Abstract

Time-of-flight optical computer designs must implicitly or explicitly allow for the synchronization of all signals at all interaction points. This paper details algorithms for calculating delays required for synchronization of optical systems, as well as the sensitivity of these systems to variations in delays from their nominal values. These algorithms, which are applied to graph models of systems, form the basis for an optical systems design methodology in which the designer develops architectures with lumped delays and idealized zero-delay devices. When applied to the system designs, the algorithms provide estimates of actual delay distributions and sensitivities.

© 1992 Optical Society of America

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References

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  1. T. K. Sharpless, “Mercury delay lines as a memory unit,” in Proceedings of the International Symposium on Large-Scale Digital Calculating Machinery, 1947 [Ann. Comput. Lab. Harvard Univ. 14, 103–109 (1948)].
  2. P. D. Denyer, D. Renshaw, VLSI Signal Processing: A Bit-Serial Approach (Addison-Wesley, Reading, Mass., 1985).
  3. C. E. Leiserson, J. B. Saxe, “Optimizing synchronous systems,” J. VLSI Comput. Syst. 1, 41–67 (1983).
  4. C. E. Leiserson, J. B. Saxe, “A mixed-integer linear programming problem which is efficiently solvable,” J. Algorithms 9, 114–128 (1988).
    [CrossRef]
  5. A. Gibbons, Algorithmic Graph Theory (Cambridge University, New York, 1985).
  6. R. G. Busacker, T. L. Saaty, Finite Graphs and Networks (McGraw-Hill, New York, 1965).
  7. S. Danø, Linear Programming in Industry (Springer-Verlag, New York, 1974).
    [CrossRef]
  8. J. P. Pratt, “The Design of Bit-Serial Optical Systems,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 1990; University Microfilms, Ann Arbor, Mich.).
  9. D. B. Sarrazin, H. F. Jordan, V. P. Heuring, “Fiber optic delay line memory,” Appl. Opt. 29, 627–637 (1990).
    [CrossRef] [PubMed]
  10. M. A. Plonus, Applied Electromagnetics (McGraw-Hill, New York, 1978).
  11. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).
  12. S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
    [CrossRef]
  13. M. N. Islam, “Ultrafast all-optical logic gates based on soliton trapping in fibers,” Opt. Lett. 14, 1257–1259 (1989).
    [CrossRef] [PubMed]
  14. N. Christofides, Graph Theory (Academic, New York, 1975).

1990

1989

1988

C. E. Leiserson, J. B. Saxe, “A mixed-integer linear programming problem which is efficiently solvable,” J. Algorithms 9, 114–128 (1988).
[CrossRef]

1985

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

1983

C. E. Leiserson, J. B. Saxe, “Optimizing synchronous systems,” J. VLSI Comput. Syst. 1, 41–67 (1983).

Alferness, R. C.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Buhl, L. L.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Busacker, R. G.

R. G. Busacker, T. L. Saaty, Finite Graphs and Networks (McGraw-Hill, New York, 1965).

Christofides, N.

N. Christofides, Graph Theory (Academic, New York, 1975).

Danø, S.

S. Danø, Linear Programming in Industry (Springer-Verlag, New York, 1974).
[CrossRef]

Denyer, P. D.

P. D. Denyer, D. Renshaw, VLSI Signal Processing: A Bit-Serial Approach (Addison-Wesley, Reading, Mass., 1985).

Eisenstein, G.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Gibbons, A.

A. Gibbons, Algorithmic Graph Theory (Cambridge University, New York, 1985).

Harvey, G. T.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Heuring, V. P.

Islam, M. N.

Jordan, H. F.

Korotky, S. K.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Leiserson, C. E.

C. E. Leiserson, J. B. Saxe, “A mixed-integer linear programming problem which is efficiently solvable,” J. Algorithms 9, 114–128 (1988).
[CrossRef]

C. E. Leiserson, J. B. Saxe, “Optimizing synchronous systems,” J. VLSI Comput. Syst. 1, 41–67 (1983).

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).

Plonus, M. A.

M. A. Plonus, Applied Electromagnetics (McGraw-Hill, New York, 1978).

Pratt, J. P.

J. P. Pratt, “The Design of Bit-Serial Optical Systems,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 1990; University Microfilms, Ann Arbor, Mich.).

Read, P. H.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Renshaw, D.

P. D. Denyer, D. Renshaw, VLSI Signal Processing: A Bit-Serial Approach (Addison-Wesley, Reading, Mass., 1985).

Saaty, T. L.

R. G. Busacker, T. L. Saaty, Finite Graphs and Networks (McGraw-Hill, New York, 1965).

Sarrazin, D. B.

