Abstract

The optimum design of free-space optical interconnection systems utilizing diffractive optics is determined from a practical engineering standpoint for systems ranging from space invariant to fully space variant. System volume is calculated in terms of parameters such as the f-number of the diffractive lens, the wavelength of light, and also the total number, size, and separation of the optical sources and detectors. Performance issues such as interconnection complexity, diffraction efficiency, and signal-to-noise ratio are discussed. Diffractive optics fabricated by electron-beam direct-write techniques are used to provide experimental results for both shuffle-exchange and twin-butterfly free-space optical interconnects.

© 1994 Optical Society of America

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References

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  1. J. W. Goodman, “Optics as an interconnect technology,” in Optical Processing and Computing, H. H. Arsenault, ed. (Academic, New York, 1989), pp. 1–32.
  2. G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Mass. Inst. Technol. Tech. Rep. 854, 17–24 (1989).
  3. A. L. Decegama, Parallel Processing Architectures and VLSI Hardware, (Prentice-Hall, Englewood Cliffs, N.J., 1989), Vol. 1, pp. 192–193.
  4. H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing, 2nd ed. (McGraw-Hill, New York, 1990), pp. 113–174.
  5. B. Maggs, T. Leighton, “Fast algorithms for routing around faults on multibutterflies and randomly wired splitter networks,” IEEE Trans. Comput. 41, 478–587 (1992).
  6. L. G. Valiant, “Graph-theoretic properties in computational complexity,” J. Comput. Syst. Sci. 13, 278–285 (1988).
    [CrossRef]
  7. F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
    [CrossRef]
  8. A. Lohmann, G. Stucke, W. Stork, “Optical perfect shuffle,” Appl. Opt.25, 1530–1531 (1986).
    [CrossRef]
  9. S. H. Lin, T. F. Krille, J. F. Walkup, “2-D optical multistage interconnection networks,” in Digital Optical Computing, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.752, 209–216(1987).
  10. A. Lohmann, “What classical optics can do for the digital optical computer,” Appl. Opt. 25, 1543–1549 (1986).
    [CrossRef] [PubMed]
  11. G. Lohman, A. Lohmann, “Optical interconnection network utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).
  12. Q. W. Song, F. T. S. Yu, “Generalized perfect shuffle using optical spatial filtering,” Appl. Opt. 27, 1222–1223 (1988).
    [CrossRef] [PubMed]
  13. K. Brenner, A. Huang, “Optical implementations of the perfect shuffle interconnection,” Appl. Opt. 27, 135–137 (1988).
    [CrossRef] [PubMed]
  14. C. Stirk, R. A. Athale, M. W. Haney, “Folded perfect shuffle optical processor,” Appl. Opt. 27, 202–203 (1988).
    [CrossRef] [PubMed]
  15. A. Sawchuk, I. Glaser, “Geometries for optical implementations of the perfect shuffle,” in Optical Computing ’88, P. Chavel, J. W. Goodman, G. Roblin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 270–282 (1988).
  16. M. W. Haney, J. J. Levy, “Low loss free-space perfect shuffle network,” in 1990 International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (ICO Secretariat, Kobe, Japan), p. 85.
  17. M. W. Haney, “Optoelectronic shuffle exchange network for multiprocessing architectures,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TuX5.
  18. M. R. Feldman, C. C. Guest, “Interconnect density capabilities of computer-generated holograms for optical interconnection of very-large-scale-integrated circuits,” Appl. Opt. 28, 3134–3137 (1989).
    [CrossRef] [PubMed]
  19. Code V is a registered trademark of Optical Research Associates, Pasadena, Calif.
  20. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computers,” Appl. Opt. 5, 1739–1748 (1967).
    [CrossRef]
  21. J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
    [CrossRef]
  22. G. Keiser, Optical Fiber Communications, 2nd ed. (McGraw-Hill, New York, 1991), Chap. 7.2, pp. 274–297.
  23. R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
    [CrossRef] [PubMed]
  24. K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated hologram fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
    [CrossRef] [PubMed]
  25. K. S. Urquhart, H. Farhoosh, S. H. Lee, “Diffractive lens utilizing orthogonal cylindrical Fresnel zone planes,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng1211, 184–190 (1990).

1993

1992

B. Maggs, T. Leighton, “Fast algorithms for routing around faults on multibutterflies and randomly wired splitter networks,” IEEE Trans. Comput. 41, 478–587 (1992).

