Abstract

Successful development, fabrication, and deployment of optical interconnects and computing systems depend on how easily the optical components and light beams can be aligned. An interconnection system difficult or time-consuming to align is costly to develop and may be unreliable. In this paper a probability theoretical framework is developed for analyzing the alignability, that is, the degree of difficulty of aligning the devices and the light beams, of a given optical interconnection system. The alignability measure is related to the other performance measures of an interconnect such as the power transfer efficiency, SNR, and the spatial and temporal bandwidths. The cost of the development and deployment of an optical processor or interconnection system can be estimated from knowledge of the alignability.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  2. M. R. Feldman, S. C. Esener, C. C. Guest, S. H. Lee, “Comparisons Between Optical and Electrical Interconnects Based on Power and Speed Considerations,” Appl. Opt. 27, 1742–1751 (1988).
    [CrossRef] [PubMed]
  3. Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989).
  4. D. Tsang, “Alignment and Performance Tradeoffs for Free-Space Optical Interconnections,” in Ref. 3, pp. 146–149.
  5. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).
  6. C. Miller, S. Mettler, I. White, Optical Fiber Splices and Connectors (Marcel Dekker, New York, 1986).
  7. J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 302–306.
  8. J. Bufton, “Lasers in Remote Sensing, Communications, and Operations on Space Platforms,” in Laser/Optoelectronics in Engineering (Springer-Verlag, New York, 1988), pp. 647–658.

1988

1984

J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Athale, R.

J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Bufton, J.

J. Bufton, “Lasers in Remote Sensing, Communications, and Operations on Space Platforms,” in Laser/Optoelectronics in Engineering (Springer-Verlag, New York, 1988), pp. 647–658.

Esener, S. C.

Feldman, M. R.

Gaskill, J.

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 302–306.

Goodman, J.

J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Guest, C. C.

Kung, S-Y.

J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lee, S. H.

Leonberger, F.

J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Mettler, S.

C. Miller, S. Mettler, I. White, Optical Fiber Splices and Connectors (Marcel Dekker, New York, 1986).

Miller, C.

C. Miller, S. Mettler, I. White, Optical Fiber Splices and Connectors (Marcel Dekker, New York, 1986).

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

Tsang, D.

D. Tsang, “Alignment and Performance Tradeoffs for Free-Space Optical Interconnections,” in Ref. 3, pp. 146–149.

White, I.

C. Miller, S. Mettler, I. White, Optical Fiber Splices and Connectors (Marcel Dekker, New York, 1986).

Appl. Opt.

Proc. IEEE

J. Goodman, F. Leonberger, S-Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Other

Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989).

D. Tsang, “Alignment and Performance Tradeoffs for Free-Space Optical Interconnections,” in Ref. 3, pp. 146–149.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

C. Miller, S. Mettler, I. White, Optical Fiber Splices and Connectors (Marcel Dekker, New York, 1986).

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 302–306.

J. Bufton, “Lasers in Remote Sensing, Communications, and Operations on Space Platforms,” in Laser/Optoelectronics in Engineering (Springer-Verlag, New York, 1988), pp. 647–658.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

(a) Distribution of x-offset errors. Time allowed for alignment = 30 s. (b) Distribution of y-offset errors. Time allowed for alignment = 30 s. (c) Distribution of x-offset errors. Time allowed for alignment = 90 s. (d) Distribution of y-offset errors. Time allowed for alignment = 90 s.

Fig. 2
Fig. 2

Horizontal and vertical lateral offsets between the centers of the device and spot.

Fig. 3
Fig. 3

Gaussian probability density fxy(x,y) as a function of the overall cost measure (OCM = k/σ).

Fig. 4
Fig. 4

Worst case of a perfect alignment with efficiency η = 100%.

Fig. 5
Fig. 5

Probability of perfect alignment P100 as a function of d and OCM.

Fig. 6
Fig. 6

(a) Efficiency of power transfer as a function of normalized offset (ξ/s) for d > s. [The dotted lines represent linear approximations to Eq. (8).] (b) Efficiency of power transfer as a function of the normalized offset (ξ/s) for ds. [The dotted lines represent linear approximations to Eqs. (8) and (10).]

Fig. 7
Fig. 7

Maximum offset ξ(f)/s as a function of the minimum efficiency sought f%. [The dotted lines represent linear approximations to Eq. (11).]

Fig. 8
Fig. 8

For d = s and 50 < η < 100 the linear approximation (2) is better than linear approximation (1) to the efficiency η.

Fig. 9
Fig. 9

Variation of the probability Pf with d for various values of f.

Fig. 10
Fig. 10

Variation of probability Pf with f for various values of device radius d.

Fig. 11
Fig. 11

Variation of alignability with the radius of the device for various values of the OCM.

Fig. 12
Fig. 12

Variation of alignability with the OCM for various values of the device size.

Fig. 13
Fig. 13

(a) Results of fifty simulated alignments of a BOI with d = 42 μm and s = 40 μm so that A = 0.7. (b) Results of fifty simulated alignments of a BOI with d = 42 μm and s = 40 μm so that A = 0.95. (c) Results of fifty simulated alignments of a BOI with d = 42 μm and s = 40 μm so that A = 0.25.

Fig. 14
Fig. 14

Optical interconnection system consisting of several beams of light and optical devices.

Fig. 15
Fig. 15

Free-space optical crossbar interconnection system.

Equations (28)

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

OCM = α 1 t c o + α 2 D c p + α 3 g ( λ ) + α 4 d + α 5 s + α 6 F ,
η = power delivered to the device source power × 100 ( % )
f X Y ( x , y ) = ( 1 2 π σ 2 ) exp [ - ( x 2 + y 2 ) / 2 σ 2 ) ,
OCM = k / σ ,
d > s ,
x 2 + y 2 < d - s .
P 100 = Prob ( perfect alignment with η = 100 % ) , = 0 for d < s , = 1 - exp [ - ( d - s ) 2 / 2 σ 2 ] for d s .
P f = Prob ( alignment with f % η 100 % ) .
η = 100 %             for ξ < d - s ,
= 0             for ξ > d + s ,
= ( 50 / π ) [ ( d / s ) 2 ( θ 1 - sin θ 1 ) + ( θ 2 - sin θ 2 ) ] %             otherwise .
θ 1 = 2 cos - 1 [ ( d 2 - s 2 + ξ 2 ) / 2 d ξ ] ,
θ 2 = 2 cos - 1 [ ( s 2 - d 2 + ξ 2 ) / 2 s ξ ] .
η = 100 ( d / s ) 2 % for ξ < ( s - d ) .
ξ ( f ) d + s - f s / 50             for d > s ,
d + s - f s 2 / ( 50 d )             for d < s .
ξ ( f ) π s ( 100 - f ) / 200.
P f = 0             for d < s and f > 100 ( d / s ) % ,
= 1 - exp [ - ξ 2 ( f ) / 2 σ 2 ]             otherwise .
A = 1 100 0 100 P f d f ,
0 < A 1.
A = 1 - π 8 ( σ s ) [ erf ( d + s σ 2 ) - erf ( d - s σ 2 ) ] ,
total alignment = j = 1 N alignment of j th BOI .
OCM tot = j = 1 N OCM j .
Φ E = Prob ( total alignment with E % η 100 % ) = j = 1 N P f j ,
P f j = Prob ( an alignment in j th BOI with f j % η 100 % ) ,
E = 100 j = 1 N f j 100 ,
A tot = 1 100 0 100 Φ E d E = j = 1 N A j ,

Metrics