Saxe, J. B.

C. E. Leiserson, J. B. Saxe, “A mixed-integer linear programming problem which is efficiently solvable,” J. Algorithms 9, 114–128 (1988).
[CrossRef]

C. E. Leiserson, J. B. Saxe, “Optimizing synchronous systems,” J. VLSI Comput. Syst. 1, 41–67 (1983).

Sharpless, T. K.

T. K. Sharpless, “Mercury delay lines as a memory unit,” in Proceedings of the International Symposium on Large-Scale Digital Calculating Machinery, 1947 [Ann. Comput. Lab. Harvard Univ. 14, 103–109 (1948)].

Veselka, L. L.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

Appl. Opt.

IEEE J. Lightwave Technol.

S. K. Korotky, G. Eisenstein, R. C. Alferness, L. L. Veselka, L. L. Buhl, G. T. Harvey, P. H. Read, “Fully connectorized high-speed Ti:LiNbO3 switch/modulator for time-division multiplexing and data encoding,” IEEE J. Lightwave Technol. LT-3, 1–6 (1985).
[CrossRef]

J. Algorithms

C. E. Leiserson, J. B. Saxe, “A mixed-integer linear programming problem which is efficiently solvable,” J. Algorithms 9, 114–128 (1988).
[CrossRef]

J. VLSI Comput. Syst.

C. E. Leiserson, J. B. Saxe, “Optimizing synchronous systems,” J. VLSI Comput. Syst. 1, 41–67 (1983).

Opt. Lett.

Other

A. Gibbons, Algorithmic Graph Theory (Cambridge University, New York, 1985).

R. G. Busacker, T. L. Saaty, Finite Graphs and Networks (McGraw-Hill, New York, 1965).

S. Danø, Linear Programming in Industry (Springer-Verlag, New York, 1974).
[CrossRef]

J. P. Pratt, “The Design of Bit-Serial Optical Systems,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 1990; University Microfilms, Ann Arbor, Mich.).

M. A. Plonus, Applied Electromagnetics (McGraw-Hill, New York, 1978).

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).

N. Christofides, Graph Theory (Academic, New York, 1975).

T. K. Sharpless, “Mercury delay lines as a memory unit,” in Proceedings of the International Symposium on Large-Scale Digital Calculating Machinery, 1947 [Ann. Comput. Lab. Harvard Univ. 14, 103–109 (1948)].

P. D. Denyer, D. Renshaw, VLSI Signal Processing: A Bit-Serial Approach (Addison-Wesley, Reading, Mass., 1985).

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Figures (11)

Fig. 1
Fig. 1

Digital system with SME’s.

Fig. 2
Fig. 2

Digital system lacking SME’s.

Fig. 3
Fig. 3

Graph representation of Fig. 2.

Fig. 4
Fig. 4

Delay in a bit-serial adder.

Fig. 5
Fig. 5

Delay models.

Fig. 6
Fig. 6

Delays to the interaction point.

Fig. 7
Fig. 7

Reference delays to the interaction point.

Fig. 8
Fig. 8

Lithium niobate switch and delay model.

Fig. 9
Fig. 9

Delay circuit example.

Fig. 10
Fig. 10

Delay circuit model.

Fig. 11
Fig. 11

Switch Timing.

Tables (1)

Tables Icon

Table I Delay Uncertainties for Fig. 9

Equations (16)

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

s 5 ( k ) = s 1 ( k - 1 ) s 2 ( k ) s 3 ( k - 2 ) .
v V ,             P i , P j S v , P i w 0 - P j w 0 = P i w 1 - P j w 1 ,
f i = { 0 : edge i not in circuit 1 : edge i in circuit and in circulation direction - 1 : edge i in circuit and against circulation direction
F w 0 = F w 1 .
F Δ w = 0.
w 0 i + Δ w i m i ,             1 i E ,
i = 1 E ( w 0 + Δ w ) i
F Δ w = 0 ,             w 0 + Δ w m
x = w 0 + Δ w - m
F x = b ,             x 0 ,
minimize c · x subject to F x = b and x 0.
T ( v , T c ) : v V             j , : e j A i ( v ) ,             w j w j - T c , T c Real             n , : e n A 0 ( v ) ,             w n w n + T c .
While there exist w i < m i , apply T ( v k , m i - w i ) ,
U σ ( out ) j = max s states [ max inputs i U σ ( in ) i ] ,             i C ( s , j ) ;
U max ( out ) j = max s states [ max inputs i U max ( in ) i ] ,             i C ( s , j ) ;
U min ( out ) j = max s states [ max inputs i U min ( in ) i ] ,             i C ( s , j ) .

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