1991

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
[CrossRef] [PubMed]

1989

G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Mass. Inst. Technol. Tech. Rep. 854, 17–24 (1989).

M. R. Feldman, C. C. Guest, “Interconnect density capabilities of computer-generated holograms for optical interconnection of very-large-scale-integrated circuits,” Appl. Opt. 28, 3134–3137 (1989).
[CrossRef] [PubMed]

1988

1986

1967

A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computers,” Appl. Opt. 5, 1739–1748 (1967).
[CrossRef]

J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[CrossRef]

Athale, R. A.

Brenner, K.

Burch, J. J.

J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[CrossRef]

Decegama, A. L.

A. L. Decegama, Parallel Processing Architectures and VLSI Hardware, (Prentice-Hall, Englewood Cliffs, N.J., 1989), Vol. 1, pp. 192–193.

Esener, S.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Esener, S. C.

Farhoosh, H.

K. S. Urquhart, H. Farhoosh, S. H. Lee, “Diffractive lens utilizing orthogonal cylindrical Fresnel zone planes,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng1211, 184–190 (1990).

Feldman, M. R.

Ford, J. E.

Glaser, I.

A. Sawchuk, I. Glaser, “Geometries for optical implementations of the perfect shuffle,” in Optical Computing ’88, P. Chavel, J. W. Goodman, G. Roblin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 270–282 (1988).

Goodman, J. W.

J. W. Goodman, “Optics as an interconnect technology,” in Optical Processing and Computing, H. H. Arsenault, ed. (Academic, New York, 1989), pp. 1–32.

Guest, C. C.

Haney, M. W.

C. Stirk, R. A. Athale, M. W. Haney, “Folded perfect shuffle optical processor,” Appl. Opt. 27, 202–203 (1988).
[CrossRef] [PubMed]

M. W. Haney, J. J. Levy, “Low loss free-space perfect shuffle network,” in 1990 International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (ICO Secretariat, Kobe, Japan), p. 85.

M. W. Haney, “Optoelectronic shuffle exchange network for multiprocessing architectures,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TuX5.

Huang, A.

Keiser, G.

G. Keiser, Optical Fiber Communications, 2nd ed. (McGraw-Hill, New York, 1991), Chap. 7.2, pp. 274–297.

Kiamilev, F.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Krille, T. F.

S. H. Lin, T. F. Krille, J. F. Walkup, “2-D optical multistage interconnection networks,” in Digital Optical Computing, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.752, 209–216(1987).

Krishnamoorthy, A. V.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Lee, S. H.

K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated hologram fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
[CrossRef] [PubMed]

R. Paturi, D. T. Lu, J. E. Ford, S. C. Esener, S. H. Lee, “Parallel algorithms based on expander graphs for optical computing,” Appl. Opt. 30, 917–927 (1991).
[CrossRef] [PubMed]

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

K. S. Urquhart, H. Farhoosh, S. H. Lee, “Diffractive lens utilizing orthogonal cylindrical Fresnel zone planes,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng1211, 184–190 (1990).

Leighton, T.

B. Maggs, T. Leighton, “Fast algorithms for routing around faults on multibutterflies and randomly wired splitter networks,” IEEE Trans. Comput. 41, 478–587 (1992).

Levy, J. J.

M. W. Haney, J. J. Levy, “Low loss free-space perfect shuffle network,” in 1990 International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (ICO Secretariat, Kobe, Japan), p. 85.

Lin, S. H.

S. H. Lin, T. F. Krille, J. F. Walkup, “2-D optical multistage interconnection networks,” in Digital Optical Computing, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.752, 209–216(1987).

Lohman, G.

G. Lohman, A. Lohmann, “Optical interconnection network utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

Lohmann, A.

G. Lohman, A. Lohmann, “Optical interconnection network utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

A. Lohmann, “What classical optics can do for the digital optical computer,” Appl. Opt. 25, 1543–1549 (1986).
[CrossRef] [PubMed]

A. Lohmann, G. Stucke, W. Stork, “Optical perfect shuffle,” Appl. Opt.25, 1530–1531 (1986).
[CrossRef]

Lohmann, A. W.

Lu, D. T.

Maggs, B.

B. Maggs, T. Leighton, “Fast algorithms for routing around faults on multibutterflies and randomly wired splitter networks,” IEEE Trans. Comput. 41, 478–587 (1992).

