ,     k < n / 2 , B k A = a n - 1 a n - 2     a k + 1 a 0 a k - 1     a n / 2 ,   a n / 2 - 1   a 1 a k ,     kn / 2 .
p ,   q p ,   q , a 0 = a k , p ,   q p 2 k - n / 2 ,   q ± 1 , a 0 a k ,
Z = 1 + 2 2 k - n 1 / 2 , tan   γ = 2 k - n / 2 .
B k A = a n - k - 1 a n - 2     a n - k a n - 1 a n - k - 2   a n / 2 ,   a n / 2 - 1     a 1 a 0     k < n / 2 , B k A = a n - k - 1 a n - 2     a n / 2 ,   a n / 2 - 1   a n - k a n - 1 a n - k - 2     a 1 a 0     kn / 2 .
p ,   q p ,   q , a 0 = a n - 1 , p ,   q p 2 n / 2 - 1 ,   q ± 2 n - k - 1 , a 0 a n - 1 ,
Z = 2 2 n - k - 1 + 2 n - 2 1 / 2 , tan   γ = 2 k - n / 2 .

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