Marchand, P.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Paris, D. P.

Paturi, R.

Sawchuk, A.

A. Sawchuk, I. Glaser, “Geometries for optical implementations of the perfect shuffle,” in Optical Computing ’88, P. Chavel, J. W. Goodman, G. Roblin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 270–282 (1988).

Siegel, H. J.

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing, 2nd ed. (McGraw-Hill, New York, 1990), pp. 113–174.

Song, Q. W.

Stein, R.

Stirk, C.

Stork, W.

A. Lohmann, G. Stucke, W. Stork, “Optical perfect shuffle,” Appl. Opt.25, 1530–1531 (1986).
[CrossRef]

Stucke, G.

A. Lohmann, G. Stucke, W. Stork, “Optical perfect shuffle,” Appl. Opt.25, 1530–1531 (1986).
[CrossRef]

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Mass. Inst. Technol. Tech. Rep. 854, 17–24 (1989).

Urquhart, K. S.

K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated hologram fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
[CrossRef] [PubMed]

K. S. Urquhart, H. Farhoosh, S. H. Lee, “Diffractive lens utilizing orthogonal cylindrical Fresnel zone planes,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng1211, 184–190 (1990).

Valiant, L. G.

L. G. Valiant, “Graph-theoretic properties in computational complexity,” J. Comput. Syst. Sci. 13, 278–285 (1988).
[CrossRef]

Walkup, J. F.

S. H. Lin, T. F. Krille, J. F. Walkup, “2-D optical multistage interconnection networks,” in Digital Optical Computing, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.752, 209–216(1987).

Yu, F. T. S.

Appl. Opt.

IEEE Trans. Comput.

B. Maggs, T. Leighton, “Fast algorithms for routing around faults on multibutterflies and randomly wired splitter networks,” IEEE Trans. Comput. 41, 478–587 (1992).

J. Comput. Syst. Sci.

L. G. Valiant, “Graph-theoretic properties in computational complexity,” J. Comput. Syst. Sci. 13, 278–285 (1988).
[CrossRef]

J. Lightwave Technol.

F. Kiamilev, P. Marchand, A. V. Krishnamoorthy, S. Esener, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Mass. Inst. Technol. Tech. Rep.

G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Mass. Inst. Technol. Tech. Rep. 854, 17–24 (1989).

Opt. Eng.

G. Lohman, A. Lohmann, “Optical interconnection network utilizing diffraction gratings,” Opt. Eng. 27, 893–900 (1988).

Opt. Lett.

Proc. IEEE

J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[CrossRef]

Other

G. Keiser, Optical Fiber Communications, 2nd ed. (McGraw-Hill, New York, 1991), Chap. 7.2, pp. 274–297.

Code V is a registered trademark of Optical Research Associates, Pasadena, Calif.

A. Sawchuk, I. Glaser, “Geometries for optical implementations of the perfect shuffle,” in Optical Computing ’88, P. Chavel, J. W. Goodman, G. Roblin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.963, 270–282 (1988).

M. W. Haney, J. J. Levy, “Low loss free-space perfect shuffle network,” in 1990 International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (ICO Secretariat, Kobe, Japan), p. 85.

M. W. Haney, “Optoelectronic shuffle exchange network for multiprocessing architectures,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TuX5.

A. L. Decegama, Parallel Processing Architectures and VLSI Hardware, (Prentice-Hall, Englewood Cliffs, N.J., 1989), Vol. 1, pp. 192–193.

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing, 2nd ed. (McGraw-Hill, New York, 1990), pp. 113–174.

A. Lohmann, G. Stucke, W. Stork, “Optical perfect shuffle,” Appl. Opt.25, 1530–1531 (1986).
[CrossRef]

S. H. Lin, T. F. Krille, J. F. Walkup, “2-D optical multistage interconnection networks,” in Digital Optical Computing, R. Arrathoon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.752, 209–216(1987).

K. S. Urquhart, H. Farhoosh, S. H. Lee, “Diffractive lens utilizing orthogonal cylindrical Fresnel zone planes,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng1211, 184–190 (1990).

J. W. Goodman, “Optics as an interconnect technology,” in Optical Processing and Computing, H. H. Arsenault, ed. (Academic, New York, 1989), pp. 1–32.

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Figures (15)

Fig. 1
Fig. 1

Space-invariant OIM implementation of the shuffle-exchange interconnection: (a) expanded, (b) condensed.

Fig. 2
Fig. 2

Space-semivariant OIM implementation of the shuffle-exchange interconnection.

Fig. 3
Fig. 3

Space-variant OIM implementation of the shuffle-exchange interconnection.

Fig. 4
Fig. 4

Space-semivariant system as modeled in Code V. Only one of the four lenslets and only five sources are shown.

Fig. 5
Fig. 5

Geometrical output spot diagrams for the system shown in Fig. 4. The spot diagrams on the left are for a simple spherical diffractive lens, while those on the right include aspheric terms.

Fig. 6
Fig. 6

Space-variant system as modeled in Code V. The figure shows the source at one corner being imaged to the detector at the opposite corner. The upper part is the XZ view, while the lower part is the YZ view.

Fig. 7
Fig. 7

SEM photomicrographs of the diffractive lenslet array for performing the shuffle-exchange interconnection: (a) the intersection of the four off-axis lenslets, (b) the central portion of one of the four off-axis lenslets.

Fig. 8
Fig. 8

Intersection of four quadrants of the input for the shuffle-exchange interconnection. The input array extends to 64 × 64.

Fig. 9
Fig. 9

Experimental output of the shuffle-exchange interconnection showing shuffling of the input. The output extends to 64 × 64.

Fig. 10
Fig. 10

Netlist for a 64-node twin-butterfly interconnection.

Fig. 11
Fig. 11

SEM photomicrograph (150×) of a portion of an 8 × 8 array of regularly spaced lenslets for input illumination of the twin-butterfly interconnection.

Fig. 12
Fig. 12

SEM photomicrograph (150×) of a portion of an 8 × 8 array of off-axis lenslets for SV twin-butterfly interconnection.

Fig. 13
Fig. 13

Reconstruction from an 8 × 8 twin-butterfly optical interconnection with all 64 sources illuminated: (a) simulated input, (b) simulated output, (c) experimental output.

Fig. 14
Fig. 14

Same as Fig. 13 but with all except the left column of the 64 sources illuminated.

Fig. 15
Fig. 15

Same as Fig. 13 but with only the right three columns (24 sources) illuminated.

Tables (3)

Tables Icon

Table 1 Optical Interconnection Module Volume Calculationsa

Tables Icon

Table 2 Light Throughput of the Three Optical Interconnection Module Designs

Tables Icon

Table 3 Signal-to-Noise Ratio Resultsa

Equations (26)

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

D ( i ) = 2 i - 1 ,             1 i ( N / 2 ) , D ( i ) = 2 i - N ,             ( N / 2 + 1 ) i N ,
t ( f x , f y ) = cos ( π Δ f x ) cos ( π Δ f y ) ,
PSF = F { t ( f x , f y ) } = δ ( x - Δ 2 ) δ ( y - Δ 2 ) + δ ( x + Δ 2 ) δ ( y - Δ 2 ) + δ ( x - Δ 2 ) δ ( y + Δ 2 ) + δ ( x + Δ 2 ) δ ( y + Δ 2 ) ,
V ( N s ) 1.5 ( d s ) 3 f # ,
N s < ( d s 4 λ f # ) 2 ,
η tot = η holo η OIM .
BER = 0.5 [ 1 - erf ( SNR 2 2 ) ] ,
V = L s d s 2 N s .
AR = L s d s N s .
f # = 2 3 d d s 2 N s ,
L s = 9 2 f # d s N s .
d off = ± d s 6 ( N s - 1 ) .
D eff = 2 [ d s 2 N s 2 - d s 6 ( 2 N s - 1 ) ] 2 3 d s 2 N s ,
f # 2 3 d 2 3 d s 2 N s .
L s 3 f # d s 2 N s .
d 1 = d s w s 2 λ ,
f = d 1 d 2 d 1 + d 2 .
D eff = 2 [ d 1 d s 2 ( N s - 1 ) d 1 + d 2 + d s 2 ] 2 ( d 1 d s 2 N s d 1 + d 2 ) ,
d 2 2 f # d s 2 N s .
L s d s ( 2 f # 2 N s + w s λ ) .
d 2 < ( d s ) 2 2 λ .
N s < ( d s 4 λ f # ) 2 .
S = η + 1 P I 2 w s .
N = N s i 1 η i P I A i ,
S = ( η + 1 ) 2 P I w s .
N = j ( η j P I A j i 1 η i P I A i ) .

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